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Learning compatibility coefficients for relaxation labeling processes
 IEEE Trans. Pattern Anal. Machine Intell
, 1994
"... AbstractRelaxation labeling processes have been widely used in many different domains including image processing, pattern recognition, and artificial intelligence. They are iterative procedures that aim at reducing local ambiguities and achieving global consistency through a parallel exploitation o ..."
Abstract

Cited by 44 (5 self)
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AbstractRelaxation labeling processes have been widely used in many different domains including image processing, pattern recognition, and artificial intelligence. They are iterative procedures that aim at reducing local ambiguities and achieving global consistency through a parallel exploitation of contextual information, which is quantitatively expressed in terms of a set of “compatibility coefficients. ” The problem of determining compatibility coefficients has received a considerable attention in the past and many heuristic, statisticalbased methods have been suggested. In this paper, we propose a rather different viewpoint to solve this problem: we derive them attempting to optimize the performance of the relaxation algorithm over a sample of training data; no statistical interpretation is given: compatibility coefficients are simply interpreted as real numbers, for which performance is optimal. Experimental results over a novel application of relaxation are given, which prove the effectiveness of the proposed approach. Index Terms Compatibility coefficients, constraint satisfaction, gradient projection, learning, neural networks, nonlinear
The Dynamics of Nonlinear Relaxation Labeling Processes
, 1997
"... We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symm ..."
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Cited by 37 (11 self)
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We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symmetry condition is met, the algorithm possesses a Liapunov function which turns out to be (the negative of) a wellknown consistency measure. This follows almost immediately from a powerful result of Baum and Eagon developed in the context of Markov chain theory. Moreover, it is seen that most of the essential dynamical properties of the algorithm are retained when the symmetry restriction is relaxed. These properties are also shown to naturally generalize to higherorder relaxation schemes. Some applications and implications of the presented results are finally outlined.
Autoassociative Learning in Relaxation Labeling Networks
, 1997
"... We address the problem of training relaxation labeling processes, a popular class of parallel iterative procedures widely employed in pattern recognition and computer vision. The approach discussed here is based on a theory of consistency developed by Hummel and Zucker, and contrasts with a recently ..."
Abstract

Cited by 6 (3 self)
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We address the problem of training relaxation labeling processes, a popular class of parallel iterative procedures widely employed in pattern recognition and computer vision. The approach discussed here is based on a theory of consistency developed by Hummel and Zucker, and contrasts with a recently introduced learning strategy which can be regarded as heteroassociative, i.e., what is actually learned is the association between patterns rather than the patterns themselves. The proposed learning model is instead autoassociative and involves making a set of training patterns consistent, in the sense rigorously defined by Hummel and Zucker; this implies that they become local attractors of the relaxation labeling dynamical system. The learning problem is formulated in terms of solving a system of linear inequalities, and a straightforward iterative algorithm is presented to accomplish this. The learning model described here allows one to view the relaxation labeling process as a kind of ...
Pattern, R.ecognition Letters ELSEVIER Pattern Recognition Letters 18 (1997) 312 Autoassociative learning in relaxation labeling networks
, 1996
"... We address the problem of training relaxation labeling processes, a popular class of parallel iterative procedures widely employed in pattern recognition and computer vision. The approach discussed here is entirely based on a theory of consistency developed by Hummel and Zucker, and contrasts with a ..."
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We address the problem of training relaxation labeling processes, a popular class of parallel iterative procedures widely employed in pattern recognition and computer vision. The approach discussed here is entirely based on a theory of consistency developed by Hummel and Zucker, and contrasts with a recently introduced leaming strategy which can be regarded as heteroassociative, i.e., what is actually learned is the association between patterns rather than the patterns themselves. The proposed learning model is instead autoassociative and involves making a set of training patterns consistent, in the sense rigorously defined by Hummel and Zucker; this implies that they become local attractors of the relaxation labeling dynamical system. The learning problem is formulated in terms of solving a system of linear inequalities, and a straightforward iterative algorithm is presented to accomplish this. The attractive feature of this algorithm is that it solves the system when it admits a solution, and automatically yields the best approximation solution when this is not the case. The learning model described here allows one to view the relaxation labeling process as a kind of asymmetric associative memory, the effectiveness of which is demonstrated experimentally. © 1997 Elsevier Science B.V.