Applied Probability Lecture 5 Tina Kapur

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Presentation transcript:

Applied Probability Lecture 5 Tina Kapur

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

Review Friday: Vocabulary Random variable Discrete vs. continuous random variable PDF Uniform PDF Gaussian PDF Bayes rule / Conditional probability Marginal Probability

Gaussian PDF

Objective Probabilistic Segmentation of MRI images.

Objective Probabilistic Segmentation of MRI images.

Today and Tomorrow Lecture: Bayesian Segmentation of MRI –Inputs and outputs –Mechanics Lab/Recitation: Implementation using Matlab.

Bayesian Segmentation of MRI: Inputs and Outputs

Input: 256x256 MRI image

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)

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.

Bayes Rule for Segmentation

In MRI Segmentation:

Bayes Rule for Segmentation In MRI Segmentation: What is P(x|  P  P(  x 

Bayesian Segmentation of MRI: Mechanics Create class-conditional Gaussian density models from training data

Bayesian Segmentation of MRI: Mechanics Create class-conditional Gaussian density models from training data Use Uniform priors on the classes

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

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

Recitation/Lab Start MRI Segmentation Lab