Maximum Posterior Mode Research Articles

A new hybrid model of convolutional neural networks and hidden Markov chains for image classification.

Convolutional neural networks (CNNs) have lately proven to be extremely effective in image recognition. Besides CNN, hidden Markov chains (HMCs) are probabilistic models widely used in image processing. This paper presents a new hybrid model composed of both CNNs and HMCs. The CNN model is used for feature extraction and dimensionality reduction and the HMC model for classification. In the new model, named CNN-HMC, convolutional and pooling layers of the CNN model are applied to extract features maps. Also a Peano scan is applied to obtain several HMCs. Expectation-Maximization (EM) algorithm is used to estimate HMC's parameters and to make the Bayesian Maximum Posterior Mode (MPM) classification method used unsupervised. The objective is to enhance the performances of the CNN models for the image classification task. To evaluate the performance of our proposal, it is compared to six models in two series of experiments. In the first series, we consider two CNN-HMC and compare them to two CNNs, 4Conv and Mini AlexNet, respectively. The results show that CNN-HMC model outperforms the classical CNN model, and significantly improves the accuracy of the Mini AlexNet. In the second series, it is compared to four models CNN-SVMs, CNN-LSTMs, CNN-RFs, and CNN-gcForests, which only differ from CNN-HMC by the second classification step. Based on five datasets and four metrics recall, precision, F1-score, and accuracy, results of these comparisons show again the interest of the proposed CNN-HMC. In particular, with a CNN model of 71% of accuracy, the CNN-HMC gives an accuracy ranging between 81.63% and 92.5%.

Equivalence between LC-CRF and HMM, and Discriminative Computing of HMM-Based MPM and MAP

Practitioners have used hidden Markov models (HMMs) in different problems for about sixty years. Moreover, conditional random fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We propose two contributions: First, we show that the basic linear-chain CRFs (LC-CRFs), considered as different from HMMs, are in fact equivalent to HMMs in the sense that for each LC-CRF there exists an HMM—that we specify—whose posterior distribution is identical to the given LC-CRF. Second, we show that it is possible to reformulate the generative Bayesian classifiers maximum posterior mode (MPM) and maximum a posteriori (MAP), used in HMMs, as discriminative ones. The last point is of importance in many fields, especially in natural language processing (NLP), as it shows that in some situations dropping HMMs in favor of CRFs is not necessary.

Synthetic aperture radar image segmentation using fuzzy label field‐based triplet Markov fields model

The recently proposed triplet Markov random fields (TMF) model is very suitable for dealing with non-stationary image segmentation. However, influenced by multiplicative speckle noise, synthetic aperture radar image (SAR) is dim and blurred in the boundaries of different areas, making it difficult to locate boundary accurately in the segmentation process. Thus, in this study, the authors propose a new segmentation algorithm using fuzzy label field-based TMF model for SAR images. In the proposed algorithm, the value of each site in the label field is extended from a finite discrete set in the classical TMF model to a continuous one, in order to describe the memberships of each pixel to different classes. A fuzzy energy function is constructed to describe the joint prior distribution of the fuzzy label field and the auxiliary field. The construction of fuzzy energy function also takes into account four direction information and degree of difference between neighbouring pixels. Iterative conditional estimation method and maximum posterior mode criterion are applied to implement parameter estimation and segmentation. Experimental results on simulated data and real SAR images demonstrate the effectiveness of the proposed algorithm.

Unsupervised multi-class segmentation of SAR images using triplet Markov fields models based on edge penalty

Non-Gaussian triplet Markov random fields (TMF) model is suitable for dealing with multi-class segmentation of nonstationary and non-Gaussian synthetic aperture radar (SAR) images. However, the segmentation of SAR images utilizing this model still fails to resolve the misclassifications due to the inaccuracy of edge location. In this paper, we propose a new unsupervised multi-class segmentation algorithm by fusing the traditional energy function of TMF model with the principle of edge penalty. Through the introduction of the penalty function based on local edge strength information, the new energy function could prevent segment from smoothing across boundaries. Then we optimize the objective function that stems from the new energy function to obtain an iterative multi-region merging Bayesian maximum posterior mode (MPM) segmentation equation for the new segmentation algorithm. The effectiveness of the proposed algorithm is demonstrated by application to simulated data and real SAR images.

Fast algorithm based on triplet Markov fields for unsupervised multi-class segmentation of SAR images

Non-Gaussian triplet Markov fields (TMF) model is suitable for dealing with multi-class segmentation of non-stationary and non-Gaussian synthetic aperture radar (SAR) images. Considering the complexity of the model and algorithm, as well as the requirement of real-time, and robust and efficient processing of SAR images, a fast algorithm based on TMF for unsupervised multi-class segmentation of SAR images is proposed in this paper. For the speckle noise in SAR images, numerical characteristic, threshold selection and QuadTree decomposition criterion are researched firstly. With the new method, a SAR image can quickly be mapped into an edge-based pixon-representation, which results in a coarse decomposition in smooth regions, and a fine decomposition in edges. Then by combining TMF model with the pixon-representation of SAR image, a new potential energy function of TMF based on pixon-representation is derived. Finally, the segmentation is finished by Bayesian maximum posterior mode (MPM). The effectiveness of the fast TMF algorithm is demonstrated by applying it to simulated data and real SAR images.

Turbo Segmentation of Textured Images

We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.

Multichannel Deconvolution of Seismic Signals Using Statistical MCMC Methods

In this paper, we propose two multichannel blind deconvolution algorithms for the restoration of two-dimensional (2D) seismic data. Both algorithms are based on a 2D reflectivity prior model, and use iterative multichannel deconvolution procedures which deconvolve the seismic data, while taking into account the spatial dependency between neighboring traces. The first algorithm employs in each step a modified maximum posterior mode (MPM) algorithm which estimates a reflectivity column from the corresponding observed trace using the estimate of the preceding reflectivity column. The second algorithm takes into account estimates of both the preceding and subsequent columns in the estimation process. Both algorithms are applied to synthetic and real data and demonstrate better results compared to those obtained by a single-channel deconvolution method. Expectedly, the second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm.

Blind marine seismic deconvolution using statistical MCMC methods

In order to improve the resolution of seismic images, a blind deconvolution of seismic traces is necessary, since the source wavelet is not known and cannot be considered as a stationary signal. The reflectivity sequence is modeled as a Gaussian mixture, depending on three parameters (high and low reflector variances and reflector density), on the wavelet impulse response, and on the observation noise variance. These parameters are unknown and must be estimated from the recorded trace, which is the reflectivity convolved with the wavelet, plus noise. Two methods are compared in this paper for the parameter estimation. Since we are considering an incomplete data problem, we first consider maximum likelihood estimation by means of a stochastic expectation maximization (SEM) method. Alternatively, proper prior distributions can be specified for all unknown quantities. Then, a Bayesian strategy is applied, based on a Monte Carlo Markov Chain (MCMC) method. Having estimated the parameters, one can proceed to the deconvolution. A maximum posterior mode (MPM) criterion is optimized by means of an MCMC method. The deconvolution capability of these procedures is checked first on synthetic signals and then on the seismic data of the IFREMER ESSR4 campaign, where the wavelet duration blurs the reflectivity, and on the SMAVH high-resolution marine seismic data.