Surface deformation models for nonrigid 3D shape recovery

Three-dimensional detection and shape recovery of a nonrigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here, we introduce an approach to creating such models for deformable 3D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3D deformation models. We show that these models can be used to accurately model a wide range of deforming 3D surfaces from video sequences acquired under realistic conditions.     

A factorization-based approach for articulated nonrigid shape, motion and kinematic chain recovery from video

Recovering articulated shape and motion, especially human body motion, from video is a challenging problem with a wide range of applications in medical study, sport analysis and animation, etc. Previous work on articulated motion recovery generally requires prior knowledge of the kinematic chain and usually does not concern the recovery of the articulated shape. The non-rigidity of some articulated part, e.g. human body motion with nonrigid facial motion, is completely ignored. We propose a factorization-based approach to recover the shape, motion and kinematic chain of an articulated object with nonrigid parts altogether directly from video sequences under a unified framework. The proposed approach is based on our modeling of the articulated non-rigid motion as a set of intersecting motion subspaces. A motion subspace is the linear subspace of the trajectories of an object. It can model a rigid or non-rigid motion. The intersection of two motion subspaces of linked parts models the motion of an articulated joint or axis. Our approach consists of algorithms for motion segmentation, kinematic chain building, and shape recovery. It handles outliers and can be automated. We test our approach through synthetic and real experiments and demonstrate how to recover articulated structure with non-rigid parts via a single-view camera without prior knowledge of its kinematic chain.     

Adaptive-size meshes for rigid and nonrigid shape analysis andsynthesis

A physically based modeling method that uses adaptive-size meshes to model surfaces of rigid and nonrigid objects is presented. The initial model uses an a priori determined mesh size. However, the mesh size increases or decreases dynamically during surface reconstruction to locate nodes near surface areas of interest (like high curvature points) and to optimize the fitting error. Further, presented with multiple 3-D data frames, the mesh size varies as the data surface undergoes nonrigid motion. This model is used to reconstruct 3-D surfaces, analyze the nonrigid motion, track the corresponding points in nonrigid motion, and create graphic animation and visualization. The method was tested on real range data, on simulated nonrigid motion, and on real data for the left ventricular motion     

Generation of steady three- and four-dimensional entangled states via quantum-jump-based feedback

A scheme is presented for generating steady three- (four-) dimensional entangled states for two atoms trapped in a strongly dissipative single-mode (double-mode) cavity via quantum-jump-based feedback. The cavity decay is no longer undesirable, but plays an integral part in the schemes. Numerical results show that the target states could be obtained from any initial states via quantum-jump-based feedback. Moreover, our scheme is insensitive to moderate fluctuations of experimental parameters and detection inefficiencies without atomic decay since the system can always reach the target state. Nevertheless, the atomic decay still plays a negative role in the current scheme. The scheme can be generalized to realize $N$ -dimensional entanglement for two atoms.     

Surface shape reconstruction of a nonrigid transport object usingrefraction and motion

The appearance of a pattern behind a transparent, moving object is distorted by refraction at the moving object's surface. An algorithm for reconstructing the surface shape of a nonrigid transparent object, such as water, from the apparent motion of the observed pattern is described. This algorithm is based on the optical and statistical analysis of the distortions. It consists of four steps: extraction of optical flow, averaging of each point trajectory obtained from the optical flow sequence, calculation of the surface normal using optical characteristics, and reconstruction of the surface. The algorithm is applied to both synthetic and real images to demonstrate its performance     

Continuous anisotropic representation of coarse-grained potentials for proteins by spherical harmonics synthesis

A new method is presented for extracting statistical potentials dependent on the relative side chain and backbone orientations in proteins. Coarse-grained, anisotropic potentials are constructed for short-, medium-, and long-range interactions using the Boltzmann method and a database of non-homologous protein structures. The new orientation-dependent potentials are analyzed using a spherical harmonics decomposition method with real eigenfunctions. This method permits a more realistic, continuous angular representation of the coarse-grained potentials. Results of tests for discriminating the native protein conformations from large sets of decoy proteins, show that the new continuous distance- and orientation-dependent potentials present significantly improved performance. Novel graphical representations are developed and used to depict the orientational dependence of the interaction potentials. These new continuous anisotropic statistical potentials could be instrumental in developing new computational methods for structure prediction, threading and coarse-grained simulations.     

