A Geometric Approach to Image Labeling
We introduce a smooth non-convex approach in a novel geometric framework which complements established convex and non-convex approaches to image labeling. The major underlying concept is a smooth manifold of probabilistic assignments of a prespecified set of prior data (the “labels”) to given image data. The Riemannian gradient flow with respect to a corresponding objective function evolves on the manifold and terminates, for any \(\delta > 0\), within a \(\delta \)-neighborhood of an unique assignment (labeling). As a consequence, unlike with convex outer relaxation approaches to (non-submodular) image labeling problems, no post-processing step is needed for the rounding of fractional solutions. Our approach is numerically implemented with sparse, highly-parallel interior-point updates that efficiently converge, largely independent from the number of labels. Experiments with noisy labeling and inpainting problems demonstrate competitive performance.
KeywordsImage labeling Assignment manifold Fisher-Rao metric Riemannian gradient flow
FÅ, SP and CS thank the German Research Foundation (DFG) for support via grant GRK 1653. BS was supported by the European Research Council (project SIGMA-Vision).
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