A probabilistic segmentation method for IVUS images Tesis

Centro de Investigación en Matemáticas A.C.

A probabilistic segmentation method

for IVUS images

Tesis

que para obtener el grado de

Maestro en Ciencias con Especialidad en

Computación y Matemáticas Industriales

presenta

Eduardo Gerardo Mendizabal Ruiz

Director de Tesis

Dr. Mariano José J. Rivera Meraz

Codirector de Tesis

Dr. Ioannis A. Kakadiaris

Guanajuato, Gto. Marzo del 2008

Abstract

Complications attributed to cardiovascular disease (CVD) are currently the main cause of deathworldwide. It is known that the majority of adverse CVD-related events are due to coronary arterydiseases: a condition in which fatty lesions called plaques are formed on the walls of those vesselswhich nourish the heart with blood.

During the past decade, intravascular ultrasound (IVUS) has become an increasingly importanttool in clinical and research application. IVUS is a catheter based medical imaging technique thatproduces cross-sectional images of blood vessels and is particularly useful for studying atheroscleroticdiseases.

Segmentation of the lumen and media-adventitia borders in IVUS images is an important problemfor many applications in the study of atherosclerotic deceases. It can provide assessment of thevascular wall, information about the nature of atherosclerotic lesions and even plaque shape andsize.

In this thesis, we present a probabilistic approach for the semi-automatic segmentation of theluminal border on IVUS images. Specically, we parameterize the lumen contour using a sum ofGaussian functions that are deformed by the minimization of a cost function formulated using aprobabilistic approach.

For the optimization of the cost function, we introduce a novel method that linearly combinesthe descent directions of the steepest descent and BFGS optimization methods within a trust regionthat improves convergence.

In addition, we introduce a multi-scale approach for the segmentation that increases the speedof segmentation.

Finally, we present a method for segmentation of IVUS sequences that makes use of the segmenta-tion results from previous frames, in order to accelerate and increase the quality of the segmentationof the consecutive frames.

Results of our proposed method on 20 MHz IVUS images are presented and discussed in orderto demonstrate the eectiveness of our approach.

A mis padres Patricia y Eduardo.

Agradecimientos

Primero que nada quiero agradecer a mis padres a quien dedico este trabajo, ya que sin su apoyonunca hubiera alcanzado esta meta tan importante para mi. Gracias padre, por que eres unainspiración para mi y algun día quiero llegar a ser un gran cientíco como tu. A mi madre porquesu amor y comprensión han sido mi motivacin para seguir adelante.

Quiero agradecer a el profesor Mariano Rivera por su apoyo, ideas y supervición para la elabo-ración de este trabajo y al profesor Ioannis A. Kakadiaris por darme la oportunidad de trabajar conel en Houston que fue donde inició este trabajo.

A mi hermana Adriana colega en la ciencia y compañera en dicha y tristeza. A mi cuñadoAlejandro por las pláticas acerca de todo, las ideas locas, los juegos y los consejos.

A mis amigos (los vagos): Enrique, Guicho, los gemelos, Javis, Iram y el huesos; y mis amigas:Vicky, Mirella, Marion, Tania, etc. por el cotorro y los buenos momentos que hemos compartidoy que me ha servido de distracción para no volverme loco mientras estudiaba la maestría.

A mis amigos no vagos: Jorge Alfonzo por ser compañero de ideas, espectativas y loqueras yHugo por su amistad de tantos años.

A mis colegas y amigos de Guanajuato: Josué (que en estos momentos seguro está dormido,!limpia la casa!!), Carlos por sus gritos, Angel y Grace por darme de comer cuando no habia nadaen la casa, Jordi por convencerme de usar Linux y las pláticas tan interesantes y a Edna, Pablo,Juanita, Luz, Oscar y Angulo por su amistad.

A Gallo Muerto #5: Ivvan, Leonel, Victor y Sergio por los momentos de música y cotorreo quesiempre eran buenos para desestresar.

Finalmente quiero agradecer a CIMAT por darme la oportunidad de estudiar la maestría, por losconocimientos y por el apoyo económico recibido. Igualmente agradezco a CONACYT por el apoyoeconómico brindado para el estudio de mi postgrado.

Contents

1 Introduction 15

1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 Document Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Background 17

2.1 Anatomy and Physiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.1 Arterial Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.2 Pathology of Atherosclerosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Imaging Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.2 Intravascular Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.3 IVUS Images Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Previous Work 27

3.1 Previous Approaches to IVUS segmentation problem . . . . . . . . . . . . . . . . . . 27

3.2 Shape-driven Segmentation of IVUS Images . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Shape Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.2 Shape Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.3 Lumen Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.4 Media/adventitia Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.5 Lumen Segmentation Results with Unal et al. Method . . . . . . . . . . . . . 30

4 Proposed work 33

4.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.1 Probability Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.2 Cost Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Segmentation Method Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.1 Lumen contour parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.2 Likelihoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

10 CONTENTS

4.2.3 Optimization Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.3.1 Steepest descent method . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2.3.2 BFGS method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2.3.3 Steepest descent + BFGS optimization within a trust region (G+BFGSoptimization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2.4 Multi-scale Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.5 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3 Probabilistic Segmentation of IVUS Images with G+BFGS Method . . . . . . . . . . 45

4.3.1 Proposed Method Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3.2 Video Sequence Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5 Results and Discussion 49

5.1 Lumen Segmentation of Fixed IVUS Images . . . . . . . . . . . . . . . . . . . . . . . 49

5.1.1 Segmentation process examples . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.1.2 Segmentation on shifted images . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 Segmentation on IVUS Video Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.4 Results on IVUS Images with Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 Conclusions 63

6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

List of Figures

1.1 Lumen/intima and media/adventitia borders on IVUS image . . . . . . . . . . . . . 16

2.1 Blood vessel anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Stages of atherosclerotic plaque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Common ultrasound transducer congurations and examples . . . . . . . . . . . . . 20

2.4 Ultrasound signal and signal-envelope . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.5 IVUS B-mode image before and after log-compression . . . . . . . . . . . . . . . . . 21

2.6 Overview of IVUS catheter placement within the arterial system. . . . . . . . . . . . 22

2.7 B-Mode IVUS representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.8 Catheter congurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.9 L-mode IVUS image from pullback sequence . . . . . . . . . . . . . . . . . . . . . . . 23

2.10 A Comparison of 20MHz and 40MHz IVUS images. . . . . . . . . . . . . . . . . . . . 25

2.11 IVUS artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1 Unal et al. segmentation method result, example 1 . . . . . . . . . . . . . . . . . . . 31



3.4 Unal et al. segmentation method result on an unseen IVUS image dierent fromthose used for training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.5 Unal et al. segmentation method result on a shifted IVUS image . . . . . . . . . . . 32

4.1 IVUS regions with same gray-level distribution . . . . . . . . . . . . . . . . . . . . . 34

4.2 Lumen contour in Cartesian and polar B-mode representations . . . . . . . . . . . . 34

4.3 Contour function on IVUS B-mode representation . . . . . . . . . . . . . . . . . . . 35

4.4 Sigmoid function example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.5 User-provided prior information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.6 Empirical likelihoods for foreground and background . . . . . . . . . . . . . . . . . . 38

4.7 Contribution-control function ψ(ρ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.8 Proposed descent direction trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.9 Adjustment of the lumen contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

12 LIST OF FIGURES

5.1 A typical IVUS image to segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2 segmentation progress in step 1 of the multi-scale method . . . . . . . . . . . . . . . 50

5.3 Segmentation progress in step 2 of the multi-scale method . . . . . . . . . . . . . . . 50



5.6 Segmentation result of IVUS image of Fig. 5.1 . . . . . . . . . . . . . . . . . . . . . . 51

5.7 90 shifted version of IVUS image of Fig. 5.1 . . . . . . . . . . . . . . . . . . . . . . 52

5.8 Segmentation result of IVUS image of Fig. 5.7 . . . . . . . . . . . . . . . . . . . . . . 52

5.9 Video-sequence segmentation process . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.10 Segmentation of 5 consecutive frames in Cartesian representation . . . . . . . . . . . 55

5.11 Histogram and cumulative histogram of the RMS between A and MS1. . . . . . . . . 56

5.12 Histogram and cumulative histogram of the RMS between A and MS2. . . . . . . . . 56

5.13 Histogram and cumulative histogram of the RMS between MS1 and MS2. . . . . . . 57

5.14 Cumulative histograms of the RMS between A vs. MS1, A vs. MS2 and MS1 vs. MS2. 57

5.15 IVUS image with shadow artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.16 Segmentation result of image in Fig. 5.15 . . . . . . . . . . . . . . . . . . . . . . . . 58

5.17 IVUS image with ringdown, guidewire and shadow artifacts . . . . . . . . . . . . . . 59


5.19 IVUS image with large guidewire artifact . . . . . . . . . . . . . . . . . . . . . . . . 60


5.21 IVUS image with side branch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.22 Segmentation result of IVUS image in Fig. 5.21 . . . . . . . . . . . . . . . . . . . . . 61

5.23 Segmentation result of IVUS image in Fig. 5.21 with a less smooth segmenting curve 62

List of Tables

5.1 Performance evaluation for lumen area compared to manual segmentation. . . . . . . 53

14 LIST OF TABLES

Chapter 1

Introduction

Complications attributed to cardiovascular disease (CVD) are currently the main cause of deathworldwide. It is known that the majority of adverse CVD-related events are due to coronary arterydisease: a condition in which fatty lesions called plaques are formed on the walls of those vesselswhich nourish the heart with blood. These plaques may grow to sucient magnitude such thatblood ow is partially occluded. More critically, the sudden rupture of a plaque may lead to arapidly-progressing stenotic condition in which the blood supply is entirely cut o from a region ofthe heart. This condition may cause death.

Medical imaging has had tremendous advances in the last decade. Like that of providing struc-tural and functional imaging of the human body through a number of invasive, and non-invasive,methods which generate sensed data at varying degrees of resolution. In particular, contrast angiog-raphy is the standard technique for detecting and evaluating coronary artery disease. In recent years,a number of limitations of this technique have become apparent; these include the two-dimensionalnature of the images, the absence of information about the blood vessel wall, insensitivity to sub-stantial plaque burden in outwardly remodeled vessels and inability to detect vessel wall disruptionduring angioplasty. To overcome these limitations, intravascular ultrasound (IVUS) was developedtowards the end of the 1980's and has been rened and its clinical importance assessed through the1990's. IVUS is an invasive imaging technique capable of providing high-resolution, cross-sectionalimages of the interior of human blood vessels in real time; this allows to have morphological infor-mation of the vessel and by consequence of the plaque.

