lec11: active contour and level set for medical image segmentation

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MEDICAL IMAGE COMPUTING (CAP 5937) LECTURE 11: Active Contour and Level Set for Medical Image Segmentation Dr. Ulas Bagci HEC 221, Center for Research in Computer Vision (CRCV), University of Central Florida (UCF), Orlando, FL 32814. [email protected] or [email protected] 1 SPRING 2017

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Page 1: Lec11: Active Contour and Level Set for Medical Image Segmentation

MEDICAL IMAGE COMPUTING (CAP 5937)

LECTURE 11: Active Contour and Level Set for Medical Image Segmentation

Dr. Ulas BagciHEC 221, Center for Research in Computer Vision (CRCV), University of Central Florida (UCF), Orlando, FL [email protected] or [email protected]

1SPRING 2017

Page 2: Lec11: Active Contour and Level Set for Medical Image Segmentation

Outline• Active Contour (Snake)• Level Set• Applications

2

Page 3: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation• Active contours and active surfaces are means of model-

driven segmentation. Their use enforces closed and smooth boundaries for each segmentation irrespective of the image content.

3

Page 4: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation• Active contours and active surfaces are means of model-

driven segmentation. Their use enforces closed and smooth boundaries for each segmentation irrespective of the image content.

• Data-driven (region) approaches: Objects in an image appear homogeneous

4

Page 5: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation• Active contours and active surfaces are means of model-

driven segmentation. Their use enforces closed and smooth boundaries for each segmentation irrespective of the image content.

• Data-driven (region) approaches: Objects in an image appear homogeneous

• Model-driven (boundary) approaches: Ideal object boundary are predicted. The boundary is assumed to be smooth and closed.

5

Page 6: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation• Active contours and active surfaces are means of model-

driven segmentation. Their use enforces closed and smooth boundaries for each segmentation irrespective of the image content.

• Data-driven (region) approaches: Objects in an image appear homogeneous

• Model-driven (boundary) approaches: Ideal object boundary are predicted. The boundary is assumed to be smooth and closed.

6

Page 7: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation

7

Page 8: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation

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Page 9: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation

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Page 10: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation

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Page 11: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation

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Page 12: Lec11: Active Contour and Level Set for Medical Image Segmentation

Motivation

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Page 13: Lec11: Active Contour and Level Set for Medical Image Segmentation

Active Contours (Snake)• First introduced in 1987 by Kass et al, and gained popularity

since then.

• Represents an object boundary or some other salient image feature as a parametric curve.

• An energy functional E is associated with the curve.

• The problem of finding object boundary is cast as an energy minimization problem.

13

Page 14: Lec11: Active Contour and Level Set for Medical Image Segmentation

A Snake is a parametric curve!

14

The course of the snake smoothly follows high intensity gradients if the gradients reliably reflect the object boundary. Otherwise, a smooth boundary is generated bridging regions of noisy data or missing gradients. Such an active contour is particularly well suited to segment an object instance in an image where thedata are distorted by noise or artefacts

Page 15: Lec11: Active Contour and Level Set for Medical Image Segmentation

Frameworks for Snakes• A higher level process or a user initializes any curve close to

the object boundary.• The snake then starts deforming and moving towards the

desired object boundary.• In the end it completely “shrink-wraps” around the object.

15

Page 16: Lec11: Active Contour and Level Set for Medical Image Segmentation

Deformable Models• Deformable models are curves or surfaces defined within an

image domain that can move under the influence of internal forces,

16

Page 17: Lec11: Active Contour and Level Set for Medical Image Segmentation

Deformable Models• Deformable models are curves or surfaces defined within an

image domain that can move under the influence of internal forces, which are defined within the curve or surface itself,

17

Page 18: Lec11: Active Contour and Level Set for Medical Image Segmentation

Deformable Models• Deformable models are curves or surfaces defined within an

image domain that can move under the influence of internal forces, which are defined within the curve or surface itself, and external forces, which are computed from the image data.

18

Page 19: Lec11: Active Contour and Level Set for Medical Image Segmentation

Deformable Models• Deformable models are curves or surfaces defined within an

image domain that can move under the influence of internal forces, which are defined within the curve or surface itself, and external forces, which are computed from the image data.

19

The internal forces are designed to keep the model smooth during deformation.

The external forces are defined to move the model toward an object boundary or other desired features within an image.

