컴퓨터비전을 위한 그래프정합과 고차그래프정합: 새로운 알고리즘과 분석에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 8. 이경무.Establishing image feature correspondences is fundamental problem in computer vision and machine learning research fields. Myriad of graph matching algorithms have been proposed to tackle this problem by regarding correspondence problem as a graph matching problem. However, the graph matching problem is challenging since there are various types of noises in real world scenarioe.g., non-rigid motion, view-point change, and background clutter. The objective of this dissertation is to propose robust graph matching algorithms for feature correspondence task in computer vision and to investigate an effective graph matching strategy. For the purpose, at first, two robust simulation based graph matching algorithms are introduced: the one is based on Random Walks simulation and the other is based on Markov Chain Monte Carlo sampling simulation. Secondly, two different graph matching formulations and their transformal relation are studied since equivalence between two formulations are not well studied in graph matching fields. It is demonstrated that conventional graph matching algorithms can solve both types of formulations by proposing conversion principle between two formulations. Finally, these whole statements are extended into hypergraph matching problem by introducing two robust hypergraph matching algorithms which are based on Random Walks and Markov Chain Monte Carlo, by relating two different hypergraph matching formulations, and by reinterpreting previous hypergraph matching algorithms into their counterpart formulations. Throughout chapters in this dissertation, comparative and extensive experiments verify characteristics of formulations, transformal relations, and algorithms. Synthetic graph matching problems as well as real image feature correspondence problems are performed in various and severe noise conditions.Chapter 1 Introduction 1 1.1 Graph Matching Problem 1 1.1.1 Graph Matching for Computer Vision 1 1.1.2 Graph Matching Formulation 2 1.1.3 Extension to Hypergraph Matching 5 1.2 Outline of Dissertation 6 Chapter 2 Graph Matching via Random Walks 9 2.1 Introduction 9 2.1.1 Related Works 10 2.2 Problem Formulation 12 2.2.1 Graph Matching Formulation 12 2.2.2 Hypergraphs Matching Formulation 13 2.3 Graph Matching via Random Walks 16 2.3.1 Random Walks for Graph Matching 16 2.3.2 Reweighting Jumps for Graph Matching 19 2.4 Hypergraph Matching via Random Walks 22 2.4.1 Hypergraph Random Walks 22 2.4.2 Reweighting Jumps for Hypergraph Matching 23 2.5 Experiments 26 2.5.1 Random Graph Matching 27 2.5.2 Synthetic Point Matching 34 2.5.3 Image Sequence Matching 37 2.5.4 Image Feature Matching 39 2.6 Conclusion 44 Chapter 3 Graph Matching via Markov Chain Monte Carlo 45 3.1 Introduction 45 3.2 Graph Matching Formulation 47 3.3 Algorithm 49 3.3.1 State Transition 49 3.3.2 Energy Formulation 49 3.3.3 Data-Driven Proposal 51 3.4 Hypergraph Extension 53 3.4.1 Hypergraph Matching Problem 53 3.4.2 Energy Formulation & Data-Driven Proposal 54 3.5 Experiment 54 3.5.1 Random Graph Matching Problem 54 3.5.2 Random Hypergraph Matching Problem 58 3.6 Conclusion 59 Chapter 4 Graph and Hypergraph Matching Revisited 63 4.1 Introduction 63 4.2 Related Works 65 4.3 Two Types of Formulations 66 4.3.1 Adjacency-based Formulation 67 4.3.2 Affinity-based Formulation 69 4.3.3 Relation between Two Formulations 70 4.4 Affinity Measures 72 4.5 Existing Methods & Re-interpretations 74 4.5.1 Spectral Matching 74 4.5.2 Integer Projected Fixed Point 75 4.5.3 Reweighted Random Walks Matching 76 4.5.4 Factorized Graph Matching 77 4.6 High-order Methods & Reinterpretations 78 4.6.1 Hypergraph Matching by Zass and Shashua 81 4.6.2 SVD-based Hypergraph Matching 82 4.6.3 Tensor Power Iteration based Hypergraph Matching 82 4.6.4 Reweighted Random Walks for Hypergraph Matching 83 4.6.5 Discrete Hypergraph Matching 85 4.7 Experiments & Comparison 85 4.8 Conclusion 102 Chapter 5 Conclusion 105 5.1 Summary and Contribution of Dissertation 105 5.2 Future Works 107 Bibliography 109 국문 초록 117Docto

Hashing for Similarity Search: A Survey

Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this paper, we present a survey on one of the main solutions, hashing, which has been widely studied since the pioneering work locality sensitive hashing. We divide the hashing algorithms two main categories: locality sensitive hashing, which designs hash functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance measure and search scheme in the hash coding space

