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227
Shape Matching and Object Recognition Using Shape Contexts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform ..."
Abstract

Cited by 1255 (19 self)
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We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape con texts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; reg ularized thin plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning trans form. We treat recognition in a nearestneighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.
Svmknn: Discriminative nearest neighbor classification for visual category recognition
 in CVPR
, 2006
"... We consider visual category recognition in the framework of measuring similarities, or equivalently perceptual distances, to prototype examples of categories. This approach is quite flexible, and permits recognition based on color, texture, and particularly shape, in a homogeneous framework. While n ..."
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Cited by 211 (7 self)
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We consider visual category recognition in the framework of measuring similarities, or equivalently perceptual distances, to prototype examples of categories. This approach is quite flexible, and permits recognition based on color, texture, and particularly shape, in a homogeneous framework. While nearest neighbor classifiers are natural in this setting, they suffer from the problem of high variance (in biasvariance decomposition) in the case of limited sampling. Alternatively, one could use support vector machines but they involve timeconsuming optimization and computation of pairwise distances. We propose a hybrid of these two methods which deals naturally with the multiclass setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice. The basic idea is to find close neighbors to a query sample and train a local support vector machine that preserves the distance function on the collection of neighbors. Our method can be applied to large, multiclass data sets for which it outperforms nearest neighbor and support vector machines, and remains efficient when the problem becomes intractable for support vector machines. A wide variety of distance functions can be used and our experiments show stateoftheart performance on a number of benchmark data sets for shape and texture classification (MNIST, USPS, CUReT) and object recognition (Caltech101). On Caltech101 we achieved a correct classification rate of 59.05%(±0.56%) at 15 training images per class, and 66.23%(±0.48%) at 30 training images. 1.
The calculi of emergence: Computation, dynamics, and induction
 Physica D
, 1994
"... Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how modelbuilding observers infer from measurements the computational capabilities embedded ..."
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Cited by 79 (14 self)
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Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how modelbuilding observers infer from measurements the computational capabilities embedded in nonlinear processes. An observer’s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference. The discovery of structure in an environment depends more critically and subtlely, though, on how those resources are organized. The descriptive power of the observer’s chosen (or implicit) computational model class, for example, can be an overwhelming determinant in finding regularity in data. This paper presents an overview of an inductive framework — hierarchicalmachine reconstruction — in which the emergence of complexity is associated with the innovation of new computational model classes. Complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. Illustrative examples are drawn from the onset of unpredictability in nonlinear systems, finitary nondeterministic processes, and
Developmental Models of Herbaceous Plants for Computer Imagery Purposes
, 1988
"... In this paper we present a method for modeling herbaceous plants, suitable for generating realistic plant images and animating developmental processes. The idea is to achieve realism by simulating mechanisms which control plant growth in nature. The developmental approach to the modeling of plant a ..."
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Cited by 76 (10 self)
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In this paper we present a method for modeling herbaceous plants, suitable for generating realistic plant images and animating developmental processes. The idea is to achieve realism by simulating mechanisms which control plant growth in nature. The developmental approach to the modeling of plant architecture is extended to the modeling of leaves and flowers. The method is expressed using the formalism of Lsystems.
Surface matching via currents
 IPMI 2005. LNCS
, 2005
"... Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriat ..."
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Cited by 63 (1 self)
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Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural transformation properties from differential forms. We impose a Hilbert space structure on currents, whose norm gives a convenient and practical way to define a matching functional. Using this Hilbert space norm, we also derive and implement a surface matching algorithm under the large deformation framework, guaranteeing that the optimal solution is a onetoone regular map of the entire ambient space. We detail an implementation of this algorithm for triangular meshes and present results on 3D face and medical image data. 1
Voxelbased morphometry using the ravens maps: Methods and validation using simulated longitudinal atrophy
 NeuroImage
, 2001
"... Statistical analysis of anatomical maps in a stereotaxic space has been shown to be a useful tool in populationbased studies for quantifying local anatomical differences or changes, without a priori assumptions about the location and extent of the regions of interest. This paper presents an extensi ..."
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Cited by 57 (17 self)
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Statistical analysis of anatomical maps in a stereotaxic space has been shown to be a useful tool in populationbased studies for quantifying local anatomical differences or changes, without a priori assumptions about the location and extent of the regions of interest. This paper presents an extension and validation of a previously published methodology, referred to as RAVENS, for characterizing regional atrophy in the brain. A new method for elastic, volumepreserving spatial normalization, which allows for accurate quantification of very localized atrophy, is used. The RAVENS methodology was tested on images with simulated atrophy within two gyri: precentral and superior temporal. It was found to accurately determine the regions of atrophy, despite their localized nature and the interindividual variability of cortical structures. Moreover, it was found to perform substantially better than the voxelbased morphology method of SPM’99. Improved sensitivity was achieved at the expense of human effort involved in defining a number of sulcal curves that serve as constraints on the 3D elastic warping. © 2001 Academic Press
Computational anatomy: Shape, growth, and atrophy comparison via diffeomorphisms
 NeuroImage
, 2004
"... Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examine ..."
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Cited by 50 (2 self)
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Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g a G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(d) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.
Face Verification across Age Progression
 in Proc. IEEE Conf. Computer Vision and Pattern Recognition
, 2005
"... Abstract—Human faces undergo considerable amounts of variations with aging. While face recognition systems have been proven to be sensitive to factors such as illumination and pose, their sensitivity to facial aging effects is yet to be studied. How does age progression affect the similarity between ..."
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Cited by 46 (6 self)
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Abstract—Human faces undergo considerable amounts of variations with aging. While face recognition systems have been proven to be sensitive to factors such as illumination and pose, their sensitivity to facial aging effects is yet to be studied. How does age progression affect the similarity between a pair of face images of an individual? What is the confidence associated with establishing the identity between a pair of age separated face images? In this paper, we develop a Bayesian age difference classifier that classifies face images of individuals based on age differences and performs face verification across age progression. Further, we study the similarity of faces across age progression. Since age separated face images invariably differ in illumination and pose, we propose preprocessing methods for minimizing such variations. Experimental results using a database comprising of pairs of face images that were retrieved from the passports of 465 individuals are presented. The verification system for faces separated by as many as nine years, attains an equal error rate of 8.5%. Index Terms—Age progression, face recognition, face verification, probabilistic eigenspaces, similarity measure. I.
Matching with shape contexts
 IEEE Workshop on Contentbased access of Image and VideoLibraries
, 2000
"... Summary. We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solving for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning tr ..."
Abstract

Cited by 42 (2 self)
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Summary. We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solving for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin–plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearestneighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. We also demonstrate that shape contexts can be used to quickly prune a search for similar shapes. We present two algorithms for rapid shape retrieval: representative shape contexts, performing comparisons based on a small number of shape contexts, and shapemes, using vector quantization in the space of shape contexts to obtain prototypical shape pieces. Results are presented for silhouettes, handwritten digits and visual CAPTCHAs. 1
Is Anything Ever New? Considering Emergence
 IN
, 1994
"... This brief essay reviews an approach to defining and then detecting the emergence of complexity in nonlinear processes. It is, in fact, a synopsis of Reference [1] that leaves out the technical details in an attempt to clarify the motivations behind the approach. The central puzzle ..."
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Cited by 35 (4 self)
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This brief essay reviews an approach to defining and then detecting the emergence of complexity in nonlinear processes. It is, in fact, a synopsis of Reference [1] that leaves out the technical details in an attempt to clarify the motivations behind the approach. The central puzzle