Page 20: Lec11: Active Contour and Level Set for Medical Image Segmentation

Active Contour Modeling• The contour is defined in the (x, y) plane of an image as a parametric

curve

• Contour is said to possess an energy (Esnake) which is defined as the sum of the three energy terms.

• The energy terms are defined cleverly in a way such that the final position of the contour will have a minimum energy (Emin)

• Therefore our problem of detecting objects reduces to an energy minimization problem.

20

int intsnake ernal external constraE E E E= + +

What are these energy terms which do the trick for us ?

1s0))s(y),s(x()s( ≤≤=ν

Page 21: Lec11: Active Contour and Level Set for Medical Image Segmentation

Internal Energy• The smoothness energy at contour point v(s) could be

evaluated as

21

Elasticity/stretching Stiffness/bending

sdd

dsd

sssEin 2

2)()())((

22

ννβαν +=

Then, the interior energy (smoothness) of the whole snake

∫=1

0inin ds))s((EE ν]}1,0[s|)s({ ∈= νC

Page 22: Lec11: Active Contour and Level Set for Medical Image Segmentation

Internal Energy

22

5v4v

3v

2v

1v 6v

7v

8v10v

9v

elastic energy(elasticity)

i1ivdsd νν −≈ +

bending energy(stiffness)

1ii1i1iii1i2

2

2)()(dsd

−+−+ ν+ν−ν=ν−ν−ν−ν≈ν

)( iii y,x=ν

2n)( ℜ∈= −1n210 ,....,,, ννννC

Page 23: Lec11: Active Contour and Level Set for Medical Image Segmentation

Internal Energy

10/13/15

23

Elasticity Stiffness

i1ivdsd νν −≈ +

11112

2

2)()( −+−+ +−=−−−≈ iiiiiiidsd νννννννν

∑−

=−++ +−+−=

1

0

211

21 |2|||

n

iiiiiiinE νννβννα

)( iii y,x=ν

2n)( ℜ∈= −1n210 ,....,,, ννννC

Min energy when curve minimizes length of contour…..... …...........is smooth

Page 24: Lec11: Active Contour and Level Set for Medical Image Segmentation

External Energy• The external energy describes how well the curve matches

the image data locally• Numerous forms can be used, attracting the curve toward

different image features

24

Page 25: Lec11: Active Contour and Level Set for Medical Image Segmentation

External (Image) Energy• Suppose we have an image I(x,y)• Can compute image gradient at any point• Edge strength at pixel (x,y) is• External energy of a contour point v=(x,y) could be

25

|)y,x(I|∇)I,I(I yx=∇

22 |),(||)(|)( yxIIEex ∇−=∇−= vv

∑−

=

=1

0)(

n

iiexex EE ν discrete case

}ni0|{ i <≤= νC

∫=1

0

))(( dssEE exex ν continuous case ]}1,0[s|)s({ ∈= νC

■ External energy term for the whole snake is

Page 26: Lec11: Active Contour and Level Set for Medical Image Segmentation

Basic Elastic Snake

26

• The total energy of a basic elastic snake is

continuous case

discrete case

∫∫ ∇−⋅=1

0

21

0

2 ds|))s(v(I|ds|dsdv|E α

∑∑−

=

=+ ∇−−⋅=

1n

0i

2i

1n

0i

2i1i |)v(I||vv|E α

elastic smoothness term(interior energy)

image data term(exterior energy)

]}1,0[s|)s({ ∈= νC

}ni0|{ i <≤= νC

(PS. bending energy can be added under elastic term)

Page 27: Lec11: Active Contour and Level Set for Medical Image Segmentation

Basic Elastic Snake

27

This can make a curve shrink

(to a point)∑−

=

⋅=1

0

2n

iiin LE α

21

1

0

21 )()( ii

n

iii yyxx −+−⋅= +

=+∑α

∑−

=

∇−=1n

0i

2iiex |)y,x(I|E

21

0

2 |),(||),(| iiy

n

iiix yxIyxI∑

=

+−=

)y,x,....,y,x,y,x()ni0|( 1n1n1100i −−=<≤= νC

C

ii-1 i+1

i+2

Li-1 Li

Li+1

Page 28: Lec11: Active Contour and Level Set for Medical Image Segmentation

Find Contour C that minimizes E(C)

28

2iiy

1n

0i

2iix

2i1i

1n

0i

2i1i |)y,x(I||)y,x(I|)yy()xx()(E ∑∑

=+

=+ +−−+−⋅= αC

Optimization problem for function of 2n variables- can compute local minima via gradient descent- more robust option: dynamic programming

