Variational Image Segmentation and Cosegmentation with the Wasserstein Distance

We present novel variational approaches for segmenting and cosegmenting images. Our supervised segmentation approach extends the classical Continuous Cut approach by a global appearance-based data term enforcing closeness of aggregated appearance statistics to a given prior model. This novel data term considers non-spatial, deformation-invariant statistics with the help of the Wasserstein distance in a single global model. The unsupervised cosegmentation model also employs the Wasserstein distance for finding the common object in two images. We introduce tight convex relaxations for both presented models together with efficient algorithmic schemes for computing global minimizers. Numerical experiments demonstrate the effectiveness of our models and the convex relaxations.

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