Non-rigid 3D shape tracking from multiview video

We present a fast and efficient non-rigid shape tracking method for modeling dynamic 3D objects from multiview video. Starting from an initial mesh representation, the shape of a dynamic object is tracked over time, both in geometry and topology, based on multiview silhouette and 3D scene flow information. The mesh representation of each frame is obtained by deforming the mesh representation of the previous frame towards the optimal surface defined by the time-varying multiview silhouette information with the aid of 3D scene flow vectors. The whole time-varying shape is then represented as a mesh sequence which can efficiently be encoded in terms of restructuring and topological operations, and small-scale vertex displacements along with the initial model. The proposed method has the ability to deal with dynamic objects that may undergo non-rigid transformations and topological changes. The time-varying mesh representations of such non-rigid shapes, which are not necessarily of fixed connectivity, can successfully be tracked thanks to restructuring and topological operations employed in our deformation scheme. We demonstrate the performance of the proposed method both on real and synthetic sequences.     

Local commute-time guided MDS for 3D non-rigid object retrieval

In this paper, we propose a 3D non-rigid shape retrieval method based on canonical shape analysis. Our main idea is to transform the problem of non-rigid shape retrieval into a rigid shape retrieval problem via the well-known multidimensional scaling (MDS) approach and random walk on graphs. We first segment the non-rigid shape into local partitions based on its salient features. Then, we calculate a local MDS problem for each partition, where the local commute time distance is used as weighting function in order to preserve local shape details. Finally, we aggregate the set of local MDS problems as a global constrained problem. The constraint is formulated using the biharmonic function between local salient features. In contrast to MDS method, the proposed local MDS is computationally efficient, parameters free and gives isometry-invariant forms with minimum features distortion. Due to these advantageous properties, the proposed method achieved good retrieval accuracy on non-rigid shape benchmark datasets.     

A methodology for shape matching of non-rigid structures based on integrated graphical information

Shape matching is a long-studied problem and lies at the core of many applications in statistical shape analysis, virtual reality and human–computer interaction. This paper presents an automatic dense correspondence method to match the mesh vertices of two 3D shapes under near-isometric and non-rigid deformations. The goal is achieved by combining three types of graphic structure information. The method includes three major steps: first, we describe the vertices based on three types of graphical information, Euclidean structure information, Riemannian structure information, and conformal structure information; second, the match between two shapes is formulated as an optimization problem and a novel objective function is proposed; third, we resolve the optimal solution by using the projected descent optimization procedure to solve the objective function. The method is tested on various shape pairs with different poses, surface details, and topological noises. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several challenging 3D shape matching datasets where we achieve superior performance to existing methods.     

深度特征融合的非刚性三维形状局部匹配

针对海量、异构三维形状匹配与智能检索技术的需求,提出了一种基于级联卷积神经网络(F-PointCNN)深度特征融合的三维形状局部匹配方法.首先,采用特征袋模型,提出几何图像表示方法,该几何图像不仅能够有效区分同类异构的非刚性三维模型,而且能够揭示大尺度不完整三维模型的结构相似性.其次,构建级联卷积神经网络学习框架F-PointCNN,其中,BoF-CNN从几何图像中学习深度全局特征,建立融合局部特征与全局特征的点特征表示;进而对Point-CNN进行点特征的细化与提纯,生成具有丰富信息的深度融合特征,有效提高形状特征的区分性与鲁棒性.最终,通过交叉矩阵度量方法高效实现非刚性三维模型的局部形状匹配.在公开的非刚性三维模型数据库的实验结果表明,该方法提取的特征在大尺度变换的形状分类及局部形状匹配中具有更强的识别力与更高的匹配精度.     

Non-Rigid Stereo Factorization

In this paper we address the problem of recovering 3D non-rigid structure from a sequence of images taken with a stereo pair. We have extended existing non-rigid factorization algorithms to the stereo camera case and presented an algorithm to decompose the measurement matrix into the motion of the left and right cameras and the 3D shape, represented as a linear combination of basis-shapes. The added constraints in the stereo camera case are that both cameras are viewing the same structure and that the relative orientation between both cameras is fixed. Our focus in this paper is on the recovery of flexible 3D shape rather than on the correspondence problem. We propose a method to compute reliable 3D models of deformable structure from stereo images. Our experiments with real data show that improved reconstructions can be achieved using this method. The algorithm includes a non-linear optimization step that minimizes image reprojection error and imposes the correct structure to the motion matrix by choosing an appropriate parameterization. We show that 3D shape and motion estimates can be successfully disambiguated after bundle adjustment and demonstrate this on synthetic and real image sequences. While this optimization step is proposed for the stereo camera case, it can be readily applied to the case of non-rigid structure recovery using a monocular video sequence. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Feature-Preserved 3D Canonical Form

