Local Histogram based Segmentation using the Wasserstein Distance

Kangyu Ni
University of California, Los Angeles (UCLA)

We propose a nonparametric region-based active contour model for segmenting cluttered scenes. This model is unsupervised and assumes that pixel intensity is independently identically distributed. The proposed segmentation energy consists of a geometric regularization term that penalizes the length of region boundaries, and a region-based image term that uses the probability density function (or histogram) of pixel intensity to distinguish different regions. More specifically, the region data encourages partitioning the image domain so that the local histograms within each region are approximately uniform. The solutions of the proposed model do not need to differentiate histograms. The similarity between normalized histograms is measured by the Wasserstein distance with exponent 1, which is able to compare both continuous and discontinuous histograms in a reasonable manner. We employ a fast global minimization method based on Bresson el al. to solve the proposed model. The advantages of this method include less computational time compared with the standard PDE minimization method by gradient descent of the associated Euler-Lagrange equation and the ability to find a global minimizer. Moreover, our proposed model has several desired properties due to the use of the Wasserstein distance. In particular, the proposed model is contrast invariant and intrinsically insensitive to noise.

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