However, the advantages that IVUS can provide are not fully exploited due to certain problems.Specically, one of these problems is that the image sequences generated by IVUS are sometimesdicult to interpret, even by experts, making their fully-automated segmentation an open problemeven after over a decade of research.

Given that IVUS sequences may be hundreds to thousands of frames long, the manual segmenta-tion of a complete sequence is strictly prohibited and time-consuming. Even when possible, manualsegmentation still suers from inter- and intra-observer variability due to its high level of subjec-tivity: studies show that surprisingly large dierences (i.e., up to 20%) in the cross-sectional areaof luminal segmentations provided by the same observer may be possible [15]. Thus, an automaticsegmentation method for IVUS images is needed.

Automated segmentation of IVUS sequences has been a topic of interest since at least, the early1990's. The primary objectives of the majority of the algorithms are to delineate the lumen/intimaand media/adventitia borders (Fig. 1.1) with little or no human intervention. In atheroscleroticcases, we may refer to the region between these borders simply as the plaque.

16 Introduction

Figure 1.1: Lumen/intima and media/adventitia borders on IVUS image.

1.1 Objectives

The goal of this work is to develop a computational method for luminal border segmentation onIVUS images with minimal human intervention. This method should be fast, capable of segmentingvideo sequences, and robust to IVUS artifacts.

1.2 Contributions

The main contributions of this work are: 1) a probabilistic approach to the segmentation problemthat introduces a new parameterization of the lumen contour using a sum of Gaussian functions thatis deformed by the minimization of a cost function formulated using Markov-random eld modelswith a Bayesian; 2) a novel minimization method that linearly combines the descent directionsof the steepest descent and BFGS optimization methods within a trust region that stabilizes theconvergence; and 3) a multi-scale approach that increases considerably the speed of convergence.

1.3 Document Outline

Chapter 2 provides background to this work, both from the computer-science and the anatomicperspectives. Chapter 3 presents the state-of-the-art and previous works on IVUS segmentation.Chapter 4 presents our proposed work and some of the implementation details of these algorithms.In chapter 5, results are shown and discussed. Chapter 6 shows the conclusions.

Chapter 2

Background

In this chapter we introduce background on normal and pathological anatomy as the concepts behindthe ultrasound imaging in general and IVUS imaging in particular.

2.1 Anatomy and Physiology

To understand which structures are imaged under IVUS, the blood vessel anatomy is briey de-scribed.

2.1.1 Arterial Anatomy

The vessel wall is composed of multiple concentric layers (Fig. 2.1). In direct contact with the lumen(blood) is the tunica intima, which consists of three layers. The layer immediately adjacent to thelumen is the endothelium; this consists of a single layer of cells which act as a semipermeable barrierbetween the wall interior and the lumen. The remainder of the intima consists of a small layer ofconnective tissue (usually underdeveloped except in larger vessels) followed by the internal elasticmembrane. This elastic layer is, proportionally, much thicker than the other two layers.

Supporting the intima is the middle arterial layer, the tunica media. The media consists primarilyof layered smooth muscle cells, but in larger arteries may contain a greater degree of elastic tissue.Its homogeneous nature implies that, internally, it is fairly echofree (i.e. dark) under ultrasound.Hence, if the media is of sucient scale to be resolved, it will appear as a dark band near the luminalborder. It is bounded on the outside by the external elastic membrane.

The outermost layer of the artery is the tunica adventitia. This consists of irregularly-arrangedconnective tissue (collagen) and elastin. As the adventitia is the vessel's interface to surroundingstructures, it is normal to observe various features adjacent to it and apparently embedded within it(e.g., smaller vessels). Therefore, the adventitia could be considered not as a vessel layer in itself, butas a region of connective tissue which merges the vessel into surrounding structures; the adventitiaoften has no well-dened outer boundary.

2.1.2 Pathology of Atherosclerosis

Coronary artery disease (CAD) occurs as a result of atherosclerosis, a condition in which fatty lesionscalled plaques gradually build up on the walls of the coronary arteries (Fig. 2.2). Atherosclerosis is

18 Background

Figure 2.1: Blood vessel anatomy. (Credit: Maastricht, November 2005. Stijn A.I. Ghesquierewww.applesnail.net).

characterized by intima thickening, brosis, calcication, necrosis, and hemorrhage [9]. In the past,gradual fat deposition and consequent luminal narrowing (stenosis) of the coronary arteries werethought to be the culprit factors in CAD-induced coronary events. Now, it is instead believed thatthe majority of heart attacks are caused by inammation of the coronary arteries and thromboticcomplications. The process of atherosclerotic plaque formation is considered to be an inammatory,response-to-injury phenomenon; it is initiated by injury of the endothelium or smooth muscle cellsof the artery wall [24]. Damage may occur through various means: ow alterations which leadto shear stress, especially at vessel bifurcations; degradation due to age; intrinsic abnormalities inthe vessel wall; changes in blood chemistry; free radicals; diabetes; genetic alterations; infectiousmicroorganisms; hypertension; or elevated LDL cholesterol among other causes [9][25].

In particular, the disruption of a coronary plaque may lead to the creation of a thrombus or aectan existing thrombus superimposed on the plaque itself. If this brings about rapid stenosis, partiallyor entirely occluding blood ow, it may lead to critical ischemic events such as acute myocardialinfarction or sudden cardiac death.

2.2 Ultrasound

Ultrasound refers to the use of high-frequency acoustic waves (i.e., in the MHz range) for obtainingsignals which provide information about the interior structure of an object. In general, an ultrasoundpulse or wavelet is generated by a piezoelectric transducer which is coupled with the object surface;the subsequent reections from the object's interior are recorded for a brief period of time, generatinga 1-D time-domain signal. The principles of ultrasound imaging are very similar to the principlesof optics. For instance, reections only occur at the interface between objects of diering acousticimpedance (analogously, index of refraction). Hence, the interior of acoustically homogeneous objects

2.2 Ultrasound 19

Figure 2.2: Stages of atherosclerotic plaque growth beginning with a normal artery (left),and potentially advancing to a highly stenotic and calcied lesion (right). (Credit: SHAPEhttp://www.shapesociety.org).

are said to be echofree, hypoechoic, or echolucent. Acoustically heterogeneous objects are said to beechogenic or hyperechoic and generate stronger acoustic backscatter. In most medical applicationsof ultrasound, acoustically opaque objects are also encountered and frequently present a confoundingfactor. For instance, calcication (including bone) are highly echo-reective, so any feature behindthem in the path of the wavelet, are in shadow and generally cannot be imaged.

As the wave propagates, some of its energy is lost due to reection. However, a much greaterportion of the energy in the wave is lost due to absorption. This can be compensated by amplifyingthe returned signal according to a monotonically increasing function, which is essentially the inverseof the expected attenuation. This is referred to as time-gain compensation (TGC). Although TGCdoes not provide improvements with respect to signal to noise ratio (the SNR of the signal decreasesas attenuation increases), it renders an approximately consistent energy level across time to theresulting signal.

2.2.1 Imaging Modes

The simplest type of ultrasound imaging is termed A-mode; in this case, the 1-D ultrasound signalsthemselves (called A-lines) are plotted as a function of depth. This imaging mode is of limitedutility, but may be used to measure distances or the size of internal organs. The A-line signalsfrequently have a bandpass lter applied to them that is centered around the transducer frequency.This provides an improved SNR, eliminating non-linear reections and other noise.

B-mode imaging generates a more familiar and more easily interpreted 2-D image. In this case,an array of transducers or a single mechanically-actuated transducer, is used to rapidly retrieve A-lines from a number of directions which, when interpreted geometrically, typically radiate outwardin a disc or fan shape (Fig. 2.3).

We let the time-domain signal from a particular direction θ be yθ(t). To form a gray-level image,each point in time for each signal must have a gray level associated with it. Usually, the mapping is

20 Background

done so that brighter gray levels are associated with reections of greater amplitude [1]. One wayto do this is to take the envelope of the signal, so that the output will be real and non-negative(Fig. 2.4). For visualization, the dynamic range is often mapped using logarithmic compression(Fig. 2.5). M-mode refers to a video display of B-mode images, so organ dynamics may be viewedand measured over time.

As typical ultrasound B-mode imaging generates sequences of 2-D images, it is possible to gen-erate a 3-D volume of an object by sweeping the imaging plane along its structure. Viewing a sliceof this volume perpendicular to the imaging plane produces an L-mode image. This image mode iscommon in intravascular ultrasound and will be discussed later.

(a) (b) (c) (d)

Figure 2.3: Common ultrasound transducer congurations and examples: fan congura-tion (a) and example (b): fetal ultrasound (Credit: Towner County Medical Center.http://www.tcmedcenter.com); disc conguration (c) and example (d): cross-sectional interior ofa coronary artery.

Figure 2.4: Reected ultrasound signal (solid line) and its envelope (dashed line).

2.2 Ultrasound 21

(a)

(b)

Figure 2.5: IVUS B-mode image: (a) envelope of the signal; (b) envelope of the signal after log-compression.

2.2.2 Intravascular Ultrasound

Intravascular ultrasound (IVUS), as the name suggests, is designed to image the interior of a bloodvessel by being placed within the vessel itself. The IVUS sensor is part of a catheter assemblywhich is advanced percutaneously to the vessel of interest. For coronary imaging in humans, theentry point is the femoral artery in the leg (Fig. 2.6). The images that IVUS provide are typicallygenerated at video framerates (15 to 30 frames/s) and are cross-sectional with respect to the vesselaxis. Thus, ultrasound signals are emitted and received radially and scan-converted into a B-Mode2-D image (Fig. 2.7). For easier visualization the image is converted from polar (Fig. 2.7(a)) toCartesian coordinates (Fig. 2.7(b)), obtaining the familiar disk-shaped. To accomplish this type ofradial imaging, there are two primary types of IVUS catheter: single and multi-array transducercatheters. Those with a single transducer element must be mechanically rotated to achieve a 360

view of the surrounding vessel (Fig. 2.8(a)). In multi-array congurations, solid-state catheters aresurrounded by a series of transducers which are essentially activated in series, achieving a similareect (Fig. 2.8(b)). These catheters are currently constructed with up to 64 transducer elements.

