几何处理论文：纹理保持的模型尺寸调整与变形算法.doc

几何处理论文：纹理保持的模型尺寸调整与变形算法【中文摘要】随着三维扫描获取技术的发展,数字几何媒体已经在工业制造、生物医药、数字娱乐、数字文化遗产保护等方面取得了广泛的应用,数字几何处理技术,特别是基于网格(Mesh)模型的数字几何处理技术得到了相应的发展。为了避免创建新模型的繁琐的工作,许多人开始考虑重用已有的模型组件或者设计来创建新的模型。为了在新的场景和环境中重用已有模型,通常需要对模型进行一些改造。其中一种主要的改造方式是对物体进行尺寸调整操作：例如,使物体模型沿正交的方向或维度进行尺寸的拉伸或者收缩。通过对模型运行全局统一的放缩操作通常会使模型的某些部分或者某些特征发生改变或扭曲,例如,如果对一个圆形的结构沿某一特定方向进行拉伸,圆形就无法保持了。为了解决这个问题,Kraevoy et al.将图像处理中的尺寸调整算法推广到了三维几何处理领域,提出了一种非均匀的模型尺寸调整方法。他们的方法对网格中每一个三角面片的可放缩程度进行估算,该放缩程度表征了该三角面片对放缩操作的敏感度。依照不同的可放缩敏感度,不同的三角面片被不同程度的放缩,最终通过改变几何细节部分在尺寸改变后的模型中的相对比例,来保持模型重要的几何细节特征。然而,许多实际的物体的模型通常含有各种各样的复杂的几何纹理。对于这些模型,单纯应用现有的非均匀模型尺寸调整方法无法生成理想的尺寸调整之后的结果模型,因为包含纹理的模型即使其基本表面相对比较简单,由于几何纹理区域的存在,各三角面片可放缩敏感度的计算会被极大地影响,因而导致最后的结果模型的几何细节或纹理发生扭曲改变。基于现有的模型尺寸调整算法,在本文中,我们首先提出了一种基于几何纹理迁移的保持几何纹理的非均匀模型尺寸调整方法。对于一个输入模型,我们的方法首先将模型的几何纹理提取出来,分别得到单独的几何纹理信息和不包含几何纹理的基网格模型。然后,我们对基网格模型进行保持几何细节的非均匀模型尺寸调整。最后,几何纹理信息通过纹理合成的方式,在经过非均匀放缩的基网格模型表面上进行重建。利用模型表面尺寸调整前后的自然相关性,带有多种几何纹理的网格模型可以被自动的进行尺寸调整和几何纹理恢复。通过这几个步骤,我们可以得到一个不但保持模型的重要的几何细节特征,而且保持模型的几何纹理的外观的尺寸调整后的结果模型。最后,我们将上述的保持几何纹理的算法推广到了一般意义上的变形操作,包括旋转变形、扭转变形等等,提出了保持几何纹理的模型变形算法。与保持纹理的尺寸调整算法类似,变形算法包括几何纹理提取、基网格模型变形和几何纹理重建几个步骤。实验结果证明,本文中的方法在模型尺寸调整和变形的过程中,能够自动的、有效的保持模型的几何纹理和几何细节。【英文摘要】With the development of 3D scanning Technology,3D digital media has been widely used in industrial manufacturing, biomedical, digital entertainment, and digital cultural heritage protection and so on. Digital geometry processing technologies, especially those based on 3D mesh, have been well developed. To avoid the tedious tasks of creating new models from scratch, a trend towards reuse of existing models has emerged. In order to reuse such models in new assemblies or scenes, some reshaping operation may be needed. One of the principal ways of reshaping objects is through the resizing operation, i.e. scaling or stretching the object in several orthogonal directions or dimensions.Resizing by simply applying a global scaling usually causes distortions of various parts and features. For example, a round component element of the model would not still be round if we stretch it along a specific direction. To solve this problem, Kraevoy et al.1 introduced the resizing method original used in image processing to 3D geometry processing, presented a non-homogeneous model resizing method. In their method, for an input mesh, they estimate the degree can be scaled of each triangular facet of the mesh as the vulnerability. According to various vulnerabilities, different triangular facets are scaled differently; and finally important geometric features can be preserved at the cost of changing the relative scale of the geometric features in the resized model. However, many practical objects contain various geometric textures. For these kinds of models, such methods alone cannot produce reasonably scaled models because the regions with geometric textures will significantly affect the estimation of vulnerability, while the overall perceived shape is similar.Inspired by such non-homogeneous model resizing method, in this paper, we first present an automatic model resizing method based on geometric texture transfer. For an input mesh model, we first extract geometric textures from the underlying surfaces using segmentation, get filtered geometric texture information and base mesh without geometric textures. Then, we apply non-homogeneous model resizing process to base mesh, and finally extracted geometric textures are reconstructed on the surface of resized base mesh. By utilizing the natural correspondence before and after scaling, our method improves the non-homogeneous scaling of models with various geometric textures. Through these steps, we get a scaled model which preserves the geometric features along with the relative scale of the geometric textures.Finally, we extend the geometric texture preservation method to general deformation processes, including rotation and twisting. Similar to the geometric texture preservation resizing method, deformation method involves geometric texture extraction, base mesh deformation and geometric texture reconstruction.Experimental results show that our method can effectively and automatically preserves geometric textures during the model resizing and deformation process.【关键词】几何处理 尺寸调整 变形【英文关键词】Geometry Processing Resizing Deformation【目录】纹理保持的模型尺寸调整与变形算法摘要8-10ABSTRACT10-11第一章 引言12-171.1 三维模型尺寸调整(Resizing)与变形(Deformation)概述12-151.2 本文主要工作概述15-17第二章 相关知识17-222.1 拉普拉斯运算(Laplacian)17-182.2 几何纹理及其合成技术18-192.3 积分不变量(Integral Invariant)19-202.4 单纯形(Simplex)变换与骨架(Skeleton)20-22第三章 纹理分割与提取22-323.1 纹理分割22-253.1.1 几何特征量的选取22-233.1.2 基于Mean Shift的聚类分割算法23-253.2 纹理提取25-323.2.1 基于隐式光顺的基模型获取26-303.2.2 基于拉普拉斯的几何纹理信息获取与编码30-32第四章 模型尺寸调整与变形32-434.1 非各向同性的网格尺寸调整32-364.1.1 尺寸放缩敏感度计算32-334.1.2 基于模型栅格化的尺寸调整33-364.1.3 模型重建364.2 骨架驱动的网格变形36-434