形状的全尺度可视化表示与识别

目的视觉目标的形状特征表示和识别是图像领域中的重要问题。在实际应用中,视角、形变、遮挡和噪声等干扰因素造成识别精度较低,且大数据场景需要算法具有较高的学习效率。针对这些问题,本文提出一种全尺度可视化形状表示方法。方法在尺度空间的所有尺度上对形状轮廓提取形状的不变量特征,获得形状的全尺度特征。将获得的全部特征紧凑地表示为单幅彩色图像,得到形状特征的可视化表示。将表示形状特征的彩色图像输入双路卷积网络模型,完成形状分类和检索任务。结果通过对原始形状加入旋转、遮挡和噪声等不同干扰的定性实验,验证了本文方法具有旋转和缩放不变性,以及对铰接变换、遮挡和噪声等干扰的鲁棒性。在通用数据集上进行形状分类和形状检索的定量实验,所得准确率在不同数据集上均超过对比算法。在MPEG-7数据集上精度达到99.57%,对比算法的最好结果为98.84%。在铰接和射影变换数据集上皆达到100%的识别精度,而对比算法的最好结果分别为89.75%和95%。结论本文提出的全尺度可视化形状表示方法,通过一幅彩色图像紧凑地表达了全部形状信息。通过卷积模型既学习了轮廓点间的形状特征关系,又学习了不同尺度间的形状特征关系。本文方法...     

An analytical representation of conformal mapping for genus-zero implicit surfaces and its application to surface shape similarity assessment

This paper develops an analytical representation of conformal mapping for genus-zero implicit surfaces based on algebraic polynomial functions, and its application to surface shape similarity assessment. Generally, the conformal mapping often works as a tool of planar or spherical parameterization for triangle mesh surfaces. It is further exploited for implicit surface matching in this study. The method begins with discretizing one implicit surface by triangle mesh, where a discrete harmonic energy model related to both the mesh and the other implicit surface is established based on a polynomial-function mapping. Then both the zero-center constraint and the landmark constraints are added to the model to ensure the uniqueness of mapping result with the Möbius transformation. By searching optimal polynomial coefficients with the Lagrange–Newton method, the analytical representation of conformal mapping is obtained, which reveals all global and continuous one-to-one correspondent point pairs between two implicit surfaces. Finally, a shape similarity assessment index for (two) implicit surfaces is proposed through calculating the differences of all the shape index values among those corresponding points. The proposed analytical representation method of conformal mapping and the shape assessment index are both verified by the simulation cases for the closed genus-zero implicit surfaces. Experimental results show that the method is effective for genus-zero implicit surfaces, which will offer a new way for object retrieval and manufactured surface inspection.     

A new shape decomposition scheme for graph-based representation

Nowadays, the part-based representation of a given shape plays a significant role in shape-related applications, such as those involving content-based retrieval, object recognition, and so on. In this paper, to represent both 2-D and 3-D shapes as a relational structure, i.e. a graph, a new shape decomposition scheme, which recursively performs constrained morphological decomposition (CMD), is proposed. The CMD method adopts the use of the opening operation with the ball-shaped structuring element, and weighted convexity to select the optimal decomposition. For the sake of providing a compact representation, the merging criterion is applied using the weighted convexity difference. Therefore, the proposed scheme uses the split-and-merge approach. Finally, we present experimental results for various, modified 2-D shapes, as well as 3-D shapes represented by triangular meshes. Based on the experimental results, it is believed that the decomposition of a given shape coincides with that based on human insight for both 2-D and 3-D shapes, and also provides robustness to scaling, rotation, noise, shape deformation, and occlusion.     

Object representation and recognition in shape spaces

In this paper, we describe a shape space based approach for invariant object representation and recognition. In this approach, an object and all its similarity transformed versions are identified with a single point in a high-dimensional manifold called the shape space. Object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space. This approach produced promising results in 2D object recognition experiments: it is invariant to similarity transformations and is relatively insensitive to noise and occlusion. Potentially, it can also be used for 3D object recognition.     

