基于形状分析的三维点云模型压缩
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摘要
随着三维扫描和相关建模技术的快速发展,三维数字几何模型作为一种新兴的数字媒体,已逐渐融入到人们的生产和生活中,在三维游戏,影视特效,计算机仿真,自主导航,工业检测,逆向工程,医疗诊断以及数字文化遗产保护等方面取得了日益广泛的应用。在这种趋势下,三维模型的数量和复杂度越来越大,不断增长的三维模型的数据量对于存储空间以及网络传输(尤其是无线网传输)都带来了巨大的压力。在这种情况下,三维模型压缩是一个有效的解决方案。所以,在过去的近二十年间,三维模型的压缩成为一个研究的热点。
本文深入研究了三维点云模型压缩的理论基础,技术特点以及国内外研究现状,针对当前研究中存在的问题,我们将三维形状分析技术引入到模型压缩领域。具体的,借助于模型的表面分割和对称性分析技术,我们提出了两种三维点云模型压缩方案。本文的主要工作和创新点包括：
1.提出了一种基于形状模式分析的点云模型压缩算法
算法首先根据点的主曲率方向把模型的表面分割成一些四边形的面片；然后把四边形的面片参数化到一个二维的平面上并进行重采样；重采样之后,面片可以用一个二维的高度图来描述；基于高度图描述,我们对这些四边面片进行相似性分析,形状相似的面片被聚为一类,称为一个形状模式；具有相同形状模式的面片可以计算一个代表面片,这样,每一个面片只需要存储与代表面片的误差即可。解码时,只根据变换参数和代表面片即可恢复出模型的大致形状,然后随着面片的误差图像的恢复,模型会慢慢的变得精细,实现了对点云模型的渐进式压缩与传输。
2.提出了一种基于加权PCA的点云模型对称性检测算法
对称性检测算法基于对模型的迭代重加权PCA分析,算法的执行过程如下：首先使用每个点元的面积作为权重,执行一次加权PCA确定一个近似的对称平面作为初始平面；然后通过迭代的方法一步步的调整这个近似的对称平面,使之趋向于完美的对称平面(主对称平面)。在每一次迭代中,我们首先根据一个距离度量来更新每个点元的权重,然后使用新的权重执行加权PCA来确定一个新的对称平面。对于每一个近似的对称平面,我们会计算一个与之相关的对称度。如果当前的对称平面与上一次迭代中的对称平面足够接近或者迭代次数超过了给定的阈值,迭代就会终止。迭代终止后,最后一次迭代过程中的对称平面即作为我们要找的主对称平面。
3.提出了一种基于对称性分析的点云模型压缩算法
算法基于对模型的平面反射对称性分析,能处理任意拓扑结构的模型。据我们所知,这是第一个利用模型的高层对称信息对模型进行有效压缩的算法。对于一个给定的三维点云模型,算法首先检测出模型的主对称平面并基于对称性检测确定三个正交平面。然后,通过分析模型表面在这三个平面上的投影,把模型的表面分割成一些四边形的面片以及剩余部分,四边形的面片又可分为对称的面片对以及不对称的单独面片。对于四边形的面片,可以使用对称性来进行预测,并用嵌入式零树小波(EZW)编码器进行编码。对于剩余部分,则使用基于八叉树(OT)的点云数据编码器进行编码。由于EZW编码器以及OT编码器的渐进特性,我们获得了一个一般的渐进式点云模型编码器。而且我们把绝大部分的模型表面表示成了高度域,并使用对称性做了预测,所以算法能获得很高的压缩效率。实验结果也表明,本算法比当前点云模型压缩的其它算法取得了更好的R-D性能。
With the development of3D scanning and modeling technologies, three dimensional models have become more and more widely used, as a new type of emerging digital media. They have found applications in many fields such as video gaming, movie special effects, computer simulation, autonomous navigation, industrial inspection, reverse engineering, medical diagnosis and digital cultural protection. As a result, increasingly more point set surfaces data are being produced, which give rise to a growing demand on effective compression schemes to efficiently utilize the storage, the processing and/or the bandwidth resources. Hence,3D model compression has become a hot topic in the past two decades.