Page 29: Lec11: Active Contour and Level Set for Medical Image Segmentation

Constraint Forces (Econstraints)• Initial snake result can be nudged where it goes wrong, simply add

extra external energy terms to

• Pull nearby points toward cursor, or

• Push nearby points away from cursor

29

∑−

= −−=

1

02

2

||

n

i ipull p

rEν

∑−

= −+=

1

02

2

||

n

i ipush p

rEν

Page 30: Lec11: Active Contour and Level Set for Medical Image Segmentation

Ex: If Only External Force is Used

30

Red: initial contourGreen: final contour

Credit: Scot Acton

Page 31: Lec11: Active Contour and Level Set for Medical Image Segmentation

Gradient Descent31

⎥⎦

⎤⎢⎣

⎡−−

=∂∂∂∂

yExE

E∇−

negative gradient at point (x,y) gives direction of the steepest descent towards lower values of function E

• Example: minimization of functions of 2 variables

),( 00 yx

),( yxE

y

x

Page 32: Lec11: Active Contour and Level Set for Medical Image Segmentation

Gradient Descent32

Et ∇⋅Δ−=′ pp

• Example: minimization of functions of 2 variables),( yxE

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅Δ−⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟⎠

⎞⎜⎜⎝

⎛′′

∂∂∂∂

yExE

tyx

yx

Stop at a local minima where 0!

=∇E

y

x

),( 00 yx

update equation for a point p=(x,y)

Page 33: Lec11: Active Contour and Level Set for Medical Image Segmentation

Gradient Descent33

• Example: minimization of functions of 2 variables

High sensitivity wrt. the initialisation !!

),( yxE

x

y

Page 34: Lec11: Active Contour and Level Set for Medical Image Segmentation

Gradient Descent in Snakes34

simple elastic snake energy

tE' Δ⋅∇−=CCupdate equation for the whole snake

t...

yx...yx

'y'x...'y'x

1n

1n

0

0

yExE

yExE

1n

1n

0

0

1n

1n

0

0

Δ⋅

⎟⎟⎟⎟⎟⎟

⎜⎜⎜⎜⎜⎜

⎟⎟⎟⎟⎟⎟

⎜⎜⎜⎜⎜⎜

=

⎟⎟⎟⎟⎟⎟

⎜⎜⎜⎜⎜⎜

∂∂∂∂

∂∂∂∂

C

21

1

0

21 )()( ii

n

iii yyxx −+−⋅+ +

=+∑α

2iiy

1n

0i

2iix1n01n0 |)y,x(I||)y,x(I|)y,,y,x,,x(E ∑

=−− +−=!!

here, energy is a function of 2n variables

C

Page 35: Lec11: Active Contour and Level Set for Medical Image Segmentation

Dynamic Programming for Snakes• Please Read

– Interactive Segmentation with Intelligent Scissors by E. Mortensen and W. Barrett,

– Using Dynamic Programming for Solving variational Problems in Vision by AA. Amini et al, where authors used dynamic programming for image segmentation tasks.

35

Page 36: Lec11: Active Contour and Level Set for Medical Image Segmentation

Ex: Corpus Collasum

36

Page 37: Lec11: Active Contour and Level Set for Medical Image Segmentation

Problems with Snakes

10/13/15

37

• Depends on number and spacing of control points• Snake may over-smooth the boundary• Initialization is crucial• Not trivial to prevent curve self intersecting

• May not follow topological changes of objects

Page 38: Lec11: Active Contour and Level Set for Medical Image Segmentation

Level Sets• A limitation of active contours based on parametric curves of

the form f(s) (snakes, b-snakes,…) is that it is challenging to change the topology of the curve as it evolves.

• If the shape changes dramatically, curve reparameterization may also be required.

• An alternative representation for such closed contours is to use level sets (LS).– LS evolve to fit and track objects of interest by modifying the

underlying embedding function instead of curve function f(s)

38

Page 39: Lec11: Active Contour and Level Set for Medical Image Segmentation

Image Segmentation with Level Sets• Contour evolution (Sethian and Osher, 1988)• Level sets for closed contours

– Zero-crossing(s) of a characteristic function define the curve

– Fit and track objects of interest by modifying the underlying embedding function instead of the curve f(s)

– Efficient algorithm• A small strip around the locations of the current zero-crossing

needs to updated at each step

39

( , )x yφ

Fast Marching Methods

Page 40: Lec11: Active Contour and Level Set for Medical Image Segmentation

Moving Interfaces• 2D Moving Curves• 3D Moving Surfaces

Ex:– Interfaces between water and oil– Propagating front of bush fire– Deformable elastic solid

40

water

air

Page 41: Lec11: Active Contour and Level Set for Medical Image Segmentation

Evolving Curves and Surfaces

41

Only velocity component normal to surface is important!

