A common framework for curve evolution, segmentation and anisotropic diffusion

In recent years, curve evolution has developed into an important tool in Computer Vision and has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. The underlying principle is the evolution of a simple closed curve whose points move in the direction of the normal with prescribed velocity. A fundamental limitation of the method as it stands is that it cannot deal with important image features such as triple points. The method also requires a choice of an "edge-strength" function, defined over the image domain. Indicating the likelihood of an object boundary being present at any point in the image domain. This implies a separate preprocessing step, in essence precomputing approximate boundaries in the presence of noise. One also has to choose the initial curve. It is shown here that the different versions of curve evolution used in Computer Vision together with the preprocessing step can be integrated in the form of a new segmentation functional which overcomes these limitations and extends curve evolution models. Moreover, the numerical solutions obtained retain sharp discontinuities or "shocks", thus providing sharp demarcation of object boundaries.