Piece-wise Constant Image Segmentation with a Deep Image Prior Approach

Image segmentation is a key topic in image processing and computer vision and several approaches have been proposed in the literature to address it. The formulation of the image segmentation problem as the minimization of the Mumford-Shah energy has been one of the most commonly used techniques in the last past decades. More recently, deep learning methods have yielded a new generation of image segmentation models with remarkable performance. In this paper we propose an unsupervised deep learning approach for piece-wise image segmentation based on the so called Deep Image Prior by parameterizing the Mumford-Shah functional in terms of the weights of a convolutional neural network. Several numerical experiments on both biomedical and natural images highlight the goodness of the suggested approach. The implicit regularization provided by the Deep Image Prior model allows to also consider noisy input images and to investigate the robustness of the proposed technique with respect to the level of noise.