基于变分方法的网格处理

发布时间：2018-06-12 00:29

本文选题：网格去噪 + 分片常数空间　；参考：《中国科学技术大学》2015年博士论文

【摘要】：随着三维扫描技术以及计算机性能的提高,三角网格曲面处理已经成为计算机图形学领域中的热门研究方向之一。其研究内容主要包括网格重建、去噪、分割、简化、参数化、编辑等。经过几十年众多专家学者的努力,网格曲面处理方法已经得到了良好的发展,许多成熟、高效的算法被提出。其在计算机图形学、工业制造以及逆向工程中扮演越来越重要的角色。本文主要研究网格去噪,网格分割以及网格简化三个问题。针对这三个方向中存在的一些问题(比如去噪中的不保特征,分割方法的不稳定性,分割结果不是足够语义等),本文提出了一些有效的解决方法。具体内容包含以下几个部分。第一章中,本文首先介绍网格曲面处理,Total-Variation相关的基础知识；其次分别从研究背景,研究现状和本文所作的贡献三个方面对网格去噪、网格分割与网格简化这三个网格处理问题进行阐述,最后给出了全文内容的结构安排。第二章中,本文首先对全文中使用的符号进行统一定义,其次根据已有的分片线性空间在图形学某些应用中存在的问题,提出并定义了网格上的分片常数空间,以及与该空间相关的微分算子与内积公式,进而给出了网格曲面上Total-Variation范数的严格定义。接着本章将分片常数空间与分片线性空间进行比较,比较结果显示分片常数空间在图形学应用领域有着明显的优越性。第三章中,本文主要讨论基于变分方法的保特征的网格去噪问题。网格去噪中存在的最大的困难是去除噪音的同时如何保持住网格的尖锐特征(比如一些尖锐边与角),并且不产生阶梯效应(staircase)。基于分片常数空间以及Total-Variation (TV)良好的保特征的性质,本文提出一种十分有效的保特征的网格去噪方法,并且提供了两个估计公式自动地计算算法的参数,同时也证明了该去噪模型在某种意义下连续地依赖其参数。为了求解该去噪问题,本文提出使用分裂算子与增广拉格朗日方法的有效迭代算法对其进行求解。最后本文从各个方面将提出的去噪方法与现有的去噪方法进行比较。实验结果显示,对CAD网格与non-CAD网格,本文中提出的方法得到的结果均优于其它去噪方法的结果,并且计算速度很快。另外,对于小尺度的特征,本文中提出的算法也能得到很好的结果并且避免产生阶梯效应。第四章中,本文主要讨论基于part-type的网格分割问题。大多数现有的分割方法或者太依赖于初始值,或者分割结果不够语义。针对这些问题,本文提出了一种新的基于三角形的稳定、有效的变分分割方法。首先结合网格的高阶信息,本文定义了四种新的拉普拉斯矩阵。与经典的拉普拉斯矩阵相比,这些新定义的拉普拉斯矩阵能够反映出更多正确的语义信息。考虑到三角形一般情况下不是均匀地分布在网格上,基于分片常数空间以及经典的图像中的Mumford-Shah模型,本文提出了一种基于三角形的变分分割模型。由于本文中提出的分割方法是对三角形进行聚类,因此能够得到真正意义上的基于区域聚类的分割结果。另外,由于本文中提出的变分分割模型是一个非凸的优化问题,因此,我们提出了一种有效的初始化方法使模型变得稳定。为了进一步地改善分割结果,本文提出了一种简单有效的用户交互技术(如果需要的话)。最后本文通过Princeton Segmentation Benchmark数据库与其它分割方法进行比较,比较结果显示本文的方法具有明显的优势。第五章中,本文主要讨论基于surface-type网格分割与基于分片常数逼近的网格简化。根据前面章节的讨论,我们发现网格去噪与分割均属于从不同程度上对网格进行简化。利用分片常数空间的良好性质以及网格光滑与网格简化的相似性,本文提出了一种基于surface-type的网格分割方法。事实上,对surface-type的网格分割结果的边界进行提取,即可实现对网格的简化。随后本文提出利用第三章中的去噪模型获取网格模型的分片常数逼近。实验结果显示基于surface-type的分割方法与基于去噪模型的分片常数逼近方法均能得到相当满意的结果。第六章对全文进行总结,并且提出一些与本文内容相关的值得研究的问题。
[Abstract]:With the improvement of 3D scanning technology and computer performance, triangular mesh surface processing has become one of the most popular research fields in the field of computer graphics. Its main contents include mesh reconstruction, denoising, segmentation, simplification, parameterization, editing and so on. Through the efforts of many experts and scholars for several decades, the grid surface processing method has been used After a good development, many mature and efficient algorithms have been proposed. They play a more and more important role in computer graphics, industrial manufacturing and reverse engineering. This paper mainly deals with three problems of mesh denoising, mesh segmentation and mesh simplification. For example, there are some problems in the three directions (such as non noise reduction). Characteristics, the instability of the segmentation method, the segmentation result is not enough semantics, etc. This paper proposes some effective solutions. The specific contents include the following sections.
In the first chapter, this paper first introduces the grid surface processing and the basic knowledge of Total-Variation. Secondly, from the three aspects of the research background, the research status and the contribution of this paper, the three grid processing problems of grid denoising, mesh segmentation and mesh simplification are expounded, and the structure of the full text content is given at the end.
In the second chapter, this paper first defines the symbols used in the full text. Secondly, according to the existing problems in the application of the existing piecewise linear space in some graphics applications, we propose and define the partition constant space on the grid, as well as the differential operator and the inner product formula related to the space, and then give the Total-Variat on the grid surface. The strict definition of the ion norm. Then this chapter compares the piecewise constant space with the piecewise linear space. The comparison results show that the partition constant space has obvious advantages in the field of graphics applications.
