Convexity Shape Prior for Binary Segmentation

Lena Gorelick, Olga Veksler, Yuri Boykov, Claudia Nieuwenhuis

In IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), vol. 39, no. 2, pp. 258-271, Feb. 2017.


Convexity is a known important cue in human vision. We propose shape convexity as a new high-order regularization constraint for binary image segmentation. In the context of discrete optimization, object convexity is represented as a sum of 3-clique potentials penalizing any 1-0-1 configuration on all straight lines. We show that these non-submodular potentials can be efficiently optimized using an iterative trust region approach. At each iteration the energy is linearly approximated and globally optimized within a small trust region around the current solution. While the quadratic number of all 3-cliques is prohibitively high, we design a dynamic programming technique for evaluating and approximating these cliques in linear time. We also derive a second order approximation model that is more accurate but computationally intensive. We discuss limitations of our local optimization and propose gradual non-submodularization scheme that alleviates some limitations. Our experiments demonstrate general usefulness of the proposed convexity shape prior on synthetic and real image segmentation examples. Unlike standard second-order length regularization, our convexity prior does not have shrinking bias, and is robust to changes in scale and parameter selection.

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