l15_seg.pdf

7/30/2019 l15_seg.pdf

1/80

MIT OpenCourseWarehttp://ocw.mit.edu

HST.582J / 6.555J / 16.456J Biomedical Signal and Image ProcessingSpring 2007

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
http://ocw.mit.edu/http://ocw.mit.edu/termshttp://ocw.mit.edu/termshttp://ocw.mit.edu/

7/30/2019 l15_seg.pdf

2/80

Introduction to Medical ImageSegmentation

HST 582

Harvard-MIT Division of Health Sciences and TechnologyHST.582J: Biomedical Signal and Image Processing, Spring 2007Course Director: Dr. Julie Greenberg

Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signaland Image Processing,Spring 2007.MIT OpenCourseWare(http://ocw.mit.edu), Massachusetts Institute of Technology.Downloaded on[DD Month YYYY].

7/30/2019 l15_seg.pdf

3/80

Outline

Applications Terminology

Probability Review Intensity-Based Classification

Prior models Morphological Operators


7/30/2019 l15_seg.pdf

4/80

Applications of Segmentation

Image Guided Surgery Surgical Simulation

Neuroscience Studies Therapy Evaluation


7/30/2019 l15_seg.pdf

5/80

Interactive Segmentation


MRI image sequence removed due to copyright restrictions.

7/30/2019 l15_seg.pdf

6/80


Image Guided Surgery

Surgical Simulation


Photo removed due to copyright restrictions.

Two doctors working with a surgical simulation device.

7/30/2019 l15_seg.pdf

7/80


Neuroscience Studies


7/30/2019 l15_seg.pdf

8/80

Statistical Map of Cortical Thinning:

Aging

p < 10-6

Courtesy of Bruce Fischl. Used with permission.

Thanks to Drs. Randy Buckner and David Salat for supplying this slide.Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signaland Image Processing,Spring 2007.MIT OpenCourseWare(http://ocw.mit.edu), Massachusetts Institute of Technology.Downloaded on[DD Month YYYY].

Th M i f C ti l Thi i

7/30/2019 l15_seg.pdf

9/80

The Movie of Cortical Thinningwith Aging

2.52.753.02.02.252.5

Courtesy of Bruce Fischl. Used with permission.


7/30/2019 l15_seg.pdf

10/80


Therapy Evaluation Multiple Sclerosis

Examples Later in talk

Knee Cartilage Repair


7/30/2019 l15_seg.pdf

11/80

Results: Segmentation ofFemoral & Tibial Cartilage

MRI Image Model-BasedSegmentation

Manual Segmentation

Source: Kapur, Tina. Model based three dimensional medical image segmentation. MIT Ph.D. thesis, 1999.


7/30/2019 l15_seg.pdf

12/80

Limitations of ManualSegmentation

slow (up to 60 hours per scan) variable (up to 15% between experts)

[Warfield + 2000]


7/30/2019 l15_seg.pdf

13/80

The Automatic SegmentationChallenge

An automated segmentation method needs toreconcile

Gray-level appearance of tissue

Characteristics of imaging modality

Geometry of anatomy


7/30/2019 l15_seg.pdf

14/80

Terminology: Segmentation

Graphics Community: Any process that turns images into models

Another Frequent Usage (HST 582):

Labeling images according to tissue type (e.g.White / Gray Matter)

Another: Dividing imagery into Major Anatomical

SubdivisionsCite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signaland Image Processing,Spring 2007.MIT OpenCourseWare(http://ocw.mit.edu), Massachusetts Institute of Technology.Downloaded on[DD Month YYYY].

7/30/2019 l15_seg.pdf

15/80

Hierarchical Approach (Brain)David Kennedy, MGH / Martinos Center

Segmentinto lobes Parcellate into functional areas


N t i D i ti Hi h

7/30/2019 l15_seg.pdf

16/80

Neuroanatomic Description Hierarchy:

WHOLE

BRAIN/STRUCTURE

Courtesy of David N. Kennedy, Ph.D. Used with permission.


Image removed due tocopyright restrictions.




Stages of Anatomic Analysis

7/30/2019 l15_seg.pdf

17/80

Stages of Anatomic AnalysisOriginal Subcortical Parc. Cortical Parcellation

General Segmentation. White Matter Parc.Courtesy of David N. Kennedy, Ph.D. Used with permission.

Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signaland Image Processing,Spring 2007.MIT O enCourseWare htt ://ocw.mit.edu Massachusetts Institute of Technolo .Downloaded on DD Month YYYY .