Measuring the dissimilarity between non-rigid objects is a challenging problem in 3D shape retrieval. One potential solution is to construct the models’ 3D canonical forms (i.e., isometry-invariant representations in 3D Euclidean space) on which any rigid shape matching algorithm can be applied. However, existing methods, which are typically based on embedding procedures, result in greatly distorted canonical forms, and thus could not provide satisfactory performance to distinguish non-rigid models. In this paper, we present a feature-preserved canonical form for non-rigid 3D watertight meshes. The basic idea is to naturally deform original models against corresponding initial canonical forms calculated by Multidimensional Scaling (MDS). Specifically, objects are first segmented into near-rigid subparts, and then, through properly-designed rotations and translations, original subparts are transformed into poses that correspond well with their positions and directions on MDS canonical forms. Final results are obtained by solving nonlinear minimization problems for optimal alignments and smoothing boundaries between subparts. Experiments on two non-rigid 3D shape benchmarks not only clearly verify the advantages of our algorithm against existing approaches, but also demonstrate that, with the help of the proposed canonical form, we can obtain significantly better retrieval accuracy compared to the state of the art.     

A Bayesian approach to simultaneously recover camera pose and non-rigid shape from monocular images

In this paper we bring the tools of the Simultaneous Localization and Map Building (SLAM) problem from a rigid to a deformable domain and use them to simultaneously recover the 3D shape of non-rigid surfaces and the sequence of poses of a moving camera. Under the assumption that the surface shape may be represented as a weighted sum of deformation modes, we show that the problem of estimating the modal weights along with the camera poses, can be probabilistically formulated as a maximum a posteriori estimate and solved using an iterative least squares optimization. In addition, the probabilistic formulation we propose is very general and allows introducing different constraints without requiring any extra complexity. As a proof of concept, we show that local inextensibility constraints that prevent the surface from stretching can be easily integrated.An extensive evaluation on synthetic and real data, demonstrates that our method has several advantages over current non-rigid shape from motion approaches. In particular, we show that our solution is robust to large amounts of noise and outliers and that it does not need to track points over the whole sequence nor to use an initialization close from the ground truth.     

Reconstruction of non-rigid 3D shapes from stereo-motion

Several non-rigid structure from motion methods have been proposed so far in order to recover both the motion and the non-rigid structure of an object. However, these monocular algorithms fail to give reliable 3D shape estimates when the overall rigid motion of the sequence is small. Aiming to overcome this limitation, in this paper we propose a novel approach for the 3D Euclidean reconstruction of deformable objects observed by an uncalibrated stereo rig. Using a stereo setup drastically improves the 3D model estimation when the observed 3D shape is mostly deforming without undergoing strong rigid motion. Our approach is based on the following steps. Firstly, the stereo system is automatically calibrated and used to compute metric rigid structures from pairs of views. Afterwards, these 3D shapes are aligned to a reference view using a RANSAC method in order to compute the mean shape of the object and to select the subset of points which have remained rigid throughout the sequence. The selected rigid points are then used to compute frame-wise shape registration and to robustly extract the motion parameters from frame to frame. Finally, all this information is used as initial estimates of a non-linear optimization which allows us to refine the initial solution and also to recover the non-rigid 3D model. Exhaustive results on synthetic and real data prove the performance of our proposal estimating motion, non-rigid models and stereo camera parameters even when there is no rigid motion in the original sequence.     

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.     

SR-SIHKS：一种非刚体全局形状特征

非刚体由于姿态变化会产出多样的形变,因此非刚体的形状检索比刚体更具挑战性。形状特征提取是非刚体三维模型形状检索的关键问题。为了提高非刚体形状检索的准确度,提出了一种非刚体全局形状特征提取方法。此方法的核心思想是将稀疏表示（Sparse Representation,SR）理论用于对尺度无关的热核特征（Scale Invariant Heat Kernel Signature,SIHKS）进行稀疏编码,因此被称为SR-SIHKS。改进了SIHKS局部特征的提取方法,根据所处理的模型库来自适应地确定热扩散时间参数;采用K-SVD算法来训练字典,借助Batch-OMP算法实现局部特征的稀疏编码;将非刚体三维模型的所有局部特征的稀疏编码汇聚为全局形状特征。实验结果表明,SR-SIHKS具有比SIHKS和HKS更优的检索效果。     

3D head model classification by evolutionary optimization of the Extended Gaussian Image representation

Classification of 3D head models based on their shape attributes for subsequent indexing and retrieval are important in many applications, as in hierarchical content-based retrieval of these head models for virtual scene composition, and the automatic annotation of these characters in such scenes. While simple feature representations are preferred for more efficient classification operations, these features may not be adequate for distinguishing between the subtly different head model classes. In view of these, we propose an optimization approach based on genetic algorithm (GA) where the original model representation is transformed in such a way that the classification rate is significantly enhanced while retaining the efficiency and simplicity of the original representation. Specifically, based on the Extended Gaussian Image (EGI) representation for 3D models which summarizes the surface normal orientation statistics, we consider these orientations as random variables, and proceed to search for an optimal transformation for these variables based on genetic optimization. The resulting transformed distributions for these random variables are then used as the modified classifier inputs. Experiments have shown that the optimized transformation results in a significant improvement in classification results for a large variety of class structures. More importantly, the transformation can be indirectly realized by bin removal and bin count merging in the original histogram, thus retaining the advantage of the original EGI representation.     

