Deformable Model Retrieval Based on Topological and Geometric Signatures

With the increasing popularity of 3D applications such as computer games, a lot of 3D geometry models are being created. To encourage sharing and reuse, techniques that support matching and retrieval of these models are emerging. However, only a few of them can handle deformable models, i.e., models of different poses, and these methods are generally very slow. In this paper, we present a novel method for efficient matching and retrieval of 3D deformable models. Our research idea stresses on using both topological and geometric features at the same time. First, we propose Topological Point Ring (TPR) analysis to locate reliable topological points and rings. Second, we capture both local and global geometric information to characterize each of these topological features. To compare the similarity of two models, we adapt the Earth Mover Distance (EMD) as the distance function, and construct an indexing tree to accelerate the retrieval process. We demonstrate the performance of the new method, both in terms of accuracy and speed, through a large number of experiments

Indexing and Retrieval of 3D Articulated Geometry Models

In this PhD research study, we focus on building a content-based search engine for 3D articulated geometry models. 3D models are essential components in nowadays graphic applications, and are widely used in the game, animation and movies production industry. With the increasing number of these models, a search engine not only provides an entrance to explore such a huge dataset, it also facilitates sharing and reusing among different users. In general, it reduces production costs and time to develop these 3D models. Though a lot of retrieval systems have been proposed in recent years, search engines for 3D articulated geometry models are still in their infancies. Among all the works that we have surveyed, reliability and efficiency are the two main issues that hinder the popularity of such systems. In this research, we have focused our attention mainly to address these two issues. We have discovered that most existing works design features and matching algorithms in order to reflect the intrinsic properties of these 3D models. For instance, to handle 3D articulated geometry models, it is common to extract skeletons and use graph matching algorithms to compute the similarity. However, since this kind of feature representation is complex, it leads to high complexity of the matching algorithms. As an example, sub-graph isomorphism can be NP-hard for model graph matching. Our solution is based on the understanding that skeletal matching seeks correspondences between the two comparing models. If we can define descriptive features, the correspondence problem can be solved by bag-based matching where fast algorithms are available. In the first part of the research, we propose a feature extraction algorithm to extract such descriptive features. We then convert the skeletal matching problems into bag-based matching. We further define metric similarity measure so as to support fast search. We demonstrate the advantages of this idea in our experiments. The improvement on precision is 12\% better at high recall. The indexing search of 3D model is 24 times faster than the state of the art if only the first relevant result is returned. However, improving the quality of descriptive features pays the price of high dimensionality. Curse of dimensionality is a notorious problem on large multimedia databases. The computation time scales exponentially as the dimension increases, and indexing techniques may not be useful in such situation. In the second part of the research, we focus ourselves on developing an embedding retrieval framework to solve the high dimensionality problem. We first argue that our proposed matching method projects 3D models on manifolds. We then use manifold learning technique to reduce dimensionality and maximize intra-class distances. We further propose a numerical method to sub-sample and fast search databases. To preserve retrieval accuracy using fewer landmark objects, we propose an alignment method which is also beneficial to existing works for fast search. The advantages of the retrieval framework are demonstrated in our experiments that it alleviates the problem of curse of dimensionality. It also improves the efficiency (3.4 times faster) and accuracy (30\% more accurate) of our matching algorithm proposed above. In the third part of the research, we also study a closely related area, 3D motions. 3D motions are captured by sticking sensor on human beings. These captured data are real human motions that are used to animate 3D articulated geometry models. Creating realistic 3D motions is an expensive and tedious task. Although 3D motions are very different from 3D articulated geometry models, we observe that existing works also suffer from the problem of temporal structure matching. This also leads to low efficiency in the matching algorithms. We apply the same idea of bag-based matching into the work of 3D motions. From our experiments, the proposed method has a 13\% improvement on precision at high recall and is 12 times faster than existing works. As a summary, we have developed algorithms for 3D articulated geometry models and 3D motions, covering feature extraction, feature matching, indexing and fast search methods. Through various experiments, our idea of converting restricted matching to bag-based matching improves matching efficiency and reliability. These have been shown in both 3D articulated geometry models and 3D motions. We have also connected 3D matching to the area of manifold learning. The embedding retrieval framework not only improves efficiency and accuracy, but has also opened a new area of research

