hst.582j / 6.555j / 16.456j biomedical signal and image ... · introduction to medical image...
TRANSCRIPT
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MIT OpenCourseWare http://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.
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Introduction to Medical Image Segmentation
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 Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Outline
• Applications• Terminology• Probability Review• Intensity-Based Classification• Prior models• Morphological Operators
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Applications of Segmentation
• Image Guided Surgery• Surgical Simulation• Neuroscience Studies• Therapy Evaluation
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Interactive Segmentation
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
MRI image sequence removed due to copyright restrictions.
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Applications of Segmentation
• Image Guided Surgery• Surgical Simulation
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Photo removed due to copyright restrictions.Two doctors working with a surgical simulation device.
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Applications of Segmentation
• Neuroscience Studies
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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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 Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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The Movie of Cortical Thinning with Aging
2.5 2.75 3.02.0 2.25 2.5Courtesy of Bruce Fischl. Used with permission.
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Applications of Segmentation
• Therapy Evaluation– Multiple Sclerosis
• Examples Later in talk
– Knee Cartilage Repair
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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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.
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Limitations of Manual Segmentation
• slow (up to 60 hours per scan) • variable (up to 15% between experts)
[Warfield + 2000]
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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The Automatic Segmentation Challenge
An automated segmentation method needs to reconcile– Gray-level appearance of tissue– Characteristics of imaging modality– Geometry of anatomy
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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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 Subdivisions
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Hierarchical Approach (Brain)David Kennedy, MGH / Martinos Center
• Segment into lobes• Parcellate into functional areas
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Neuroanatomic Description Hierarchy:
WHOLE BRAIN/STRUCTURE
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 Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Image removed due tocopyright restrictions.
Image removed due tocopyright restrictions.
Image removed due tocopyright restrictions.
Image removed due tocopyright restrictions.
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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 Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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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
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Discrete Random Variable
• Characterized by Probability Mass Function(PMF) – (sometimes called Distribution)– Maps values x to their Probabilities P(x)
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Continuous Random Variables
• Define Cumulative Distribution Function (CDF) on RV x
• Non-Decreasing• Sometimes called Distribution Function
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Continuous Random Variables...
• Define Probability Density Function (PDF)
• Easy to show, using Fundamental Theorem of Calculus:
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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More on PDFs : p(x)
• Non Negative• Integrates to One• (Value can be Greater than One)
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Conditional Probability
• Define Conditional Probability:
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Bayes’ Rule (easy to show)
• Frequent Situation:– A: State of the World– B: Measurement– P(B|A) : Measurement Model– P(A) : A-Priori Model
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Intensity-Based Segmentation
• Statistical Classification– ML – MAP, a-priori models– KNN
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Segmentation
• Easy Segmentation– Tissue/Air (except bone in MR)– Bone in CT
• Feasible Segmentation– White Matter/Gray Matter– M.S. Lesions
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Statistical Classification
• Probabilistic model of intensity as a function of (tissue) class
• Intensity data• Prior model
Classification ofvoxels
[Duda, Hart 78]
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Measurement Model
• Characterize sensor
p(x|tissue class J)
probabilitydensity
intensity Tissue class conditional modelof signal intensity
mean for tissue J
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Example
intensity
p(x|gray matter)
p(x|white matter)
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Maximum Likelihood Classification
• Measure intensity, xo, and we want to know the tissue class
• Pick tissue class that maximizes L• L is not a probability
– Called: Likelihood
)|()( joj TCxpTCL =
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Example - revisited
white matter
threshold
gray matter
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Anatomical Knowledge
• A priori model– Before the measurement is considered
)( jTCP
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MAP Classifier
• Choose TC to Maximize the A Posterioriprobability
)()()|()|(
0xpTCPTCxpxTCP o
o =
posteriorprobability
measurementmodel
not important
prior
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Measurement Model
• Training data– Get an expert to label some of the voxels
• Optional: Use a parametric model– Assume functional form
• Popular choice: Gaussian
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Gaussian Density – 1D
• Why?– Central Limit Theorem– Makes math easy (when doing parameter
estimation)
σ
μ
2
2
2)(
21),,( σ
μ
σπσμ
−−
=x
exG
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Choosing σ and μ
• Use training data:• ML parameter estimation
• MAP tissue classifier with Gaussian measurement model: choose tissue class to maximize:
∑=i
iYN1μ ∑ −=
iiY
N22 )(1 μσ
{ }NYYY ,...,, 21
...)(),,(
)|( jojjoj
TCPxGxTCP
σμ=
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Gaussian Density – 2d Data
• ExampleX = proton density intensity
T2 weighted intensity
Vector Gaussian
)()(
21
2
1
||)2(
1),,( MXMXN
T
eXMG −Σ−− −
Σ=Σ
π
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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2D Gaussian: Example
iso probability contour is
ellipse
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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 lesions
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Multiple Sclerosis
Provided by S Warfield
Courtesy Elsevier, Inc., http://www.sciencedirect.com. Used with permission.
PDw T2w
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Dual Echo MRI Feature Space
csf
gmwm
severelesions
air
T2 In
tens
ity
PD IntensityCite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Detail
• MS Lesions are “graded phenomenon” in MRI, and can be anywhere on the curve
gmwm
lesionscsf
healthymild
severe
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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 Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Background: Intensity Inhomogeneities in MRI
• MRI signal derived from RF signals…• Intra Scan Inhomogeneities
– “Shading” … from coil imperfections– interaction with tissue?
• Inter Scan Inhomogeneities– Auto Tune– Equipment Upgrades
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Estimate intensity correctionusing residuals based on current posteriors.
Compute tissue posteriors using current intensity correction.
