A Real-Time solution to the image segmentation problem: CNN-Movels

2D Image segmentation has been a main issue in image analysis since the very early years. Traditional literature usually classifies segmentation approaches as area-based or contourbased. In the second class, among dozens of different approaches, Active Contours have recently gained more and more interest. Active contours (also known as deformable models) are open or closed curves that can accurately fit to the contours of objects featuring almost any kind of shape. These models are called active because they automatically respond to specific characteristics of the points of the image, by changing their shape consequently. For example, an active contour can respond to the edgeness values of the image points. A particular type of active contour is the snake: it responds both to the characteristics of the points of the image (through the minimization of a quantity called external energy), and to specific internal laws ruling its shape and way of deformation, tending to minimize a quantity called internal energy (Kass et al., 1988; Lai & Chin, 1995). It usually consist of elastic curves that, located over an image, evolve from their initial shapes and positions in order to adapt themselves to the notable characteristics of the scene. This evolution comes as a result of the combined action of external and internal forces. The external forces lead the snakes towards features of the image, whereas internal forces model the elasticity of the curves. In a parametric representation, a snake appears as a curve u(s)=(x(s),y(s)), s [0,1], with u(0)=u(1). Its internal energy is often defined as