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Efficient Hypergraph Clustering
"... Data clustering is an essential problem in data mining, machine learning and computer vision. In this paper we present a novel method for the hypergraph clustering problem, in which second or higher order affinities between sets of data points are considered. Our algorithm has important theoretical ..."
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Data clustering is an essential problem in data mining, machine learning and computer vision. In this paper we present a novel method for the hypergraph clustering problem, in which second or higher order affinities between sets of data points are considered. Our algorithm has important theoretical properties, such as convergence and satisfaction of first order necessary optimality conditions. It is based on an efficient iterative procedure, which by updating the cluster membership of all points in parallel, is able to achieve state of the art results in very few steps. We outperform current hypergraph clustering methods especially in terms of computational speed, but also in terms of accuracy. Moreover, we show that our method could be successfully applied both to higherorder assignment problems and to image segmentation. 1
RealTime Exact Graph Matching with Application in Human Action Recognition
"... Abstract. Graph matching is one of the principal methods to formulate the correspondence between two set of points in computer vision and pattern recognition. However, most formulations are based on the minimization of a difficult energy function which is known to be NPhard. Traditional methods sol ..."
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Abstract. Graph matching is one of the principal methods to formulate the correspondence between two set of points in computer vision and pattern recognition. However, most formulations are based on the minimization of a difficult energy function which is known to be NPhard. Traditional methods solve the minimization problem approximately. In this paper, we show that an efficient solution can be obtained by exactly solving an approximated problem instead of approximately solving the original problem. We derive an exact minimization algorithm and successfully applied to action recognition in videos. In this context, we take advantage of special properties of the time domain, in particular causality and the linear order of time, and propose a novel spatiotemporal graphical structure. Keywords: Spacetime graph, Hypergraph matching, Action recognition 1
Fast exact matching and correspondence with hypergraphs on spatiotemporal data
, 2012
"... Graphs and hypergraphs are frequently used to recognize complex and often nonrigid patterns in computer vision, either through graph matching or pointset matching with graphs. Most formulations resort to the minimization of a difficult energy function containing geometric or structural terms, fre ..."
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Graphs and hypergraphs are frequently used to recognize complex and often nonrigid patterns in computer vision, either through graph matching or pointset matching with graphs. Most formulations resort to the minimization of a difficult energy function containing geometric or structural terms, frequently coupled with data attached terms involving appearance information. Traditional methods solve the minimization problem approximately, for instance with spectral techniques. In this paper we deal with data embedded in a 3D ”spacetime”, for instance in action recognition applications. We show that, in this context, we can take advantage of special properties of the time domain, in particular causality and the linear order of time. We show that the complexity of the exact matching problem is far inferior to the complexity of the general problem and we derive an algorithm calculating the exact solution. As a second contribution, we propose a new graphical structure which is elongated in time. We argue that, instead of approximately solving the original problem, a better solution can be obtained by exactly solving an approximated problem. An exact minimization algorithm is derived for this structure and successfully applied to action recognition in videos.
Joint optimization for consistent multiple graph matching
 IN: ICCV
, 2013
"... The problem of graph matching in general is NPhard and approaches have been proposed for its suboptimal solution, most focusing on finding the onetoone node mapping between two graphs. A more general and challenging problem arises when one aims to find consistent mappings across a number of grap ..."
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The problem of graph matching in general is NPhard and approaches have been proposed for its suboptimal solution, most focusing on finding the onetoone node mapping between two graphs. A more general and challenging problem arises when one aims to find consistent mappings across a number of graphs more than two. Conventional graph pair matching methods often result in mapping inconsistency since the mapping between two graphs can either be determined by pair mapping or by an additional anchor graph. To address this issue, a novel formulation is derived which is maximized via alternating optimization. Our method enjoys several advantages: 1) the mappings are jointly optimized rather than sequentially performed by applying pair matching, allowing the global affinity information across graphs can be propagated and explored; 2) the number of concerned variables to optimize is in linear with the number of graphs, being superior to local pair matching resulting in O(n2) variables; 3) the mapping consistency constraints are analytically satisfied during optimization; and 4) offtheshelf graph pair matching solvers can be reused under the proposed framework in an ‘outofthebox’ fashion. Competitive results on both the synthesized data and the real data are reported, by varying the level of deformation, outliers and edge densities.
Graduated ConsistencyRegularized Optimization for Multigraph Matching
"... Abstract. Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NPhard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more genera ..."