This thesis makes a comprehensive study of the existing work on point-based3D model compression. Based on the problems found in the previous works, we introduce the3D shape analysis technology into the field of3D model compression. Specially, with the help of surface patch segmentation and symmetry analysis, we propose two compression schemes for3D point-based models. The contributions of the thesis mainly include:
1. Compression algorithm based on shape pattern analysis
The algorithm proceeds as follows. First, the model surface is segmented into square patches according to the principal directions of the surfel. Then, the square patch is parameterized onto a2D domain and regularly resampled. After resampling, the patch can be described as a height map. Using the height maps, we do the self-similarity analysis between patches. The patches which have the similar shape are classified into one cluster, called a shape pattern. For the patches in a same shape pattern, a representative patch is computed; then the patch can be represented as the representative patch plus the error correction. When decoding, the profile of the model can be quickly constructed using the representative patches and transformation parameters. Then with the decoding of the error image, the model can be refined little by little, thus implementing progressive compression of3D point-based models.
2. Symmetry detection algorithm based on iteratively re-weighted principal component analysis (PCA)
The iteratively re-weighted PCA process works as follows. An initial approximate symmetry plane is computed through a weighted PCA process, using the area of each surfel as its weight. Thereafter, the approximate symmetry plane is refined iteratively. In each iteration, we firstly update each surfel's weight based on a distance metric at that surfel, and secondly conduct the weighted PCA to refine the approximate symmetry plane. For each approximate symmetry plane, an associated symmetry metric is computed. The iteration will stop to give the final approximate symmetry plane when the new symmetry plane and the previous one are closely enough or the number of iterations goes beyond a threshold.
3. Compression algorithm based on symmetry analysis
The algorithm is suitable for progressive compression of generic3D point-based models based on planar reflective symmetry analysis. To the best of our knowledge, this work pioneers in analyzing and utilizing high-level symmetry information for efficient encoding of point-based3D models. Given a point-based model, the proposed algorithm identifies the primary symmetry plane and, based on which, determines three orthogonal projection planes. By analyzing the model surface's projections on these planes, the surface is segmented into portions which are classified into symmetric height fields, non-symmetric height fields, and the remaining surface portion. Symmetry based prediction and embedded zerotree wavelet coders are employed for compact coding of the former two types, and octree-based encoder is employed for the last type of portion. As a result, we have made a point-based3D model encoder that achieves generic applicability and excellent rate-distortion performance at the same time, as demonstrated by experiments.
本文深入研究了三维点云模型压缩的理论基础,技术特点以及国内外研究现状,针对当前研究中存在的问题,我们将三维形状分析技术引入到模型压缩领域。具体的,借助于模型的表面分割和对称性分析技术,我们提出了两种三维点云模型压缩方案。本文的主要工作和创新点包括：
1.提出了一种基于形状模式分析的点云模型压缩算法
算法首先根据点的主曲率方向把模型的表面分割成一些四边形的面片；然后把四边形的面片参数化到一个二维的平面上并进行重采样；重采样之后,面片可以用一个二维的高度图来描述；基于高度图描述,我们对这些四边面片进行相似性分析,形状相似的面片被聚为一类,称为一个形状模式；具有相同形状模式的面片可以计算一个代表面片,这样,每一个面片只需要存储与代表面片的误差即可。解码时,只根据变换参数和代表面片即可恢复出模型的大致形状,然后随着面片的误差图像的恢复,模型会慢慢的变得精细,实现了对点云模型的渐进式压缩与传输。
2.提出了一种基于加权PCA的点云模型对称性检测算法
对称性检测算法基于对模型的迭代重加权PCA分析,算法的执行过程如下：首先使用每个点元的面积作为权重,执行一次加权PCA确定一个近似的对称平面作为初始平面；然后通过迭代的方法一步步的调整这个近似的对称平面,使之趋向于完美的对称平面(主对称平面)。在每一次迭代中,我们首先根据一个距离度量来更新每个点元的权重,然后使用新的权重执行加权PCA来确定一个新的对称平面。对于每一个近似的对称平面,我们会计算一个与之相关的对称度。如果当前的对称平面与上一次迭代中的对称平面足够接近或者迭代次数超过了给定的阈值,迭代就会终止。迭代终止后,最后一次迭代过程中的对称平面即作为我们要找的主对称平面。
3.提出了一种基于对称性分析的点云模型压缩算法
算法基于对模型的平面反射对称性分析,能处理任意拓扑结构的模型。据我们所知,这是第一个利用模型的高层对称信息对模型进行有效压缩的算法。对于一个给定的三维点云模型,算法首先检测出模型的主对称平面并基于对称性检测确定三个正交平面。然后,通过分析模型表面在这三个平面上的投影,把模型的表面分割成一些四边形的面片以及剩余部分,四边形的面片又可分为对称的面片对以及不对称的单独面片。对于四边形的面片,可以使用对称性来进行预测,并用嵌入式零树小波(EZW)编码器进行编码。对于剩余部分,则使用基于八叉树(OT)的点云数据编码器进行编码。由于EZW编码器以及OT编码器的渐进特性,我们获得了一个一般的渐进式点云模型编码器。而且我们把绝大部分的模型表面表示成了高度域,并使用对称性做了预测,所以算法能获得很高的压缩效率。实验结果也表明,本算法比当前点云模型压缩的其它算法取得了更好的R-D性能。
