Combining Belief Networks and Neural Networks for Scene Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Class of Discrete Multiresolution Random Fields and Its Application to Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Semi-iterative Inferences with Hierarchical Energy-Based Models for Image Analysis
EMMCVPR '99 Proceedings of the Second International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision and Image Understanding
Dynamic Trees for Unsupervised Segmentation and Matching of Image Regions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Kalman filtering in pairwise Markov trees
Signal Processing
Fuzzy Markov Random Fields versus Chains for Multispectral Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Interpretation of complex scenes using dynamic tree-structure Bayesian networks
Computer Vision and Image Understanding
EURASIP Journal on Applied Signal Processing
Quad tree decomposition of fused image of sunspots for classifying the trajectories
ICAI'06 Proceedings of the 7th WSEAS International Conference on Automation & Information
Fuzzy pairwise Markov chain to segment correlated noisy data
Signal Processing
Computing the latitudes of sunspot trajectories and speed of sunspots with intelligent methods
SSIP'08 Proceedings of the 8th conference on Signal, Speech and image processing
Parallel Hidden Hierarchical Fields for Multi-scale Reconstruction
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
IEEE Transactions on Image Processing
Multiband segmentation based on a hierarchical Markov model
Pattern Recognition
Robust computation of mutual information using spatially adaptive meshes
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
An extension of the standard mixture model for image segmentation
IEEE Transactions on Neural Networks
Dirichlet Gaussian mixture model: Application to image segmentation
Image and Vision Computing
A novel gray image representation using overlapping rectangular NAM and extended shading approach
Journal of Visual Communication and Image Representation
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Noncasual Markov (or energy-based) models are widely used in early vision applications for the representation of images in high-dimensional inverse problems. Due to their noncausal nature, these models generally lead to iterative inference algorithms that are computationally demanding. In this paper, we consider a special class of nonlinear Markov models which allow one to circumvent this drawback. These models are defined as discrete Markov random fields (MRF) attached to the nodes of a quadtree. The quadtree induces causality properties which enable the design of exact, noniterative inference algorithms, similar to those used in the context of Markov chain models. We first introduce an extension of the Viterbi algorithm which enables exact maximum a posteriori (MAP) estimation on the quadtree. Two other algorithms, related to the MPM criterion and to Bouman and Shapiro's (1994) sequential-MAP (SMAP) estimator are derived on the same hierarchical structure. The estimation of the model hyper parameters is also addressed. Two expectation-maximization (EM)-type algorithms, allowing unsupervised inference with these models are defined. The practical relevance of the different models and inference algorithms is investigated in the context of image classification problem, on both synthetic and natural images