  Two-region image segmentation is the process of dividing an image into two
regions of interest, i.e., the foreground and the background. To this aim, Chan
et al. [Chan, Esedo\=glu, Nikolova, SIAM Journal on Applied Mathematics 66(5),
1632-1648, 2006] designed a model well suited for smooth images. One drawback
of this model is that it may produce a bad segmentation when the image contains
oscillatory components. Based on a cartoon-texture decomposition of the image
to be segmented, we propose a new model that is able to produce an accurate
segmentation of images also containing noise or oscillatory information like
texture. The novel model leads to a non-smooth constrained optimization problem
which we solve by means of the ADMM method. The convergence of the numerical
scheme is also proved. Several experiments on smooth, noisy, and textural
images show the effectiveness of the proposed model.