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Abstract. Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NPhard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more general problem of matching N attributed graphs to each other, i.e. labeling their common node correspondences such that a certain compatibility/affinity objective is optimized. This multigraph matching problem involves two key ingredients affecting the overall accuracy: a) the pairwise affinity matching score between two local graphs, and b) global matching consistency that measures the uniqueness and consistency of the pairwise matching results by different sequential matching orders. Previous work typically either enforces the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across different graph pairs; or separates score optimizing and consistency synchronization in two steps. This paper is motivated by the observation that affinity score and consistency are mutually affected and shall be tackled jointly to capture their correlation behavior. As such, we propose a novel multigraph matching algorithm to incorporate the two aspects by iteratively approximating the globaloptimal affinity score, meanwhile gradually infusing the consistency as a regularizer, which improves the performance of the initial solutions obtained by existing pairwise graph matching solvers. The proposed algorithm with a theoretically proven convergence shows notable efficacy on both synthetic and public image datasets. 1
Graphbased inference with constraints for object detection and segmentation
, 2013
"... For many fundamental problems of computer vision, adopting a graphbased framwork can be straightforward and very effective. In this thesis, I propose several graphbased inference methods tailored for different computer vision applications. It starts from studying contourbased object detection me ..."
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For many fundamental problems of computer vision, adopting a graphbased framwork can be straightforward and very effective. In this thesis, I propose several graphbased inference methods tailored for different computer vision applications. It starts from studying contourbased object detection methods. Compared to other image cues, the outline contour (silhouette) is invariant to lighting conditions and variations in object color and texture. More importantly, it can efficiently represent image structures with large spatial extents. Because of these advantages, contour information is widely used in object detection and recognition methods. However, the contourbased methods mainly suffer from the fact that the contour is not very distinctive and informative, especially when considered locally. We made several efforts to address this problem. The first effort we made is not directly related to graphbased modeling but rather to increase the distinctness of contour matching. We propose a novel technique that significantly improves the performance of oriented chamfer matching on images with cluttered background. Different to other matching methods, which only measures how well a template fits to an edge map, we evaluate
GraphBased Deformable 3D Object Matching
, 2015
"... We present a method for efficient detection of deformed 3D objects in 3D point clouds that can handle large amounts of clutter, noise, and occlusion. The method generalizes well to different object classes and does not require an explicit deformation model. Instead, deformations are learned based ..."
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We present a method for efficient detection of deformed 3D objects in 3D point clouds that can handle large amounts of clutter, noise, and occlusion. The method generalizes well to different object classes and does not require an explicit deformation model. Instead, deformations are learned based on a few registered deformed object instances. The approach builds upon graph matching to find correspondences between scene and model points. The robustness is increased through a parametrization where each graph vertex represents a full rigid transformation. We speed up the matching through greedy multistep graph pruning and a constanttime feature matching. Quantitative and qualitative experiments demonstrate that our method is robust, efficient, able to detect rigid and nonrigid objects and exceeds state of the art.
Spectral Norm Regularization of Orthonormal Representations for
"... Recent literature [1] suggests that embedding a graph on an unit sphere leads to better generalization for graph transduction. However, the choice of optimal embedding and an efficient algorithm to compute the same remains open. In this paper, we show that orthonormal representations, a class of un ..."
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Recent literature [1] suggests that embedding a graph on an unit sphere leads to better generalization for graph transduction. However, the choice of optimal embedding and an efficient algorithm to compute the same remains open. In this paper, we show that orthonormal representations, a class of unitsphere graph embeddings are PAC learnable. Existing PACbased analysis do not apply as the VC dimension of the function class is infinite. We propose an alternative PACbased bound, which do not depend on the VC dimension of the underlying function class, but is related to the famous Lovász ϑ function. The main contribution of the paper is SPORE, a SPectral regularized ORthonormal Embedding for graph transduction, derived from the PAC bound. SPORE is posed as a nonsmooth convex function over an elliptope. These problems are usually solved as semidefinite programs (SDPs) with time complexity O(n6). We present, Infeasible Inexact proximal (IIP): an Inexact proximal method which performs subgradient procedure on an approximate projection, not necessarily feasible. IIP is more scalable than SDP, has an O ( 1√ T) convergence, and is generally applicable whenever a suitable approximate projection is available. We use IIP to compute SPORE where the approximate projection step is computed by FISTA, an accelerated gradient descent procedure. We show that the method has a convergence rate of O ( 1√ T The proposed algorithm easily scales to 1000’s of vertices, while the standard SDP computation does not scale beyond few hundred vertices. Furthermore, the analysis presented here easily extends to the multiple graph setting. 1