A Pixel Dissimilarity Measure That Is Insensitive to Image Sampling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonrigid Image Registration Using Dynamic Higher-Order MRF Model
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
A comparative study of energy minimization methods for markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
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In this paper, we propose a new method for solving the Markov random field (MRF) energies with higher-order smoothness priors. The main idea of the proposed method is a graph conversion which decomposes higher-order cliques as hierarchical auxiliary nodes. For a special class of smoothness priors which can be formulated as gradient-based potentials, we introduce an efficient representation of an auxiliary node called a gradient node. We denote a graph converted using gradient nodes as a hierarchical gradient node (HGN) graph. Given a label set L, the computational complexity of message passings of HGN graphs are reduced to O(|L|2) from exponential complexity of a conventional factor graph representation. Moreover, as the HGN graph can integrate multiple orders of the smoothness priors inside its hierarchical structure, this method provides a way to combine different smoothness orders naturally in MRF frameworks. For optimizing HGN graphs, we apply the tree-reweighted (TRW) message passing which outperforms the belief propagation. In experiments, we show the efficiency of the proposed method on the 1D signal reconstructions and demonstrate the performance of the proposed method in three applications: image denoising, sub-pixel stereo matching and nonrigid image registration.