| Three-dimensional surface reconstructed often contains noise because the original data contains noise. It is not conducive to following research and application. So removing surface geometric noise becomes an important research field of computer vision.The thesis introduced the classical ROF model for image denoising at first. The model can preserve edges of image while denoising, which is its advantage. But there are some disadvantages in the model, such as making images appear the phenomenon of step, and being not good at maintaining the texture.Non-local means is a new method rising in the image restoration field now. It removes noise taking use of the cyclical pattern and the redundant content in the image, and the effect is very good. Another feature is that it is better to maintain the image texture information. Therefore, the combination of non-local means and ROF model will play out the advantages of both, denoising and preserving texture information.Three-dimensional surface reconstruction based on slice images segmentation is easier to implement. The thesis extended the two-dimensional image segmentation to three-dimensional. Surfaces obtained by this method were processed by the following new method.The Heaviside function of a level set function provides equivalent binary image expression of an implicit surface described by zero level set of a continuous signed distant function, based on which the variational models of image denoising can be extended to geometric noise removal of a surface. We propose a Non-Local variational model of geometric noise removal of surfaces and present its Split Bregman algorithm, where, the energy functional include a regularizers in Non-Local TV(Total Variation) form, Non-Local PM(Perona Malik) form and a penalty term to avoid the re-initialization of level set functions. Some numerical experiments for geometric noise removal show that the model can preserve the edge feature very well and has high computational efficiency. |
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