This paper proposes an image segmentation model based on the active contour model, the Mumford-Shah functional and the image decomposition process. Generally speaking, the active contour model detects boundaries in images from sharp intensities variations and the Mumford-Shah model finds smooth regions from homogeneous intensities. Our model merges these two complementary approaches while considering the Four Color Theorem to globally partition any given image. We also consider the textural part lying in natural images by separating it from the geometric part, which contains the meaningful objects, to help the segmentation process. Our segmentation model is experimented with a 1-D signal and 2-D images.