For a typical study, continuously pulling back the sensor within its sheath allows a length of vesselto be imaged smoothly, (i.e., with no vessel wall friction). These pullback sequences may be analyzedmanually or reconstructed for a 3-D view of the vessel. Frequently, pullback sequences are viewedin L-mode (Fig. 2.9), where the 3-D structure of the vessel is more apparent. However, becausethe catheter is not always centered in the vessel, the wall appears to have sharp discontinuities asthe catheter shifts toward and away from the wall during pullback and recording. In many cases,pullback sequences are gated according to an electrocardiogram (ECG) signal in order to alleviatesome of the motion artifacts caused by the heart.

2.2.3 IVUS Images Properties

Dynamic Range. The term dynamic range refers to the range and precision of measurements aparticular sensor is able to capture. It is often expressed as a ratio of the maximum measurable valuedivided by the minimum dierentiable value in bits. Though this ignores potential non-linearity ofthe measurement spectrum, it is a convenient tool for inter-sensor and inter-datatype comparison.Applied to ultrasound, typical gray-level B-mode images have a dynamic range of about 8 bits(log2

2561 ). The raw ultrasound data from which B-mode images are derived may have a dynamic

range of 12 to 16 bits. While intentional reduction of the dynamic range of a signal is not generallybenecial, it is a common practice due to the constraints of the viewing hardware.

22 Background

Figure 2.6: Overview of IVUS catheter placement within the arterial system.(Credit: Montana StateUniversity. http://www.montana.edu/wwwai/imsd/diabetes/myocard.htm and Yale-New HavenHospital. http://www.ynhh-healthlibrary.org)

(a) (b) (c)

Figure 2.7: B-Mode IVUS representations: (a) IVUS image in polar representation; (b) IVUS imagein Cartesian representation; (c) the visible regions of this image: (A) the area occupied by theIVUS catheter; (B) The lumen; (C) the intima; (D) the media; (E) the adventitia and surroundingtissues.

2.2 Ultrasound 23

(a)

(b)

Figure 2.8: Catheter congurations: (a) single rotating transducer; (b) multi transducer array.(Credit: Normatem. http://www.normatem.com/vp.html)

(a) (b)

Figure 2.9: L-mode IVUS image from pullback sequence: (a) B-mode Cartesian IVUS image, theline indicates the transverse cut; (b) L-mode image from pullback sequence corresponding to thetransverse cut.

24 Background

Resolution. Due to the small scale of most vessels, the images generated by IVUS are necessarilyof much greater resolution than images generated by other ultrasound (and many non-ultrasound) invivo medical imaging methods. Since spatial resolution increases with transducer frequency, IVUScatheters typically operate in the 20 to 40 MHz range. However, attenuation also increases withfrequency, so we do not expect to image very far beyond the vessel border. Due to the rotationaltomographic nature of IVUS images, their spatial resolution is highly variable within a single image.Previous studies have divided IVUS image resolution into three components: axial, lateral, andout-of-plane. In image space, the axial direction is strictly away from the catheter and the lateraldirection is along any path at a constant distance from the catheter. The out-of-plane direction is,as the name suggests, perpendicular to both of these and is generally less of a concern; it primarilydecides the slice thickness of the IVUS image.

Axial resolution is much better than lateral, as we might expect. Notice how lateral sampling islimited by the hardware (i.e., the radial sampling rate and transducer size), whereas axial resolutionis limited only by the acoustic wavelength. Out-of-plane resolution is decided by the beam widthand actually improves as distance from the catheter increases. Lateral resolution degrades linearlywith distance from the catheter, while axial resolution is constant [8].

Speckle Noise. Speckle noise refers both to the seemingly random point-like artifacts visible inthe lumen and to the more organized interference patterns apparent even in relatively homogeneoustissues. The eects of speckle tend to increase with increasing catheter frequency, hence the lumen in20 MHz images (Fig. 2.10(a)) appears relatively echofree compared to 40MHz images (Fig. 2.10(b)).

In the past, speckle intensities have been modeled using a number of dierent distributions, thesimplest being Gaussian. The majority of later research eorts made the assumption that speckleintensities could be modeled using the Rayleigh distribution, similar to any object imaged underultrasound [10].

Other artifacts. After the piezoelectric transducer is excited to generate the initial ultrasoundwavelet, it takes some time for it to cease vibrating. This leads to an artifact called ringdown [6],which causes the appearance of one or more bright concentric rings close to the center of the IVUSframe (Fig. 2.11 (A)). These rings are usually cropped by the imaging software creating a lower limitfor the distance that a tissue must be from the catheter for it to be captured in the image.

Two common sources of acoustic shadowing artifact include the guidewire (Fig. 2.11 (B)) andecho-opaque calcication (Fig. 2.11 (C)). The guidewire may produce a series of partial rings due towire reverberation or wire/catheter interreections, followed by more distant shadowing behind thewire. Calcication does not produce these false reections, but may obscure a far greater portion ofthe image through shadowing.

2.2 Ultrasound 25

(a) (b)

Figure 2.10: A Comparison of (a) 20MHz and (b) 40MHz IVUS images. In both cases, the lumenborder has been outlined.

Figure 2.11: IVUS artifacts: (A) ringdown artifact; (B) guidewire artifact; (C) shadow due to plaquecalcication.

26 Background

Chapter 3

Previous Work

In the following section we describe some of the previous attempts for IVUS image segmentation.Also presented is the formulation, results, and deciencies of the recently-proposed method thatinspired our proposed work.

3.1 Previous Approaches to IVUS segmentation problem

So far, a number of segmentation techniques have been developed for IVUS data analysis. A greatportion of this work is based on local properties of image pixels, namely gradient based activesurfaces [12] and pixel intensity combined with gradient active contours [13]. Graph search was alsoinvestigated using local pixel features and gradient associated with line pattern correlation [30][29].

Another portion of the IVUS segmentation work was based on more global or region information.Texture-based morphological processing was considered [18]. Gray level variances were then usedfor the optimization of a maximum a posteriori (MAP) estimator modeling ultrasound speckleand contour geometry [11]. Despite all this research, in 2001 a clinical expert consensus fromthe American College of Cardiology [17] reported that no IVUS edge detection method had foundwidespread acceptance by clinicians.

Recently, the most reported successful approaches are based on contour detection using theminimization of a cost function of the boundary contours or deformable models. Among the rstapproaches, Sonka et al.[26] implemented a knowledge-based graph searching method, incorporatinga priori knowledge on coronary artery anatomy and a selected region of interest prior to the auto-matic border detection. Brusseau et al. [4] exploited an automatic method for detecting the luminalborder based on an active contour that evolves until it optimally separates regions with dierentstatistical properties.

Quite a few variations of active contour models exist in the literature. Some of them use gray-levelas intensity gradient information to create a potential eld in which the active contour is deformedby the minimization of an energy function[2]. However, since texture has proven to be an importantfeature for the analysis of generic images [16], other approaches make use of texture features todeform the model.

Regarding [7], texture features are computed using moments within a small local window aroundeach pixel, then clustering based on the Fuzzy C means algorithm is preformed in order to detectregions with the same texture pattern. Later morphological contour smoothing and boundary de-tection methods (Sobel lter) are used to segment the contours of the vessel layers. In [21] and [3]instead of using a heuristically constructed, potential eld, a priori knowledge is introduced: the

28 Previous Work

active contour is deformed on a likelihood map in order to obtain regions with homogeneous texturedescription, that is, maximizing the likelihood of the set of pixels to represent the same object.

Discrete wavelet frame (DWF) decomposition is proposed in [19] for detecting and characterizingtexture properties in the neighborhood of each pixel. This is a method similar to the discrete wavelettransform that uses a lter bank to decompose the image into a set of sub-bands. The main dierencebetween DWT and DWF is that in the latter, the output of the lter bank is not sub-sampled. Then,a low-pass lter is used in order to get smooth contours and eliminate discontinuities.

Some authors make use of the temporal information of the IVUS sequence, which results in a3D segmentation where, in most cases, the L-mode of the IVUS image is used. Cardinal et al. [5]propose a 3D IVUS segmentation model based on the fast-marching method and the use of gray-levelprobability density functions (PDF) of the vessel wall structure. The gray-level distribution of thewhole IVUS pullback is modeled with a mixture of Rayleigh PDFs computed using the expectation-maximization algorithm.

One of the latest approaches to IVUS image segmentation presented in the 2006 MICCAI con-ference, is the shape-driven segmentation of intravascular ultrasound images method by Unal etal.[28]; since our proposed method is inspired by this work, we will give more details on this approach.

3.2 Shape-driven Segmentation of IVUS Images

The technique presented by Unal et al. is a shape-driven approach to segmentation of the arterialwall from IVUS images in the B-Mode polar representation. The lumen and the adventitia contourare constrained with a smooth, closed geometrical shape model obtained statistically from trainingdata; then a non-parametric probability-density-based image energy function is used for driving thesegmentation.

3.2.1 Shape Model

The inner and outer arterial walls are modeled using an implicit shape representation by embeddingperiodic contours C ε Ω implicitly as the zero-level set of a signed distance function φ : R2 → Ω:

C = (x, y) ∈ Ω|φ(x, y) = 0 (3.1)

in the B-mode polar representation domain Ω ⊂ R2; where φ(x, y) < 0 is inside and φ(x, y) > 0 isoutside the contour.

To construct the statistical shape models, a set of N IVUS images manually segmented1 by anexpert are used. This set of images will be denominated training set.

The N contours of lumen φl1, ..., φ

lN, and media/adventitia φa

1 , ..., φaN of the training set are

radially aligned by cropping from the uppermost row coordinate where the contours can start, andthe lowermost row coordinate where the media/adventitia contours can end.

Then, the mean lumen φlmean = 1

N

∑Ni=1 φ

li and the mean media/adventitia φa

mean = 1N

∑Ni=1 φ

ai

shapes are calculated.

1In this case, manual segmentation consist in delineating the lumen and media/adventitia contours on the IVUSimages.

3.2 Shape-driven Segmentation of IVUS Images 29

3.2.2 Shape Space

In order to construct the shape space, shape variability matrices Sl and Sa are computed by sub-tracting the means from their corresponding contour of each shape in the training set.

