融合形状特征的MRG骨架树三维检索方法

提出一种基于MRG骨架树的三维模型检索方法。根据多分辨率Reeb图(MRG)的原理,提取反映模型拓扑特征的Reeb图骨架并且映射成树形结构,分析了节点的拓扑属性。针对拓扑属性在形状特征上的表达能力不足,在节点相应区域提取离散曲率和面积比例描绘局部的形状特征。有效地结合了模型的拓扑特征和形状特征计算模型的相似度。该方法突出了模型的整体拓扑特征和形状特征,实验结果表明了该方法的高效性和鲁棒性。     

一种MRG骨架树的三维模型检索方法

根据多分辨率Reeb图（MRG）原理,依据测地线函数分割模型,有效地提取反映模型拓扑结构的Reeb图骨架。进而,映射Reeb图为树结构,分析各骨架节点的拓扑属性,并提取其相应区域的离散曲率信息作为局部形状属性。最终,有效结合拓扑和几何形状特征,计算模型的相差度。该方法突出了模型的总体拓扑特征以及模型的表面细节,一系列的实验结果验证了其高效性、鲁棒性。     

A framework for dynamic implicit curve approximation by an irregular discrete approach

The approximation of implicit planar curves by line segments is a very classical problem. Many algorithms use interval analysis to approximate this curve, and to handle the topology of the final reconstruction. In this article, we use discrete geometry tools to build an original geometrical and topological representation of the implicit curve. The polygonal approximation contains few segments, and the Reeb graph permits to sum up efficiently the shape and the topology of the curve. Furthermore, we propose two algorithms to process local cells refinement and local cells grouping schemes. We illustrate these schemes with a global system that efficiently handles manual or automatic fast updates on the global reconstruction, by considering topological or geometrical constraints. We also compare the speed and the quality of our approach with two classical methods.     

Automatic 3D Shape Co-Segmentation Using Spectral Graph Method

Co-analyzing a set of 3D shapes is a challenging task considering a large geometrical variability of the shapes. To address this challenge, this paper proposes a new automatic 3D shape co-segmentation algorithm by using spectral graph method.Our method firstly represents input shapes as a set of weighted graphs and extracts multiple geometric features to measure the similarities of faces in each individual shape.Secondly all graphs are embedded into the spectral domain to find meaningful correspondences across the set.After that we build a joint weighted matrix for the graph set and then apply normalized cut criterion to find optimal co-segmentation of the input shapes.Finally we evaluate our approach on different categories of 3D shapes, and the experimental results demonstrate that our method can accurately co-segment a wide variety of shapes, which may have different poses and significant topology changes.     

Fragment oriented molecular shapes

Molecular shape is an important concept in drug design and virtual screening. Shape similarity typically uses either alignment methods, which dynamically optimize molecular poses with respect to the query molecular shape, or feature vector methods, which are computationally less demanding but less accurate. The computational cost of alignment can be reduced by pre-aligning shapes, as is done with the Volumetric-Aligned Molecular Shapes (VAMS) method. Here, we introduce and evaluate fragment oriented molecular shapes (FOMS), where shapes are aligned based on molecular fragments. FOMS enables the use of shape constraints, a novel method for precisely specifying molecular shape queries that provides the ability to perform partial shape matching and supports search algorithms that function on an interactive time scale. When evaluated using the challenging Maximum Unbiased Validation dataset, shape constraints were able to extract significantly enriched subsets of compounds for the majority of targets, and FOMS matched or exceeded the performance of both VAMS and an optimizing alignment method of shape similarity search.     

Robust Structure‐Based Shape Correspondence

We present a robust method to find region‐level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the shapes, and devise an adapted graph‐matching technique, from which we infer correspondences between shape regions. The simplified shape graphs are designed to primarily capture the overall structure of the shapes, without reflecting precise information about the geometry of each region, which enables us to find correspondences between shapes that might have significant geometric differences. Moreover, due to the special care we take to ensure the robustness of each part of our pipeline, our method can find correspondences between shapes with different representations, such as triangular meshes and point clouds. We demonstrate that the region‐wise matching that we obtain can be used to find correspondences between feature points, reveal the intrinsic self‐similarities of each shape and even construct point‐to‐point maps across shapes. Our method is both time and space efficient, leading to a pipeline that is significantly faster than comparable approaches. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several benchmarks where we achieve comparable or superior performance to existing methods.     