Page 42: Lec11: Active Contour and Level Set for Medical Image Segmentation

Describe curve as Level Sets of a Function42

�(x, y) = x

2 + y

2 � 1 = 0

Isocontour is the unit circle (implicit represt.)

Page 43: Lec11: Active Contour and Level Set for Medical Image Segmentation

Describe curve as Level Sets of a Function

43

�(x, y) = x

2 + y

2 � 1 = 0

A few isocontours of twodimensional function (circle)Along with some representativenormals.

GRADIENT:

5� = (@�

@x

,

@�

@y

)

Page 44: Lec11: Active Contour and Level Set for Medical Image Segmentation

Describe curve as Level Sets of a Function

44

~N =5�

|5 �|Then, unit normal (outward) is

Page 45: Lec11: Active Contour and Level Set for Medical Image Segmentation

Describe curve as Level Sets of a Function

45

~N =5�

|5 �|Then, unit normal (outward) is

On Cartesian grid, we need to approximate this equation (ex. Finite difference techniques):

@�

@x

⇡ �i+1 � �i

�x

Page 46: Lec11: Active Contour and Level Set for Medical Image Segmentation

Describe curve as Level Sets of a Function

46

~N =5�

|5 �|Then, unit normal (outward) is

On Cartesian grid, we need to approximate this equation (ex. Finite difference techniques):

@�

@x

⇡ �i+1 � �i

�x

Mean curvature of the interface is defined as the divergence of the normal ~N = (n1, n2)

= r.

~

N =@n1

@x

+@n2

@y

= r.(r�

|r�| )

Page 47: Lec11: Active Contour and Level Set for Medical Image Segmentation

Describe curve as Level Sets of a Function

47

~N =5�

|5 �|Then, unit normal (outward) is

On Cartesian grid, we need to approximate this equation (ex. Finite difference techniques):

@�

@x

⇡ �i+1 � �i

�x

Mean curvature of the interface is defined as the divergence of the normal ~N = (n1, n2)

= r.

~

N =@n1

@x

+@n2

@y

= r.(r�

|r�| )

Page 48: Lec11: Active Contour and Level Set for Medical Image Segmentation

Variational Formulations and LS• Transition from Active Contours:

– contour v(t) → front γ(t)– contour energy → forces FA FC

– image energy → speed function kI

• Level set:– The level set c0 at time t of a function ψ(x,y,t)

is the set of arguments { (x,y) , ψ(x,y,t) = c0 }– Idea: define a function ψ(x,y,t) so that at any time,

γ(t) = { (x,y) , ψ(x,y,t) = 0 }• there are many such ψ• ψ has many other level sets, more or less parallel to γ• only γ has a meaning for segmentation, not any other level set of ψ

48

Page 49: Lec11: Active Contour and Level Set for Medical Image Segmentation

49

Usual choice for ψ: signed distance to the front γ(0)⎧ - d(x,y, γ) if (x,y) inside the front

ψ(x,y,0) = ⎨ 0 “ on “⎩ d(x,y, γ) “ outside “

00

00 0 0 0

0 00

00

00

00

0000

00

0000

-1-1-1-1

-1-1

-1-1

-1-1-1-1

-1-1-1-1

-1-1

-1 -1 -1 -1-2 -2 -2 -2

-2-2

-2-2-2-2

-2-2

-2 -2 -3 -3-3-3

-3-3

11

11

11

11

1111

1111

1111

11

1 1 1 11 1

11

22

222

22

222

2222

2222

22

22 2 2 2 2

22

2

33

333

33

33

33333

33

3

33

33 4

44

44

4

44444

44

4

44

4

7

55

55

555

5

55

66

6 6

γ(t)ψ(x,y,t)

ψ(x,y,t)

0

-2

5

Page 50: Lec11: Active Contour and Level Set for Medical Image Segmentation

Front Propagation

50

∂ψ∂t

+ ˆ k I ⋅ FA + FG (κ)( ) ⋅ ∇ψ = 0

link between spatial and temporal derivatives,but not the same type of motion as contours!