7/30/2019 l15_seg.pdf

18/80

Probability Review

Discrete Random Variables (RV) Probability Mass Functions (PMF)

Continuous Random Variables

Cumulative Distribution Functions (CDF)

Probability Density Functions (PDF)

Conditional Probability

Bayes Rule


7/30/2019 l15_seg.pdf

19/80

Discrete Random Variable Characterized by Probability Mass Function

(PMF)

(sometimes called Distribution)

Maps valuesx to their Probabilities P(x)


7/30/2019 l15_seg.pdf

20/80

Continuous Random Variables

Define Cumulative Distribution Function(CDF) on RV x

Non-Decreasing Sometimes calledDistribution Function


7/30/2019 l15_seg.pdf

21/80

Continuous Random Variables...

Define Probability Density Function (PDF)

Easy to show, using FundamentalTheorem of Calculus:


7/30/2019 l15_seg.pdf

22/80

More on PDFs :p(x)

Non Negative Integrates to One

(Value can be Greater than One)


7/30/2019 l15_seg.pdf

23/80

Conditional Probability

Define Conditional Probability:


7/30/2019 l15_seg.pdf

24/80

Bayes Rule (easy to show)

Frequent Situation: A: State of the World

B: Measurement

P(B|A) : Measurement Model

P(A) : A-Priori Model


7/30/2019 l15_seg.pdf

25/80

7/30/2019 l15_seg.pdf

26/80

Segmentation

Easy Segmentation Tissue/Air (except bone in MR)

Bone in CT

Feasible Segmentation

White Matter/Gray Matter

M.S. Lesions


7/30/2019 l15_seg.pdf

27/80

Statistical Classification

Probabilistic model ofintensity as a function of(tissue) class

Intensity data

Prior model

Classification of

voxels

[Duda, Hart 78]


7/30/2019 l15_seg.pdf

28/80

7/30/2019 l15_seg.pdf

29/80

Example

intensity

p(x|gray matter)p(x|white matter)


7/30/2019 l15_seg.pdf

30/80

7/30/2019 l15_seg.pdf

31/80

Example - revisited

white matterthreshold

gray matter


7/30/2019 l15_seg.pdf

32/80

Anatomical Knowledge

A priori model Before the measurement is considered

)( jTCP


7/30/2019 l15_seg.pdf

33/80

7/30/2019 l15_seg.pdf

34/80

Measurement Model

Training data Get an expert to label some of the voxels

Optional: Use a parametric model

Assume functional form

Popular choice: Gaussian


7/30/2019 l15_seg.pdf

35/80

7/30/2019 l15_seg.pdf

36/80

Choosing and Use training data:

ML parameter estimation

MAP tissue classifier with Gaussian measurement

model: choose tissue class to maximize:

= i iYN1

= i iYN22

)(

1

{ }NYYY ,...,, 21

...

)(),,(

)|(jojj

oj

TCPxG

xTCP

=


7/30/2019 l15_seg.pdf

37/80

7/30/2019 l15_seg.pdf

38/80

2D Gaussian: Example

iso probabilitycontour is

ellipse


7/30/2019 l15_seg.pdf

39/80

Multiple Sclerosis Example Dual echo MRI

1 x 1 x 3 mm

Registered slice pairs

Proton density image Good: white/gray

Bad: gray/csf

T2-weighted image Good: CSF/ Not so good: white/gray

Good: MS lesionsCite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signaland Image Processing,Spring 2007.MIT OpenCourseWare(http://ocw.mit.edu), Massachusetts Institute of Technology.Downloaded on[DD Month YYYY].

7/30/2019 l15_seg.pdf

40/80

Multiple Sclerosis

Provided by S Warfield

Courtesy Elsevier, Inc., http://www.sciencedirect.com. Used with permission.

PDw T2w

http://www.sciencedirect.com/http://www.sciencedirect.com/

7/30/2019 l15_seg.pdf

41/80

D t il

7/30/2019 l15_seg.pdf

42/80

Detail

MS Lesions are graded phenomenon in

MRI, and can be anywhere on the curve

gmwm

lesionscsf

healthy

mild

severe


7/30/2019 l15_seg.pdf

43/80

Multiple Sclerosis

Courtesy Elsevier, Inc.,http://www.sciencedirect.com. Used with permission.