E-Step
EM-Segmentation
M-StepProvided by T Kapur
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Dual Echo Longitudinal Study
PDw T2w
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Tissue classification
No Intensity Correction EM Segmentation
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Prior Models
• Average Brain• Structurally-Conditioned Models• Markov Random Fields (MRF)
– Ising– Potts
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Average Brain Models
• Construct a spatial prior model by averaging tissue distributions over a population [MNI].
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Source: Pohl, Kilian M. "Prior Information for Brain Parcellation." MIT Ph.D. thesis, 2005.
Provided by Kilian Pohl
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P(white matter | x y)
Provided by Kilian Pohl
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Source: Pohl, Kilian M. "Prior Information for Brain Parcellation." MIT Ph.D. thesis, 2005.
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Structurally-Conditioned Prior Models
• From (Kapur 1999)– Modeling Global Geometric Relationships
between Structures
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• Relative Geometry Models • Motivate Using Knee MRI • Brain MRI Example
Modeling Global Geometric Relationships between Structures
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Segmented Knee MRIFemur
Tibia
Femoral Cartilage
Tibial Cartilage
MERL, SPL, MIT, CMUSurgical Simulation(Sarah Gibson, PI)
Source: Kapur, Tina. “Model based three dimensional medical image segmentation.” MIT Ph.D. thesis, 1999.
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Motivation
• Primary Structures– image well– easy to segment
• Secondary Structures– image poorly– relative to primary
Tibial Cartilage
Femoral Cartilage
Tibia
Femur
Source: Kapur, Tina. “Model based three dimensional medical image segmentation.” MIT Ph.D. thesis, 1999.
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Relative Geometric Prior Approach
• Select primary/secondary structures• Measure geometric relation between
primary and secondary structures from training data
• Given novel image– segment primary structures– use geometric relation as prior on secondary
structure in EM-MF SegmentationProvided by T Kapur
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Segment Primary Structures:Femur, Tibia
Seed Region Growing Boundary Localization
Source: Kapur, Tina. “Model based three dimensional medical image segmentation.” MIT Ph.D. thesis, 1999.
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Status
• Have Bone
• Want Cartilage
Provided by T Kapur
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Measure Geometric Relationship between Primary and Secondary
Structures Femur
Tibia
Femoral CartilageTibial Cartilage
• Using primitives such as– distances between surfaces– local normals of primary structures– local curvature of primary structures– etc.
Provided by T Kapur
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Femur
Tibia
Femoral CartilageTibial Cartilage
Measure Geometric Relationship between Primary and Secondary
Structures
Ze)P(CartilagCartilage)x|nP(
)Bone|CartilageP(x
pointclosest at (femur) bone tonormal n(femur)boneon point closest todistance
sss
s
s
s
, ∈≅
∈
≡≡
ρ
ρ
Provided by T KapurCite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Estimate of Cartilage)x|nP( sss , ∈ρ
Cartilage)Fem.x|nP( sss , ∈ρ Cartilage)Tib.x|nP( sss , ∈ρSource: Kapur, Tina. “Model based three dimensional medical image segmentation.” MIT Ph.D. thesis, 1999.
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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.
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kNN combined with Atlas
•Simon Warfield
•Use Atlas to control kNN Classifier•Resolve contrast failure
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Overlapping distributions
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Lesion classification
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Lesion classification
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Multiple Sclerosis
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PDw T2w
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Morphological Operations
• Erosion• Dilation• Opening• Closing
• [Haralick + 1989]
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Morphological Operators...
• Ubiquitous simple tools. Useful for ad-hoc clean-up of results from Statistical Classification.
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Dilation• Binary (or Boolean) images• Represent image by a set of coordinate
vectors of pixels with value 1
{ }B b A, a somefor ,| ∈∈+=≡⊕ baccBAimage
Typical structure elements: 11 1
11
111
1
vector addition
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Dilation• Continuous analogy• Makes structures fatter
1
zero
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Erosion• Erosion is dual of dilation
– complement A– reflect B (negate coordinates)– dilate– complement result
BABA ˆ⊕=⊗
•Frequently, B is symmetric and then reflection can be ignored
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Erosion• Erosion by simple S.E.’s makes structures
thinner• Analog analogy:
1 zero
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Opening
• Opening = Erode then Dilate
Break thin connections
Removes small junk
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Closing
• Closing = Dilate then Erode• Can attach objects that have become
fragmented
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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”
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Connectivity
• Define neighbor relation
– There are some inconsistencies that a 6-neighbor relation can fix
4-neighbor 8-neighbor
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Finding Connected Components
• N = 1• Repeat until all pixels are labeled
– Pick an unmarked 1 pixel– Label it, and all of its 1 neighbors, N– N N + 1
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Connected Components: Example
• Boolean image
• Each separate object get a unique label
1
1
1
1zero
1
2
3
4zero
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Selected References• [Duda and Hart1973] Duda, R. and Hart, P.1973. Pattern Classification and Scene
Analysis. John Wiley and Sons.• [Gonzales + 2001] R Gonzales and R Woods. Digital Image Processing, 2nd Ed.
Prentice Hall 2001.• [Haralick + 1989 ] R Haralick and S Steinberg. Image Analysis Using
Mathematical Morphology. IEEE Transactions PAMI 1989.• [Kapur 1999] T Kapur. Model Based Three Dimensional Medical Imaging
Segmentation. PhD Thesis, MIT EECS, 1999.• [Warfield + 2000] S Warfield, J Rexilius, M Kaus, F Jolesz, R Kikinis. Adaptive
template moderated spatial varying statistical classification. Med. Image Analysis, 2000.
• [Wells + 1996] W Wells, E Grimson, R Kikinis, F Jolesz. Adaptive segmentation of MRI data. IEEE Trans. Med. Img. 15, 1996.
Cite as: William (Sandy) Wells. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].