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Image segmentation is an important branch of computer vision. Its aim is to extract meaningful lying in objects images, either by dividing images into contiguous semantic regions, or by extracting one or several objects more specific in images, such as medical structures. In general, image segmentation task is very difficult to achieve it since natural images are diverse, complex and the way we perceive them, vary according to individuals. More than a decade ago, a promising mathematical framework, based on variational models and partial differential equations, have been investigated to solve the image segmentation problem. This new approach benefits from well-established mathematical theories that allow people to analyze, understand and extend segmentation methods. Moreover, this framework is defined in a continuous setting which makes the proposed models independent with respect to the grid of digital images.