PDw T2w SegmentationCite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signaland Image Processing,Spring 2007.MIT OpenCourseWare(http://ocw.mit.edu), Massachusetts Institute of Technology.Downloaded on[DD Month YYYY].

Images from Dr. Simon Warfield removed

due to copryight restrictions.
http://www.sciencedirect.com/http://www.sciencedirect.com/

7/30/2019 l15_seg.pdf

44/80

EM-Segmentation

7/30/2019 l15_seg.pdf

45/80

Estimate intensity correctionusing residuals based oncurrent posteriors.

Compute tissue posteriorsusing current intensity

correction.

E-Step

M-Step

Provided by T Kapur


7/30/2019 l15_seg.pdf

46/80

7/30/2019 l15_seg.pdf

47/80

7/30/2019 l15_seg.pdf

48/80

Prior Models Average Brain

Structurally-Conditioned Models

Markov Random Fields (MRF)

Ising

Potts


7/30/2019 l15_seg.pdf

49/80

Average Brain Models Construct a spatial prior model by

averaging tissue distributions over apopulation [MNI].


7/30/2019 l15_seg.pdf

50/80

Source: Pohl, Kilian M. "Prior Information for Brain Parcellation." MIT Ph.D. thesis, 2005.

Provided by Kilian Pohl


7/30/2019 l15_seg.pdf

51/80

7/30/2019 l15_seg.pdf

52/80

Modeling Global Geometric

7/30/2019 l15_seg.pdf

53/80

Relative Geometry Models

Motivate Using Knee MRI

Brain MRI Example

Modeling Global Geometric

Relationships between Structures


7/30/2019 l15_seg.pdf

54/80

Motivation

7/30/2019 l15_seg.pdf

55/80

Primary Structures image well

easy to segment

Secondary Structures image poorly

relative to primary

Tibial Cartilage

Femoral Cartilage

Tibia

Femur



7/30/2019 l15_seg.pdf

56/80

7/30/2019 l15_seg.pdf

57/80

7/30/2019 l15_seg.pdf

58/80

Status Have Bone

Want Cartilage

Provided by T Kapur


7/30/2019 l15_seg.pdf

59/80

7/30/2019 l15_seg.pdf

60/80

Estimate of Cartilage)x|nP( sss ,

7/30/2019 l15_seg.pdf

61/80

Cartilage)Fem.x|nP( sss , Cartilage)Tib.x|nP( sss ,



7/30/2019 l15_seg.pdf

62/80

7/30/2019 l15_seg.pdf

63/80

7/30/2019 l15_seg.pdf

64/80

7/30/2019 l15_seg.pdf

65/80

Lesion classification

7/30/2019 l15_seg.pdf

66/80


Images from Dr. Simon Warfield removeddue to copryight restrictions.

7/30/2019 l15_seg.pdf

67/80

7/30/2019 l15_seg.pdf

68/80

Morphological Operations Erosion

Dilation

Opening

Closing

[Haralick + 1989]


7/30/2019 l15_seg.pdf

69/80

7/30/2019 l15_seg.pdf

70/80

Dilation

7/30/2019 l15_seg.pdf

71/80

Continuous analogy

Makes structuresfatter

1

zero


Erosion

7/30/2019 l15_seg.pdf

72/80

Erosion is dual of dilation complement A

reflect B (negate coordinates)

dilate

complement result

BABA =

Frequently, B is symmetric and then reflection canbe ignored


Erosion

7/30/2019 l15_seg.pdf

73/80

Erosion by simple S.E.s makes structuresthinner

Analog analogy:

1 zero


7/30/2019 l15_seg.pdf

74/80

7/30/2019 l15_seg.pdf

75/80

Closing Closing = Dilate then Erode

Can attach objects that have becomefragmented


7/30/2019 l15_seg.pdf

76/80

Erosion and Dilation Common trick in brain isolation de-

scalping Erode it

to disconnect brain from head Dilate it

But only mark pixels that were originally brain


7/30/2019 l15_seg.pdf

77/80

Connectivity Define neighbor relation

There are some inconsistencies that a 6-neighbor relation can fix

4-neighbor 8-neighbor


7/30/2019 l15_seg.pdf

78/80

Finding Connected Components N = 1

Repeat until all pixels are labeled

Pick an unmarked1pixel

Label it, and all of its 1 neighbors, N NN + 1


7/30/2019 l15_seg.pdf

79/80

7/30/2019 l15_seg.pdf

80/80

Documents

l15_seg.pdf