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Novel Spectral Representations and Sparsity-Driven Algorithms for Shape Modeling and Analysis.

机译：用于形状建模和分析的新颖光谱表示和稀疏驱动算法。

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摘要

In this dissertation, we focus on extending classical spectral shape analysis by incorporating spectral graph wavelets and sparsity-seeking algorithms. Defined with the graph Laplacian eigenbasis, the spectral graph wavelets are localized both in the vertex domain and graph spectral domain, and thus are very effective in describing local geometry. With a rich dictionary of elementary vectors and forcing certain sparsity constraints, a real life signal can often be well approximated by a very sparse coefficient representation. The many successful applications of sparse signal representation in computer vision and image processing inspire us to explore the idea of employing sparse modeling techniques with dictionary of spectral basis to solve various shape modeling problems.;Conventional spectral mesh compression uses the eigenfunctions of mesh Laplacian as shape bases, which are highly inefficient in representing local geometry. To ameliorate, we advocate an innovative approach to 3D mesh compression using spectral graph wavelets as dictionary to encode mesh geometry. The spectral graph wavelets are locally defined at individual vertices and can better capture local shape information than Laplacian eigenbasis. The multi-scale SGWs form a redundant dictionary as shape basis, so we formulate the compression of 3D shape as a sparse approximation problem that can be readily handled by greedy pursuit algorithms.;Surface inpainting refers to the completion or recovery of missing shape geometry based on the shape information that is currently available. We devise a new surface inpainting algorithm founded upon the theory and techniques of sparse signal recovery. Instead of estimating the missing geometry directly, our novel method is to find this low-dimensional representation which describes the entire original shape. More specifically, we find that, for many shapes, the vertex coordinate function can be well approximated by a very sparse coefficient representation with respect to the dictionary comprising its Laplacian eigenbasis, and it is then possible to recover this sparse representation from partial measurements of the original shape. Taking advantage of the sparsity cue, we advocate a novel variational approach for surface inpainting, integrating data fidelity constraints on the shape domain with coefficient sparsity constraints on the transformed domain. Because of the powerful properties of Laplacian eigenbasis, the inpainting results of our method tend to be globally coherent with the remaining shape.;Informative and discriminative feature descriptors are vital in qualitative and quantitative shape analysis for a large variety of graphics applications. We advocate novel strategies to define generalized, user-specified features on shapes. Our new region descriptors are primarily built upon the coefficients of spectral graph wavelets that are both multi-scale and multi-level in nature, consisting of both local and global information. Based on our novel spectral feature descriptor, we developed a user-specified feature detection framework and a tensor-based shape matching algorithm.;Through various experiments, we demonstrate the competitive performance of our proposed methods and the great potential of spectral basis and sparsity-driven methods for shape modeling.
机译：本文通过结合光谱图小波和稀疏性算法来扩展经典光谱形状分析。光谱图小波由图拉普拉斯特征根定义，既位于顶点域又位于图光谱域，因此在描述局部几何方面非常有效。借助丰富的基本向量字典并强制使用某些稀疏性约束，通常可以通过非常稀疏的系数表示很好地逼近真实信号。稀疏信号表示在计算机视觉和图像处理中的许多成功应用激发了我们探索使用稀疏建模技术和频谱基字典来解决各种形状建模问题的想法。常规频谱网格压缩使用网格拉普拉斯算子的本征函数作为形状基，在表示局部几何图形方面效率非常低。为了改善这一点，我们提倡一种创新的3D网格压缩方法，该方法使用频谱图小波作为字典来编码网格几何形状。谱图小波局部定义在各个顶点上，比拉普拉斯本征基能更好地捕获局部形状信息。多尺度SGW形成了一个冗余的字典作为形状基础，因此我们将3D形状的压缩公式化为一个稀疏的近似问题，可以通过贪婪的追踪算法轻松解决。表面修补是指基于缺失形状几何的完成或恢复。关于当前可用的形状信息。我们设计了一种基于稀疏信号恢复的理论和技术的新的表面修复算法。我们的新颖方法不是找到直接缺失的几何形状，而是找到能够描述整个原始形状的低维表示形式。更具体地说，我们发现，对于许多形状，相对于包含其拉普拉斯本征基数的字典，顶点坐标函数可以通过非常稀疏的系数表示很好地近似，然后可以从局部测量中恢复该稀疏表示。原来的形状。利用稀疏提示，我们提倡一种新颖的变体方法来进行表面修复，将形状域上的数据保真度约束与变换域上的系数稀疏性约束相结合。由于拉普拉斯特征根基的强大特性，我们的方法的修复结果趋于与其余形状保持全局一致。信息性和区分性特征描述符对于各种图形应用程序的定性和定量形状分析至关重要。我们提倡使用新颖的策略来定义形状上通用的，用户指定的特征。我们的新区域描述符主要建立在频谱图子波的系数上，该子波本质上是多尺度和多层次的，由局部和全局信息组成。基于我们新颖的光谱特征描述符，我们开发了用户指定的特征检测框架和基于张量的形状匹配算法。通过各种实验，我们证明了所提出方法的竞争性能以及光谱基础和稀疏性的巨大潜力-驱动的形状建模方法。

著录项

  • 作者

    Zhong, Ming.;

  • 作者单位

    State University of New York at Stony Brook.;

  • 授予单位 State University of New York at Stony Brook.;
  • 学科 Computer science.;Optics.
  • 学位 Ph.D.
  • 年度 2016
  • 页码 171 p.
  • 总页数 171
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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