基于几何小波的多目标图像分割与地震去噪
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摘要
在图像分割领域中,图像中噪声的压制、弱边界的有效识别和拓扑变化的处理至关重要。基于曲线演化理论的测地线活动轮廓(Geodesic Active Contour-GAC)是当前流行的技术方案之一。Curvelet变换是一种多尺度、多方向的“几何小波(Geometric Wavelet)”,它实现了二维二阶连续可微奇异性(C2-singularity)分段连续目标的最优稀疏表达。本中提出一种基于Curvelet的GAC(或CGS)方法,并且应用于复杂图像中多目标的分割。
大多活动轮廓(Active Contour或Snake)方法和现有的多尺度Snake都在原始图像域演化,从初始位置走过大片背景区域才到达目标边界,导致CPU计算代价大。基于小波(Wavelet)的活动轮廓中,由一维小波的张量积构成的二维小波只能处理点奇异问题,对于沿边界的曲线奇异性无能为力,识别边界能力差。当前基于几何小波的分割技术只与传统活动轮廓相结合,不能处理多目标时的拓扑变化。本文研究目的即解决上述这些缺陷。研究方法和过程主要为:结合水平集(Level Set)将Curvelet嵌入GAC,使得算法在分割多目标时自如处理拓扑变化;在Curvelet二进制尺度空间进行轮廓线的演化和移植,粗糙尺度上演化快,节省了计算量;用Curvelet阈值代替传统的基于梯度的边界地图(Edge Map),解决Curvelet尺度系列产生边界地图系列的问题,实现每尺度的边界地图与本尺度尺寸相同。本文对基于Curvelet的GAC进行了强噪声、弱边界条件下真实图像的实验,结果表明CGS在同时压制噪声和识别边界两方面都达到了理想的效果。
地震数据携带大量信息,可供人们研究地质结构,噪声的存在使得难以进行可靠研究,因此如何有效去除噪声,成为地震资料处理一大难题。地震去噪部分,本文将Wavelet和Curvelet联合去噪方法首次引入地震随机去噪领域,目的是为实际工程提供方法借鉴和参考结果。算法基本思想为:迭代进行Wavelet和Curvelet分解,其约束条件是一个变换域系数的l1模最小化的优化问题。本文将其与传统方法和其他多尺度方法进行诸多地震数据图像的比较研究,结果表明Wavelet和Curvelet联合方法比其他方法达到更优良的去噪结果。
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.
大多活动轮廓(Active Contour或Snake)方法和现有的多尺度Snake都在原始图像域演化,从初始位置走过大片背景区域才到达目标边界,导致CPU计算代价大。基于小波(Wavelet)的活动轮廓中,由一维小波的张量积构成的二维小波只能处理点奇异问题,对于沿边界的曲线奇异性无能为力,识别边界能力差。当前基于几何小波的分割技术只与传统活动轮廓相结合,不能处理多目标时的拓扑变化。本文研究目的即解决上述这些缺陷。研究方法和过程主要为:结合水平集(Level Set)将Curvelet嵌入GAC,使得算法在分割多目标时自如处理拓扑变化;在Curvelet二进制尺度空间进行轮廓线的演化和移植,粗糙尺度上演化快,节省了计算量;用Curvelet阈值代替传统的基于梯度的边界地图(Edge Map),解决Curvelet尺度系列产生边界地图系列的问题,实现每尺度的边界地图与本尺度尺寸相同。本文对基于Curvelet的GAC进行了强噪声、弱边界条件下真实图像的实验,结果表明CGS在同时压制噪声和识别边界两方面都达到了理想的效果。
地震数据携带大量信息,可供人们研究地质结构,噪声的存在使得难以进行可靠研究,因此如何有效去除噪声,成为地震资料处理一大难题。地震去噪部分,本文将Wavelet和Curvelet联合去噪方法首次引入地震随机去噪领域,目的是为实际工程提供方法借鉴和参考结果。算法基本思想为:迭代进行Wavelet和Curvelet分解,其约束条件是一个变换域系数的l1模最小化的优化问题。本文将其与传统方法和其他多尺度方法进行诸多地震数据图像的比较研究,结果表明Wavelet和Curvelet联合方法比其他方法达到更优良的去噪结果。
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.
引文
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