We present a new image segmentation algorithm based on graph cuts. Our main tool is separation of each pixel p from a special point outside the image by a cut of a minimum cost. Such a cut creates a group of pixels Cp around each pixel. We show that these groups Cp are either disjoint or nested in each other, and so they give a natural segmentation of the image. In addition, this property allows an efficient implementation of the algorithm because for most pixels p the computation of Cp is not performed on the whole graph. We inspect all Cp's and discard those which are not interesting, for example if they are too small. This procedure automatically groups small components together or merges them into nearby large clusters. Effectively extracting significant non-intersecting closed contours performs our segmentation. We present interesting segmentation results on real and artificial images.