PDE-based Variational Level Set Image Segmentation Methods

Image processing is the basis of computer vision and an important component of image understanding as well. At present, it mainly concerns with the following aspects: image pre-processing, image segmentation, object recognition etc. Thereinto, image segmentation takes a crucial position in image processing. With more and more applications of image segmentation in every field, traditional linear methods have displayed some limitations.Recently, the nonlinear methods, especially image segmentation methods based on PDEs have attracted more and more attentions.Compared to traditional image segmentation approaches, PDE-based ones have many prominent virtues: such as more accuracy, being able to directly deal with some image features which is easy for flexible descriptions with various mathematical models. Among PDE-based image segmentation techniques, variation and level set approaches are two useful and important mathematical tools, based on which active contour models embody the advantages of PDE methods over traditional ones. However, these two methods have their own insufficiency on some aspects, for example, variation-based parametric active contour model has difficulty in dealing with the adaptability of topological changes, while level set based geometric active contour model is generally not an energy minimization model .Variational level set methods which are an ideal and efficient tool take on all the virtues of them.Generally, PDE-based image segmentation includes three kinds of methods: edge-based, region-based, edge and region-based methods. The first one has better effect for images with better contrast, but is not suitable to noisy and blurry images. The second one makes use of images' regional information, and has better optimal segmentation effects.The third one which utilizes both the edge and regional information may obtain better segmentation effects for some segmentation applications. Based on analyzing two classic variational level set models in detail, the author puts forward a new edge and region based variational level method, at the same time, concludes the corresponding gradient flow equation, and proves the unconditional stability of the model as well. So when solving the gradient flow equation, it's better to use the implicit iteration method instead of explicit one which is restricted with time step.