COLOR DOPPLER FLOW IMAGE ANALYSIS -...

CHAPTER 5

COLOR DOPPLER FLOW IMAGE ANALYSIS

5.1 INTRODUCTION

Doppler echocardiography is the most direct and theoretically accurate technique for

assessing blood flow [Miguel, 2002]. Combining blood velocity with the cross-sectional area of

the orifice through which the blood is flowing provides the basis to quantify blood flow

[Pinjari, 2009]. Color Doppler flow is the initial approach currently used for the diagnosis of

mitral regurgitation and stenosis [Hari, 1998]. This capability has generated great excitement

about the use of the technique for identifying valvular, congenital, and other forms of heart

disease, as the color flow image imparts spatial information to the Doppler data. To

inexperienced Doppler users, the color flow display makes the Doppler data more readily

understandable because of the avoidance of complex spectral velocity displays.

In this chapter a comprehensive discussion of color Doppler flow image analysis is

presented. It includes the following: understanding of the Doppler images, interpretation,

segmentation using Fast SQL K-Means Color clustering algorithm, pixel-classification based

segmentation, and qualitative feature extraction.

The major research contribution with respect to Doppler images is the analysis of Doppler

images using some novel methods for various image processing techniques, statistical methods,

pattern recognition, etc.

5.2 BASICS OF COLOR DOPPLER IMAGES

Doppler echocardiography is an integral part of almost every ultrasonic examination of the

heart. Thus knowledge of Doppler principles is essential for anyone involved with

echocardiography [Ashraf, 2006] [Feigenbaum, 1993]. It is primarily a technique for recording

the manner in which blood moves within the cardiovascular system. Blood flowing through the

heart and blood vessels can be either laminar or turbulent. Laminar flow occurs when the

CHAPTER 5 - COLOR DOPPLER FLOW IMAGE ANALYSIS

123

majority of flow is moving in the same direction and at similar velocities. Turbulent flow

occurs when flow is disturbed, by a stenosis or regurgitation.

By convention, flow that is moving away from the transducer is encoded in blue and flow

that is moving toward the transducer is encoded in red (that is, BART – Blue Away Red

Toward) as shown in Figure 5.1 (a).

.

Fig. 5.1 Doppler images (a) Color flow direction during early systole (Normal patient

(b) Abnormal patient (severe MR)

5.2.1 THE MEANING OF COLOR

The position of the transducer or probe is at the apex or head of patient (marked with red

arrow). So the blue color pattern shows that the flow is away from the probe and similarly red

color shows the flow toward the probe. When a mosaic color pattern is seen in the image

signifies abnormality (severe MR in the case of Figure 5.1(b)).

Fig. 5.2 Three color bars from a color flow system. When there is no flow, black is displayed (center) in

the standard bar (left), flow toward the transducer at the top is in red, flow away in blue.

Progressively faster velocities are displayed in brighter shades of red or blue. The center bar is in an

enhanced map, and the right bar in a variance map.

In addition to this color scheme, three color bars also appear on the right top corner or left

top corner of the image as shown in Figure 5.1 (a) and (b). These colors contain useful

information. As shown in Figure 5.2, in addition to simple direction, velocity information is

Apex

Color

Bar Color

Bar


124

also displayed. Progressively increasing velocities are encoded in varying hues of either red or

blue. The more dull the hue, the slower the velocity. The brighter the hue, faster is the relative

velocity. In the color bar shown in the center of Figure 5.2, the colors have been “enhanced” so

that the hues of red are increased from very dull red to bright yellow and the hues of blue are

increased from very dull blue to a bright pale blue.

The enhanced map helps a beginner to understand the relationship between velocity and

color. The bar at the right demonstrates variance. As will be seen later, color is also used to

display turbulent flow and allows an operator to discriminate between normal and abnormal

flow states [Joseph, 2010].

5.2.2 INTERPRETING COLOR DOPPLER IMAGES

Doppler flow imaging is fairly a complex technology, which therefore can be influenced by

many technical factors. Perhaps the most useful application of color flow imaging is in the

detection of valvular regurgitation. Typically, the following abnormalities can be studied using

color Doppler image analysis:

Valvular Regurgitation

o Aortic insufficiency

o Tricuspid Regurgitation

o Pulmonic insufficiency

Valvular Stenosis

o Mitral Stenosis

o Aortic Stenosis

o Tricuspid and Pulmonic Stenosis

The regurgitation and stenosis diseases can easily be identified based on the mosaic color

pattern present in the various cardiac chambers. For example, MR and AR abnormalities are

shown in Figure 5.3(a) and 5.3(b) respectively.

