三维形状特征提取技术研究进展

三维形状模型广泛应用于工业设计、教育、生物医药、动画娱乐、文物保护等多个领域中。三维形状模型的特征提取是计算机图形学和模式识别领域的重要问题,近年来受到学者的广泛关注。尤其是具有铰链、关节等的非刚性三维形状通常会发生变形,进一步增加了形状特征提取的难度。主要研究、分析、总结了近几年出现的刚性三维形状和非刚性三维形状的特征提取算法,分析了三维形状特征提取的难点,给出了三维形状特征提取的发展进程。介绍了近年来三维形状特征匹配研究领域中常用的一些测试数据库,重点探讨了非刚性三维形状的特征匹配方法,并展望了三维形状特征提取、特征匹配的未来发展方向。     

Visual Attention for Rendered 3D Shapes

Understanding the attentional behavior of the human visual system when visualizing a rendered 3D shape is of great importance for many computer graphics applications. Eye tracking remains the only solution to explore this complex cognitive mechanism. Unfortunately, despite the large number of studies dedicated to images and videos, only a few eye tracking experiments have been conducted using 3D shapes. Thus, potential factors that may influence the human gaze in the specific setting of 3D rendering, are still to be understood. In this work, we conduct two eye‐tracking experiments involving 3D shapes, with both static and time‐varying camera positions. We propose a method for mapping eye fixations (i.e., where humans gaze) onto the 3D shapes with the aim to produce a benchmark of 3D meshes with fixation density maps, which is publicly available. First, the collected data is used to study the influence of shape, camera position, material and illumination on visual attention. We find that material and lighting have a significant influence on attention, as well as the camera path in the case of dynamic scenes. Then, we compare the performance of four representative state‐of‐the‐art mesh saliency models in predicting ground‐truth fixations using two different metrics. We show that, even combined with a center‐bias model, the performance of 3D saliency algorithms remains poor at predicting human fixations. To explain their weaknesses, we provide a qualitative analysis of the main factors that attract human attention. We finally provide a comparison of human‐eye fixations and Schelling points and show that their correlation is weak.     

On-the-fly Curve-skeleton Computation for 3D Shapes

The curve-skeleton of a 3D object is an abstract geometrical and topological representation of its 3D shape. It maps the spatial relation of geometrically meaningful parts to a graph structure. Each arc of this graph represents a part of the object with roughly constant diameter or thickness, and approximates its centerline. This makes the curve-skeleton suitable to describe and handle articulated objects such as characters for animation. We present an algorithm to extract such a skeleton on-the-fly, both from point clouds and polygonal meshes. The algorithm is based on a deformable model evolution that captures the object's volumetric shape. The deformable model involves multiple competing fronts which evolve inside the object in a coarse-to-fine manner. We first track these fronts' centers, and then merge and filter the resulting arcs to obtain a curve-skeleton of the object. The process inherits the robustness of the reconstruction technique, being able to cope with noisy input, intricate geometry and complex topology. It creates a natural segmentation of the object and computes a center curve for each segment while maintaining a full correspondence between the skeleton and the boundary of the object.     

A Frequency-Domain Approach to Watermarking 3D Shapes

This paper presents a robust watermarking algorithm with informed detection for 3D polygonal meshes. The algorithm is based on our previous algorithm [ 22 ] that employs mesh‐spectral analysis to modify mesh shapes in their transformed domain. This paper presents extensions to our previous algorithm so that (1) much larger meshes can be watermarked within a reasonable time, and that (2) the watermark is robust against connectivity alteration (e.g., mesh simplification), and that (3) the watermark is robust against attacks that combine similarity transformation with such other attacks as cropping, mesh simplification, and smoothing. Experiment showed that our new watermarks are resistant against mesh simplification and remeshing combined with resection, similarity transformation, and other operations..     

Matching of 3D polygonal arcs

We define a distance measure between 3D polygonal arcs of equal length, and show that the minimum value of this distance measure is the smallest eigenvalue of a certain matrix. Using this, we develop a mismatch measure and a matching algorithm for 3D polygonal arcs of unequal lengths     

A Survey on Partial Retrieval of 3D Shapes

Content-based shape retrieval techniques can facilitate 3D model resource reuse, 3D model modeling, object recognition, and 3D content classification.Recently more and more researchers have attempted to solve the problems of partial retrieval in the domain of computer graphics, vision, CAD, and multimedia.Unfortunately, in the literature, there is little comprehensive discussion on the state-of-the-art methods of partial shape retrieval.In this article we focus on reviewing the partial shape retrieval methods over the last decade, and help novices to grasp latest developments in this field.We first give the definition of partial retrieval and discuss its desirable capabilities.Secondly, we classify the existing methods on partial shape retrieval into three classes by several criteria, describe the main ideas and techniques for each class, and detailedly compare their advantages and limits.We also present several relevant 3D datasets and corresponding evaluation metrics, which are necessary for evaluating partial retrieval performance.Finally, we discuss possible research directions to address partial shape retrieval.     

