Markov random field

About: Markov random field is a research topic. Over the lifetime, 5669 publications have been published within this topic receiving 179568 citations. The topic is also known as: MRF.

Handwriting Recognition: Soft Computing and Probabilistic Approaches

Abstract: In this book, we introduce several methods for recognising unconstrained handwritten words and digits using hidden Markov models (HMMs) and Markov random field (MRF) models. Since the hidden Markov model (HMM) is stochastic finite state automation, it is able to represent a sequence of features. we used HMMs to model features that are extracted from outer contours of images to form sequences. To overcome the limitation of HMMs in modelling structural information, we used structural models, which are based on the best sequences of states, to represent structural information and enhance the performance of HMMs. In addition, we presented a procdure to model relationships between spectral components using 2-D HMMs, where the spectral features are extracted by Fourier descriptor. This method can be used to recognise two-dimensional shapes as well as handwritten digits. Markov random field models are appropriate to model two-dimensional features of handwritten words and digits. The most important merit of Markov random field models is that they provide flexible and natural methods for modelling the interaction between spatially related random variables in their neighbourhood systems via designed clique functions. In MRF model, the global optimum can be derived from local information in term of clique functions. This book also describes methods to use MRFs to model structural relationships between line-segments for recognising handwritten words and to model both structural and statistical information for recognising handwritten digits. Relaxation labelling is used to maximise the global compatibility of MRF models. To evaluate the proposed methods, we had conducted experiments on two databases: handwritten word database and handwritten digit database. Both databases are taken from USPS CEDAR CDROM1. The recognition rates for handwritten words are from 69.0% to 96.5% among top 1 to top 5 positions with only 7.5 training images per word on the average. The recognition rates for handwritten digits range from 96.48\% to 98.37% with different methods. These results show our method can achieve recognition rates comparable to that reported in the literature recently.

VPRS-Based Regional Decision Fusion of CNN and MRF Classifications for Very Fine Resolution Remotely Sensed Images

Abstract: Recent advances in computer vision and pattern recognition have demonstrated the superiority of deep neural networks using spatial feature representation, such as convolutional neural networks (CNNs), for image classification. However, any classifier, regardless of its model structure (deep or shallow), involves prediction uncertainty when classifying spatially and spectrally complicated very fine spatial resolution (VFSR) imagery. We propose here to characterize the uncertainty distribution of CNN classification and integrate it into a regional decision fusion to increase classification accuracy. Specifically, a variable precision rough set (VPRS) model is proposed to quantify the uncertainty within CNN classifications of VFSR imagery and partition this uncertainty into positive regions (correct classifications) and nonpositive regions (uncertain or incorrect classifications). Those “more correct” areas were trusted by the CNN, whereas the uncertain areas were rectified by a multilayer perceptron (MLP)-based Markov random field (MLP-MRF) classifier to provide crisp and accurate boundary delineation. The proposed MRF-CNN fusion decision strategy exploited the complementary characteristics of the two classifiers based on VPRS uncertainty description and classification integration. The effectiveness of the MRF-CNN method was tested in both urban and rural areas of southern England as well as semantic labeling data sets. The MRF-CNN consistently outperformed the benchmark MLP, support vector machine, MLP-MRF, CNN, and the baseline methods. This paper provides a regional decision fusion framework within which to gain the advantages of model-based CNN, while overcoming the problem of losing effective resolution and uncertain prediction at object boundaries, which is especially pertinent for complex VFSR image classification.

Restriction of a Markov random field on a graph and multiresolution statistical image modeling

Abstract: The association of statistical models and multiresolution data analysis in a consistent and tractable mathematical framework remains an intricate theoretical and practical issue. Several consistent approaches have been proposed previously to combine Markov random field (MRF) models and multiresolution algorithms in image analysis: renormalization group, subsampling of stochastic processes, MRFs defined on trees or pyramids, etc. For the simulation or a practical use of these models in statistical estimation, an important issue is the preservation of the local Markovian property of the representation at the different resolution levels. It is shown that this key problem may be studied by considering the restriction of a Markov random field (defined on some simple finite nondirected graph) to a part of its original site set. Several general properties of the restricted field are derived. The general form of the distribution of the restriction is given. "Locality" of the field is studied by exhibiting a neighborhood structure with respect to which the restricted field is an MRF. Sufficient conditions for the new neighborhood structure to be "minimal" are derived. Several consequences of these general results related to various "multiresolution" MRF-based modeling approaches in image analysis are presented.

Unsupervised change detection using fuzzy c-means and MRF from remotely sensed images

Abstract: In this paper, a novel change detection approach is proposed using fuzzy c-means (FCM) and Markov random field (MRF). First, the initial change map and cluster (changed and unchanged) membership probability are generated through applying FCM to the difference image created by change vector analysis (CVA) method. Then, to reduce the over-smooth results in the traditional MRF, the spatial attraction model is integrated into the MRF to refine the initial change map. The adaptive weight is computed based on the cluster membership and distances between the centre pixel and its neighbourhood pixels instead of the equivalent value of the traditional MRF using the spatial attraction model. Finally, the refined change map is produced through the improved MRF model. Two experiments were carried and compared with some state-of-the-art unsupervised change detection methods to evaluate the effectiveness of the proposed approach. Experimental results indicate that FCMMRF obtains the highest accuracy among methods used ...