Fig. 5.3 Valvular Defects in Apical four chamber view (a) Severe MR (b) Severe AR


125

Fig. 5.4 Stenosis Defects in Apical four chamber view (a) MS (b) AS

Similarly, MS and AS with mosaic colors are shown in Figure 5.4(a) and 5.4(b)

respectively [Paul, 2011]. In contrast, a normal color Doppler image will not carry the mosaic

color pattern, but either red or blue uniform color as shown in Figure 5.5.

Fig. 5.5 Color Doppler image with uniform color pattern (Normal patient)

Color flow Doppler echocardiography also has an extremely useful role in the assessment

of congenital abnormalities [Pinjari, 2009]. By superimposing flow data on the two-

dimensional echocardiogram, recognition of abnormal flows is easy in many disorders. For

example, Atrial septal defect, Ventricular septal defects are some of the abnormalities that can

easily be identified.

5.3 SEGMENTATION OF COLOR DOPPLER IMAGES

This section discusses three novel methods to segment the color Doppler images. Without

extracting the color portion of the image, the analysis either difficult or impossible [Ashraf,

2006]. Therefore, the primary goal is to design a fast, accurate, and robust algorithm to identify


126

the color segment and analyze the pixel data associated with it. Following three methods are

proposed in this research work:

a) Fast SQL based K-Means Color Clustering Algorithm

b) Accelerated SQL K-Means Color Clustering Algorithm

c) Pixel-Classification Algorithm

The first two methods are based upon the grayscale versions discussed in Chapter 3, and the

third is a fast rule based classification algorithm which does not require database and SQL.

5.3.1 FAST SQL BASED K-MEANS COLOR CLUSTERING ALGORITHM

The proposed method of segmenting the color Doppler image is an extension of the

algorithm shown in Section 3.5. The primary difference between the two methods is the

dimension.

CData CCentroid

CEucl CCVCD

CSI

i j R G B

Fig. 5.6 Schema for fast SQL based K-Means Clustering Algorithm

Step 1: [Initialize CData with image pixel data]

CData

i x y R G B

j x y R G B

i d1 d2 d3

i j R G B

i x y R G B

1

2

3

4

..

..

..

n


127

Step 2: [Initialize CCentroid with 3 rows from CData]

CData CCentroid

Step 3: [Initialize CEucl table with Euclidean distances from each pixel to each of the

centroids]

CData

CEucl

CCentroid

Step 4: [Initialize CCVCD table]

Euclidean

distance

i x y R G B

1

2

3

4

..

..

..

n

j x y R G B

1

2

3

i d1 d2 d3

1

2

3

4

n

i x y R G B

1

2

3

4

..

..

..

n

j x y R G B

1

2

3

random

selection

i j R G B

1 3

2 3

3 2

4 3

.. ..

.. ..

n 1


128

Step 5: [Iterate and Update tables: CVCD, CCentroid, and CEucl]

CCentroid

CEucl

CCVCD

Fig. 5.7 Flow showing the initialization and update steps

Since the Doppler images are pseudo color images, where RGB values of the color region

are different but the rest of the pixels is same, it is important to extend the grayscale

segmentation algorithm to suit the color version by replacing val attribute with three attributes

R, G, and B. Figure 5.6 shows the modified schema. The table CData is to store the color pixel

data (RGB values) and its spatial locations (x and y co-ordinates).

Similarly, CCentroid plays the same role as that of Centroid table for grayscale 2D echo

images except that all three color pixel data must be stored. This concept is extended to all

other tables as well, except CEucl, because in this table only the three distances need to be

stored and k is 3. The working of the proposed algorithm can be pictorially depicted in

i j R G B

1 2

2 3

3 3

4 3

.. ..

.. ..

n 1

j x y R G B

1

2

3

i d1 d2 d3

1

2

3

4

n

Find the Euclidean distance

from every centroid to all pixels

in CData

Assign cluster #

to all pixels

Find new means

from each

cluster data


129

Figure 5.7. The first three steps are initialization steps and executed only once, whereas step 4

which in turn consists of substeps are primarily to update CCentroid, CEucl, and CVCD tables.

The iteration is terminated after some definite number of iterations specified by the user. Again

all clustering activities are carried out within database tables and no PL/SQL statements are

used in the implementation.