三维可变形物体的特征点层次提取

针对不同姿态下的三维可变形物体特征点一致性问题,提出了一种基于样例学习的特征点层次提取方法。该方法首先提取出三维模型的外部特征点;其次,根据外部特征点在不同姿态下所具有的局部特征相似性,采用热核信号和支持向量机识别出外部特征点的语义标签;最后,根据语义标签和测地距离,层次地提取出三维模型的其它语义特征点。实验结果表明,该方法能很好地得到三维可变形物体的各种语义上的有效特征点。     

基于Hausdorff距离的图形快速匹配

本文提出了一种快速的图形匹配算法。将图形的角点作为匹配特征，利用HU矩中的重心计算方法得到角点的重心作为原点，在此基础上运用金字塔算法缩放角点对重心的距离以适应图形的比例变化。运用Hausdorff距离计算图形间的相似度，实现了一种快速的图形匹配算法。实验中运用零件图形进行匹配，结果证明，本文中提出的匹配算法不仅具有一定的鲁棒性，而且匹配速度快，是一种高效率的匹配算法。     

Data‐Driven Sparse Priors of 3D Shapes

We present a sparse optimization framework for extracting sparse shape priors from a collection of 3D models. Shape priors are defined as point‐set neighborhoods sampled from shape surfaces which convey important information encompassing normals and local shape characterization. A 3D shape model can be considered to be formed with a set of 3D local shape priors, while most of them are likely to have similar geometry. Our key observation is that the local priors extracted from a family of 3D shapes lie in a very low‐dimensional manifold. Consequently, a compact and informative subset of priors can be learned to efficiently encode all shapes of the same family. A comprehensive library of local shape priors is first built with the given collection of 3D models of the same family. We then formulate a global, sparse optimization problem which enforces selecting representative priors while minimizing the reconstruction error. To solve the optimization problem, we design an efficient solver based on the Augmented Lagrangian Multipliers method (ALM). Extensive experiments exhibit the power of our data‐driven sparse priors in elegantly solving several high‐level shape analysis applications and geometry processing tasks, such as shape retrieval, style analysis and symmetry detection.     

利用飞行时间三维相机的非刚体形状三维重建

针对目前基于飞行时间原理的三维测距相机捕获数据分辨率低、噪声大,无法直接使用的问题,提出一种非刚体形状三维重建算法.首先对不同角度拍摄的深度图像数据进行分割、去噪等预处理;然后对生成的网格序列进行刚体对齐、选取关键帧网格,以减少运动模糊和数据冗余的影响,并进行全局非刚体配准和网格变形来减少静物或人体扫描中的非刚体误差;...     

Nonrigid Matching of Undersampled Shapes via Medial Diffusion

We introduce medial diffusion for the matching of undersampled shapes undergoing a nonrigid deformation. We construct a diffusion process with respect to the medial axis of a shape, and use the quantity of heat diffusion as a measure which is both tolerant of missing data and approximately invariant to nonrigid deformations. A notable aspect of our approach is that we do not define the diffusion on the shape's medial axis, or similar medial representation. Instead, we construct the diffusion process directly on the shape. This permits the diffusion process to better capture surface features, such as varying spherical and cylindrical parts, as well as combine with other surface‐based diffusion processes. We show how to use medial diffusion to detect intrinsic symmetries, and for computing correspondences between pairs of shapes, wherein shapes contain substantial missing data.     

Sparse Non‐rigid Registration of 3D Shapes

Non‐rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non‐rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an ?₂‐norm regularization on the local transformation differences. However, the ?₂‐norm regularization tends to bias the solution towards outliers and noise with heavy‐tailed distribution, which is verified by the poor goodness‐of‐fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non‐rigid registration (SNR) method with an ?₁‐norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi‐resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large‐scale deformations as well as outliers and noise.     