A multimedia retrieval framework based on semi-supervised ranking and relevance feedback

We present a new framework for multimedia content analysis and retrieval which consists of two independent algorithms. First, we propose a new semi-supervised algorithm called ranking with Local Regression and Global Alignment (LRGA) to learn a robust Laplacian matrix for data ranking. In LRGA, for each data point, a local linear regression model is used to predict the ranking scores of its neighboring points. A unified objective function is then proposed to globally align the local models from all the data points so that an optimal ranking score can be assigned to each data point. Second, we propose a semi-supervised long-term Relevance Feedback (RF) algorithm to refine the multimedia data representation. The proposed long-term RF algorithm utilizes both the multimedia data distribution in multimedia feature space and the history RF information provided by users. A trace ratio optimization problem is then formulated and solved by an efficient algorithm. The algorithms have been applied to several content-based multimedia retrieval applications, including cross-media retrieval, image retrieval, and 3D motion/pose data retrieval. Comprehensive experiments on four data sets have demonstrated its advantages in precision, robustness, scalability, and computational efficiency.     

CM-BOF: visual similarity-based 3D shape retrieval using Clock Matching and Bag-of-Features

Content-based 3D object retrieval has become an active topic in many research communities. In this paper, we propose a novel visual similarity-based 3D shape retrieval method (CM-BOF) using Clock Matching and Bag-of-Features. Specifically, pose normalization is first applied to each object to generate its canonical pose, and then the normalized object is represented by a set of depth-buffer images captured on the vertices of a given geodesic sphere. Afterwards, each image is described as a word histogram obtained by the vector quantization of the image’s salient local features. Finally, an efficient multi-view shape matching scheme (i.e., Clock Matching) is employed to measure the dissimilarity between two models. When applying the CM-BOF method in non-rigid 3D shape retrieval, multidimensional scaling (MDS) should be utilized before pose normalization to calculate the canonical form for each object. This paper also investigates several critical issues for the CM-BOF method, including the influence of the number of views, codebook, training data, and distance function. Experimental results on five commonly used benchmarks demonstrate that: (1) In contrast to the traditional Bag-of-Features, the time-consuming clustering is not necessary for the codebook construction of the CM-BOF approach; (2) Our methods are superior or comparable to the state of the art in applications of both rigid and non-rigid 3D shape retrieval.     

基于最优最小生成树的三维模型形状优化方法

针对海量、异构、复杂的三维模型高效形状分析需求,提出基于最优最小生成树的三维模型形状优化方法。首先基于三维模型最小生成树（3D-MST）构造模型的结构描述;其次通过拓扑结构与几何形状检测并结合双边滤波与熵权值分布进行局部优化,获得模型的优化MST表示;最终基于优化的Laplacian谱特征,结合薄板样条函数（TPS）,实现模型的形状分析与相似性检测。实验结果表明,所提方法不仅有效地保留了模型的形状特征,而且可高效地实现复杂模型的稀疏优化表示,能进一步提高几何处理与形状检索的高效性和增强鲁棒性。     

Modeling Real Objects for Kansei-based Shape Retrieval

A large number of 3D models are created on computers and available for networks. Some content-based retrieval technologies are indispensable to find out particular data from such anonymous datasets. Though several shape retrieval technologies have been developed, little attention has been given to the points on human＇s sense and impression （as known as Kansei） in the conventional techniques, In this paper, the authors propose a novel method of shape retrieval based on shape impression of human＇s Kansei. The key to the method is the Gaussian curvature distribution from 3D models as features for shape retrieval. Then it classifies the 3D models by extracted feature and measures similarity among models in storage.     

3D anatomical shape atlas construction using mesh quality preserved deformable models

3D anatomical shape atlas construction has been extensively studied in medical image analysis research, owing to its importance in model-based image segmentation, longitudinal studies and populational statistical analysis, etc. Among multiple steps of 3D shape atlas construction, establishing anatomical correspondences across subjects, i.e., surface registration, is probably the most critical but challenging one. Adaptive focus deformable model (AFDM) [1] was proposed to tackle this problem by exploiting cross-scale geometry characteristics of 3D anatomy surfaces. Although the effectiveness of AFDM has been proved in various studies, its performance is highly dependent on the quality of 3D surface meshes, which often degrades along with the iterations of deformable surface registration (the process of correspondence matching). In this paper, we propose a new framework for 3D anatomical shape atlas construction. Our method aims to robustly establish correspondences across different subjects and simultaneously generate high-quality surface meshes without removing shape details. Mathematically, a new energy term is embedded into the original energy function of AFDM to preserve surface mesh qualities during deformable surface matching. More specifically, we employ the Laplacian representation to encode shape details and smoothness constraints. An expectation–maximization style algorithm is designed to optimize multiple energy terms alternatively until convergence. We demonstrate the performance of our method via a set of diverse applications, including a population of sparse cardiac MRI slices with 2D labels, 3D high resolution CT cardiac images and rodent brain MRIs with multiple structures. The constructed shape atlases exhibit good mesh qualities and preserve fine shape details. The constructed shape atlases can further benefit other research topics such as segmentation and statistical analysis.