5.3.2 ALGORITHM AND ITS IMPLEMENTATION

The algorithm for the color Doppler images is same as the algorithm shown in Figure 3.8 of

Chapter 3 with a difference in the number of dimensions which is 3. All other steps will remain

same.

SQL Statements for Initialization Steps

The image pixel values (RGB) are read from the image and stored in the table CData using

parameterized method as shown below:

Step 1:

Insert into CData (i, x, y, R, G, B)

Values (:i, :x, :y, :R, :G, :B);

The next step is to select three random pixel data from CData and this is accomplished by

calling random number generator.

Step 2:

Insert into CCentroid (

Select 1, x, y, R, G, B

From CData

Where i = ……..; % select first random row number from CData



From CData

Where i = ……..; % select second random row number from CData



From CData


130

Where i = ……..; % select third random row number from CData

To initialize CEucl table, the Euclidean distance is computed from each row of CCentroid

to all the rows in CData and so populated. Three distances corresponding to each cluster and is

shown below:

Step 3:

INSERT into CEucl (

SELECT i, sqrt(power((CData.R-c1.R),2) + power((CData.G-c1.G),2) +

power((CData.B-c1.B),2)) as d1,

sqrt(power((CData.R-c2.R),2) + power((CData.G-c2.G),2) +

power((CData.B-c2.B),2)) as d2,

sqrt(power((CData.R-c3.R),2) + power((CData.G-c3.G),2) +

power((CData.B-c3.B),2)) as d3

FROM CData, (SELECT * FROM CCentroid where j = 1) c1,

(SELECT * FROM CCentroid where j = 2) c2,

(SELECT * FROM CCentroid where j = 3) c3)

ORDER BY i;

This single SQL statement finds the distances for all the pixels in one go. Next three steps

are iterated so that the most similar pixels can be assigned the appropriate cluster ids.

Step 4:

Since the number of rows in CCentroid is 3, it can be updated directly using the following

SQL statement:

UPDATE CCentroid c3

SET (j, R, G, B) ="

( SELECT c1.j, c2.R, c2.G, c2.B

FROM CCentroid c1, ( SELECT j, Avg(R) as R, Avg(G) as G, Avg(B) as B

FROM CCVCD Group by j) c2

WHERE c1.j = c2.j(+) and c1.j = c3.j) ;

As explained in the initialization step, all the rows of CEucl are deleted using TRUNCATE

statement and the newly computed distances are inserted using the following statement:

INSERT into CEucl (i, d1, d2, d3)

( SELECT i, sqrt(power((e2.R-c1.R), 2) + power((e2.G-c1.G), 2)


131

+ power((e2.B-c1.B), 2)) as d1,

sqrt(power((e2.R-c2.R), 2) + power((e2.G-c2.G), 2)

+ power((e2.B-c2.B), 2)) as d2,

sqrt(power((e2.R-c3.R), 2) + power((e2.G-c3.G), 2)

+ power((e2.B-c3.B), 2)) as d3

FROM CData e2,

(SELECT j, x, y, NVL(R,0) as R, NVL(G,0) as G, NVL(B,0) as B

FROM CCentroid WHERE j = 1) c1,


FROM CCentroid where j = 2) c2,


FROM CCentroid WHERE j = 3) c3

);

Next step is to find the smallest distance out of d1, d2, and d3 and assign the cluster id for

each of the pixels. However, before doing this operation the CCVCD rows must be truncated

and the cluster id updated in the table CCVCD as shown here.

INSERT INTO CCVCD (i, j, R, G, B)

( SELECT v1.i,

CASE when d1 <= d2 and d1 <= d3 then 1

when d2 <= d3 and d2 <= d1 then 2

when d3 <= d2 and d3 <= d1 then 3

END as j, v1.R, v1.G, v1.B

FROM CEucl v2, CData v1

WHERE v1.i = v2.i

);

So the value of j is calculated with a simple Case statement and this is repeated for each

pixel. This completes the last statement in the iteration. After this statement the control goes

back to update of CCentroid table so that the new means are calculated from the most recent

groups. After the specified number of iterations, the loop terminates. To show each cluster

distinctly, some random color is assigned to pixels of each cluster. This task is also carried out

using SQL statement as below:

INSERT INTO CSI (i, j, R, G, B)

( SELECT i, j,

Decode(j, 1, 34, 2, 178, 3, 0),


132

Decode(j, 1, 34, 2, 34, 3, 255),

Decode(j, 1, 178, 2, 34, 3, 255)

FROM CCVCD

);

The three colors chosen are: <34, 78, 0>, <34, 34, 255>, and <178, 34, 255>. The final

segmented image, therefore, will contain only three distinct color objects. The output of the

color Doppler image segmented using this technique is shown in Figure 5.8 and Figure 5.9.

