Spatially Adaptive Regularization in Image Segmentation

We present a total-variation-regularized image segmentation model that uses local regularization parameters to take into account spatial image information. We propose some techniques for defining those parameters, based on the cartoon-texture decomposition of the given image, on the mean and median filters, and on a thresholding technique, with the aim of preventing excessive regularization in piecewise-constant or smooth regions and preserving spatial features in nonsmooth regions. Our model is obtained by modifying a well-known image segmentation model that was developed by T. Chan, S. Esedoḡlu, and M. Nikolova. We solve the modified model by an alternating minimization method using split Bregman iterations. Numerical experiments show the effectiveness of our approach.