Principal component analysis (PCA) is then carried out on both variability matrices to obtain amodel that represents each shape as variations around the mean; then, any contour can be approx-imated by

φl(ω) = φlmean +

k∑i=1

ωliU

li , (3.2)

where ωl = ωl1, ω

l2, ..., ω

lk are the weights associated with the rst k principal modes U l

i . Now anylumen and media/adventitia contour can be represented by a vector of weights associated with therst k principal modes of the lumen data.

The weights for any shape can be found using the following equation:

ωl = UTl (φl − φl

mean) . (3.3)

For the segmentation, the shape weights will evolve iteratively to deform the contour towardsthe lumen and media/adventitia borders on the image.

3.2.3 Lumen Segmentation

For the segmentation of the lumen, the shape model is initialized automatically using some priorinformation. Then, the contours are evolved by minimizing the following regional probabilisticenergy equation:

Elumen(ωl) =∫

Ω

−χin(x)log(Pin(I(x))dx+∫

Ω

χout(x)log(Pout(I(x))dx , (3.4)

where χ is an indicator function for inside and outside the contour and x = (x, y) are thecoordinates of a pixel with intensity.

I(x) = maxy0ε[0 y]

1y − y0 + 1

y∑yi=y0

I(x, yi) . (3.5)

The probability distribution Pin and Pout are estimated using a Gaussian Kernel density estima-tor: P (q) = 1

Nσ

∑Ni=1K( q−qi

σ ), where N is the number of pixels inside or outside the contour and

K(p) = 1√2πexp(−p2

2 ) with a heuristically calculated standard deviation value.

Using the Euler-Lagrange equations to nd the gradient ow of the lumen contours representedby the weight vector, we obtain the ordinary dierential equation to solve :

∂ωli

∂t=

∫C

−log( Pin(I(x))Pout(I(x))

)U lidx , (3.6)

where U li is the corresponding eigenshape.

30 Previous Work

3.2.4 Media/adventitia Segmentation

Taking into account that the media is observed as a thin black line and the adventitia tissue appearsvery bright because its echogenic characteristics, it is possible to employ the edge information forthe media/adventitia segmentation. A smoother version of the gradient is employed as the dierencebetween the average intensity of a square above and below the current pixel position.

Then, the evolution of the media/adventitia contour is computed using the average intensityof two oriented windows above and below the contour and the edge based energy derived into itsordinary dierential equation:

∂ωai

∂t=

∫C

∇G(x)Uai dx (3.7)

3.2.5 Lumen Segmentation Results with Unal et al. Method

The lumen segmentation part of this method was implemented and tested on images from our IVUSimage database. Figures 3.1, 3.2 and 3.3 depict the segmentation result for three images similar tothose used for training. As we can observe in these examples, the method was successful in ndingthe segmenting-contour.

Figure 3.4 depicts the segmentation result of an unseen image dierent from those used fortraining. It is evident that the method was not able to segment the luminal border. In the sameway, Fig 3.5 depicts the segmentation result of an angular-shifted version of image in Fig. 3.1 (shiftingin polar representation is equivalent to rotation in Cartesian representation). Despite this imagebeing the same that was previously segmented, the segmentation method fails because the shiftingconverts this image into an image dierent from those in the training set.

Previous IVUS image segmentation methods are almost always hampered by noise and artifactspresented in the IVUS images. Although active shape models have been shown to be robust to thisproblem, a training phase is required to provide the statistical knowledge that allows for segmentationof new images. However, having a training set that is suciently representative of all possible IVUSimages is a dicult task, due to the dierent shapes that the vessels can take and the variabilityof the IVUS catheters. In these cases, an IVUS image that is dissimilar in shape to those in thetraining set will be very dicult to segment with this method.

In summary, previous techniques were not able to solve the segmentation problem eciently dueto IVUS artifacts, and those that have shown better performance require a prior training phase.Next, we present a probabilistic approach for segmentation of the lumininal border of IVUS imagesthat do not require training and is robust to artifacts.

3.2 Shape-driven Segmentation of IVUS Images 31

(a) (b) (c)

Figure 3.1: Unal et al. segmentation method result, example 1: (a) IVUS image to segment; (b)segmentation result on polar representation; (c) segmentation result on Cartesian representation.

(a) (b) (c)


(a) (b) (c)


32 Previous Work

(a) (b) (c)

Figure 3.4: Unal et al. segmentation method result on an unseen IVUS image dierent from thoseused for training: (a) IVUS image to segment; (b) segmentation result on polar representation; (c)segmentation result on Cartesian representation.

(a) (b) (c)

Figure 3.5: Unal et al. segmentation method result on a shifted IVUS image: (a) IVUS imageto segment; (b) segmentation result on polar representation; (c) segmentation result on Cartesianrepresentation.

Chapter 4

Proposed work

Segmentation of the lumen by regular segmentation methods (those that assign a label to the pixelson the image to be segmented) is very dicult due to the characteristics and artifacts of the IVUSimages previously presented in section 2.2.3. In 20MHz IVUS images, the lumen and some regionsof the adventitia and surrounding tissues may have similar gray-level distribution (gure 4.1).Attempting to segment with these methods will result in an incorrect segmentation, with two ormore regions labeled as lumen. Similary, calcication shadows and guidewire artifacts (gure 2.11)could lead to an incorrect segmentation. Shadows may be labeled as lumen because of their darkness,and the region of the guidewire artifact that is inside the luminal border will be labeled as non-lumendue to its brightness.

To overcome these problems, we would like to nd the luminal border ([28][21] [5][3][2][4]) insteadof labeling the pixels that are lumen. This way, we will know that all the pixels within the luminalborder correspond to lumen.

Then, our proposed method makes use of a parametric curve that is deformed using a formulationbased on the work presented by Rivera et al.[23][22] for segmentation. This formulation avoids thenecessity of a training phase ([28][5][21]) making it robust to "unseen" IVUS images. The details ofour proposed formulation are presented next.

4.1 Formulation

Similarly with [28], we employ the B-mode polar IVUS image representation since it is the originalacquisition format and computations are much simpler due to the 1D appearance of the segmentingcontours (Fig. 4.2).

Thus, in the IVUS image domain Ω ⊂ R2, we dene the gray-level pixel intensity as I(x) fora pixel with coordinates x = (θ, r) where (θ, r) ⊂ Ω are the angle and radius of the IVUS imagerespectively (Fig. 4.3). In this domain, we parametrize the lumen contour as a function f(θ, C) thatdepends on the angle and the parameters C.

4.1.1 Probability Function

Since the contour delineates the luminal border, all the pixels inside this contour would correspondto lumen (foreground or class 1), while the pixels outside this contour would correspond to non-lumen (background or class 2). The class for each pixel in the image can be determined using the

34 Proposed work

Figure 4.1: IVUS regions with same gray-level distribution. (A) lumen, (B) adventitia and sur-rounding tissues.

Figure 4.2: Lumen contour in Cartesian (left) and polar (right) B-mode representations.

4.1 Formulation 35

Figure 4.3: Contour function on IVUS B-mode representation.

signed distance function:

g(x,C) = f(θ, C)− r, (4.1)

where the pixels with positive value have higher probability of corresponding to lumen and thosewith negative value of corresponding to non-lumen.

We use a sigmoid function (Fig. 4.4) to dene the probability Pin(x) of each pixel x to belongto the class lumen as follows:

Pin(x) =1

1 + e−λ(f(θ,C)−r). (4.2)

Using this formulation, the pixels far and above the contour will have a probability close to one forbelonging to lumen, while the pixels far and below the contour will have probability close to zero.For the pixels near the contour, depending on the value of λ and their distance to the contour, theprobability for these pixels of belonging to lumen will be around 0.5.

Figure 4.4: Sigmoid function example.

36 Proposed work

4.1.2 Cost Function

Inspired in the Bayesian formulation for image segmentation proposed by Rivera et. al. ([23][22]),we propose the cost function:

U(C) =∑

x

Pin(x,C)2d1(x) + Pout(x,C)2d2(x) . (4.3)

The functions d1 and d2 are dened as:

dk(x) = −log(vk(x, φk)) , (4.4)

where vk(x, φk) is the normalized likelihood of the pixel x to be generated by a model k withparameters φk. For our binary segmentation case:

P (x,C) = Pin(x,C) (4.5)

Pout(x,C) = (1− P (x,C)) . (4.6)

Since the square of a sigmoid function can be emulated with the same sigmoid function usingdierent values of λ, using equations (4.5) and (4.6) and we can rewrite equation (4.3) as:

U(C) =∑

x

P (x,C)d1(x) + (1− P (x,C))d2(x) . (4.7)

4.2 Segmentation Method Details

In order to implement the proposed formulation, we codify prior information in the contour parametriza-tion and likelihood functions. The optimization method is also an important issue since it willdetermine the velocity of convergence. In the following subsections we will describe the selectedcontour parametrization and how the likelihoods are obtained. In addition, techniques to acceleratethe segmentation of single images and a video sequences are described.

4.2.1 Lumen contour parametrization

Since we would like a smooth, close geometry curve for the lumen contour, we propose to model oursegmenting-contour using a mixture of Gaussians (radial basis function based parametrization). Thissimplify the calculus and give us the advantage that the smoothness of the curve can be controlled bytwo parameters: the number of Gaussians and the standard deviation. To reduce the computationcomplexity, we have decided to x the number of Gaussians N , and use the same standard deviationσ for all the Gaussians. Then, the lumen contour f(θ, C) for the parameters C = (C0, C1, ..., CN ) ismodeled with:

f(θ, C) = C0 +N∑

i=1

Ci exp(− 12σ2

(θ − µi)2) . (4.8)

Here, C0 is an oset value to move the curve without changing the shape and Ci ∀ i > 0 are thecoecients that control the contribution of each Gaussian i (with a xed value of mean µi) to thecurve (note that the number of Gaussians will be dim(C)− 1).

An important characteristic of the IVUS images in B-mode polar representation is the periodicitythat allows the transformation to B-mode Cartesian representation (the disk shape on Fig. 2.7(b)).Since the segmented images will be normally transformed to Cartesian representation for a betterunderstanding and visualization, it is necessary for our lumen contour to be periodical too.

4.2 Segmentation Method Details 37

In an IVUS image with width w, it is necessary to consider the pixels with angles θw−1 and θ0as the same point to add periodicity. Then, depending on the means and standard deviations, theGaussians in the beginning of the image will contribute to the end of the curve and the Gaussianson the end of the image will contribute to the beginning of the curve.

