Convex Histogram-Based Joint Image Segmentation with Regularized Optimal\n Transport Cost

2016/10/05 by Nicolas Papadakis, Papadakis, Nicolas, Julien Rabin +1
Computer Science · #Advanced Image and Video Retrieval Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image Retrieval and Classification Techniques #Medical Image Segmentation Techniques #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1610.01400

openalex publication_date 2016/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate in this work a versatile convex framework for multiple image\nsegmentation, relying on the regularized optimal mass transport theory. In this\nsetting, several transport cost functions are considered and used to match\nstatistical distributions of features. In practice, global multidimensional\nhistograms are estimated from the segmented image regions, and are compared to\nreferring models that are either fixed histograms given a priori, or directly\ninferred in the non-supervised case. The different convex problems studied are\nsolved efficiently using primal-dual algorithms. The proposed approach is\ngeneric and enables multi-phase segmentation as well as co-segmentation of\nmultiple images.\n

Citations

• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Optimal approximations by piecewise smooth functions and associated variational problems
• The Earth Mover's Distance as a Metric for Image Retrieval
• Fast projection onto the simplex and the \pmb l_\mathbf 1 l 1 ball

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