Combinatorial Optimization Algorithms for Hypergraph Matching with Application to Posture Identification in Embryonic Caenorhabditis elegans

Point-set matching defines the task in computer vision of identifying a one-to-one alignment between two sets of points. Existing techniques rely on simple relationships between point-sets in order to efficiently find optimal correspondences between larger sets. Modern methodology precludes application to more challenging point-set matching tasks which benefit from interdependent modeling. This thesis addresses a gap in combinatorial optimization literature by enhancing leading methods in both graph matching and multiple object tracking (MOT) to more flexibly use data-driven point-set matching models. Presented contributions are inspired by Caenorhabditis elegans, a transparent free-living roundworm frequently studied in developmental biology and neurobiology. The C. elegans embryo, containing around 550 cells at hatch, can be used for cell tracking studies to understand how cell movement drives the development of specific embryonic tissues and organ functions. The development of muscle cells complicates analyses during late-stage development, as embryos begin twitching due to muscular activity. The sporadic twitches cause cells to move violently and unpredictably, invalidating traditional cell tracking approaches. The embryo possesses seam cells, a set of 20 cells which together act as fiducial markers to approximate the coiled embryo's body. Novel optimization algorithms and data-driven hypergraphical models leveraging the correlated movement among seam cells are used to forward research on C. elegans embryogenesis. We contribute two optimization algorithms applicable in differing conditions to interdependent point-set matching. The first algorithm, Exact Hypergraph Matching (EHGM), exactly solves the n-adic assignment problem by casting the problem as hypergraph matching. The algorithm obtains solutions to highly interdependent seam cell identification models. The second optimization algorithm, Multiple Hypothesis Hypergraph Tracking (MHHT), adapts traditional multiple hypothesis tracking with hypergraphical data association. Results from both studies highlight improved performance over established methods while providing adaptable optimization tools for multiple academic communities. The canonical point-set matching task is solved efficiently under strict assumptions of frame-to-frame transformations. Challenging situations arising from non-rigid displacements between frames will complicate established methods. Particularly, limitations in fluorescence microscopy paired with muscular twitching in late-stage embryonic C. elegans yield adversarial point-set matching tasks. Seam cell identification is cast as an assignment problem; detected cells in images are uniquely identified through a combinatorial optimization algorithm. Existing graph matching methods are underequipped to contextualize the coiled embryonic position in sparsely imaged samples. Both the lack of an effective point-set matching model and an efficient algorithm for solving the resulting optimization problem limit computationally driven solutions to identify seam cells in acquired image volumes. We cast the n-adic problem as hypergraph matching and present an exact algorithm to solve the resulting optimization problem. EHGM adapts the branch-and-bound paradigm to dynamically identify a globally optimal correspondence; it is the first algorithm capable of solving the underlying optimization problem. Our algorithm and accompanying data-driven hypergraphical models identify seam cells more accurately than established point-set matching methods. The final hours of embryogenesis encompass the moments in which C. elegans assumes motor control and begins exhibiting behavior. Rapid imaging of the seam cells provides insight into the embryo’s movement as a proxy for behavior. However, seam cell tracking is especially challenging due to both muscular twitching and the low dose required to gently image the embryo without perturbing development. Current methods in MOT rely on independent object trajectories undergoing smooth motion to effectively track large numbers of objects. Multiple Hypothesis Tracking (MHT) is the foremost method for challenging MOT tasks, yet the method cannot model correlated object movements. We contribute Multiple Hypothesis Hypergraph Tracking (MHHT) as an extension of MHT, which performs interdependent object tracking by jointly representing objects as a hypergraph. We apply MHHT to track seam cell nuclei during late-stage embryogenesis. Data-driven hypergraphical models more accurately track seam cells than traditional MHT based approaches. Analysis of time-lapse embryonic postures and behavioral motifs reveal a stereotyped developmental progression in C. elegans. Further analysis uncovers late-stage motility defects in unc-13 mutants

Multiple structure recovery with T-linkage

reserved2noThis work addresses the problem of robust fitting of geometric structures to noisy data corrupted by outliers. An extension of J-linkage (called T-linkage) is presented and elaborated. T-linkage improves the preference analysis implemented by J-linkage in term of performances and robustness, considering both the representation and the segmentation steps. A strategy to reject outliers and to estimate the inlier threshold is proposed, resulting in a versatile tool, suitable for multi-model fitting “in the wild”. Experiments demonstrate that our methods perform better than J-linkage on simulated data, and compare favorably with state-of-the-art methods on public domain real datasets.mixedMagri L.; Fusiello A.Magri, L.; Fusiello, A