Fig. 5.8 Application of Segmentation algorithm to Normal patient image (a) Original color Doppler

image (b) Segmented using Fast color SQL K-Means algorithm

Fig. 5.9 Application of Segmentation algorithm to Abnormal patient image (a) Original color Doppler

image (b) Segmented using Fast color SQL K-Means algorithm

Looking at the segmented images of both normal and abnormal images, it can be inferred

that the intended results are not obtained. In other words, the color portion of the image is not

separately appearing as a cluster using normal K-Means technique.

The main drawback is that K-Means is an unsupervised learning method. But for the

current application a semi-supervised learning is required so that all the color pixels can be into

a cluster and the rest could go into another cluster.


133

5.3.3 MODIFICATIONS TO FAST SQL COLOR K-MEANS ALGORITHM

The grayscale pixels in the color Doppler images do not contribute to the analysis. Hence,

the color portion need to be extracted and the rest of the pixels must be dropped. SQL approach

can be used for the clustering process and most of the unnecessary pixels can be removed,

making the clustering faster as shown here.

SELECT *

FROM CData

WHERE NOT( ((R = G) and (G = B)) or (Abs(R - G) <= 16) or (Abs(G - B) <= 16));

(a) (b) (c)

Fig. 5.10 Clustering only the color segment (a) original image with color pixels grabbed from the color

Doppler image (b) Clustered output (k = 3) and # of iterations = 4

(c) Clustered output, k = 3, # of iterations = 30

When the intensity values of RGB are all same, the pixels will not be selected as they are

pure grayscale pixels. The constant 16 that appears in the SQL statement is the threshold being

used to check pixels whose RG or GB values are close to 16 so that those pixels can also be

classified as grayscale. Typically a color Doppler image has 30% color pixels and the

remaining 70% grayscale pixels and therefore this method would improve the running time.

However, this method does not enhance the clustering quality as shown in Figure 5.10(b).

With the number of iterations being set to 30, there is some improvement shown where the

innermost red color is delineated and shown as yellow color in the output of Fig 5.10(c).

5.3.4 PIXEL CLASSIFICATION METHOD

The drawbacks of the clustering methods discussed here are as follows:

The K-Means method is slow as both the grayscale and color pixels are considered

for clustering purpose

When mosaic color is present, the clustering does not provide any useful

information


134

The modified SQL method is faster, but this again suffers the same shortcoming as

specified above

Therefore, a robust, accurate, fast method has to be designed so that the color segment can

provide both qualitative and quantitative information. In this section a novel method called

"Pixel Classification" coupled with image morphological operations is proposed.

When the color Doppler image pixels are carefully analyzed it can be noticed that except

what is seen visually as color all other pixels belong to grayscale as shown in Figure 5.11(a).

(a) (b)

Fig. 5.11 Types of pixels in a color Doppler image (a) color Doppler image (b) Single pixel with RGB

components and the distances between them

Instead of applying the time consuming and complicated K-Means clustering, a simple

pixel based classification method can be used to identify the color and grayscale pixels. The

method works as follows: Scanning through the image from top left top corner to bottom right

corner pixel-by-pixel and classify each pixel using the following logic into appropriate clusters.

Here, only two clusters are assumed, first is the grayscale pixels (Cg) and the second is the

color pixels (Cc).

if (d1 = 0 and d2 = 0 and d3 = 0) or (d1 ≤ T or d2 ≤ T or d3 ≤ T)

then Cg ← pi

else Cc ← pi

where, d1, d2, and d3 are the distances between RG, GB, and RB. All pixels in the cluster Cg

are background pixels and all pixels in cluster Cc are the foreground pixels. The distances can

be calculated using Manhattan formula. Normally to apply quantification on the segmented

image it should be a single object. But, as shown in Figure 5.12(a), it would always contain

breaks and gaps in the color segment region. To overcome this problem a series of image

manipulations are done as shown in the block diagram 5.12. The gaps in the semi-segmented

d1

d2

d3

p3[252,252,252]

p1[140,43,0]

p2 [72,72,72]