κ = div ∇ψ∇ψ

%

& '

(

) *

constant “force”(balloon pressure)

ψ(x,y,t+1) - ψ(x,y,t)

extension of the speed function kI(image influence)

smoothing “force”depending on the local curvature κ(contour influence)

spatial derivative of ψ

product of influences

Page 51: Lec11: Active Contour and Level Set for Medical Image Segmentation

Front Propagation

51

• Speed function:– kI is meant to stop the front on the object’s boundaries– similar to image energy: kI(x,y) = 1 / ( 1 + || ∇I (x,y) || )– only makes sense for the front (level set 0)– yet, same equation for all level sets

→ extend kI to all level sets, defining

– possible extension:

k̂I

k̂I (x,y) = kI(x’,y’)where (x’,y’) is the point in the front closest to (x,y)

^( such a kI (x,y) depends on the front location )

Page 52: Lec11: Active Contour and Level Set for Medical Image Segmentation

Reconstruction of Surfaces from Unorganized Data Points

52

Reconstruction of a rat brain from data of MRI slices

Page 53: Lec11: Active Contour and Level Set for Medical Image Segmentation

CVPR 2005: Level Set Segmentation (>1800 citation)

53

Ultrasound image segmentation.

Chunming Li et al.LS Evolution without reinitialization: a new variational formulation.

Page 54: Lec11: Active Contour and Level Set for Medical Image Segmentation

Vein Segmentation with Level Set

54

Page 55: Lec11: Active Contour and Level Set for Medical Image Segmentation

Spinal Cord Quantification - MRI• Atrophy (Multiple-

Sclerosis) is generally assessed by measuring the cross-sectional areas at specific levels (typically C2–C5) along the cervical cord.

• Spinal cord under analysis can be characterized by a bright structure against a dark background.

• Segmentation is necessary for accurate and automatic quantification

55

Page 56: Lec11: Active Contour and Level Set for Medical Image Segmentation

Spinal Cord Segmentation in MRI 56

Surface evolution during the segmentation process of spinal cord from the MRI image (the number in the left corner of each image represents the number of elapsed iterations)

Selective contrast

Credit: Dougherty, MIP.

Page 57: Lec11: Active Contour and Level Set for Medical Image Segmentation

Cyst Segmentation from Breast US Images

57

Contour extraction of cyst form ultrasound breast image via merging multipleinitial level sets. Images courtesy of Yezzi, Georgia Institute of Technology.

Page 58: Lec11: Active Contour and Level Set for Medical Image Segmentation

Shape Constraints for LV Segmentation – Cardiac MRI (Yuanquan Wang, et al, Shape Analysis in Medical Image Analysis )

• Extensive techniques available for cardiac imaging provide qualitative and quantitative information about the morphology and function of the heart and great vessels

58

Page 59: Lec11: Active Contour and Level Set for Medical Image Segmentation

Shape Constraints for LV Segmentation – Cardiac MRI (Yuanquan Wang, et al, Shape Analysis in Medical Image Analysis )

• Extensive techniques available for cardiac imaging provide qualitative and quantitative information about the morphology and function of the heart and great vessels

• Many clinically established diagnosis indices such as wall thickness, myocardial motion, ejection fraction, and circumferential shortening of myocardial fibers are evaluated by the segmentation results of MRIs.

59

Page 60: Lec11: Active Contour and Level Set for Medical Image Segmentation

Shape Constraints for LV Segmentation – Cardiac MRI (Yuanquan Wang, et al, Shape Analysis in Medical Image Analysis )

• Extensive techniques available for cardiac imaging provide qualitative and quantitative information about the morphology and function of the heart and great vessels

• Many clinically established diagnosis indices such as wall thickness, myocardial motion, ejection fraction, and circumferential shortening of myocardial fibers are evaluated by the segmentation results of MRIs.

• In clinical practice, the LV segmentation task is often performed manually by an experienced clinician. Manual segmentation of the LV, however, is tedious, time consuming, subjective and irreproducible.

60

Page 61: Lec11: Active Contour and Level Set for Medical Image Segmentation

Cardiac MRI – Short Axis

61

• A major difficulty in segmentation of the cardiac MR images is the intensity inhomogeneity due to the radio-frequency coils or acquisition sequences.

