  We modify the total-variation-regularized image segmentation model proposed
by Chan, Esedoglu and Nikolova [SIAM Journal on Applied Mathematics 66, 2006]
by introducing local regularization that takes into account spatial image
information. We propose some techniques for defining local regularization
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. We solve the modified model
by using split Bregman iterations. Numerical experiments show the effectiveness
of our approach.