135

image is taken care by applying mathematical morphological dilation operator using the

following [5, 5] structuring element:

11111

11111

11111

11111

11111

Fig. 5.12 Overview of pixel classification based segmentation and other image processing

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

Fig. 5.13 Segmentation using Pixel Classification Method (a) Segmented image (b) Dilated image (c)

Gaussian blur (d) Binary image after applying Threshold, T = 80

To fill the gaps in the dilated image, a Gaussian blurring filter with σ = 1.55 and kernel size

of 14 is applied. Finally, the blurred image is applied with a threshold of 80. Figures 5.13(a) to

(d) show the output of all these operations.

Color Doppler Image

Pixel Classification Algorithm

Semi Segmented image

Gaussian Blur Filter

Convert to Grayscale and apply

Threshold

Morphology Filter (Dilation)

Qualitative Analysis

Fig. 5.13(a)

Quantitative Analysis

Fig. 5.13(d)


136

5.4 COLOR SEGMENT BOUNDARY TRACING – ACTIVE CONTOUR

BASED METHOD

The morphological based object identification and extraction of region of interest was

discussed in the previous section. However, it has few drawbacks especially tracking the exact

boundary of the color segment. To address this issue the contour based approach is adopted and

its implementation is discussed in this section.

In the case of 2D echo images, the initial contour is marked inside the cardiac cavity and it

moves towards the endocardial boundary. However, in the present case the contour must trace

the outer boundary of the color segment. That is, the contour shrinks. This is achieved by

setting the constant value, c0 to positive which is used to define binary level set function as

initial contour. On the other hand, if c0 is negative, the contour will expand. All the other steps

in the algorithm shown in Figure 4.14 remain same.

Fig. 5.14 Sample color segmentation. Left-side images are original images and the right-side are the

boundary traced images.

The working of this modified algorithm for the color Doppler images is shown in Figure

5.14. Here, the original images are shown in the left-side and the right-side images in each row


137

are the output after applying the active contour algorithm. It can be observed that the outer

boundary of the color portion alone is traced and the pixels inside this contour can be used for

quantitative and qualitative analysis. For instance, to determine the severity of Mitral

Regurgitation and Mitral Stenosis can be studied through this method. Another popular method

is based on Vena Contracta measurement and is discussed in [Tae-Ho, 2006].

The advantage of this method over the previous one is that the actual color pixel data of the

ROI is available. But in the previous method the data in the segment is totally blurred with

Gaussian method, dilated with a large kernel and so on. This spoils the whole data which then

can not be used for future analysis. However, it may be useful for quantitative analysis.

5.5 QUALITATIVE ANALYSIS

Following techniques are used to analyze the segmented color region:

1. Color Histogram Analysis

2. Texture Analysis [Mihran, 1998]

3. Statistical Analysis

4. Edge Density Analysis

In the histogram analysis, mean and standard deviation for each color channel (RGB color

space is used) is computed. Texture analysis includes energy, entropy, contrast, edge

frequency, and homogeneity calculations as proposed by Haralick and K. Shanmugam. The

third method is to employ kurtosis and skewness properties to correlate the normal patient and

the abnormal patient image color patterns. Finally, a novel method of finding the edge density

is proposed.


138

Fig. 5.15 Color separation and analysis of color Doppler images.

To study the data pattern of the above said method requires a fundamental preprocessing of

the Doppler images. First task is to separate the RGB color channels and compute the above

said parameters that are relevant. A schematic is shown in Figure 5.15 to explain this process.

5.5.1 COLOR HISTOGRAM ANALYSIS

Color allows images to reveal many pathological characteristics (Tamai, 1999). Color also

plays an important role in morphological diagnosis (Nishibori, Tsumura, & Miyake, 2004). In

Doppler images color is related to abnormality (MR, MS, etc) and reveals the velocity of blood

flow in the ventricles and atriums.

Original Image

Red Channel Green Channel Blue Channel

Histogram

(Mean & SD)

Texture

(Contrast & ED)

Histogram

(Mean & SD)

Texture

(Contrast & ED)

Histogram

(Mean & SD)

Texture

(Contrast & ED)

For data mining related analysis

Segmented

Image


139

Color Space

A color space is defined as a model for representing color in terms of intensity values.

