Lecture_05.ppt
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Transcript of Lecture_05.ppt
![Page 2: Lecture_05.ppt](https://reader038.fdocuments.us/reader038/viewer/2022100802/577ccf2b1a28ab9e788f0f5a/html5/thumbnails/2.jpg)
Review Timeline/Administrivia
• Friday: vocabulary, Matlab• Monday: start medical segmentation project• Tuesday: complete project• Wednesday: 10am exam• Lecture: 10am-11am, Lab: 11am-12:30pm• Homework (matlab programs):
– PS 4: due 10am Monday– PS 5(project): due 12:30pm Tuesday
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Review Friday: Vocabulary
• Random variable• Discrete vs. continuous random variable• PDF• Uniform PDF• Gaussian PDF• Bayes rule / Conditional probability• Marginal Probability
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Gaussian PDF
2var
22
2)(
21)(
iance
mean
x
exP
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Objective
Probabilistic Segmentation of MRI images.
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Objective
Probabilistic Segmentation of MRI images.
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Today and Tomorrow
• Lecture: Bayesian Segmentation of MRI– Inputs and outputs– Mechanics
• Lab/Recitation: Implementation using Matlab.
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Bayesian Segmentation of MRI: Inputs and Outputs
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Bayesian Segmentation of MRI: Inputs and Outputs
• Input: 256x256 MRI image
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Bayesian Segmentation of MRI: Inputs and Outputs
• Input: 256x256 MRI image• Given knowledge base
– # classes 3: WM (1), GM (2), CSF(3)– Training data (manual segmentations)
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Bayesian Segmentation of MRI: Inputs and Outputs
• Input: 256x256 MRI image• Given knowledge base
– # classes 3: WM (1), GM (2), CSF(3)– Training data (manual segmentations)
• Output: segmented image with labels 1,2,3.
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Bayes Rule for Segmentation
)()()|()|(
BPAPABPBAP
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Bayes Rule for Segmentation
)()()|()|(
BPAPABPBAP
i
PxPx )()|()P(
:x ofy probabilit marginal the is P(x) where
ii
i
PxPPxPxPxPx
)()|()()|(
)P()()|()|P(
ii
ii
iii
In MRI Segmentation:
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Bayes Rule for Segmentation
)()()|()|(
BPAPABPBAP
i
PxPx )()|()P(
:x ofy probabilit marginal the is P(x) where
ii
i
PxPPxPxPxPx
)()|()()|(
)P()()|()|P(
ii
ii
iii
In MRI Segmentation:
What is P(x|PP(x
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Bayesian Segmentation of MRI: Mechanics
• Create class-conditional Gaussian density models from training data
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Bayesian Segmentation of MRI: Mechanics
• Create class-conditional Gaussian density models from training data
• Use Uniform priors on the classes
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Bayesian Segmentation of MRI: Mechanics
• Create class-conditional Gaussian density models from training data
• Use Uniform priors on the classes• Use Bayes rule to compute Posterior
probabilities for each class
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Bayesian Segmentation of MRI: Mechanics
• Create class-conditional Gaussian density models from training data
• Use Uniform priors on the classes• Use Bayes rule to compute Posterior
probabilities for each class• Assign label of M-A-P class =>
segmentation
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Recitation/Lab
• Start MRI Segmentation Lab