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Shock Graphs and Shape Matching
, 1998
"... We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a ..."
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Cited by 207 (34 self)
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We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...
Visibility, Occlusion, and the Aspect Graph
, 1987
"... In this paper we study the ways in which the topology of the image of a polyhedron changes with changing viewpoint. We catalog the ways that the topological appearance, or aspect, can change. This enables us to find maximal regions of viewpoints of the same aspect. We use these techniques to constru ..."
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Cited by 88 (7 self)
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In this paper we study the ways in which the topology of the image of a polyhedron changes with changing viewpoint. We catalog the ways that the topological appearance, or aspect, can change. This enables us to find maximal regions of viewpoints of the same aspect. We use these techniques to construct the viewpoint space partition (VSP), a partition of viewpoint space into maximal regions of constant aspect, and its dual, the aspect graph. In this paper we present tight bounds on the maximum size of the VSP and the aspect graph and give algorithms for their construction, first in the convex case and then in the general case. In particular, we give bounds on the maximum size of Q(n 2 ) and Q (n 6 ) under an orthographic projection viewing model and of Q(n 3 ) and Q(n 9 ) under a perspective viewing model. The algorithms make use of a new representation of the appearance of polyhedra from all viewpoints, called the aspect representation or asp. We believe that this representation...
ViewBased Object Recognition Using Saliency Maps
, 1998
"... We introduce a novel viewbased object representation, called the saliency map graph (SMG), which captures the salient regions of an object view at multiple scales using a wavelet transform. This compact representation is highly invariant to translation, rotation (image and depth), and scaling, and ..."
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Cited by 49 (9 self)
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We introduce a novel viewbased object representation, called the saliency map graph (SMG), which captures the salient regions of an object view at multiple scales using a wavelet transform. This compact representation is highly invariant to translation, rotation (image and depth), and scaling, and offers the locality of representation required for occluded object recognition. To compare two saliency map graphs, we introduce two graph similarity algorithms. The first computes the topological similarity between two SMG's, providing a coarselevel matching of two graphs. The second computes the geometrical similarity between two SMG's, providing a finelevel matching of two graphs. We test and compare these two algorithms on a large database of model object views.
A similaritybased aspectgraph approach to 3d object recognition
 International Journal of Computer Vision
, 2004
"... Abstract. This paper describes a viewbased method for recognizing 3D objects from 2D images. We employ an aspectgraph structure, where the aspects are not based on the singularities of visual mapping but are instead formed using a notion of similarity between views. Specifically, the viewing spher ..."
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Cited by 25 (0 self)
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Abstract. This paper describes a viewbased method for recognizing 3D objects from 2D images. We employ an aspectgraph structure, where the aspects are not based on the singularities of visual mapping but are instead formed using a notion of similarity between views. Specifically, the viewing sphere is endowed with a metric of dissimilarity for each pair of views and the problem of aspect generation is viewed as a ”segmentation ” of the viewing sphere into homogeneous regions. The viewing sphere is sampled at regular (5 degree) intervals and an iterative procedure is used to combine views using the metric into aspects with a prototype representing each aspect, in a ”regiongrowing ” regime which stands in contrast to the usual ”edge detection ” styles to computing the aspect graph. The aspect growth is constrained such that two aspects of an object remain distinct under the given similarity metric. Once the database of 3D objects is organized as a set of aspects and prototypes for these aspects for each object, unknown views of database objects are compared with the prototypes and the results are ordered by similarity. We use two similarity metrics for shape, one based on curve matching and the other based on matching shock graphs, which for a database of 64 objects and unknown views of objects for the database give (90.3%, 74.2%, 59.7%) and (95.2%, 69.0%, 57.5%), respectively, for the top three matches; identification based on the top three matches is 98 % and 100%, respectively. The result of indexing unknown views of objects not in the database also produce intuitive matches. We also develop a hierarchical indexing scheme the goal of which is to prune unlikely objects at an early stage to improve the efficiency of indexing, resulting in savings of 35 % at the top level and of 55 % at the next level, cumulatively. 1.
Adaptive Tracking and Model Registration Across Distinct Aspects
 in International Conference on Intelligent Robots and Systems
, 1995
"... A model registration system capable of tracking an object through distinct aspects in realtime is presented. The system integrates tracking, pose determination, and aspect graph indexing. The tracking combines steerable filters with normalized crosscorrelation, compensates for rotation in 2D and is ..."
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Cited by 20 (5 self)
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A model registration system capable of tracking an object through distinct aspects in realtime is presented. The system integrates tracking, pose determination, and aspect graph indexing. The tracking combines steerable filters with normalized crosscorrelation, compensates for rotation in 2D and is adaptive. Robust statistical methods are used in the pose estimation to detect and remove mismatches. The aspect graph is used to determine when features will disappear or become difficult to track and to predict when and where new features will become trackable. The overall system is stable and is amenable to realtime performance. 1 Introduction Maintaining object registration over time (tempo ral registration) can be defined as the ability to retain uptodate objectsensor pose relationships over relative motion. Registration is useful in several domains; as an example consider enhanced reality applications such as an interactive repair manual. In this application technicians look th...
A Computational Model of View Degeneracy
, 1999
"... We quantify the observation by Kender and Freudenstein [24] that degenerate views occupy a significant fraction of the viewing sphere surrounding an object. For a perspective camera geometry ,we introduce a computational model that can be used to estimate the probability that a view degeneracy will ..."
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Cited by 6 (2 self)
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We quantify the observation by Kender and Freudenstein [24] that degenerate views occupy a significant fraction of the viewing sphere surrounding an object. For a perspective camera geometry ,we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a poly hedral object. For a ty5 cal recognition sy stem parameterization,view degeneracies ty pically occur with probabilities of 20% and,depending on the parameterization,as high as 50%. We discuss the impact of view degeneracy on the problem of object recognition and,for a particular recognition framework, relate the cost of object disambiguation to the probability of view degeneracy . To reduce this cost,we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view. In order to validate both our view degeneracy model as well as our active focal length control m...
Progress in Computer Vision at the University of Massachusetts
, 1994
"... 1 This report summarizes progress in image understanding research at the University of Massachusetts over the past year. Many of the individual efforts discussed in this paper are further developed in other papers in this proceedings. The summary is organized into several areas: 1. Mobile Robot Navi ..."
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Cited by 5 (3 self)
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1 This report summarizes progress in image understanding research at the University of Massachusetts over the past year. Many of the individual efforts discussed in this paper are further developed in other papers in this proceedings. The summary is organized into several areas: 1. Mobile Robot Navigation 2. Motion and Stereo Processing 3. KnowledgeBased Interpretation of Static Scenes 4. Image Understanding Architecture The research program in computer vision at UMass has as one of its goals the integration of a diverse set of research efforts into a system that is ultimately intended to achieve realtime image interpretation in a variety of vision applications. 1. Mobile Robot Navigation The initial focus of the mobile robot navigation project (Fennema and Hanson 1990b) has been on the development of a system for goal oriented navigation through a partially modeled, unchanging environment which contains no unmodeled obstacles. This simplified environment is intended to provide a fou...