Typically, a color space defines a one- to four-dimensional space. A color component, or a

color channel, is one of the dimensions. A color dimensional space (i.e. one dimension per

pixel) represents the gray-scale space. The following two models are commonly used in color

image retrieval system. Several color spaces, such as RGB, HSV, CIE L*a*b, and CIE L*u*v,

have been developed for different purposes. RGB color space is used in this research work.

RGB Color Model

The RGB color model is composed of the primary colors Red, Green, and Blue. This

system defines the color model that is used in most color CRT monitors and color raster

graphics. They are considered the "additive primaries" since the colors are added together to

produce the desired color. The RGB model uses the Cartesian coordinate system as shown in

Figure 5.16(a).

(a) (b) (c)

Fig. 5.16 RGB Color Model (a) Schematic of RGB Color Cube (b) 24-bit RGB Color Cube

(c) Color cube

The diagonal from (0,0,0) black to (1,1,1) white which represents the grayscale. Figure

5.16(b) is a view of the 24-bit RGB color cube and (c) represents another color view.

Color Histogram

After selecting a color space, an effective color descriptor should be developed in order to

represent the color of the global or regional areas. Several color descriptors have been

developed from various representation schemes, such as color histograms (Quyang & Tan,


140

2002), color moments (Yu et al., 2002), color edge (Gevers & Stokman, 2003), color texture

(Guan & Wada, 2002), and color correlograms (Moghaddam, Khajoie, & Rouhi, 2003). For

example, color histogram, which represents the distribution of the number of pixels for each

quantized color bin, is an effective representation of the color content of an image. The color

histogram can not only easily characterize the global and regional distribution of colors in an

image, but also be invariant to rotation about the view axis. A typical color histogram is shown

in Figure 5.17.

(a) RGB color Doppler image (b) Grayscale image Histogram

(c)Histogram of Red Channel (d) Histogram of Green Channel

(e) Histogram of Blue Channel

Fig. 5.17 Color Histogram without segmentation

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 50 100 150 200 250

0

2000

4000

6000

8000

10000

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 50 100 150 200 250


141

(a) Original segmented image of abnormal patient

(b) Red (c) Green (d) Blue

Fig. 5.18 Histogram of image shown in (a) with all 3 color channels

The color histogram can be considered as a set of vectors. For grayscale images these are

two dimensional vectors. One dimension gives the value of the gray level and the other the

count of pixels at the gray level. For color images the color histograms are composed of 4-D

vectors. Comparing Figure 5.17 with 5.18 indicates that segmentation is mandatory to obtain a

distinct histogram.

Fig. 5.19 (a) Color Histogram with segmentation of normal patient

(b) Red (c) Green (d) Blue

Fig. 5.19 Histogram of image shown in 5.19(a) with all 3 color channels


142

A similar histogram is obtained for the image of a normal patient (Figure 5.19(a)) and its

histogram of red, green, and blue channel histogram plots are shown in Figure 5.19(b), (c) and

(d) respectively. The large difference can be observed in the histogram between normal and

abnormal patient images due to the mosaic color.

Direct histogram plot of the segmented image is not useful for analysis. Hence, the

histogram mean and standard deviation of each color channel are computed. Histogram groups

the samples together that have same value. This allows the statistics to be calculated by

working with a few groups, rather than a large number of individual samples. Using this

approach, the mean and standard deviation are calculated from the histogram by the equations:

1

0

1 M

i

iHiN

(5.1)

1

0

2)(1

1 M

i

iHiN

(5.2)

where, Hi is the Histogram and i is an index that runs from 0 to M-1, and M is the number of

possible values that each sample can take on (that is 0 to 255 in our case). For instance, H50 is

the number of samples that have a value of 50. The impact of histogram on normal and

abnormal patient echo images are discussed in the results section.

5.5.2 TEXTURE ANALYSIS

In many machine vision and image processing algorithms, assumptions are made about the

uniformity of intensities in local image regions to simplify the problem space. However,

images of real objects often do not exhibit regions of uniform intensities. For example, the

image of a wooden surface is not uniform but contains variations of intensities which form

certain repeated patterns called visual texture [Mihran, 1998].

Definition

“We may regard texture as what constitutes a macroscopic region. Its structure is simply

attributed to the repetitive patterns in which elements or primitives are arranged according to

a placement rule.” [Mihran, 1998]


143

Image texture, defined as a function of the spatial variation in pixel intensities (gray

values), is useful in a variety of applications and has been a subject of intense study by many

researchers. Texture analysis is an important and useful area of study in machine vision. Most

natural surfaces exhibit texture and a successful vision system must be able to deal with the

textured world surrounding it. This section will review the importance of texture perception in

the analysis of color Doppler images in particular.

