Geometric Wavelet Based Image Segmentation With Multiple Objects And Seismic Denoising

In the field of image segmentation, it is critical to suppress image noise, recognize weak edges and deal with topological changes. The geodesic active contour(GAC) which is based on the curve evolution theory is one of the popular techniques currently. Curvelet transform is a multi-scale and multi-directional"geometric wavelet", which achieved an optimal sparse representation of two-dimensional(2D) and second-order differentiable singularity (C2-singularity) for piecewise continous objects. In this dissertation, a curvelet-based Geodesic snake(CGS) is proposed, and applied to complex image segmentation of multiple objects.Most methods based on active contours and the existing multi-scale snakes evolve the contours in the original image domain. Contours have to trudge through large image regions from the initial positions to the real edges of the objects, leading to large CPU computation cost. In the wavelet-based active contour models, the 2D wavelets built by the tensor products of 1D wavelets can only deal with point-singularities, and can not handle the curve-singularities along the edges. So they are powerless to recognize the edges of the objects. The current segmentation techniques based on geometric wavelets are only combined with the traditional active contour, and can not deal with topological changes in the case of multiple objects. The purpose of this study is to resolve these deficiencies. Research methods and the process are mainly as follows: curvelet is embedded in GACs and the algorithm is numerically implemented by level set methods, making the algorithm capable of dealing with topology changes in multiple objects segmentation. The contours are evolved and transported through the binary curvelet scale spaces. They evolve much faster in coarser scales, so the computational cost is saved. The traditional gradient-based edge maps are replaced by the ones based on curvelet threshold. The problem of generating edge map series on curvelet scale series is solved, and a certain edge map has the same size with the scale where it is located. CGS is tested on many natural images, which have either strong noise or weak edges. The experimental results show that the curvelet-based GAC can obtain expected effects in both aspects of suppressing strong noise and recognizing weak edges.Seismic data carries large amounts of information, which enables geologic researchers to study the geological structure. The presence of noise makes it difficult to conduct reliable research. So how to remove the noise effectively becomes a major challenge in seismic data processing. In the seismic denoising part of this dissertation, the combined wavelet and curvelet denoising method is firstly introduced to the field of seismic random denoising, aiming to provide new method and reference results for practical engineering. The basic concept of the combined approach is to apply the wavelet and curvelet decomposition iteratively, subjecting to an optimization problem of the l1 -norm minimization of the transform domain coefficients. The combined algorithm is compared to the traditional and the other multi-scale methods on lot of natural seismic data, and the experimental results show that the combined wavelet and curvelet denoising scheme can achieve much better results than the others.