Interactive Segmentation For Image Guided Therapy Ohad Shitrit & Tsachi Hershkovich Superviser: Dr....

Interactive Segmentation For

Image Guided Therapy

Ohad Shitrit & Tsachi Hershkovich

Superviser: Dr. Tammy Riklin Raviv

Ben-Gurion University of the Negev

What are we going to speak about?

Tsachi H. & Ohad S.

Computed Tomography

Motivation

Mathematical introduction

Problem definition

Energy

Gradient Descent

The system

Results

Conclusion & Future work

Tsachi H. & Ohad S.

Computed Tomography (CT)

Spiral Cone-Beam Scanning for Computed Tomography. Ge Wang, 2003 (All rights reserved)

Tsachi H. & Ohad S.


Spiral Cone-Beam Scanning for Computed Tomography. Ge Wang, 2003 (All rights reserved)

X-Ray Projection using radon

transform( , ) ,

attenuation

, polar axes

sP r x y ds

r

Tsachi H. & Ohad S.


Radon transform as one dimensional Fourier transform

Reconstructing the image with the inverse Fourier transform

2 ( x y)

2

{ , }( , ) (x, y)

{ , }( ,0) ( ( , )dy)

x y

x

j

x y

j xx

radon transform

x y e dxdy

x y x y e dx

2 2{ , }( ,0) (r,0) { , }( ,0) (x)x xj x j xx xx y P e dx x y P e dx

Why is there any need for interactive segmentation

?Tsachi H. & Ohad S.

Tsachi H. & Ohad S.

Why is there any need for interactive segmentation?

Volume estimation is critical for further treatment

Therapist knowledge is essential for final decisions

Fast and accurate analysis might save life

Tsachi H. & Ohad S.

Tsachi H. & Ohad S.

“Active Contour”

But first things first…

Tsachi H. & Ohad S.

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

Probabilistic Model Based on Gaussian Mixture(GM)

Tsachi H. & Ohad S.0 20 40 60 80 100 120 140 160 180 200

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Background

Object

2

22

in

in

I x

ObjectP x e

2

22

k

k

I x

Back kk

P x e

We will define the Probability of a Voxel (3D pixel) to belong to the Object Or to the Background:

A CT scan Histogram of a brain with Cerebral

hemorrhage

Tsachi H. & Ohad S.

Segmentation 2D

50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

350

400

450

500

Tsachi H. & Ohad S.

Level Set Function - x

| 0 x x x

Tsachi H. & Ohad S.

H

Mathematical Issues

Tsachi H. & Ohad S.

1 11 tanh

2 21

xH p x

e

0.5

21sech

4 2

dH

d

Mathematical Issues

[Riklin Raviv, Van Leemput, Menze, Wells, Golland, Medical Image Analysis, 2011]

Tsachi H. & Ohad S.

Problem Definition

Tsachi H. & Ohad S.

To achieve the optimized segmentation we maximize the joint distribution:

Prior

Image Likelihood User Input Smoothness

assuming conditional independence and using bayes theorm:

, ; | ; ;

ˆ log | ; log ; logarg

Parameters user

Parameters user

P I P I P

P I P U Pmax

ˆ log , ;arg P Imax


Segmentation

Parameters

Tsachi H. & Ohad S.

Energy Functional

Using the following relationship:

logE P P-Probability

E-Energy

Allows us to formulate our problem as an energy minimization problem

ˆ arg max log arg min log arg minP P E

Summing all contributions from each voxel

Tsachi H. & Ohad S.

Image Likelihood Term

log 1 logLIKELIHOODE H P H P d

x x x

,Object ObjectP N

,i ii Back Back

i

P N

Assuming Gaussian Mixtures Model (GMM)

Cost

Cost 0

Cost 0Cost

Tsachi H. & Ohad S.

Smoothness Term

SMOOTHNESSE H d

x x

Objects in nature are continuous

Trade off between smoothness and sensitivity

Fine tuning is needed

Tsachi H. & Ohad S.

User Interaction Term

1

1

Lets define user interaction clicks inside the forground and background :

L

L (1 )

; 1

; 1

obj obj kk

back back kk

obj back

L L

u

L L

u

G

G

L L L

p U p p

p U p p

x x

x x

x x

x x

x x x

x x x

log ; 1 log ;USER u uE H p U H p U d

x x x x x

Tsachi H. & Ohad S.

Gradient Descent

The gradient descent is an iterative process which leads to the minimum of the Energy term.

ˆ arg min E

USER LIKELIHOOD LENGTHTotalE E E E

, ,t t t tt

x x

Segmentation

Parameters

0Adaptive step size t= t

Tsachi H. & Ohad S.

Block Diagram – Entire System

Image

Parameters Segmentation

User


Entire System 3D

Tsachi H. & Ohad S.

Entire System 3D

Tsachi H. & Ohad S.

2 M GD

M G

M G

M G

Performance

M-Machine Segmentation

G-Ground Truth

DiceSensitivitySpecificityAccuracy

Automatic0.874±0.03

40.864±0.073

0.998±0.0019

0.996±0.0033

With user interaction

0.905±0.027

0.870±0.0630.999±0.000

30.997±0.002

2

ScorePhase

Tsachi H. & Ohad S.

Data

Provided by Dr. Ilan Shelef, Department of Radiology, Soroka University Medical Center and Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev.

Modality: CT Brilliance 64 Resolution: 512x512xZ (Z = 90-

100)X x Y x Z = 0.48 x 0.48 x

3 [mm]

Z axis with 1.5[mm] overlap

Conclusion

Semi-automatic segmentation tool

Probabilistic model

User Interface

Collaboration with Soroka Medical

Center

Tsachi H. & Ohad S.

Future work

Adjustments to other modalities (MRI)

Handle with various of structures

User-Machine dialog in the medical

world

Tsachi H. & Ohad S.

Tsachi H. & Ohad S.

User Interface

Questions?

Thank you.

Demo -http://youtu.be/Jb-6VDid37s

Interactive Segmentation For Image Guided Therapy Ohad Shitrit & Tsachi Hershkovich Superviser: Dr....

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Transcript of Interactive Segmentation For Image Guided Therapy Ohad Shitrit & Tsachi Hershkovich Superviser: Dr....