Co-occurrence Matrices

One of the defining qualities of texture is the spatial distribution of gray values. The use of

statistical features is therefore one of the early methods proposed in the machine vision

literature. In the following, we will use {I (x, y), 0 ≤ x ≤ N – 1, 0 ≤ y ≤ N – 1} to denote an N×N

echo image with G gray levels. Spatial gray level co-occurrence estimates image properties

related to second-order statistics. Haralick [Mihran, 1998] suggested the use of gray level co-

occurrence matrices (GLCM) which have become one of the most well-known and widely used

texture features. The gray level co-occurrence matrix Pd for a displacement vector d = (dx, dy)

is defined as follows. The entry of Pd is the number of occurrences of the pair of gray levels i

and j which are a distance d apart. That is, d is the distance between the pixel of interest and its

neighbor. Formally, it is given as,

Pd(i, j) = |{((r, s), (t, v)):I (r, s) = i, I (t, v) = j}| (5.3)

where (r, s), (t, v) є N × N, (t, v) = (r + dx, s + dy), |.| is the cardinality of the set.

The offset is often specified as angle and the above figure illustrates the meaning of d. In

general, given a pixel distance d, the following offset matrix can be written for various angles:

00 [0, 1], 45

0 [-1, 1], 90

0 [-1, 0], 135

0 [-1, -1]


144

Texture Properties

Useful texture features that can be computed from the co-occurrence matrix are shown in

Table 5.1.

Table 5.1 Texture Features

Sl. No Texture feature Formula

1 Energy i j

d jiP ),(2

2 Entropy i j

dd jiPjiP ),(log),(

3 Contrast i j

d jiPji ),()( 2

4 Homogeneity i j

d

ji

jiP

||1

),(

5 Correlation yx

i j

dyx jiPji

),())((

The autocorrelation function of an image is used to quantify the regularity and the

coarseness of a texture. This function is defined for an image I as:

N

u

N

v

N

u

N

v

vuI

yvxuIvuI

yx

0 0

2

0 0

),(

)(),(),(

),( (5.4)

If the texture is coarse, then the autocorrelation function will drop off slowly; otherwise, it

will drop off very rapidly. For regular textures, the autocorrelation function will exhibit peaks

and valleys [Mihran, 1998]. The experiments were conducted on the grayscale versions of the

color segment and the results are discussed later.

5.5.3 STATISTICAL ANALYSIS

One of the major drawbacks of the texture features is that not all of them provide distinct

similarity or dissimilarity between normal and abnormal patients. For example, energy,

entropy, and homogeneity features give same results for both the types of images. Hence, it is


145

required to look for some other features that can discriminate these images. Two such statistical

features have been identified as kurtosis and skewness.

Skewness

When referring to the shape of frequency or probability distributions, “skewness” refers to

asymmetry of the distribution. A distribution with an asymmetric tail extending out to the right

is referred to as “positively skewed” or “skewed to the right,” while a distribution with an

asymmetric tail extending out to the left is referred to as “negatively skewed” or “skewed to the

left.” Skewness can range from minus infinity to plus infinity.

Karl Pearson in 1895 first suggested measuring skewness by standardizing the difference

between the mean and the mode. However, the definition is used with respect to the third

moment about the mean:

3

3

1

)(

N

Y

Skewness

N

i

i

(5.5)

Skewness measured in this way is sometimes referred to as “Fisher’s skewness.” When the

deviations from the mean are greater in one direction than in the other direction, this statistic

will deviate from zero in the direction of the larger deviations.

Kurtosis

Pearson in 1905 introduced kurtosis as a measure of how flat the top of a symmetric

distribution is when compared to a normal distribution of the same variance. A distribution

with positive kurtosis is called leptokurtic, or leptokurtotic. In terms of shape, a leptokurtic

distribution has a more acute peak around the mean. A distribution with negative kurtosis is

called platykurtic, or platykurtotic. In terms of shape, a platykurtic distribution has a lower,

wider peak around the mean.

3

)(

4

4

1

N

Y

Kurtosis

N

i

i

(5.6)


146

Fig. 5.20 Schematic showing edge density calculation for an Abnormal patient

The positive kurtosis is normally seen for normal patients, whereas negative kurtosis is seen

for abnormal patients and a detailed analysis is discussed later in this chapter.