Then the periodical version of equation (4.8) is given by:

f(θ, C) = C0 +N∑

i=1

Ci exp(− 12σ2

(θ − µi)2)+

N∑i=1

Ci exp(− 12σ2

(θ + (w − 1)− µi)2)+

N∑i=1

Ci exp(− 12σ2

(θ − (w − 1)− µi)2) .

(4.9)

Finally, we impose the constraint C ≥ 0 to avoid the curve deforming "below" the image itselfand converge to a local minimum. The simplest way to impose this constraint is to square all thecoecients. Then we rewrite equation (4.9) as:

f(θ, C) = C20 +

N∑i=1

C2i exp(− 1

2σ2(θ − µi)2)+

N∑i=1

C2i exp(− 1

2σ2(θ + (w − 1)− µi)2)+

N∑i=1

C2i exp(− 1

2σ2(θ − (w − 1)− µi)2) .

(4.10)

4.2.2 Likelihoods

The likelihood vk(x, φi) is the chance for the pixel x = (θ, r) to be generated by a model k withparameters φi. We use gray-level information (i.e., the normalized histograms) in order to estimatethe likelihood of each pixel to belong to background or foreground. To estimate these distributions,the user provides samples in the form of a binary map over the IVUS image (Fig. 4.5(a)). Afterwards,the histograms of regions corresponding to foreground h1 and background h2 are computed using 50bins and then normalized (Fig. 4.5(b)). We obtain the likelihoods vin and vout by using the valueof the pixel gray-level I(x) on the normalized histogram with:

vin(x) =h1(I(x)) + ε

h1(I(x)) + h2(I(x)) + 2ε, (4.11)

where ε is a small constant that avoids a zero division, and

vout(x) = 1− vin(x) . (4.12)

The likelihood for lumen (Fig. 4.6(a)) and non-lumen (Fig. 4.6(b)) are then used for computing thedistances d1 and d2 by applying equation (4.4).

4.2.3 Optimization Method

To deform the lumen contour until it reaches the best segmentation, it is necessary to nd the valuesof C that minimize the the cost function of equation (4.7). However, because of the complexity ofthis function, it results very dicult to optimize it using analytical methods.

38 Proposed work

(a) (b)

Figure 4.5: User-provided prior information: (a) map with samples of the lumen and non-lumen;(b) 50 bins foreground and background normalized histogram.

(a) (b)

Figure 4.6: Empirical likelihoods for (a) foreground and (b) background.


A great number of numerical methods exist in the literature to approximate the solution ofoptimization problems; one of the simplest ways to solve our problem is by using the steepestdescent method. However, this approach could take a large number of iterations (i.e., time) toconverge to the solution.

Due to the non-linearity of our problem, another possibility for approximating the solution isto use the BFGS Quasi-Newton method[20]. This method uses second order information with anapproximation of the Hessian that is updated on each iteration to nd the optimal descent direction.Unfortunately, since our cost function has more than one local minima, mostly due to the similaritybetween the gray/level of lumen and some parts of the adventitia, solving a problem with thismethod could result in an incorrect over-segmentation if a big step during a certain iteration isgiven. To deal with this problem, we propose an optimization method that linearly combines thedescent directions from steepest descent (pG) and BFGS (pBFGS) methods within a trust-region,similar to the dogleg method [20]. We will refer to this method as G+BFGS optimization. Next,the details of steepest descent and BFGS will be described to introduce our proposed method.

4.2.3.1 Steepest descent method

The steepest descent method is a line search method that moves along the search direction pGk =

−∇fk, at every step k the new value for xk+1 is computed with xk+1 = xk + αkpGk .

The step length αk can be calculated in a variety of ways. A popular, inexact line search conditionstipulates that αk should rst give sucient decrease on the objective function f , as measured bythe following inequality:

f(xk + αkpk) ≤ f(xk) + c1αk∇fTk p

Gk , (4.13)

for some constant c1ε(0, 1). In other words, the reduction if f should be proportional to both the steplength αk and the directional derivative ∇fT

k pGk . This condition is known as the Armijo Condition.

The sucient decrease condition is not enough by itself to ensure that the algorithm makes rea-sonable progress, because it is satised for all suciently small values of α. To rule out unacceptablyshort steps, we introduce a second requirement called the Curvature Condition, which requires αk

to satisfy∇f(xk + αkpk)T pG

k ≥ c2∇fTk p

Gk , (4.14)

for some constant c2ε(c1, 1), where c1 is the constant from equation (4.13).

The sucient decrease and curvature conditions are known collectively as the Wolfe Ccondi-tions.

4.2.3.2 BFGS method

The Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization [20] is a method used to solvean unconstrained nonlinear optimization problem. This method is derived from the Newton'smethod, a kind of hill-climbing optimization techniques that seek the stationary point of a function,where the gradient is 0. Newton's method assumes that the function can be locally approximatedas a quadratic function in the region around the optimum, and uses the rst and second derivativesto nd the stationary point.

On BFGS the search direction pBFGSk at step k is given by the solution of the analogue of the

Newton equation:Bkp

BFGSk = −∇fk , (4.15)

where Bk is an approximation to the Hessian on that step; then the new point xk+1 is computedwith xk+1 = xk + αkp

BFGSk with ak chosen to satisfy the Wolfe conditions ((4.13) and (4.14)).

40 Proposed work

Instead of computing Bk at every iteration, it is updated in a simple manner by taking intoaccount the curvature measured in the most recent step. Suppose that we have generated a newiterate xk+1 and wish to construct a new quadratic model, of the form:

mk+1(p) = fk+1 +∇fTk+1p+

12pTBk+1p .

One reasonable requirement for Bk+1 based on the knowledge gained during the latest step is thatthe gradient of mk+1 should match the gradient of the objective function f at the latest two iter-ations xk and xk+1. Since ∇mk+1(0) is precisely ∇fk+1, the second of these conditions is satisedautomatically. The rst condition can be written mathematically as

∇mk+1(−αkpBFGSk ) = ∇fk+1 − αkBk+1p

BFGSk = ∇fk .

By rearranging we obtain:Bk+1αkp

BFGSk = ∇fk+1 −∇fk . (4.16)

To simplify the notation, it is useful to dene the vectors:

sk = xk+1 − xk, yk = ∇fk+1 −∇fk , (4.17)

so that (4.16) becomes:Bk+1sk = yk . (4.18)

We refer to this formula as the secant equation.

Given the displacement sk and the change of gradients yk, the secant equation requires that thesymmetric positive denite matrix Bk+1 maps sk into yk. This will be possible only if sk and yk

satisfy the curvature conditionsT

k yk > 0 , (4.19)

as is easily seen by multiplying equation (4.18) by sTk . When f is strongly convex, the inequality

(4.19) will be satised for any two points xk and xk+1. However, this condition will not always holdfor non-convex functions. In this case we need to enforce (4.18) explicitly, by imposing restrictionson the line search procedure that chooses α. The condition (4.18) is in fact, guaranteed to hold ifwe impose the Wolfe conditions on the line search.

To determine Bk+1, we have to solve the problem

minB

‖B −Bk‖ (4.20a)

subject to B = BT , Bsk = yk , (4.20b)

where sk and yk satisfy (4.19) and Bk is symmetric and positive denite. Using the weightedFrobenius norm, the unique solution of (4.20) is (see [20] for more details)

Bk+1 = (I − γkyksTk )Bk(I − γksky

Tk ) + γkyky

Tk , (4.21)

with

γk =1

yTk sk

. (4.22)

In order to get the descent direction pBFGSk , we need to solve the system in (4.15); which implies

solvingpBFGS

k = −B−1k fk . (4.23)

The computation of B−1k can be made by regular methods, however it is also possible to compute

directly the inverse of the Hessian approximation B−1k by using a formulation similar to the one used

to compute the Hessian approximation Bk itself.


We will denote the inverse of Bk by

Hk = B−1k ,

then the formula to update the Hessian can be derived by making a simple change in the argumentthat led to equation (4.21). Instead of imposing conditions on the Hessian approximation Bk,we impose similar conditions on their inverses Hk. The updated approximation Hk+1 must besymmetric, positive denite and must satisfy the secant equation (4.18), now written as

Hk+1yk = sk .

The condition of closeness to Hk is now specied by the following analogue of equation (4.20):

minH

‖H −Hk‖ (4.24)

subject to H = HT , Hyk = sk . (4.25)

The norm is again weighted Frobenius norm, by choosing a proper form for the norm (see [20]) weobtain a unique solution Hk+1 to equation (4.25) that is given by

Hk+1 = (I − ρkskyTk )Hk(I − ρkyks

Tk ) + ρksks

Tk , (4.26)

where

ρk =1

yTk sk

. (4.27)

Now the descent direction will be computed with

pBFGSk = −Hk∇fk . (4.28)

4.2.3.3 Steepest descent + BFGS optimization within a trust region (G+BFGS opti-mization)

On the curvature condition (4.19), when stkyk is greater than zero, the curvature of the function

is becoming more positive as the descending is approaching to a minimum. However, if stkyk < 0,

the curvature condition is not satised and a better descent direction is the negative gradient (i.e.,steepest descend direction). Additionally, we can note that for small values of the product st

kyk, thecomputation of the update formula for the Hessian, or its inverse is undened.

By design, the descent direction will be better the more positive the value of ρ is. Thus, thecontribution of the BFGS descent direction (pBFGS

k ) will be small when ρ is small, preferring steepestdescent direction pG

k . On the other hand, if the value of ρ is more positive, we want to take theBFGS descent direction pBFGS

k . Based on this analysis, we propose to compute the descent directionas a linear combination of both descent directions:

pG+BFGSk+1 = −[ψ(ρk)pBFGS

k + (1− ψ(ρk))pGk ] = − [(ψ(ρk)Hk∇fk) + ((1− ψ(ρk))∇fk)], (4.29)

where the function that controls` the contribution of each descent direction ψ(ρ) (Fig. 4.7) is denedas:

ψ(ρ) =

0 if ρ < 0

ρ2

K+ρ2 other case(4.30)

with the constant K experimentally determined to be K = 1× 10−4.

