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Harmonic shape images: A three-dimensional free-form surface representation and its applications in surface matching .

机译：谐波形状图像：三维自由曲面表示及其在曲面匹配中的应用。

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摘要

Surface matching is the process of determining whether two surfaces are equivalent in terms of shape. The usual steps in surface matching include finding the correspondences on the two surfaces being compared and computing the rigid transformation between the two surfaces. The issue of surface matching not only has theoretical importance but also has wide applications in the real world.; Unlike the matching of 2D images, the matching of 3D free-form surfaces is a much more difficult problem due to the shape and topology complexity of 3D surfaces. In general, there is no simple representation such as a matrix for 2D images that can be used to compare 3D surfaces. Issues such as surface sampling resolution, occlusion and high dimension of the pose space further complicate the problem.; In this thesis, a novel representation called Harmonic Shape Images is proposed for representing the shape of 3D free-form surfaces that are originally represented by triangular meshes. This representation is created based on the mathematical theory on harmonic maps. Given a 3D surface patch with disc topology and a selected 2D planar domain, a harmonic map is constructed by a two-step process which includes boundary mapping and interior mapping. Under this mapping, there is one to one correspondence between the points on the 3D surface patch and the resultant harmonic image. Using this correspondence relationship, Harmonic Shape Images are created by associating shape descriptors computed at each point of the surface patch at the corresponding point in the harmonic image. As a result, Harmonic Shape Images are 2D shape representations of the 3D surface patch.; Harmonic Shape Images have some properties that are important for surface matching. They are unique; their existence is guaranteed for any valid surface patches. More importantly, those images preserve both the shape and the continuity of the underlying surfaces. Furthermore, Harmonic Shape Images are not designed specifically for representing surface shape. Instead, they provide a general framework to represent surface attributes such as surface normal, color, texture and material. Harmonic Shape Images are discriminative and stable, and they are robust with respect to surface sampling resolution and occlusion. Extensive experiments have been conducted to analyze and demonstrate the properties of Harmonic Shape Images.; The usefulness of Harmonic Shape Images in surface matching is demonstrated using application examples in the real world such as face modeling and mesh watermarking. In addition, the experimental results on recognizing objects in scenes with occlusion demonstrate its successful application in object recognition. Experiments to measure the accuracy of surface registration using Harmonic Shape Images are also described.
机译：表面匹配是确定两个表面形状是否相等的过程。表面匹配的通常步骤包括找到要比较的两个表面上的对应关系，并计算两个表面之间的刚性变换。表面匹配的问题不仅具有理论上的重要性，而且在现实世界中具有广泛的应用。与2D图像的匹配不同，由于3D表面的形状和拓扑复杂性，3D自由曲面的匹配是一个更加困难的问题。通常，没有简单的表示形式，例如可用于比较3D表面的2D图像矩阵。表面采样分辨率，遮挡和姿势空间的高尺寸等问题使问题进一步复杂化。在本文中，提出了一种新颖的表示形式，称为“谐波形状图像”，用于表示最初由三角形网格表示的3D自由曲面的形状。该表示是基于谐波图的数学理论创建的。给定具有磁盘拓扑结构的3D表面补丁和选定的2D平面域，通过两步过程（包括边界映射和内部映射）构建谐波图。在此映射下，3D表面贴片上的点与生成的谐波图像之间存在一对一的对应关系。使用这种对应关系，通过在谐波图像的相应点处将在表面补丁的每个点处计算出的形状描述符关联起来，创建<谐波>形状图像。结果，谐波形状图像是3D表面贴片的2D形状表示。谐波形状图像具有一些对于表面匹配很重要的属性。它们是独特的。对于任何有效的表面补丁，它们的存在都得到了保证。更重要的是，这些图像既保留了下表面的形状又保持了连续性。此外，谐波形状图像并非专门用于表示表面形状。相反，它们提供了表示表面属性（例如表面法线，颜色，纹理和材质）的通用框架。谐波形状图像具有判别性和稳定性，并且在表面采样分辨率和遮挡方面具有鲁棒性。已经进行了广泛的实验以分析和证明谐波形状图像的特性。谐波形状图像在表面匹配中的有用性通过使用诸如面部建模和网格水印等现实世界中的应用示例得到了证明。另外，在遮挡场景中识别物体的实验结果证明了其在物体识别中的成功应用。还描述了使用谐波形状图像测量表面对准精度的实验。

著录项

  • 作者

    Zhang, Dongmei.;

  • 作者单位

    Carnegie Mellon University.;

  • 授予单位 Carnegie Mellon University.;
  • 学科 Computer Science.
  • 学位 Ph.D.
  • 年度 2000
  • 页码 161 p.
  • 总页数 161
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自动化技术、计算机技术;
  • 关键词

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