基于偏微分方程面片的网格渐进压缩与去噪

发布时间：2018-03-19 21:15

本文选题：偏微分方程　切入点：频谱方法　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：在现有的偏微分方程(PDE)方法中,Bloor-WilsonPDE(BWPDE)方法因其较高的运算效率而被广泛应用于交互几何设计、实体建模、计算机辅助制造、网格重建及医学可视化等领域。然而,BWPDE方法由于其光滑特性并不能表示带有不规整几何细节和分叉的几何模型。偏微分方程面片(Patchwise PDE,PPDE)方法通过为每个面片设立局部的坐标系统,解决了以上问题,使PDE方法可用来表示复杂几何模型。但现有PPDE方法仍不适用于三维网格信号处理,因此本文的主要目的是对现有的PPDE方法进行改进使其适用于网格信号处理,从而将其拓展到网格压缩和去噪领域。本文的具体贡献如下:(1)从面片分割、边界条件提取及面片融合三方面对现有的PPDE方法进行改进。对网格分割和边界条件提取方法的改进使得恢复出的模型能更好地保留原始模型的几何细节,而对面片融合的改进避免了原有固定点带来的存储量增大及人工干预等问题。(2)将PPDE方法的频谱特性拓展到网格压缩领域,提出了一种网格渐进压缩方法。本文通过传输PDE频谱解的低频系数来重建出粗糙的原始网格。随着更多高频系数被接受,粗糙网格被逐渐细化,恢复出原始网格更多的几何细节,从而完成渐进压缩。(3)将PPDE方法的频谱特性应用于网格去噪领域,提出了一种基于频域的网格去噪方法。本文在用PPDE方法对模型进行重建时,通过保留一定PDE解的低频系数并丢弃相应的高频系数来达到网格去噪的目的。本文通过大量实验验证了上述拓展的有效性,并从定性和定量两方面进行了详尽的比较和分析。实验结果表明,相比于其它方法,本文的网格渐进压缩算法在压缩率相同时,得到的模型更接近原始模型;在网格质量相同时,可得到更高的压缩比。另外,本文的网格去噪算法通过较少的迭代次数就能获得较理想的去噪效果且受噪声强度的影响较小,在去噪过程中也不会引起网格收缩等问题。
[Abstract]:Bloor-Wilson PDE (BWPDE) method has been widely used in interactive geometry design, solid modeling and computer aided manufacturing for its high computational efficiency. However, because of its smooth properties, the BWPDE method can not represent a geometric model with irregular geometric details and bifurcation. The partial differential equation Patchwise PDE PPDE method establishes a local coordinate system for each surface. In order to solve the above problems, PDE method can be used to represent complex geometric model. However, the existing PPDE method is still not suitable for 3D grid signal processing, so the main purpose of this paper is to improve the existing PPDE method so that it can be applied to grid signal processing. Thus it is extended to the field of mesh compression and denoising. The specific contribution of this paper is as follows:. The existing PPDE methods are improved in the aspects of boundary condition extraction and surface fusion. The improved methods of mesh segmentation and boundary condition extraction make the restored model better preserve the geometric details of the original model. However, the improvement of face slice fusion avoids the problems of increasing storage capacity and manual intervention brought by the original fixed point. The spectrum characteristics of PPDE method are extended to the field of grid compression. A progressive mesh compression method is proposed. In this paper, the rough original mesh is reconstructed by transmitting the low frequency coefficients of the PDE spectral solution. As more high frequency coefficients are accepted, the rough mesh is gradually refined. The spectral characteristics of PPDE method are applied to the field of grid denoising. A frequency domain based mesh denoising method is proposed. In this paper, the model is reconstructed by PPDE method. The purpose of mesh denoising is achieved by retaining the low frequency coefficients of a certain PDE solution and discarding the corresponding high frequency coefficients. The experimental results show that compared with other methods, the mesh progressive compression algorithm in this paper is more similar to the original model when the compression ratio is the same. When the mesh quality is the same, the compression ratio can be higher. In addition, the mesh denoising algorithm in this paper can get a better denoising effect by fewer iterations and is less affected by the noise intensity. In the process of denoising, the mesh shrinkage will not be caused.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.82

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