We propose a new method for image segmentation based on a variational regularization algorithm for image denoising. We modify the Rudin-Osher-Fatemi (ROF) model by minimizing the L^p norm of the gradient, where p > 0 is very small. The result is that we better preserve edges, while flattening regions away from the edges. This results in an automatic segmentation of the image into several regions, which does not require any prior knowledge about the number of those regions, or their intensity levels.