一种人体三维Reeb图计算方法

提出一种人体三维Reeb计算方法。利用人体三维网格数据的顶点坐标,求取顶点的测地距离,构造Morse函数,依据顶点的三角面关系提取人体三维模型的Reeb图,给出基于Reeb图的一般人体骨架结构表示。通过计算Reeb图上弧的曲率,判断是否需要增加关节节点,从而能更准确地描述人体三维模型的拓扑结构。实验结果表明,该方法计算量小、适用性广。     

Consistent Partial Matching of Shape Collections via Sparse Modeling

Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle‐consistency—namely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle‐consistent maps; in order to allow for partially similar and extra‐class shapes, we formulate the problem as a series of quadratic programs with sparsity‐inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes.     

拓扑和形状特征相结合的三维模型检索

针对整体相似性检索算法在局部细节特征上的表达能力不足,提出了一种将拓扑和形状特征相结合的三维模型相似性比较方法.首先提取三维模型的骨架,获得模型的整体拓扑特征;然后根据骨架节点将模型分解为多个子部分,并利用球面谐波算法提取每一个子部分的形状特征.模型的匹配分为3步进行:整体骨架的拓扑特征相似性比较,相对应的子部分的局部形状特征相似性比较,模型总的相似性是整体骨架相似性与对应子部分局部形状相似性的加权和.实验结果表明:该方法从整体到局部、由粗到精,综合考虑了拓扑和形状特征,较传统的考虑单一拓扑或形状特征的检索算法有较高的检索精度,同时又支持基于局部特征的相似性检索.     

On growth and formlets: Sparse multi-scale coding of planar shape

We propose a sparse representation of 2D planar shape through the composition of warping functions, termed formlets, localized in scale and space. Each formlet subjects the 2D space in which the shape is embedded to a localized isotropic radial deformation. By constraining these localized warping transformations to be diffeomorphisms, the topology of shape is preserved, and the set of simple closed curves is closed under any sequence of these warpings. A generative model based on a composition of formlets applied to an embryonic shape, e.g., an ellipse, has the advantage of synthesizing only those shapes that could correspond to the boundaries of physical objects. To compute the set of formlets that represent a given boundary, we demonstrate a greedy coarse-to-fine formlet pursuit algorithm that serves as a non-commutative generalization of matching pursuit for sparse approximations. We evaluate our method by pursuing partially occluded shapes, comparing performance against a contour-based sparse shape coding framework.     

Progressive 3D shape segmentation using online learning

In this article, we propose a progressive 3D shape segmentation method, which allows users to guide the segmentation with their interactions, and does segmentation gradually driven by their intents. More precisely, we establish an online framework for interactive 3D shape segmentation, without any boring collection preparation or training stages. That is, users can collect the 3D shapes while segment them, and the segmentation will become more and more precise as the accumulation of the shapes.Our framework uses Online Multi-Class LPBoost (OMCLP) to train/update a segmentation model progressively, which includes several Online Random forests (ORFs) as the weak learners. Then, it performs graph cuts optimization to segment the 3D shape by using the trained/updated segmentation model as the optimal data term. There exist three features of our framework. Firstly, the segmentation model can be trained gradually during the collection of the shapes. Secondly, the segmentation results can be refined progressively until users’ requirements are met. Thirdly, the segmentation model can be updated incrementally without retraining all shapes when users add new shapes. Experimental results demonstrate the effectiveness of our approach.     

Reeb graph path dissimilarity for 3D object matching and retrieval

We introduce a skeletal graph for topological 3D shape representation using Morse theory. The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function. We also propose a novel graph matching algorithm by comparing the relative shortest paths between the skeleton endpoints. Experimental results demonstrate the feasibility of the proposed topological Reeb graph as a shape signature for 3D object matching and retrieval.     

A 3D shape segmentation approach for robot grasping by parts

Neuro-psychological findings have shown that human perception of objects is based on part decomposition. Most objects are made of multiple parts which are likely to be the entities actually involved in grasp affordances. Therefore, automatic object recognition and robot grasping should take advantage from 3D shape segmentation. This paper presents an approach toward planning robot grasps across similar objects by part correspondence. The novelty of the method lies in the topological decomposition of objects that enables high-level semantic grasp planning.In particular, given a 3D model of an object, the representation is initially segmented by computing its Reeb graph. Then, automatic object recognition and part annotation are performed by applying a shape retrieval algorithm. After the recognition phase, queries are accepted for planning grasps on individual parts of the object. Finally, a robot grasp planner is invoked for finding stable grasps on the selected part of the object. Grasps are evaluated according to a widely used quality measure. Experiments performed in a simulated environment on a reasonably large dataset show the potential of topological segmentation to highlight candidate parts suitable for grasping.     

