Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is a simpler problem than the comparison of 3D surfaces by traditional shape matching methods that require pose registration, feature correspondence, or model fitting. We find that the dissimilarities be...

this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting

Example-based methods are effective for parameter estimation problems when the underlying system is simple or the dimensionality of the input is low. For complex and high-dimensional problems such as pose estimation, the number of required examples and the computational complexity rapidly become prohibitively high. We introduce a new algorithm that learns a set of hashing functions that efficiently index examples relevant to a particular estimation task. Our algorithm extends a recently developed method for locality-sensitive hashing, which finds approximate neighbors in time sublinear in the number of examples. This method depends critically on the choice of hash functions; we show how to find the set of hash functions that are optimally relevant to a particular estimation problem. Experiments demonstrate that the resulting algorithm, which we call Parameter-Sensitive Hashing, can rapidly and accurately estimate the articulated pose of human figures from a large database of example images. 1.

. Pairwise geometric histograms have been demonstrated as an effective descriptor of arbitrary 2-dimensional shape which enable robust and efficient object recognition in complex scenes. In this paper we describe how the approach can be extended to allow the representation and classification of arbitrary 2 1 2 - and 3-dimensional surface shape. This novel representation can be used in important vision tasks such as the recognition of objects with complex free-form surfaces and the registration of surfaces for building 3-dimensional models from multiple views. We apply this new representation to both of these tasks and present some promising results. 1 Introduction Finding a correspondence between two or more surfaces is a frequently encountered problem in many computer vision tasks. When surface based descriptions are used for object recognition, the hypothesis that a particular object is in a scene is confirmed by finding a good correspondence between scene and model surfaces [6]. W...

Abstract—The histogram of image intensities is used extensively for recognition and for retrieval of images and video from visual databases. A single image histogram, however, suffers from the inability to encode spatial image variation. An obvious way to extend this feature is to compute the histograms of multiple resolutions of an image to form a multiresolution histogram. The multiresolution histogram shares many desirable properties with the plain histogram including that they are both fast to compute, space efficient, invariant to rigid motions, and robust to noise. In addition, the multiresolution histogram directly encodes spatial information. We describe a simple yet novel matching algorithm based on the multiresolution histogram that uses the differences between histograms of consecutive image resolutions. We evaluate it against five widely used image features. We show that with our simple feature we achieve or exceed the performance obtained with more complicated features. Further, we show our algorithm to be the most efficient and robust.

This paper presents a new compact shape representation for retrieving line-patterns from large databases. The basic idea is to exploit both geometric attributes and structural information to construct a shape histogram. We realize this goal by computing the N-nearest neighbor graph for the lines-segments for each pattern. The edges of the neighborhood graphs are used to gate contributions to a two-dimensional pairwise geometric histogram. Shapes are indexed by searching for the line-pattern that maximizes the cross correlation of the normalized histogram bin-contents. We evaluate the new method on a database containing over 2,500 line-patterns each composed of hundreds of lines.

This paper is concerned with the retrieval of images from large databases based on their shape similarity to a query image. Our approach is based on two dimensional histograms that encode both the local and global geometric properties of the shapes. The pairwise attributes are the directed segment relative angle and directed relative position. The novelty of the proposed approach is to simultaneously use the relational and structural constraints, derivedfrom an adjacency graph, to gate histogram contributions. We investiguate the retrieval capabilities of the methodfor various queries. We also investigate the robustness of the methodtosegmentation errors. We conclude that a relational histogram of pairwise segment attributes presents a very efficient way of indexing into large databases. The optimal configuration is obtainedwhen the local features are constructed from six neighbouring segments pairs. Moreover, a sensitivity analysis reveals that segmentation errors do not affect the ...

The design of a specialised query language for content based image retrieval (CBIR) provides a means of addressing many of the problems associated with commonly used query paradigms such as query-by-example and query-by-sketch. By basing such a language on an extensible ontology which encompasses both high-level and low-level image properties and relations, one can go a long way towards bridging the semantic gap between user models of saliency and relevance and those employed by a retrieval system.

This paper presents a new similarity measure for object recognition from large libraries of line-patterns. The measure draws its inspiration from both the Hausdorff distance and a recently reported Bayesian consistency measure that has been sucessfully used for graphbased correspondence matching. The measure uses robust error-kernels to gauge the similarity of pairwise attribute relations defined on the edges of nearest neighbour graphs. We use the similarity measure in a recognition experiment which involves a library of over 1000 line-patterns. A sensitivity study reveals that the method is capable of delivering a recognition accuracy of 98%. A comparative study reveals that the method is most effective when a Gaussian kernel or Huber's robust kernel is used to weight the attribute relations. Moreover, the method consistently outperforms Rucklidge 's median Hausdorff distance. 1 Introduction Object recognition from large libraries of images holds the key to the automatic manipulati...

N.A.Thacker The purpose of this report is to introduce some basic concepts of probability and statistics necessary