Evaluation of a first-order primal-dual algorithm for MRF energy minimization
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Structured Learning and Prediction in Computer Vision
Foundations and Trends® in Computer Graphics and Vision
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We study the MAP-labeling problem for graphical models by optimizing a dual problem obtained by Lagrangian decomposition. In this paper, we focus specifically on Nes-terov's optimal first-order optimization scheme for non-smooth convex programs, that has been studied for a range of other problems in computer vision and machine learning in recent years. We show that in order to obtain an efficiently convergent iteration, this approach should be augmented with a dynamic estimation of a corresponding Lip-schitz constant, leading to a runtime complexity of O(1/?) in terms of the desired precision ?. Additionally, we devise a stopping criterion based on a duality gap as a sound basis for competitive comparison and show how to compute it efficiently. We evaluate our results using the publicly available Middlebury database and a set of computer generated graphical models that highlight specific aspects, along with other state-of-the-art methods for MAP-inference.