基于特征保持的网格模型处理技术研究
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摘要
随着三维硬件扫描技术和软件建模技术的不断发展,三维几何模型已经越来越常见,成为一种新的数字媒体形式,在许多领域得到广泛应用,例如：计算机动画、游戏,工业和机械设计、计算机仿真、数据可视化、医疗诊断等。在过去十几年里,网格模型的建模、渲染、编辑等技术取得重要发展。在网格处理中,模型显著特征的获取是一个基础问题。显著特征是指网格模型中相对比较重要的区域,该区域包含了独特的、重要的信息,它对模型的后期处理具有重要的指导作用。传统的方法主要基于法向、曲率这样的纯几何属性来识别网格的特征,但很多情况下纯几何属性并不能准确找到网格的显著特征。例如传统方法一般把高曲率区域当作是重要特征,但是大量重复的细节特征即使具有较高曲率也容易被人的视觉系统抑制,反而被高曲率包围的平坦区域更容易引起观察者的注意。
网格显著性(mesh saliency)是一种新的基于人的视觉特点来寻找模型中显著特征的方法。研究人员已经对图像的显著性进行了大量研究,并把它广泛应用于图像目标识别、图像检索、图像分割以及图像编辑等领域。网格模型因为更复杂,包含顶点位置、拓扑、法向、曲率、贴图等信息,对其进行显著性计算更为困难,时间复杂度也更高。因此针对网格显著性的研究比较少,其应用也较少。本文针对网格显著性的计算以及其在模型简化、模型缩放等技术中的应用展开深入研究,具体内容包括：
(1)现有的网格显著性计算方法通常只考虑局部显著性,本文提出一种同时考虑顶点的局部显著性和全局显著性的网格显著性计算方法。该算法以网格中顶点的离散平均曲率为基础属性来计算网格的显著性,先在不同的邻域范围内对顶点的曲率进行高斯卷积,然后根据人类视觉的中央一周围(center-surround)机制,使用多尺度高斯差分算子(Difference of Gaussian)计算顶点的局部显著性。为提高全局显著性的计算效率,该算法依据高斯卷积后的曲率对顶点进行简单聚类,然后以聚类为单位计算每类顶点同所有其它顶点的曲率差作为该类顶点的全局显著性。最后,把局部显著性和全局显著性进行加权合并,得到网格模型的显著性图。
(2)网格模型的简化是指在保持模型重要特征的基础上尽可能地减少模型中几何元素的数量。本文把网格显著性计算的结果应用于网格模型的简化,提出一种新的基于边折叠的模型简化算法。在计算折叠边的折叠代价时,同时考虑模型的几何特征和视觉显著性。视觉显著性的值作为权重使显著边获得更大的折叠代价,因此模型的重要视觉特征在简化过程中得到了更好的保护,生成的简化模型具有更好的视觉效果。
(3)网格的非均匀缩放是指在保持网格敏感特征不变的基础上,沿不同方向调整模型的大小。同一个网格模型在沿不同的方向缩放时表现出不同的敏感性,现有的网格显著性因为没有考虑方向因素,无法直接应用于网格缩放。本文提出一种新的适用于网格缩放的显著性计算方法。首先给出一种区域描述因子,反应了该区域对某一缩放方向的敏感程度,然后基于该描述因子计算区域同它的邻域的对比度,以此作为区域的显著性。为了避免被模型上的细小特征误导,采用了一种层次式的计算方法。对网格模型构造一个层次式分割,在粗约、中等和精细三个不同的分割层次上计算网格的显著性,并把各层次的计算结果用非线性的方法合成到一起。基于模型的显著性图,提出一种网格的非均匀缩放方法,把模型的每条边看做一个弹簧,通过边的伸缩来缩放模型。算法通过显著性控制每条边的缩放比例,并引入一个Laplacian项来防止模型产生严重形变。
(4)以往的网格缩放算法通常只能产生具有较好视觉效果的缩放模型,无法精确保持模型的重要特征。本文提出一种网格模型的带约束快速缩放算法,能够对模型进行全局尺寸调整,同时精确保持局部细节。该算法把待缩放模型置于一个二次B样条体中,通过调整B样条体的控制点间接实现模型的缩放。为了实现带约束缩放,B样条体的控制点被分成三类分别进行处理。其中,和模型关键特征相关的控制点引入硬约束,从而实现模型特征的精确保持,其它控制点的分布则通过使目标能量最小的优化方法求得,使模型的变形尽量均匀分布到全局。
With the development of3D scanner and modeling technology,3D geometry mod-els are becoming more and more popular which are widely used as an emerging type of digital media in computer animation, computer game, industrial and mechanical de-sign, computer simulation,3D visualization, medical diagnosis and so on. In the past decades, we have witnessed significant advances in the modeling, rendering and edit-ing of3D meshes. In the mesh processing, acquirement of salient features is a basic task. Salient features are important regions which include distinctive information and can guide the following mesh processing. The previous methods focus on using purely geometric measures such as normal and curvature to find the features. But a purely geometric measure may fail to find correct regions in many cases. For example, region-s with high curvature are usually regarded as important ones by traditional methods. However, densely repeated details, even if high in curvature, are suppressed by the hu-man visual system. A flat region in the middle of repeated high-curvature bumps will be perceived to be important.