42 Proposed work

Although the problem with the curvature condition is solved using this linear combination, whenusing BFGS, if in some step the value of the inner product of yT

k sk is very small, but positive, thenthe value of ρ becomes large. Therefore Hk+1 becomes too large resulting on a big steep, evenwhen the calculated step size α satises the Wolfe conditions ((4.13) and (4.14). This is undesirablebecause a big step could lead to an incorrect segmentation moving the lumen contour to a regionwith gray-level prole similar to that of the lumen.

To solve this problem, we propose to restrict our proposed descent direction magnitude withina trust region controlled by a xed parameter T . Thus, after obtaining pG+BFGS

k with equation(4.29), the descent direction is normalized with:

pG+BFGSk =

pG+BFGSk

‖pG+BFGSk ‖

.

The nal descent direction (Fig. 4.8) is the normalized descent direction pG+BFGSk scaled by the

parameter of thrust region T :PG+BFGS

k = T pG+BFGSk

The solution to the cost function of equation (4.7) is approximated with algorithm 4.1.

Algorithm 4.1 G+BFGS optimization

Require: Initial point x0, thrust region value T , and a tolerance ε.1: Initialize H0 = I2: pG+BFGS

k = −∇f(x0)3: Set k = 04: while ‖∇f(xk)‖ > ε do

5: pG+BFGSk = pG+BF GS

k

‖pG+BF GSk ‖

6: PG+BFGSk = T pG+BFGS

k

7: Compute the step size αk to satisfy the Wolfe conditions8: xk+1 = xk + αkP

G+BFGSk

9: sk = xk+1 − xk

10: yk = ∇f(xk + 1)−∇f(xk)11: ρk = 1

yTk sk

12: Hk+1 = (I − ρkskyTk )Hk(I − ρkyks

Tk ) + ρksks

Tk

13: pG+BFGSk+1 = −[ψ(ρk)Hk∇fk + (1− ψ(ρk))∇fk]

14: Set k = k + 115: end while

4.2.4 Multi-scale Segmentation

Since the smoothness and detail of the segmenting contour are controlled by the number of GaussiansN and the value of σ, it would be necessary to have a fair number of Gaussians depending on thewidth w of the IVUS image to be segmented. However, the larger N is, the more time will benecessary to converge to a solution, due to the hard computation required to get the gradients oneach iteration.

To accelerate the convergence of our segmentation method, we use a multi-scale approach: rst, asmall number of Gaussians Ni (3 to 5) is used, when the optimization process converges to a solutionwe will have the rst approximation to the desired segmenting-contour; then more Gaussians areadded to the lumen contour function and the optimization method is started again, using as the


Figure 4.7: Contribution-control function ψ(ρ).

Figure 4.8: Proposed descent direction trajectory.

44 Proposed work

initial point the contour of the previous segmentation; this process is repeated until the maximumnumber of Gaussians is reached. To ensure velocity in the rst adjustments and good detail in thelast ones, the value of σ is reduced as the number of Gaussians is incremented.

In order to get the starting point Ci+1 for the next step from the previous segmentation (Fig. 4.9(a)),it is necessary to adjust the last curve yi(θ) to the function with the new number of Gaussians Ni+1

(Fig. 4.9(b)). Thus, we use the non negative least squares method [14] for computing the startingpoint for the next segmentation step:

Ci+1 = minC

12[f(θ, C)− yi(θ)]2 (4.31)

s.t. : C ≥ 0 (4.32)

Since solving no negative least squares problem results trivial, we will not elaborate on details.

(a) (b)

Figure 4.9: Adjustment of the lumen contour: (a) lumen contour modeled using 5 Gaussians and (b)contour adjusted to be modeled using 10 Gaussians. The + symbol indicates the Gaussian meansand the dashed line the lumen contour.

4.2.5 Derivatives

Since the Hessian of our cost function is approximated by the BFGS part of our method, it isonly necessary to compute the rst derivative. Fortunately, given the structure of the proposedformulation, the analytical derivation of the gradient is very simple. The gradient of (4.7) is givenby:

∇U(C) =∑

x

(d1(x)− d2(x))δP (x,C)dCn

(4.33)

with

δP (x,C)dCn

=λ exp(−λ[f(θ, C)− r])

[1 + exp(−λ[f(θ, C)− r])]2δf(x,C)dCn

(4.34)

4.3 Probabilistic Segmentation of IVUS Images with G+BFGS Method 45

and

δf(x,C)dCn

=

2C0 if n = 0

2Cn[N∑

i=1

exp(− 12σ2

(θ − µi)2)+

N∑i=1

exp(− 12σ2

(θ + (w − 1)− µi)2)+

N∑i=1

exp(− 12σ2

(θ − (w − 1)− µi)2)]

otherwise(4.35)

4.3 Probabilistic Segmentation of IVUS Images with G+BFGS

Method

In this section we present our algorithm for IVUS image segmentation and a method for semi-automatic segmentation of IVUS video sequences.

4.3.1 Proposed Method Parameters

From the previous formulation, it results evident that certain parameters must be set in order tostart our proposed method:

1. The sigmoid parameter λ is related to the uncertainty around the lumen-contour; this pa-rameter controls how much the contour can be deformed on a given iteration.

2. The initial point Cinit: Since our problem has a minimum on C = 0, the initial pointCinit must be dierent from zero to avoid the trivial solution. We have found that it is aconvenient to set the oset coecient to be at least the square of one quarter of the imageheight C0[0] =

√h/4 and the rest of the coecients to be half of the oset.

3. The number of Gaussians for each of the multi-scale steps depends on the smoothnessand detail for the segmenting curve. In the rst steps we preer speed over detail, so thenumber of Gaussians should be small. On the last step the curve will be close to solution,then we can use a larger number of Gaussians to get more detail. These values form a vectorNG = N0, N1, ..., Nmax where max is the maximum number of Gaussians allowed.

4. The mean of each Gaussian: This parameter is chosen such that the Gaussians are uniformlydistributed into the image width.

5. The value of standard deviation σ for each of the multi-scale steps: in the rst steps coveragerather than accuracy is of importance. In the last step, however, the value should be less toincrease accuracy. These values form the vector Σ = σ0, σ1, ..., σmax with the values σk ateach step k.

The parameters for segmenting the lumen contour with our proposed segmentation method wereselected by experimentation on a representative set of IVUS images from our database. For theresults in the next section, we have used the following values:

• λ = 0.8.

• Number of Gaussians for each step of the multi-scale segmentation NG = 3, 7, 9, 15

46 Proposed work

• Standard deviation for each step of the multi-scale segmentation Σ = 50, 25, 20, 15

Algorithm 4.2 describes the process for a single IVUS image segmentation.

Algorithm 4.2 Probabilistic segmentation for IVUS images

Require: IVUS image I on polar representation, an array with the values of the number of Gaus-sians to be used NG = N0, N1, ..., Nmax, an array with the values of the standard deviationsΣ = σ0, σ1, ..., σmax for each step, the starting point C0 and h1 and h2 computed from themap of the luminal area.

1: Compute the normalized histograms h1 and h2 form the map.2: Compute the likelihoods vin and vout with equations (4.11)) and (4.12).3: Compute the distances d1 and d2 with equation (4.4))4: Set i = 05: while i ≤ max do6: Find the segmenting-contour yi by solving Eq. (4.7) using the G+BFGS method of algorithm

4.1.7: Find Ci+1 by solving equation (4.32).8: Set i=i+19: end while

4.3.2 Video Sequence Segmentation

Since our segmentation method requires user intervention in order to provide the binary map forthe computation of the likelihoods, segmentation of a complete IVUS video sequence would be timeconsuming since it would be necesary to provide a map for each frame.

However, based on the fact that in normal conditions two consecutive IVUS frames have similargray-level distribution for lumen and non-lumen, we propose a semi-automatic segmentation methodfor IVUS video sequences that makes use of the histogram from the previously segmented frame tocompute the likelihoods of the next frame.

In the same way, the luminal border of consecutive frames will be similar, with some variationin its shape. Then, the resulting segmentation curve of the previous frame is used as the initialpoint (one near to the solution) for the next frame, improving the speed of convergence. Based onthis principle, only the rst frame is segmented starting with a small number of Gaussians; for thesegmentation of the consecutive frames we start with the maximun or one less than the maximunnumber of Gaussians. The coecients resulting from the adjustment of the previous segmentationcontour are then used as initial point.

Additionally, it is well known that as the number of samples is increased, the gray value classdistributions are better estimated by the histogram technique. We take advantage of this fact byaccumulating the histograms of the previously segmented frames from the video sequence and usingthem on the consecutive frames. This procedure can be seen as a re-enforced learning process.

Algorithm 4.3 presents our approach for semi-automatic segmentation of IVUS video sequencesbased on our probabilistic segmentation method.

4.3 Probabilistic Segmentation of IVUS Images with G+BFGS Method 47

Algorithm 4.3 Probabilistic segmentation for IVUS video sequences

Require: An array with the values of the number of Gaussians to be usedNG = N0, N1, ..., Nmax,an array with the values of the standard deviations Σ = σ0, σ1, ..., σmax for each step, startingpoint C0 and h1 and h2 computed from the map of the luminal area of the rst frame F0.

1: Set H1 = h1 and H2 = h2.2: Set i = 03: while i <= Number of frames do4: Segment frame Fi with algorithm 4.2 using H1 and H2 as the histograms and Ci as initial

point.5: Compute h1 and h2 from the resulting segmentation of frame Fi.6: Set H1 = H1 + h1 and H2 = H2 + h2

7: Compute Ci + 1 by solving equation (4.32).8: Set i = i+ 19: end while

48 Proposed work

Chapter 5

Results and Discussion

This chapter presents the results of lumen segmentation using our proposed method on a database of20MHz IVUS images provided by the Computational Biomedicine Lab of the University of Houston.

5.1 Lumen Segmentation of Fixed IVUS Images

5.1.1 Segmentation process examples

Figure 5.1 depicts a typical IVUS image. For the segmentation of this imgage, once the histogramsand likelihoods are computed from the user-provided map, the segmentation begins with the contourcorresponding to the initial point Cinit. On Fig. 5.2, we can observe that in the rst iterations ofthe rst multi-scale step, the segmenting-contour quickly deforms and a crude approximation to theluminal border shape is reached.

