  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.

Numerical Analysis;Numerical Analysis