Mehdi N. Shirazi

Mean field decomposition of a posteriori probability for MRF-based unsupervised textured image segmentation

This paper proposes a Markov random field (MRF) model-based method for unsupervised segmentation of multispectral images consisting of multiple textures. To model such textured images, a hierarchical MRF is used with two layers, the first layer representing an unobservable region image and the second layer representing multiple textures which cover each region. This method uses the expectation-maximization (EM) method for model parameter estimation, where in order to overcome the well-noticed computational problem in the expectation step, we approximate the Baum function using mean-field-based decomposition of a posteriori probability. Given provisionally estimated parameters at each iteration in the EM method, a provisional segmentation is carried out using local a posteriori probability of each pixels region label, which is derived by mean-field-based decomposition of a posteriori probability of the whole region image.

An MRF model-based method for unsupervised textured image segmentation

This paper proposes a Markov random field (MRF) model-based method for unsupervised segmentation of images consisting of multiple textures. This method uses a hierarchical MRF with two layers, the first layer representing an unobservable region image and the second layer representing multiple textures which cover each region. This method is an iterative method based on the framework of the expectation and maximization (EM) method. We make use of an approximation for the Baum function in the expectation step. This reduces the parameter estimation to the maximum likelihood (ML) estimation given the current estimate of the region image. An estimation of the region image (image segmentation) is carried out by a deterministic relaxation method proposed by us.

A noise suppressing distance measure for competitive learning neural networks

A measure that equips competitive learning neural networks with noise suppressing capabilities in the learning phase is presented. Analysis shows that weight vectors of neural networks employing the measure are effectively protected from being trained by much shorter (and noisy) input vectors. An ART2a-like scheme is equipped with the measure, while omitting the typical noise-reduction and contrast-enhancement mechanisms of ART2a. Experiments show that this scheme is more robust to noise in the learning phase than ART2a.

Emergence of orientation-selective inhibition in the primary visual cortex: a Bayes–Markov computational model

The recent consensus is that virtually all aspects of response selectivity exhibited by the primary visual cortex are either created or sharpened by cortical inhibitory interneurons. Experimental studies have shown that there are cortical inhibitory cells that are driven by geniculate cells and that, like their cortical excitatory counterparts, are orientation selective, though less sharply tuned. The main goal of this article is to demonstrate how orientation-selective inhibition might be created by the circuitry of the primary visual cortex (striate cortex, V1) from its nonoriented geniculate inputs. To fulfill this goal, first, a Bayes–Markov computational model is developed for the V1 area dedicated to foveal vision. The developed model consists of three parts: (i) a two-layered hierarchical Markov random field that is assumed to generate the activity patterns of the geniculate and cortical inhibitory cells, (ii) a Bayesian computational goal that is formulated based on the maximum a posteriori (MAP) estimation principle, and (iii) an iterative, deterministic, parallel algorithm that leads the cortical circuitry to achieve its assigned computational goal. The developed model is not fully LGN driven and it is not implementable by the neural machinery of V1. The model, then, is transformed into a fully LGN-driven and physiologically plausible form. Computer simulation is used to demonstrate the performance of the developed models.

From Markov random field theory to the neural circuitry of striate visual cortex

The consensus is that virtually all aspects of the response selectivity exhibited by visual cortical cells are either created of sharpened by intra-cortical inhibitory cells. There is abundant experimental evidence supporting the view that the inhibitory cortical cells are orientation specific. To understand the mechanism underlying the orientation specificity of inhibitory cortical cells is a key to understand the neural circuitry of the striate visual cortex. It is the purpose of this article to show how such an orientation-specific inhibition can be achieved from the striate-cortex innervating nonoriented lateral geniculate cells. A computational model for the orientation-specific inhibition is introduced. The model consists of three parts: (a) a two-layered hierarchical Markov random field; (b) a computational goal formulated based on the maximum a posteriori estimation principle; (c) a deterministic parallel algorithm to achieve the computational goal. A physiologically-plausible firing-rate-coded neural circuit is introduced to implement the computational model.

A Computation Theory for Orientation-Selective Simple Cells Based on the MAP Estimation Principle and Markov Random Fields

A computation theory is proposed for the orientation-selective simple cells of the striate cortex. The theory consists of three parts: (a) a probabilistic computation theory based on MRFs and the MAP estimation principle which is assumed to be carried out by the visual pathway lying between the lateral geniculate nuclei and the simple cells; (b) a deterministic parallel algorithm which compute the MAP estimation approximately; and (c) a neural implementation of the algorithm.

Robust parallel segmentation of BESAG-GA USSIAN MRFs with uncertain parameters

We have developed a robust segmentation algorithm for textured images: those composed of regions of two distinct textures. The region image (the extension of the natural patches) Is modeled by a binary Besag-Marklow random field (MRF) characterized by a single parameter, whereas the covering textures are modeled by two spatially independent Gaussian random variables with region-dependent means and variances. The model parameters are unknown and assumed to be between know lower and upper bounds. The iterated conditional modes (ICM) algorithm is adopted and is made robust by using the maximin (worstcase) method. Our main theoretical result is given as the least-favorable operating point theorem. In the present study, we obtain the least favorable operating point for the mean parameters of the two spatially independent Gaussian random variables. Simulation studies show that the Algorithm has a uniform and low segmentation error over the entire Range of the model parameters. The most useful features of the Algorithm are that its use does not require full knowledge of the Model parameters or their estimates and that it can be implemented In a massively parallel manner.

A parallel robust segmentation algorithm using the maximin method for MRF texture images

A robust algorithm is proposed for the segmentation of a special class of texture images where the images are composed of regions covered with two distinct fine textures. We describe the region images with Markov random fields (MRFs) and assume that the covering fine textures are realizations of two distinct independent Gaussian random variables. The model parameters are assumed to be unknown but bounded with known lower and upper bounds. We adopt J.E. Besags (1986) iterated conditional modes (ICM) algorithm and make it robust in a maximin sense. We have previously (1998) discussed this problem in the case of two kinds of Gaussian on different regions with the same variance and different means. In this paper, we deal with the case of this problem in which the two kinds of Gaussian on the different regions have the same mean and different variances. The most attractive properties of the derived algorithm are: (a) there is no need to go through computationally expensive parameter estimations which are usually not implementable in parallel; (b) the algorithm is fully parallel; (c) the algorithm can be implemented by recurrent neural networks.

Unsupervised image segmentation using a mean field decomposition of a posteriori probability

This paper proposes a Markov random field (MRF) model-based method for unsupervised segmentation of images consisting of multiple textures. To model such textured images, a hierarchical MRF is used with two layers, the first layer representing an unobservable region image and the second layer representing multiple textures which cover each region. This method uses the Expectation and Maximization (EM) method for model parameter estimation, where in order to overcome the well-noticed computational problem in the expectation step, we approximate the Baum function using mean-field-based decomposition of a posteriori probability. Given provisionally estimated parameters at each iteration in the EM method, a provisional segmentation is carried out using local a posteriori probability (LAP) of each pixels region label, which is derived by mean-field-based decomposition of a posteriori probability of the whole region image. Simulation results show that the use of LAPs is essential to perform a good image segmentation.