Once this step converges, more Gaussians with a dierent standard deviation are added to thecurve function. In Fig. 5.3 we can observe that after adding more Gaussians and a few moreiterations, the segmenting curve begins to look more like the true lumen contour. In step three,more Gaussians are added and at the end of this step the segmenting curve is close to the solution(Fig. 5.4). The maximun number of Gaussians is used in the last step. In Fig. 5.5, it can beobserved that the nal segmenting curve is more accurate with respect to the one obtained in stepthree. Figure 5.6 depicts the segmentation result of the IVUS image of Fig. 5.1. As we can observe,our method succeeded in the segmentation of this image.

5.1.2 Segmentation on shifted images

As it was described in chapter 3, one of the problems of the Unal et al. segmentation method wasthe incapability of segmenting unseen, shifted versions of the IVUS images used for training.

Since our method does not require a training phase, any unseen image can be segmented; Fig. 5.7depicts a 90 shifted version of the IVUS image of Fig. 5.1. As we can observe in Fig. 5.8, our methodwas able to segment the shifted image with practically the same result.

50 Results and Discussion

(a) (b)

Figure 5.1: A typical IVUS image to segment. (a) image in polar representation; (b) image inCartesian representation.

(a) (b) (c) (d)

(e) (f) (g)

Figure 5.2: Segmentation progress in step 1 of the multi-scale method: initial contour (a) andsegmentation after 1 (b), 2 (c), 5 (d), 15 (e), 30 (f) and 40 (g) iterations.

(a) (b) (c) (d)

(e) (f) (g)

Figure 5.3: Segmentation progress in step 2 of the multi-scale method: initial contour (a) andsegmentation after 1 (b), 2 (c), 5 (d), 15 (e), 30 (f) and 39 (g) iterations.

5.1 Lumen Segmentation of Fixed IVUS Images 51

(a) (b) (c) (d)

(e) (f)

Figure 5.4: Segmentation progress in step 3 of the multi-scale method: initial contour (a) andsegmentation after 1 (b), 2 (c), 5 (d), 15 (e) and 17 (f) iterations.

(a) (b) (c) (d)

(e) (f)

Figure 5.5: Segmentation progress in step 4 of the multi-scale method: initial contour (a) andsegmentation after 1 (b), 2 (c), 5 (d), 15 (e) and 25 (f) iterations.

(a) (b)

Figure 5.6: Segmentation result of IVUS image of Fig. 5.1. (a) segmented image in polar represen-tation; (b) segmented image in Cartesian representation.


(a) (b)

Figure 5.7: 90 shifted version of IVUS image of Fig. 5.1. (a) image in polar representation; (b)image in Cartesian representation.

(a) (b)

Figure 5.8: Segmentation result of IVUS image of Fig. 5.7. (a) image in polar representation; (b)image in Cartesian representation.

5.2 Segmentation on IVUS Video Sequences 53

5.2 Segmentation on IVUS Video Sequences

As it was presented before on section 4.3.2, segmentation of a complete IVUS sequence is possiblewith our method in a semi-automatic way. Figure 5.9 depicts the rst and last step of the IVUSvideo-sequences segmentation method for 5 consecutive frames of an IVUS sequence. After the rstframe of the sequence is segmented (Fig. 5.9(b)) the histograms are computed and added to theprevious histograms (Fig. 5.9(d)). Then, the segmenting-contour of this frame is adjusted and usedas the starting point for the next frame segmentation (Fig. 5.9(c)). These steps are repeated untilall of the frames in the video sequence are segmented.

Figures 5.9(a), 5.9(d), 5.9(g), 5.9(j) and 5.9(m) depict the progression of the histograms. As thesegmentation process advances, the histograms are smoother and a more accurate approximation tothe gray-level distribution of the clases is obtained.

Figure 5.10 depicts the segmentation result of these 5 consecutive frames in Cartesian represen-tation.

5.3 Validation

We evaluated our method by computing the three measures of accuracy recommended by Udupaet al. [27]. Specically, we computed the false negatives (FN), false positives (FP), true negatives(TN), and true positives (TP) by counting the number of pixels that were classied as backgroundand as lumen. For a set of 100 IVUS Images manually segmented two times by an expert, theperformance results comparing with automatic segmentation are shown in table 5.1.

Table 5.1: Performance evaluation for lumen area compared to manual segmentation. TPR andTNR stand for true positive rate, and true negative rate respectively. MEAN and SD are the meanand standard deviation of the performance parameters.

.MEAN% SD%

Accuracy 98.28 0.49TPR 95.57 1.69TNR 99.43 0.29

The agreement between the automatic and manual contour segmentations were analyzed usingthe root mean squared error (RMS) given by:

RMS(θ, θ) =

√√√√ 1N

N∑i

(θi − θi)2

where θi and θi are the coordinates of each of he N points i on the contours to be compared.

Figure 5.11(a) depicts the RMS histogram of the error resulting in the comparison betweenautomatic (A) and manual segmentation 1 (MS1), in addition Fig. 5.11(b) depicts the normalizedcumulative histogram of A vs. MS1. As we can observe, the error is smaller than nine pixels andabout 80% of the images have an error of 4 pixels or less. Similarly Fig. 5.12(a) and Fig. 5.12(b)depict the RMS histogram and normalized cumulative histogram respectively in the comparisonbetween automatic and manual segmentation 2 (MS2) with similar results.


(a) (b)

.

(c) (d) (e)

(f) (g) (h)

(i) (j) (k)

(l) (m) (n)

Figure 5.9: Video-sequence segmentation process: (a) histograms used to segment frame 1; (b) frame1 segmentation result; (c) initial point for frame 2 segmentation; (d) re-computed histograms usedto segment frame 2; (e) frame 2 segmentation result; (f) initial point for frame 3 segmentation;(g) re-computed histograms used to segment frame 3; (h) frame 3 segmentation result; (i) initialpoint for frame 3 segmentation; (j) re-computed histograms used to segment frame 4; (k) frame 4segmentation result; (l) initial point for grame 5 semgnetation; (m) re-computed histograms used tosegment frame 5; (n) frame 5 segmentation result.

5.3 Validation 55

(a) (b)

(c) (d)

(e)

Figure 5.10: Segmentation of 5 consecutive frames in Cartesian representation.


Figures 5.13(a) and 5.13(b) depict the RMS histogram and normalized cumulative histogramrespectively of the comparison of MS1 and MS2. Here we can observe that the error is always lessthan 8 pixels and that about 90% of the images have an error of 4 pixels or less.

Figure 5.14 depicts the RMS normalized cumulative histogram of the three comparisons, as wecan observe, the results of our automatic segmentation method are close to the inter-variabilitybetween the manual segmentations.

(a) (b)

Figure 5.11: (a) Histogram and (b) cumulative histogram of the RMS between A and MS1.

(a) (b)

Figure 5.12: (a) Histogram and (b) cumulative histogram of the RMS between A and MS2.

5.4 Results on IVUS Images with Artifacts

The principal problem of previous segmenting methods is related to how the artifacts on the IVUSimages are handled. Figure 5.15 depicts an IVUS image with a shadow artifact due to calcied plaque.Altough this shadow could be mistakenly interpreted as lumen since it has gray-level intensitiessimilar to the lumen region, we can observe in Fig. 5.16 that our segmentation method was able tond the luminal border correctly.

Normally, the ringdown artifacts are removed by cropping the region that presents this artifact orsimply replacing it with some uniform color; however sometimes this artifact is not removed. Sinceguidewire artifacts are more dicult to remove, they are commonly found on IVUS images. Because

5.4 Results on IVUS Images with Artifacts 57

(a) (b)

Figure 5.13: (a) Histogram and (b) cumulative histogram of the RMS between MS1 and MS2.

Figure 5.14: Cumulative histograms of the RMS between A vs. MS1, A vs. MS2 and MS1 vs. MS2.

(a) (b)

Figure 5.15: IVUS image with shadow artifact: (a) image on polar representation; (b) image onCartesian representation. The arrow indicates the shadow artifact due a calcied plaque.


(a) (b)

Figure 5.16: Segmentation result of image in Fig. 5.15: (a) image in polar representation; (b) imagein Cartesian representation.

this artifact shows a bright prole, it can easily be confounded with plaque or other tissue and leadto an incorrect segmentation. Fig. 5.17 depicts an IVUS image with three artifacts: a ringdownartifact, a small guidewire artifact and a shadow artifact. Fig. 5.18 depicts the segmentation result.As we can see, none of these artifacts aected the performance of the segmentation.

Figure 5.19 depicts an IVUS image with 2 artifacts: a shadow in all the areas beyond theplaque due to calcication and a larger guidewire than the one on IVUS image in Fig. 5.17. Thesegmentation result on this image is depicted on Fig. 5.20. Again, our method was capable ofsegmenting the image, despite the shadow and the guidewire artifact.

Side branches are identied as the opening formed when the vessel being imaged bifurcates. Thisis visualized as an area of dark intensity extending from the lumen in the near eld towards thefar eld; this represents a challenge for any active-contour based segmentation method because thesegmenting contour could advance through this shadow and lead to an incorrect segmentation of theluminal border. Fig. 5.21 depicts a relative healthy vessel (i.e., only a small plaque is present) witha side branch.

In our method, the smoothness of our segmenting contour makes our method robust to sidebranches. Fig. 5.22 depicts the segmentation result of this image. For the segmentation of thisimage, we used the parameters previously presented. However, if we adjust the smoothness toachieve a better detail, the contour will tend to attempt segmentation of the side branch as lumen,and we will obtain incorrect segmentation. Fig. 5.23 depicts the segmentation result when wereduce the smoothnes of the curve to get more detail. As we can observe, the contour is closer tothe media/adventitia border than in the previous segmentation, however the side branch has beenincorrectly segmented as lumen.


(a) (b)

Figure 5.17: IVUS image with three artifacts: (a) image in polar representation; (b) image inCartesian representation. The arrows indicates the artifacts: (1) ringdown artifact; (2) guidewireartifact; (3) shadow artifact.

(a) (b)



(a) (b)

Figure 5.19: IVUS image with large guidewire artifact: (a) image in polar representation; (b) imagein Cartesian representation. The arrow indicates the guidewire artifact.

(a) (b)



(a) (b)

Figure 5.21: IVUS image with side branch: (a) image in polar representation; (b) image in Cartesianrepresentation. Arrow (1) indicates the small plaque and arrow (2) the side branch.

(a) (b)

Figure 5.22: Segmentation result of IVUS image in Fig. 5.21: (a) image in polar representation; (b)image in Cartesian representation.


(a) (b)

Figure 5.23: Segmentation result of IVUS image in Fig. 5.21 with a less smooth segmenting curve:(a) image in polar representation; (b) image in Cartesian representation.

