Estimation of generalized mixtures and its application in image segmentation

Abstract

We introduce the notion of a generalized mixture and propose some methods for estimating it, along with applications to unsupervised statistical image segmentation. A distribution mixture is said to be "generalized" when the exact nature of the components is not known, but each belongs to a finite known set of families of distributions. For instance, we can consider a mixture of three distributions, each being exponential or Gaussian. The problem of estimating such a mixture contains thus a new difficulty: we have to label each of three components (there are eight possibilities). We show that the classical mixture estimation algorithms-expectation-maximization (EM), stochastic EM (SEM), and iterative conditional estimation (ICE)-can be adapted to such situations once as we dispose of a method of recognition of each component separately. That is, when we know that a sample proceeds from one family of the set considered, we have a decision rule for what family it belongs to. Considering the Pearson system, which is a set of eight families, the decision rule above is defined by the use of "skewness" and "kurtosis". The different algorithms so obtained are then applied to the problem of unsupervised Bayesian image segmentation, We propose the adaptive versions of SEM, EM, and ICE in the case of "blind", i.e., "pixel by pixel", segmentation. "Global" segmentation methods require modeling by hidden random Markov fields, and we propose adaptations of two traditional parameter estimation algorithms: Gibbsian EM (GEM) and ICE allowing the estimation of generalized mixtures corresponding to Pearson's system. The efficiency of different methods is compared via numerical studies, and the results of unsupervised segmentation of three real radar images by different methods are presented.

Unsupervised image segmentation using triplet Markov fields

“…In particular, one may consider Stochastic Gradient (SG [35]), whose aim is to approach the maximum of the likelihood p (y) in a stochastic manner to remedy the difficulties encountered by EM. Another possibility is to use the general ''Iterative Conditional Estimation'' (ICE [25]) method, which has given good results in different classical HMF situations [4,7,10,16,22,23,30], and in more complex Markov models with a Dempster-Shafer fusion [2] or fuzzy hidden fields [31]. Moreover, first applications of ICE in a simple TMF context also gave promising results [27].…”

Color Image Segmentation using ERKFCM

“…The membership maps each element of X to a membership grade between 0 and 1. In this way, the image is considered as a fuzzy set and thus filters are designed [3]. …”

“…Image segmentation is an important tool in image processing which is partitioning an image into pixels which are homogeneous with respect to some criterion [3]. It is used for higher level image analysis task such as object recognition, data compression, image retrieval etc [2].…”

A modular approach to facial feature segmentation on real sequences

“…It has been reported that for fixed objects (and the facial features could well be considered as such) it is possible to partition the image into a globally consistent interpretation through the use of deformable templates, while using statistical shape models to enforce prior probabilities on global deformations within the same class [41]. Other recent work in image segmentation includes stochastic model-based approaches [11,25,34,52,55] morphological watershed-based region growing [43], energy diffusion [28], and graph partitioning [44]. Non-modelguided segmentation aims at separating homogeneous colour-texture regions [12], but generally do not satisfy semantic partitioning.…”