• The myocardium and surrounding tissues such as the liver have almost the same intensity profile, leading to low contrast between them.

Page 62: Lec11: Active Contour and Level Set for Medical Image Segmentation

Endocardium Segmentation - MRI

62

a Failed active contour segmentations without the circle-shape constraint. b Succeeded segmentations with the circle-shape constraint

Page 63: Lec11: Active Contour and Level Set for Medical Image Segmentation

Epicardium Segmentation - MRI63

a Epicardium extraction using new external force. b Comparison of segmentation results with and without shape (similarity) energy

the external force

without shape constraint w/ without shape constraint w/

Page 64: Lec11: Active Contour and Level Set for Medical Image Segmentation

Shape Similarity Constraint• There would be spurious edges on the myocardium, and the contrast

between myocardium and surrounding structures would be low. Authors employ the endocardium result as a priori shape and construct a new shape-similarity based constraint given by

64

R(si )−R measures the deviation of the snake contour for epicardium from a circle with radius R at snaxel si . r’s are for endocardium

Page 65: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)

• Good initialization à one major problem in snakes• Shape constraint based LS is good, but not easy to construct

shape constraint• Missing/fuzzy boundary -> leakage due to constant

propagation force– Two adjacent regions compete for the common boundary

65

Page 66: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)

• Good initialization à one major problem in snakes• Shape constraint based LS is good, but not easy to construct

shape constraint• Missing/fuzzy boundary -> leakage due to constant propagation

force– Two adjacent regions compete for the common boundary

• Tumors vary in shape, texture, size, and intensity• T1-MRI is used for detailed neuroanatomy, but not good for

precisely distinguishing tumor regions• T2-MRI is good for tumor and edema identification, but often it is

difficult to obtain high resolution• Post-contrast T1-weighted MRI is more suitable for tumor

segmentation

66

Page 67: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)

67

Without (left) and with (right) contrast agent, T1-weihted MRI

Page 68: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)• New formula modulates the propagation term using image forces to change the

direction of propagation, so that the snake shrinks when the boundary encloses parts of the background (B), and grows when the boundary is inside the tumor region (A):

68

Page 69: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)• New formula modulates the propagation term using image forces to change the

direction of propagation, so that the snake shrinks when the boundary encloses parts of the background (B), and grows when the boundary is inside the tumor region (A):

69

Region competition

Page 70: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)• New formula modulates the propagation term using image forces to change the

direction of propagation, so that the snake shrinks when the boundary encloses parts of the background (B), and grows when the boundary is inside the tumor region (A):

70

Region competition

Controls strength ofSmoothing (on active contour)

Page 71: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)• New formula modulates the propagation term using image forces to change the

direction of propagation, so that the snake shrinks when the boundary encloses parts of the background (B), and grows when the boundary is inside the tumor region (A):

71

Controls strength ofSmoothing (on LS contour)

Region competition

Controls strength ofSmoothing (on active contour)

Page 72: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)

72

Tumor probability map (orange: highly likelytumor regions) is obtained after registering pre-and post-contrast T1 MR images.

Page 73: Lec11: Active Contour and Level Set for Medical Image Segmentation

LS Evolution with Region Competition (Ho et al., ICPR 2003)

73

Tumor probability map (orange: highly likelytumor regions) is obtained after registering pre-and post-contrast T1 MR images.

This map is used to initialize proposed LS segmentation method.

Page 74: Lec11: Active Contour and Level Set for Medical Image Segmentation

Level Set Segmentation in Slicer• Following examples (slides) are from NA-MIC

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Minimal curvature

Upwind Vector

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Slide Credits and References• Credits to: M.Brady and R.Szelisky, Bagci’s CV Course 2015 Fall.• TF. Chan and L. Vese, IEEE TIP, 2001.• TF. Cootes et al. ASM and their training and applications, 1995.• Osher and Paragios (2003), Paragios, Faugeras, Chan et al.

(2005), Paragios and Sgallari (2009)• G. Strang, Lecture Notes, MIT.• Malladi, Sethian, Vemuri. IEEE PAMI 1995.• R. Szelisky, Lecture Presentations.• Sethian, JA. Fast Marching. PNAS 1996.• Osher and Fedkiw. Level set methods and dynamic implicit

surfaces.• Lim, Bagci, and Li. IEEE TBME 2013 [Willmore Flow and Level Set]• K.D. Toennies, Guide to Medical Image Analysis,

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