Mesh saliency is a new perception-inspired metric for regional importance. The image saliency has been studied extensively, and used widely in object recognition, image retrieval, image segmentation and editing. However, there are few studies on mesh saliency. The computation of mesh saliency is a challenging job, because the mesh models have more complex information than images such as vertex, topology, normal, curvature, texture and so on. In this thesis, we have performed an indepth study on mesh saliency, and discussed its application in mesh simplification and mesh resizing. The main contributions are as follows:
(1) In the previous methods, only local contrast is used to compute the mesh salien-cy. We propose a new method for saliency computation, which considers both local contrast and global rarity. According to the center-surround mechanism of human vi-sual system, the method performs a Gauss convolution on mean curvature of mesh, and uses multi-scale DoG (Difference of Gaussian) operator to compute the local contrast. To improve the computational efficiency, the method applies a simple clustering method on the mesh vertices based on Gaussian filtered curvature, and compute the global rarity of every vertex cluster to other vertices. Local contrast and global rarity are combined to get the final mesh saliency map.
(2) Mesh simplification is to reduce the geometry elements of mesh, while trying to preserve its important features. We apply the saliency map to the mesh simplification, and propose a new simplification method based on edge collapse. When computing the collapsing cost, the method considers both geometric measure and visual saliency value. The saliency value works as a weight, and makes the salient edges have bigger collapsing cost. The method preserves the salient features well in the processing of simplification, and gives more visually appealing results.
(3) Non-homogeneously mesh scaling will resize the model in different directions, and leave the vulnerable features unchanged. Existing mesh saliency can not be used in mesh resizing directly because of the neglect of resizing direction. We propose a new mesh saliency that is suitable for mesh resizing. Firstly, we bring up a region descriptor based on its vulnerability to a resizing direction, and use this descriptor to compute the region's saliency based on its contrast to neighboring regions. We build hierarchical coarse-to-fine segmentations of the input mesh, and evaluate the saliency value on different levels of segmentations. Finally these saliency values are integrated into one saliency map after applying non-linear suppression. Equipped with the saliency map, a framework for non-homogeneous mesh resizing is presented. We regard every edge as a spring, and scale the mesh by stretching the edge. We also add an Laplacian item to the energy function to avoid dramatic shape changes.
(4) The previous mesh resizing approaches usually create models with no visible artifacts, while can not precisely preserve the important features in an engineering sense. We present a novel approach for non-homogeneous mesh resizing, which can precisely preserve mesh features. The resizing is achieved by warping a B-spline volumetric grid over the mesh. Control points of B-spline volume are divided into three categories, and processed separately. The control points related to the key features are hard constrained to precisely preserve the features. And the other control points are scaled by a quadratic optimization to distribute the distortion globally.
网格显著性(mesh saliency)是一种新的基于人的视觉特点来寻找模型中显著特征的方法。研究人员已经对图像的显著性进行了大量研究,并把它广泛应用于图像目标识别、图像检索、图像分割以及图像编辑等领域。网格模型因为更复杂,包含顶点位置、拓扑、法向、曲率、贴图等信息,对其进行显著性计算更为困难,时间复杂度也更高。因此针对网格显著性的研究比较少,其应用也较少。本文针对网格显著性的计算以及其在模型简化、模型缩放等技术中的应用展开深入研究,具体内容包括：
(1)现有的网格显著性计算方法通常只考虑局部显著性,本文提出一种同时考虑顶点的局部显著性和全局显著性的网格显著性计算方法。该算法以网格中顶点的离散平均曲率为基础属性来计算网格的显著性,先在不同的邻域范围内对顶点的曲率进行高斯卷积,然后根据人类视觉的中央一周围(center-surround)机制,使用多尺度高斯差分算子(Difference of Gaussian)计算顶点的局部显著性。为提高全局显著性的计算效率,该算法依据高斯卷积后的曲率对顶点进行简单聚类,然后以聚类为单位计算每类顶点同所有其它顶点的曲率差作为该类顶点的全局显著性。最后,把局部显著性和全局显著性进行加权合并,得到网格模型的显著性图。
(2)网格模型的简化是指在保持模型重要特征的基础上尽可能地减少模型中几何元素的数量。本文把网格显著性计算的结果应用于网格模型的简化,提出一种新的基于边折叠的模型简化算法。在计算折叠边的折叠代价时,同时考虑模型的几何特征和视觉显著性。视觉显著性的值作为权重使显著边获得更大的折叠代价,因此模型的重要视觉特征在简化过程中得到了更好的保护,生成的简化模型具有更好的视觉效果。
(3)网格的非均匀缩放是指在保持网格敏感特征不变的基础上,沿不同方向调整模型的大小。同一个网格模型在沿不同的方向缩放时表现出不同的敏感性,现有的网格显著性因为没有考虑方向因素,无法直接应用于网格缩放。本文提出一种新的适用于网格缩放的显著性计算方法。首先给出一种区域描述因子,反应了该区域对某一缩放方向的敏感程度,然后基于该描述因子计算区域同它的邻域的对比度,以此作为区域的显著性。为了避免被模型上的细小特征误导,采用了一种层次式的计算方法。对网格模型构造一个层次式分割,在粗约、中等和精细三个不同的分割层次上计算网格的显著性,并把各层次的计算结果用非线性的方法合成到一起。基于模型的显著性图,提出一种网格的非均匀缩放方法,把模型的每条边看做一个弹簧,通过边的伸缩来缩放模型。算法通过显著性控制每条边的缩放比例,并引入一个Laplacian项来防止模型产生严重形变。
(4)以往的网格缩放算法通常只能产生具有较好视觉效果的缩放模型,无法精确保持模型的重要特征。本文提出一种网格模型的带约束快速缩放算法,能够对模型进行全局尺寸调整,同时精确保持局部细节。该算法把待缩放模型置于一个二次B样条体中,通过调整B样条体的控制点间接实现模型的缩放。为了实现带约束缩放,B样条体的控制点被分成三类分别进行处理。其中,和模型关键特征相关的控制点引入硬约束,从而实现模型特征的精确保持,其它控制点的分布则通过使目标能量最小的优化方法求得,使模型的变形尽量均匀分布到全局。
