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Published in:
2016 | OriginalPaper | Chapter
A Geometric Approach to Image Labeling
Authors : Freddie Åström, Stefania Petra, Bernhard Schmitzer, Christoph Schnörr
Published in: Computer Vision – ECCV 2016
Publisher: Springer International Publishing
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Abstract
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.