Use of a double Fourier series for three-dimensional shape representation

The representation of three-dimensional star-shaped objects by the double Fourier series (DFS) coefficients of their boundary function is considered. An analogue of the convolution theorem for a DFS on a sphere is developed. It is then used to calculate the moments of an object directly from the DFS coefficients, without an intermediate reconstruction step. The complexity of computing the moments from the DFS coefficients is O(N ² log N), where N is the maximum order of coefficients retained in the expansion, while the complexity of computing the moments from the spherical harmonic representation is O(N ² log ² N). It is shown that under sufficient conditions, the moments and surface area corresponding to the truncated DFS converge to the true moments and area of an object. A new kind of DFS—the double Fourier sine series—is proposed which has better convergence properties than the previously used kinds and spherical harmonics in the case of objects with a sharp point above the pole of the spherical domain.     

Voronoi diagrams of polygons: A framework for shape representation

This paper describes an efficient shape representation framework for planar shapes using Voronoi skeletons.This paper makes the following significant contributions. First a new algorithm for the construction of the Voronoi diagram of a polygon with holes is described. The main features of this algorithm are its robustness in handling the standard degenerate cases (colinearity of more than two points; co-circularity of more than three points), and its ease of implementation. It also features a robust numerical scheme to compute non-linear parabolic edges that avoids having to solve equations of degree greater than two. The algorithm has been fully implemented and tested in a variety of test inputs.Second, the Voronoi diagram of a polygon is used to derive accurate and robust skeletons for planar shapes. The shape representation scheme using Voronoi skeletons possesses the important properties of connectivity as well as Euclidean metrics. Redundant skeletal edges are deleted in a pruning step which guarantees that connectivity of the skeleton will be preserved. The resultant representation is stable with respect to being invariant to perturbations along the boundary of the shape. A number of examples of shapes with and without holes are presented to demonstrate the features of this approach.     

A two-level generative model for cloth representation and shape from shading

In this paper, we present a two-level generative model for representing the images and surface depth maps of drapery and clothes. The upper level consists of a number of folds which will generate the high contrast (ridge) areas with a dictionary of shading primitives (for 2D images) and fold primitives (for 3D depth maps). These primitives are represented in parametric forms and are learned in a supervised learning phase using 3D surfaces of clothes acquired through photometric stereo. The lower level consists of the remaining flat areas which fill between the folds with a smoothness prior (Markov random field). We show that the classical ill-posed problem-shape from shading (SFS) can be much improved by this two-level model for its reduced dimensionality and incorporation of middle-level visual knowledge, i.e., the dictionary of primitives. Given an input image, we first infer the folds and compute a sketch graph using a sketch pursuit algorithm as in the primal sketch (Guo et al., 2003). The 3D folds are estimated by parameter fitting using the fold dictionary and they form the "skeleton" of the drapery/cloth surfaces. Then, the lower level is computed by conventional SFS method using the fold areas as boundary conditions. The two levels interact at the final stage by optimizing a joint Bayesian posterior probability on the depth map. We show a number of experiments which demonstrate more robust results in comparison with state-of-the-art work. In a broader scope, our representation can be viewed as a two-level inhomogeneous MRF model which is applicable to general shape-from-X problems. Our study is an attempt to revisit Marr's idea (Marr and Freeman, 1982) of computing the 2frac12D sketch from primal sketch. In a companion paper (Barbu and Zhu, 2005), we study shape from stereo based on a similar two-level generative sketch representation.     

A new representation of shape and its use for high performance in online Arabic character recognition by an associative memory

The purpose of this study is to investigate a new representation of shape and its use in handwritten online character recognition by a Kohonen associative memory. This representation is based on the empirical distribution of features such as tangents and tangent differences at regularly spaced points along the character signal. Recognition is carried out by a Kohonen neural network trained using the representation. In addition to the Euclidean distance traditionally used in the Kohonen training algorithm to measure the similarities among feature vectors, we also investigate the Kullback–Leibler divergence and the Hellinger distance, functions that measure distance between distributions. Furthermore, we perform operations (pruning and filtering) on the trained memory to improve its classification potency. We report on extensive experiments using a database of online Arabic characters produced without constraints by a large number of writers. Comparative results show the pertinence of the representation and the superior performance of the scheme.