It is noticed that for normal images the skewness ranges from 0.98 to 1.28 whereas the

kurtosis ranges from 1.28 to 2.47. In contrast, for abnormal images the skewness ranges from

0.04 to 0.23 whereas kurtosis ranges from -0.46 to -0.86.

Original Color Doppler

Image

Pixel Classification based

Segmented Image

Get the Biggest blob

Apply Sobel Edge

Detection Operator

Compute Mean Histogram

(Edge Density)


147

5.5.4 EDGE DENSITY ANALYSIS

A feature called edge density is used primarily for color Doppler ultrasound images. This

method comprises of the following steps: segmentation of color region, grabbing the biggest

blob, converting into grayscale, applying Sobel edge detector operator, and finally computing

the mean of the histogram pattern. The entire process is shown in the form of a block diagram

in Figure 5.20.

Fig. 5.21 Schematic showing edge density calculation for a Normal patient

To begin with only the color portion of the color Doppler image is extracted. Since the

color portion, especially in abnormal patients, contains disjoint regions, the biggest region,

called the blob is extracted. This image is converted into grayscale and then the standard Sobel

operator is applied. When the image has mosaic colors the edges will be predominant

throughout the image, as shown in Figure 5.20, else not many edges will be appearing as in the

case of normal patients which can be observed from Figure 5.21. Comparing the edge patterns

of Figure 5.20 and 5.21, it is evident that the later image does not have many visible edges.

This knowledge helps in distinguishing between normal and abnormal images.

5.6 RESULTS AND DISCUSSIONS

This section presents the discussion of color Doppler image analysis. The study includes

both normal and abnormal subjects who underwent echocardiographic test by the experts. To

validate the methods explained in the previous sections, the study group consisted of 60

patients, 42 men and 18 women with 42 ± 16 years of age. Approximately 323 echo color

Doppler images, 218 abnormal and 105 normal images were used and in the abnormal category

four types of diseases: MR, MS, AR, and AS.

When the Fast SQL based K-Means algorithm is applied for color Doppler images with

k = 3 it produced the output as shown in Figure 5.22.


148

(a)

(b) Fig. 5.22 Original and segmented images of (a) normal and (b) abnormal patients

It can be observed that the segmentation does not delineate the color region which is the

main objective for analysis. Therefore, a completely different approach, called pixel

classification, may be required to solve this issue as explained already.

5.6.1 RESULTS OF PIXEL-CLASSIFICATION ALGORITHM

After applying the pixel classification method, as illustrated in Figure 5.23, the color

segment has been distinctly extracted from the original color Doppler image.

Fig. 5.23 Results of Pixel-Classification method for normal and abnormal images.


149

It can be observed visually from the results of normal and abnormal images that extracting

color region from Doppler images using the proposed method is easy.

5.6.2 RESULTS OF HISTOGRAM, TEXTURE, AND EDGE DENSITY ANALYSIS

The experiments include 17 Normal and 16 abnormal patient images after segmentation.

Figure 5.24 depicts feature called kurtosis for both normal (Images 1- 17) and abnormal

(Images from 18 to 33). For normal images its values are positive, whereas for abnormal

images it is negative.

Fig. 5.24 Bar graph of Kurtosis feature. Thick Black bars – Normal subjects, Grey Shaded bars –

Abnormal subjects. The Correlation Coefficient = -0.43271.

The correlation coefficient of these two data sets is worked out as -0.43271, which signifies

that both data is negatively correlated. This is the expected result and more than 95% of the

images show this variation. More results are shown in Chapter 10.

5.7 SUMMARY

A comprehensive discussion of color Doppler flow image analysis is presented. It includes

the following: understanding of the Doppler images, interpretation, segmentation using Fast

SQL K-Means Color clustering algorithm, pixel-classification based segmentation, and

qualitative feature extraction.

Major features such as texture, color histogram, edge density, skewness, kurtosis, etc., are

computed from the color region of the Doppler image in order to extract the hidden knowledge.

All these features prove that it is possible to automatically distinguish between normal and

abnormal patients.

-1.5 -1

-0.5 0

0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

5.5 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Ku

rto

sis

Image #

Normal

Abnormal

COLOR DOPPLER FLOW IMAGE ANALYSIS -...

Documents

Transcript of COLOR DOPPLER FLOW IMAGE ANALYSIS -...