A View of Regularized Approaches for Image Segmentation

Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image segmentation is the process of dividing an image into non-overlapping regions. These regions, which may correspond, e.g., to different objects, are fundamental for the correct interpretation and classification of the scene represented by the image. The division into regions is not unique, but it depends on the application, i.e., it must be driven by the final goal of the segmentation and hence by the most significant features with respect to that goal. Thus, image segmentation can be regarded as a strongly ill-posed problem. A classical approach to deal with ill posedness consists in incorporating in the model a-priori information about the solution, e.g., in the form of penalty terms. In this work we provide a brief overview of basic computational models for image segmentation, focusing on edge-based and region-based variational models, as well as on statistical and machine-learning approaches. We also sketch numerical methods that are applied in computing solutions to these models. In our opinion, our view can help the readers identify suitable classes of methods for solving their specific problems.