Matching 2.5D face scans to 3D models

The performance of face recognition systems that use two-dimensional images depends on factors such as lighting and subject's pose. We are developing a face recognition system that utilizes three-dimensional shape information to make the system more robust to arbitrary pose and lighting. For each subject, a 3D face model is constructed by integrating several 2.5D face scans which are captured from different views. 2.5D is a simplified 3D (x,y,z) surface representation that contains at most one depth value (z direction) for every point in the (x, y) plane. Two different modalities provided by the facial scan, namely, shape and texture, are utilized and integrated for face matching. The recognition engine consists of two components, surface matching and appearance-based matching. The surface matching component is based on a modified iterative closest point (ICP) algorithm. The candidate list from the gallery used for appearance matching is dynamically generated based on the output of the surface matching component, which reduces the complexity of the appearance-based matching stage. Three-dimensional models in the gallery are used to synthesize new appearance samples with pose and illumination variations and the synthesized face images are used in discriminant subspace analysis. The weighted sum rule is applied to combine the scores given by the two matching components. Experimental results are given for matching a database of 200 3D face models with 598 2.5D independent test scans acquired under different pose and some lighting and expression changes. These results show the feasibility of the proposed matching scheme.     

Matching and Interpolation of Shapes using Unions of Circles

While the notion of shape of an object is very intuitive, its precise definition is very elusive, and defining a useful metric for the shape distance between objects is a difficult endeavor. At the same time many successful techniques have been developed which interpolate between two objects, so in essence interpolate between shapes. W e present here work which uses a representation of objects as union of circles to define a distance between two objects and to base a method to interpolate between the two. This method can be used in a totally automatic fashion (that is, without any user intervention), or users can guide a pre-registration phase as well as a segmentation phase, after which the matched segments are interpolated pair-wise. The union of circles representation of the two objects is obtained from the Delaunay triangulation of their boundary points. The circles can be simplified to obtain smaller data sets. The circles are then optimally matched according to a distance metric between circles which is a function of their position, size, and feature, that is, a local configuration of circles. The interpolation between the two objects is then obtained by interpolating between the matched pairs of circles (the interpolations can be affine or non -affine). Examples with simple and more complex objects show how the technique can give results which correspond closely to the human notion of shape interpolation. The interpolations shown include some between a calf and a cow and between a cow and a giraffe. The examples given are in two dimensions, but all the steps except the segmentation have been implemented as well for three dimensional objects. W e also show the results of computation of distances between the objects used in our examples.     

Hierarchical Convex Approximation of 3D Shapes for Fast Region Selection

Given a 3D solid model S represented by a tetrahedral mesh, we describe a novel algorithm to compute a hierarchy of convex polyhedra that tightly enclose S. The hierarchy can be browsed at interactive speed on a modern PC and it is useful for implementing an intuitive feature selection paradigm for 3D editing environments. Convex parts often coincide with perceptually relevant shape components and, for their identification, existing methods rely on the boundary surface only. In contrast, we show that the notion of part concavity can be expressed and implemented more intuitively and efficiently by exploiting a tetrahedrization of the shape volume. The method proposed is completely automatic, and generates a tree of convex polyhedra in which the root is the convex hull of the whole shape, and the leaves are the tetrahedra of the input mesh. The algorithm proceeds bottom‐up by hierarchically clustering tetrahedra into nearly convex aggregations, and the whole process is significantly fast. We prove that, in the average case, for a mesh of n tetrahedra O(n log² n) operations are sufficient to compute the whole tree.     

3D Body Shapes Estimation from Dressed‐Human Silhouettes

Estimation of 3D body shapes from dressed‐human photos is an important but challenging problem in virtual fitting. We propose a novel automatic framework to efficiently estimate 3D body shapes under clothes. We construct a database of 3D naked and dressed body pairs, based on which we learn how to predict 3D positions of body landmarks (which further constrain a parametric human body model) automatically according to dressed‐human silhouettes. Critical vertices are selected on 3D registered human bodies as landmarks to represent body shapes, so as to avoid the time‐consuming vertices correspondences finding process for parametric body reconstruction. Our method can estimate 3D body shapes from dressed‐human silhouettes within 4 seconds, while the fastest method reported previously need 1 minute. In addition, our estimation error is within the size tolerance for clothing industry. We dress 6042 naked bodies with 3 sets of common clothes by physically based cloth simulation technique. To the best of our knowledge, We are the first to construct such a database containing 3D naked and dressed body pairs and our database may contribute to the areas of human body shapes estimation and cloth simulation.