With the development of3D scanner and modeling technology,3D geometry mod-els are becoming more and more popular which are widely used as an emerging type of digital media in computer animation, computer game, industrial and mechanical de-sign, computer simulation,3D visualization, medical diagnosis and so on. In the past decades, we have witnessed significant advances in the modeling, rendering and edit-ing of3D meshes. In the mesh processing, acquirement of salient features is a basic task. Salient features are important regions which include distinctive information and can guide the following mesh processing. The previous methods focus on using purely geometric measures such as normal and curvature to find the features. But a purely geometric measure may fail to find correct regions in many cases. For example, region-s with high curvature are usually regarded as important ones by traditional methods. However, densely repeated details, even if high in curvature, are suppressed by the hu-man visual system. A flat region in the middle of repeated high-curvature bumps will be perceived to be important.
Mesh saliency is a new perception-inspired metric for regional importance. The image saliency has been studied extensively, and used widely in object recognition, image retrieval, image segmentation and editing. However, there are few studies on mesh saliency. The computation of mesh saliency is a challenging job, because the mesh models have more complex information than images such as vertex, topology, normal, curvature, texture and so on. In this thesis, we have performed an indepth study on mesh saliency, and discussed its application in mesh simplification and mesh resizing. The main contributions are as follows:
(1) In the previous methods, only local contrast is used to compute the mesh salien-cy. We propose a new method for saliency computation, which considers both local contrast and global rarity. According to the center-surround mechanism of human vi-sual system, the method performs a Gauss convolution on mean curvature of mesh, and uses multi-scale DoG (Difference of Gaussian) operator to compute the local contrast. To improve the computational efficiency, the method applies a simple clustering method on the mesh vertices based on Gaussian filtered curvature, and compute the global rarity of every vertex cluster to other vertices. Local contrast and global rarity are combined to get the final mesh saliency map.
(2) Mesh simplification is to reduce the geometry elements of mesh, while trying to preserve its important features. We apply the saliency map to the mesh simplification, and propose a new simplification method based on edge collapse. When computing the collapsing cost, the method considers both geometric measure and visual saliency value. The saliency value works as a weight, and makes the salient edges have bigger collapsing cost. The method preserves the salient features well in the processing of simplification, and gives more visually appealing results.
(3) Non-homogeneously mesh scaling will resize the model in different directions, and leave the vulnerable features unchanged. Existing mesh saliency can not be used in mesh resizing directly because of the neglect of resizing direction. We propose a new mesh saliency that is suitable for mesh resizing. Firstly, we bring up a region descriptor based on its vulnerability to a resizing direction, and use this descriptor to compute the region's saliency based on its contrast to neighboring regions. We build hierarchical coarse-to-fine segmentations of the input mesh, and evaluate the saliency value on different levels of segmentations. Finally these saliency values are integrated into one saliency map after applying non-linear suppression. Equipped with the saliency map, a framework for non-homogeneous mesh resizing is presented. We regard every edge as a spring, and scale the mesh by stretching the edge. We also add an Laplacian item to the energy function to avoid dramatic shape changes.
(4) The previous mesh resizing approaches usually create models with no visible artifacts, while can not precisely preserve the important features in an engineering sense. We present a novel approach for non-homogeneous mesh resizing, which can precisely preserve mesh features. The resizing is achieved by warping a B-spline volumetric grid over the mesh. Control points of B-spline volume are divided into three categories, and processed separately. The control points related to the key features are hard constrained to precisely preserve the features. And the other control points are scaled by a quadratic optimization to distribute the distortion globally.
引文
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