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Advanced image segmentation methods using partial differential equations: A concise comparison

We present a survey of state-of-the-art segmentation methods that exploit partial differential equations, focusing on techniques introduced since the year 2010. The discussed approaches are mainly those based on the active contour and level set principles. The former of the two categories comprises methods utilizing parametric curve evolution based on the energy of the image function, and the resulting contour separates the homogeneous areas. In Active contours, the curve is defined explicitly; it is directly influenced by the energy in the image. Solving the partial differential equation (PDE) which describes the curve leads us towards segmentation; such a procedure, though easily implementable, nevertheless cannot automatically cope with topological changes of the segmented object. This problem is eliminated by using the level set method, which employs explicit curve definitions via a multidimensional function. In this technique, topological changes of image objects are solved wholly naturally: during the development of the level set function, the areas join or separate, and the changes need not be monitored by other algorithms. The paper comprises a description of selected publications discussing PDE-based segmentation. One of the main reasons for the continuing development of current PDE-based methods lies in the requirement for reducing the computational intensity of the algorithms ideally down to the level of real-time processing. Moreover, problems such as the solution stability and preserving of the distance function are also being currently tackled.