Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance
Motong Qiao 1*, Wei Wang 2, Michael Ng 31 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
2 Department of Mathematics, Tongji University, Shanghai 200092, China.
3 Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
Received 6 December 2012; Accepted (in revised version) 11 October 2013
Available online 14 March 2014
We present a multi-phase image segmentation method based on the histogram of the Gabor feature space, which consists of a set of Gabor-filter responses with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function, which is a metric to measure the distance of two histograms. The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2. We test our model on both simple synthetic texture images and complex natural images with two or more phases. Experimental results are shown and compared to other recent results.AMS subject classifications: 68U10
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Key words: Multi-phase texture segmentation, Wasserstein distance, Gabor filter, Mumford-Shah model.
Email: email@example.com (M. Qiao)