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Image segmentation
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==== Image segmentation using MAP and expectation–maximization ==== The [[expectation–maximization algorithm]] is utilized to iteratively estimate the a posterior probabilities and distributions of labeling when no training data is available and no estimate of segmentation model can be formed. A general approach is to use histograms to represent the features of an image and proceed as outlined briefly in this three-step algorithm: 1. A random estimate of the model parameters is utilized. 2. E step: Estimate class statistics based on the random segmentation model defined. Using these, compute the [[conditional probability]] of belonging to a label given the feature set is calculated using naive [[Bayes' theorem]]. :<math> P(\lambda \mid f_i) = \frac{P(f_i \mid \lambda) P(\lambda)}{\Sigma_{\lambda \in \Lambda} P(f_i \mid \lambda) P(\lambda)} </math> Here <math>\lambda \in \Lambda</math>, the set of all possible labels. 3. M step: The established relevance of a given feature set to a labeling scheme is now used to compute the a priori estimate of a given label in the second part of the algorithm. Since the actual number of total labels is unknown (from a training data set), a hidden estimate of the number of labels given by the user is utilized in computations. :<math> P(\lambda) = \frac{\Sigma_{\lambda \in \Lambda} P(\lambda \mid f_i)}{|\Omega|} </math> where <math>\Omega</math> is the set of all possible features. [[File:Sample segmentation HMRF-EM.png|thumb|center|Segmentation of color image using HMRF-EM model]]
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