Image Segmentation Using Hidden Markov Gauss Mixture Models

Abstract

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

Hyper-Parameter in Hidden Markov Random Field

“…It is paired with aired with its hand-labelled classified image. These photographs have also been studied by Aiyer et al (2005), Li et al (2000), Pyun et al (2007) and Pyun et al (2009). In the analysis, we To design computer-based system to measure the spatial correlation in land use, we first segment the images into manmade and natural area using a block-based classifier.…”

“…In the analysis, we use 4 × 4 sub-blocks (256 × 256 sub-blocks in total) and estimating the Gauss mixture model for manmade and natura regions using 5 training images. The block processing steps are same with those in Aiyer et al (2005) and Pyun et al (2007) and their details are omitted here. Using the estimate GMMs, we classify each sub-block into the class having the highest likelihood.…”

Isolation of Brain Tumor Segment using HMGMM

“…As the model is 2-D, computational complexity is an important issue. K. Pyun, et al(2007) proposed a segmentation method combining GMVQ and 2-D hidden Markov modeling [4]. The problem w as formulated on the basis of Bayesian statistics.…”

“…The only parameter p is unknown and estimates it jointly with the true segmentation. Use a maximum a posteriori (MAP) estimate for the true segmentation and compute the approximate maximum likelihood estimator of often referred to as the hyper parameter [4]. In the HMGMM, the MAP estimate of Z, say Z*, becomes Z*=argmax log P(Z=z|X) =argmax {log P(X|Z=z) + log P(Z|z)}.…”

“…For Segmentation, this paper uses Gauss Mixture Models (GMM) and it has been a popular tool for fitting smooth densities to data in statistics and statistical signal processing. The Gaussian probability (pdf) maximizes the differential entropy and the worst high-rate distortion rate trade off given the mean and the covariance [2], [4]. To design a GMM, employ a clustering approach using the k-Means algorithm.…”