With the development of3D scanning and modeling technologies, three dimensional models have become more and more widely used, as a new type of emerging digital media. They have found applications in many fields such as video gaming, movie special effects, computer simulation, autonomous navigation, industrial inspection, reverse engineering, medical diagnosis and digital cultural protection. As a result, increasingly more point set surfaces data are being produced, which give rise to a growing demand on effective compression schemes to efficiently utilize the storage, the processing and/or the bandwidth resources. Hence,3D model compression has become a hot topic in the past two decades.
This thesis makes a comprehensive study of the existing work on point-based3D model compression. Based on the problems found in the previous works, we introduce the3D shape analysis technology into the field of3D model compression. Specially, with the help of surface patch segmentation and symmetry analysis, we propose two compression schemes for3D point-based models. The contributions of the thesis mainly include:
1. Compression algorithm based on shape pattern analysis
The algorithm proceeds as follows. First, the model surface is segmented into square patches according to the principal directions of the surfel. Then, the square patch is parameterized onto a2D domain and regularly resampled. After resampling, the patch can be described as a height map. Using the height maps, we do the self-similarity analysis between patches. The patches which have the similar shape are classified into one cluster, called a shape pattern. For the patches in a same shape pattern, a representative patch is computed; then the patch can be represented as the representative patch plus the error correction. When decoding, the profile of the model can be quickly constructed using the representative patches and transformation parameters. Then with the decoding of the error image, the model can be refined little by little, thus implementing progressive compression of3D point-based models.
2. Symmetry detection algorithm based on iteratively re-weighted principal component analysis (PCA)
The iteratively re-weighted PCA process works as follows. An initial approximate symmetry plane is computed through a weighted PCA process, using the area of each surfel as its weight. Thereafter, the approximate symmetry plane is refined iteratively. In each iteration, we firstly update each surfel's weight based on a distance metric at that surfel, and secondly conduct the weighted PCA to refine the approximate symmetry plane. For each approximate symmetry plane, an associated symmetry metric is computed. The iteration will stop to give the final approximate symmetry plane when the new symmetry plane and the previous one are closely enough or the number of iterations goes beyond a threshold.
3. Compression algorithm based on symmetry analysis
The algorithm is suitable for progressive compression of generic3D point-based models based on planar reflective symmetry analysis. To the best of our knowledge, this work pioneers in analyzing and utilizing high-level symmetry information for efficient encoding of point-based3D models. Given a point-based model, the proposed algorithm identifies the primary symmetry plane and, based on which, determines three orthogonal projection planes. By analyzing the model surface's projections on these planes, the surface is segmented into portions which are classified into symmetric height fields, non-symmetric height fields, and the remaining surface portion. Symmetry based prediction and embedded zerotree wavelet coders are employed for compact coding of the former two types, and octree-based encoder is employed for the last type of portion. As a result, we have made a point-based3D model encoder that achieves generic applicability and excellent rate-distortion performance at the same time, as demonstrated by experiments.
引文
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