Chapter 6

Conclusions

We have presented a probabilistic, semi-automatic segmentation method for lumen segmentation ofIVUS images and video sequences, that is robust to artifacts and does not require prior training.

In addition, we have introduced our proposed G+BFGS optimization that has proven to be anideal method for this kind of problems because it is faster than the steepest descent optimization byitself. At the same time, it can be controlled to avoid big steps that lead to incorrect segmentations.

Our contour parametrization makes possible the multi-scale segmentation. This approach al-lows us to get more accurate segmenting-contours on the last step and increases considerably thesegmentation process speed on xed images and video sequences.

In our experiments, this method has demonstrated a good performance on segmenting xed20MHz IVUS images and video sequences. However, the success and accuracy of our method dependsmostly on the samples of the lumen and non-lumen area. For this reason the user-provided, binarymap is the most important step in the segmentation process: incorrect or non-representative sampleswill lead to an incorrect or inaccurate segmentation.

The importance of the initial point Cinit as a factor is undeniable. For the majority of thecases our proposed initial point will work. However, in some images where the lumen area is verysmall, our proposed initial point will be located within the plaque or even the adventitia. It wouldbe impossible for our contour to move to the luminal border. On the other hand, if the initialpoint is close to zero, it is possible that the segmenting contour converges to the trivial solutionC = 0 resulting in a null segmentation. We believe that the value for the initial point should be setaccording to the characteristics of the image (i.e. shape of lumen), however we will work on how toget rid of the trivial solution on our formulation.

Our proposed method has shown to be robust with respect to the choice of the parameters.However, it is important to dene the number of Gaussians and the standard deviations accordingto the detail we want and the desired speed. Then the smoothness of the contour is also an importantparameter to x in order to avoid problems with side branches and calcication.

6.1 Future Work

As we have commented before, the trivial solution for our problem could result in a null segmentation.We will try to remove this from our formulation by adding a penalization factor in the cost function.

64 Conclusions

Since our formulation is designed to deform the segmenting-contour until it reaches a zone withgray-values dierent from the luminal area, it is possible that the modied-intensity proposed byUnal et. al. [28] increments our accuracy on the segmentation.

Likewise, the probability distribution estimator proposed for Pin and Pout proposed by the sameauthor, could replace the histograms for estimating the gray-level distributions. We will examinethese factors in future work.

Prior detection of side branches could be a good idea to implement as well. If we previouslydetect the side branches, we could change the standard deviation (augmenting it) for a particularGaussian that is close to it. We are able to avoid incorrectly segmenting that side branch as lumenwithout sacricing detail on the rest of the contour.

For higher-frequency IVUS images (i.e., 30-40 MHz) the speckle noise will be higher. Since ourmethod uses only gray-level histograms to compute the likelihoods, the segmentation of these imageswill be impossible. To solve this problem, we believe that by incorporating texture features in our apriori information [7], we will have better likelihoods that would lead to a successful segmentationon those modalities.

Finally, media/adventitia border segmentation is still a problem to be solved by our method.The media is observed as a thin black line and the adventitia tissue appears very bright due toits echogenic characteristics [28]. We believe that this same formulation will work to segment themedia/adventitia contour by combining pixel intensities with image-gradient information [13] on thea priori information (i.e., likelihoods) with some minor modications to our segmentation method.

Bibliography

[1] J. C. Bamber. Image formation and image processing in ultrasound.http://mpss.iop.org1999/pdf/bamber.pdf, 1999.

[2] C. V. Bourantas, M. E. Plissiti, D. I. Fotiadis, V. C. Protopappas, G. V. Mpozios, C. S.Katasouras, I. C. Kourtis, M. R. Rees, and L. K. Michalis. In vivo validation of a novel semi-automated method for border detection in intravascular ultrasound images. The British Journalof Radiology, 78(926):122129, Feb 2005.

[3] Ellen Brunenberg, Oriol Pujol, Bart ter Haar Romeny, and Petia Radeva. Automatic ivussegmentation of atherosclerotic plaque with stop and go snake. In MICCAI, 2006.

[4] E. Brusseau and C. L. de Korte. Fully automatic luminal contour segmentation in intracoronaryultrasound imaging - a statistical approach. IEEE Trans. on Med. Imag., 2004.

[5] Marie-Helene Roy Cardinal, Kean Meunier, Guilles Soulez, Roch L. Maurice, Eric Therasse,and Guy Cloutier. Intravascular ultrasound image segmentation: A three-dimensional fast-marching method based on gray level distribution. IEEE Transactions on Medical Imaging,25(5):590601, May 2006.

[6] F. J. de Ana and M. O'Donnell. Ringdown reduction for an inraluminal ultrasound array usingdepth-dependent azimuthal lters. In Proc IEEE Ultrasonics Symposium, pages 17301733,2002.

[7] Esmeraldo dos Santos Filho, Makoto Yoshizawa, Akira Tanaka, and Yoshifumi Saijo. A study onintravascular ultrasound image processing. Record of Electrical and Communication EngineeringCconversazione Tohoku University, 74(2):3033, 2006.

[8] M. R. Elliott and A. J. Thrush. Measurement of resolution in intravascular ultrasound images.Physiol Meas, 17(4):259265, November 1996.

[9] C.K. Friedberg. Diseases of the Heart, chapter 16: Coronary arteriosclerosis, pages 336352.W. B. Saunders Co., 1949.

[10] D. Guo. Intravascular ultrasound speckle statistics. In Proc IEEE Engineering in Medicine andBiology Society, pages 796799, 1998.

[11] C. Haas, H. Ermert, S. Holt, P. Grewe, A. Machraoui, and J. Barmeyer. Segmentation of3d intravascular ultrasonic images based on a random eld model. Ultrasound Med. Biol.,26(2):297306, 2000.

[12] J. D. Klingensmith, R. Shekhar, and D. G. Vince. Evaluation of three-dimensional segmenta-tion algorithms for the identication of luminal and medial-adventitial borders in intravascularultrasound images. IEEE Trans. Med. Imag, 19(10):996110, Oct 2000.

66 BIBLIOGRAPHY

[13] G. Kovalski, R. Beyar, R. Shofti, and H. Azhari. Three-dimensional automatic quantitativeanalysis of intravascular ultrasound images. Ultrasound Med. Biol, 26(4):527537, 2000.

[14] Charles L. Lawson and Richard J. Hanson. Solving least squares problems. Prentice-Hall,Englewood Clis, 1974.

[15] D. S. Meier, R. M. Cothren, D. G. Vince, and J. F. Cornhill. Automated morphometry of coro-nary arteries with digital image analysis of intravascular ultrasound. Am Heart J, 133(6):681690, June 1997.

[16] Mezaris, V. Kompatsiaris, I. Strintzis, and M. G. Still image segmentation tools for object-based multimedia applications. International Journal of Pattern Recognition and ArticialIntelligence., 18(4):701726, 2004.

[17] G. S. Mintz, S. E. Nisen, W. D. Anderson, S. R. Bailey, R. Erbel, P. J. Fitzgerald, F. J. Pinto,K. Roseneld, R. J. Siegel, E. M. Tuzcu, and P. G. Yock. American college of cardiologyclinical expert consensus document on standards for acquisition, measurement and reporting ofintravascular ultrasound studies (IVUS). J. Am. Coll. Cardiol, 37(5):14781492, 2001.

[18] A. Mojsilovic, M. Popovic, N. Amodaj, R. Babic, and M. Ostojic. Automatic segmentation ofintravascular ultrasound images: a texture-based approach. Ann. Biomed. Eng., 25(6):10591071, 1997.

[19] M.Papadogiorgaki, V.Mezaris, Y.S.Chatzizisis, I.Kompatsiaris, G.D.Giannoglou, andM.G.Strintzis. A fully automated texture-based approach for the segmentation of sequential ivusimages. In 13th International Conference on Systems, Signals and Image Processing (IWSSIP2006), September 2006.

[20] J. Nocedal and S. J. Wright. Numerical Optimization. Springer, 1999.

[21] Oriol Pujol and Petia Radeva. Texture segmentation by statistical deformable models. Inter-national Journal of Image and Graphics, 4(3):433452, 2004.

[22] Mariano Rivera and Pedro P. Mayorga. Quadratic Markovian probability elds for image binarysegmentation. In Proc. ICV'07, 2007.

[23] Mariano Rivera, Omar Ocegueda, and Jose L. Marroquin. Entropy-controlled quadraticMarkov measure eld models for ecient image segmentation. IEEE Trans. Image Process-ing, 8(12):30473057, Dec. 2007.

[24] R. Ross. The pathogenesis of atherosclerosis: A perspective for the 1990s. NATURE, 362:801809, April 1993.

[25] R. Ross. Atherosclerosis: an inamatory disease. New England J Med, 340(2):115126, January1999.

[26] M. Sonka and X. Zhang. Segmentation of intravascular ultrasound images: A knowledge-basedapproach. IEEE Trans. on Medical Imaging, 14:719732, 1995.

[27] J. Udupa, Y. Jin, C. Imielinska, A. Laine, W. Shen, and S. Heymseld. Segmentation and eval-uation of adipose tissue from whole body MRI scans. In Proc. 6th International Conference onMedical Image Computing and Computer-Assisted Intervention, Montreal, Canada, November15-18, pages 635642, 2003.

[28] Gozde Unal, Susann Bucher, Stephane Carlier, Greg Slabaugh, Tong Fang, and Kaoru Tanaka.Shape-driven segmentation of intravascular ultrasound images. In Proc. International Workshopon Computer Vision for Intravascular Imaging (CVII), MICCAI, Copenhagen, Denmark., 2006.

BIBLIOGRAPHY 67

[29] C. von Birgelen, C. D. Mario, W. Li, J. C. H. Schuurbiers, C. J. Slager, P. J. de Feyter, P. W.Serruys, and J. R. T. C. Roelandt. Morphometric analysis in three-dimensional intracoronaryultrasound: an in vitro and in vivo study using a novel system for the contour detection oflumen and plaque. Am. Heart J., 132(2):516527, 1996.

[30] X. Zhang, C. R. McKay, and M. Sonka. Tissue characterization in intravascular ultrasoundimages. IEEE Trans. Med. Imag, 17(6):889899, Dec 1998.

A probabilistic segmentation method for IVUS images Tesis

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