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment

Derivation of continuous zoomable road network maps through utilization of Space-Scale-Cube

The process of performing cartographic generalization in an automatic way applied on geographic information is of highly interest in the field of cartography, both in academia and industry. Many research e↵orts have been done to implement di↵erent automatic generalization approaches. Being able to answer the research question on automatic generalization, another interesting question opens up: ”Is it possible to retrieve and visualize geographic information in any arbitrary scale?” This is the question in the field of vario-scale geoinformation. Potential research works should answer this question with solutions which provide valid and efficient representation of geoinformation in any on-demand scale. More brilliant solutions will also provide smooth transitions between these on-demand arbitrary scales. Space-Scale-Cube (Meijers and Van Oosterom 2011) is a reactive tree (Van Oosterom 1991) data structure which shows positive potential for achieving smooth automatic vario-scale generalization of area features. The topic of this research work is investigation of adaptation of this approach on an interesting class of geographic information: road networks datasets. Firstly theoretical background will be introduced and discussed and afterwards, implementing the adaptation would be described. This research work includes development of a hierarchical data structure based on road network datasets and the potential use of this data structure in vario-scale geoinformation retrieval and visualization.:Declaration of Authorship i Abstract iii Acknowledgements iv List of Figures vii Abbreviations viii 1 Introduction 1 1.1 Problem Definition 2 1.1.1 Research Questions 2 1.1.2 Objectives 3 1.2 Proposed Solution 3 1.3 Structure of the Thesis 4 1.4 Notes on Terminology 4 2 Cartographic Generalization 6 2.1 Cartographic Generalization: Definitions and Classifications 6 2.2 Generalization Operators 9 2.3 Efforts on Vario-Scale Visualization of Geoinformation 10 2.4 Efforts on Generalization of Road Networks and Similar Other Networks 16 2.4.1 Geometric Generalization of Networks 17 2.4.2 Model Generalization of Networks 18 2.5 Clarification of Interest 20 3 Theory of Road Network SSC 21 3.1 Background of an SSC 21 3.1.1 tGAP 21 3.1.2 Smoothing tGAP 23 3.2 Road Network as a ’Network’ 24 3.2.1 Short Background on Graph Theory 5 3.3 Formation of Road Network SSC 26 3.3.1 Geometry 26 3.3.2 Network Topology 27 3.3.3 Building up tGAP on The Road Network 28 3.3.4 Smoothing of Road Network SSC 31 3.3.4.1 Smoothing Elimination 32 3.3.4.2 Smoothing Simplification 32 3.4 Reading from a road network SSC 34 3.4.1 Discussion on Scale 34 3.4.2 Iterating Over The Forest 35 3.4.3 Planar Slices 35 3.4.4 Non-Planar Slices 36 4 Implementation of Road Network SSC 37 4.1 General Information Regarding The Implementation 37 4.1.1 Programming Language 37 4.1.2 RDBMS 38 4.1.3 Geometry Library 39 4.1.4 Graph Library 39 4.2 Data Structure 40 4.2.1 Node 40 4.2.2 Edge 41 4.2.3 Edge-Node-Relation 41 4.3 Software Architecture 42 4.3.1 More Detail on Building The SSC 42 4.3.1.1 Initial Data Processing 42 4.3.1.2 Network Processing 43 4.3.2 More Detail on Querying The SSC 46 4.3.2.1 Database Query 46 4.3.2.2 Building Geometry 46 4.3.2.3 Interface and Visualization 47 4.4 Results 48 5 Conclusions and Outlook 49 Bibliography 5