In the third chapter, this paper mainly discusses the problem of mesh denoising based on the variational method. The biggest difficulty in mesh denoising is how to remove the noise and keep the sharp features of the grid (such as some sharp edges and angles), and do not produce staircase. Based on the partition constant space and Total-Variation (T) V) a good feature preserving property, a very efficient mesh denoising method is proposed in this paper, and two estimation formulas are provided to automatically calculate the parameters of the algorithm. At the same time, it is proved that the denoising model depends on its parameters in a certain sense. In order to solve the denoising problem, this paper uses the splitting operator and the increase of the noise. The effective iterative algorithm of the wide Lagrange method is solved. Finally, the denoising method proposed in this paper is compared with the existing denoising method. The experimental results show that the results obtained in this paper are better than the results of other denoising methods for CAD grid and non-CAD grid, and the calculation speed is very fast. In addition, for small scale characteristics, the algorithm proposed in this paper can also get good results and avoid ladder effect.
In the fourth chapter, this paper mainly discusses the problem of grid segmentation based on part-type. Most existing segmentation methods are too dependent on the initial value, or the segmentation results are not semantic. In this paper, a new stable, effective variational cut method based on the triangle is proposed. Four new Laplasse matrices are defined. Compared with the classical Laplasse matrix, these newly defined Laplasse matrices can reflect more correct semantic information. Considering that the triangle is generally not distributed evenly on the grid, based on the partition constant space and the classical Mumford-Shah model in the image, this paper is proposed in this paper. In this paper, a triangulation based variational segmentation model is proposed. Because the segmentation method proposed in this paper is a triangle clustering, we can get the real sense of the segmentation results based on regional clustering. In addition, because the variational segmentation model proposed in this paper is a non convex optimization problem, we propose a kind of effective method. The method of initialization makes the model stable. In order to further improve the segmentation results, this paper proposes a simple and effective user interaction technology (if necessary). Finally, this paper compares the Princeton Segmentation Benchmark database with other segmentation methods, and the comparison results show that the method in this paper has obvious advantages.
In the fifth chapter, this paper mainly discusses the mesh simplification based on surface-type mesh segmentation and piecewise constant approximation. According to the discussion in the previous chapters, we find that mesh denoising and segmentation are both simplified to different degrees. The good quality of the partition constant space and the similarity of grid smooth and mesh simplification are used. In this paper, a mesh segmentation method based on surface-type is proposed. In fact, the boundary of the mesh segmentation results of surface-type is extracted, and the mesh simplification can be realized. In this paper, we use the denoising model in the third chapter to obtain the piecewise constant of the mesh model. The experimental results show the partition based on the surface-type. Both the method and the piecewise constant approximation method based on the denoising model can get fairly satisfactory results.
The sixth chapter summarizes the full text, and puts forward some issues worthy of study related to the content of this article.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TP391.41

【共引文献】