Coordinated Crowd Simulation With Topological Scene Analysis

This paper proposes a new algorithm to produce globally coordinated crowds in an environment with multiple paths and obstacles. Simple greedy crowd control methods easily lead to congestion at bottlenecks within scenes, as the characters do not cooperate with one another. In computer animation, this problem degrades crowd quality especially when ordered behaviour is needed, such as soldiers marching towards a castle. Similarly, in applications such as real‐time strategy games, this often causes player frustration, as the crowd will not move as efficiently as it should. Also, planning of building would usually require visualization of ordered evacuation to maximize the flow. Planning such globally coordinated crowd movement is usually labour intensive. Here, we propose a simple solution that is easy to use and efficient in computation. First, we compute the harmonic field of the environment, taking into account the starting points, goals and obstacles. Based on the field, we represent the topology of the environment using a Reeb Graph, and calculate the maximum capacity for each path in the graph. With the harmonic field and the Reeb Graph, path planning of crowd can be performed using a lightweight algorithm, such that any blocking of one another's paths is minimized. Comparing to previous methods, our system can synthesize globally coordinated crowd with smooth and efficient movement. It also enables control of the crowd with high‐level parameters such as the degree of cooperation and congestion. Finally, the method is scalable to thousands of characters with minimal impact to computation time. It is best applied in interactive crowd synthesis systems such as animation designs and real‐time strategy games.     

Enhancing 3D mesh topological skeletons with discrete contour constrictions

This paper describes a unified and fully automatic algorithm for Reeb graph construction and simplification as well as constriction approximation on triangulated surfaces. The key idea of the algorithm is that discrete contours – curves carried by the edges of the mesh and approximating the continuous contours of a mapping function – encode both topological and geometrical shape characteristics. Therefore, a new concise shape representation, enhanced topological skeletons, is proposed, encoding the contours’ topological and geometrical evolution. First, mesh feature points are computed. Then they are used as geodesic origins for the computation of an invariant mapping function that reveals the shape most significant features. Next, for each vertex in the mesh, its discrete contour is computed. As the set of discrete contours recovers the whole surface, each of them can be analyzed, both to detect topological changes and constrictions. Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, which we refer to as enhanced topological skeletons. Extensive experiments showed that, without any preprocessing stage, proposed algorithms are fast in practice, affine-invariant and robust to a variety of surface degradations (surface noise, mesh sampling and model pose variations). These properties make enhanced topological skeletons interesting shape abstractions for many computer graphics applications.     

Hybrid query execution engine for large attributed graphs

Graphs are widely used for modeling complicated data such as social networks, bibliographical networks and knowledge bases. The growing sizes of graph databases motivate the crucial need for developing powerful and scalable graph-based query engines. We propose a SPARQL-like language, G-SPARQL, for querying attributed graphs. The language enables the expression of different types of graph queries that are of large interest in the databases that are modeled as large graph such as pattern matching, reachability and shortest path queries. Each query can combine both structural predicates and value-based predicates (on the attributes of the graph nodes/edges). We describe an algebraic compilation mechanism for our proposed query language which is extended from the relational algebra and based on the basic construct of building SPARQL queries, the Triple Pattern. We describe an efficient hybrid Memory/Disk representation of large attributed graphs where only the topology of the graph is maintained in memory while the data of the graph are stored in a relational database. The execution engine of our proposed query language splits parts of the query plan to be pushed inside the relational database (using SQL) while the execution of other parts of the query plan is processed using memory-based algorithms, as necessary. Experimental results on real and synthetic datasets demonstrate the efficiency and the scalability of our approach and show that our approach outperforms native graph databases by several factors.     

A multiresolution descriptor for deformable 3D shape retrieval

In this paper, we present a spectral graph wavelet framework for the analysis and design of efficient shape signatures for nonrigid 3D shape retrieval. Although this work focuses primarily on shape retrieval, our approach is, however, fairly general and can be used to address other 3D shape analysis problems. In a bid to capture the global and local geometry of 3D shapes, we propose a multiresolution signature via a cubic spline wavelet generating kernel. The parameters of the proposed signature can be easily determined as a trade-off between effectiveness and compactness. Experimental results on two standard 3D shape benchmarks demonstrate the much better performance of the proposed shape retrieval approach in comparison with three state-of-the-art methods. Additionally, our approach yields a higher retrieval accuracy when used in conjunction with the intrinsic spatial partition matching.