coherent states on the circle a careful study of the physical properties of a family of coherent states on the circle introduced some years ago by de bievre and gonzalez in 1992 semiclassical behaviour of the weyl correspondence on the circle group theoretical methods in physics vol i madrid ciemat is carried out they were obtained from the weyl heisenberg coherent states in by means of the weil brezin zak transformation they are labelled by the points of the cylinder and they provide a realization of by entire functions similar to the well known fock bargmann construction in particular we compute the expectation values of the position and momentum operators on the circle and we discuss the heisenberg uncertainty relation

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

the segal bargmann coherent state transform for compact lie groups abstract let k be an arbitrary compact connected lie group we describe on k an analog of the segal bargmann coherent state transform and we prove theorem 1 that this generalized coherent state transform maps l 2 k isometrically onto the space of holomorphic functions in l 2 g where g is the complexification of k and where is an appropriate heat kernel measure on g the generalized coherent state transform is defined in terms of the heat kernel on the compact group k and its analytic continuation to the complex group g we also define a k averaged version of the coherent state transform and we prove a similar result for it theorem 2 in the appendix we describe the coherent states which motivate the definitions of these transforms in section 9 we obtain inversion formulas for both the coherent state transform and the k averaged coherent state transform theorems 3 4 as a consequence we obtain formulas for certain bergman kernels on the complex group g theorems 5 6 in section 10 we derive a general paley wiener theorem for k and we exhibit a family of convolution transforms each of which is an isometric isomorphism of l 2 k onto a certain l 2 space of holomorphic functions on g these transforms include the k averaged coherent state transform as a special case we also discuss the analogous results for r 1 the results of section 10 are theorems 7 10 finally in section 11 we discuss the case of quotient spaces we prove theorem 11 that both the coherent state transform and the k averaged coherent state transform pass in a natural way from k to k h where h is a closed connected subgroup of k

constructing descriptive and discriminative nonlinear features rayleigh coefficients in kernel feature spaces we incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination employing a unified framework in terms of a nonlinearized variant of the rayleigh coefficient we propose nonlinear generalizations of fisher s discriminant and oriented pca using support vector kernel functions extensive simulations show the utility of our approach

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

coherent states for a quantum particle on a circle the coherent states for a quantum particle on a circle are introduced the bargmann representation within the actual treatment provides the representation of the algebra where u is unitary which is a direct consequence of the heisenberg algebra but it is more adequate for the study of circular motion

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

learning smooth pattern transformation manifolds manifold models provide low dimensional representations that are useful for processing and analyzing data in a transformation invariant way in this paper we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals to construct a manifold we build a representative pattern whose transformations accurately fit various input images we examine two objectives of the manifold building problem namely approximation and classification for the approximation problem we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold we present a dc optimization scheme that is applicable to a wide range of transformation and dictionary models and demonstrate its application to the transformation manifolds generated by the rotation translation and anisotropic scaling of a reference pattern then we generalize this approach to a setting with multiple transformation manifolds where each manifold represents a different class of signals we present an iterative multiple manifold building algorithm such that the classification accuracy is promoted in the learning of the representative patterns the experimental results suggest that the proposed methods yield high accuracy in the approximation and classification of data compared with some reference methods while the invariance to geometric transformations is achieved because of the transformation manifold model

surface signatures an orientation independent free form surface representation scheme for the purpose of objects registration and matching this paper introduces anew free form surface representation scheme for the purpose of fast and accurate registration and matching accurate registration of surfaces is a common task in computer vision the proposed representation scheme captures the surface curvature information seen from certain points and produces images called surface signatures at these points matching signatures of different surfaces enables the recovery of the transformation parameters between these surfaces we propose using template matching to compare the signature images to enable partial matching another criterion the overlap ratio is used this representation scheme can be used as a global representation of the surface as well as a local one and performs near real time registration we show that the signature representation can be used to recover scaling transformation as well as matching objects in 3d scenes in the presence of clutter and occlusion applications presented include free form object matching multimodal medical volumes registration and dental teeth reconstruction from intraoral images

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

coherent states for the quantum mechanics on a compact manifold we review our recent observations concerning quantum mechanics on such compact manifolds as a circle torus and sphere

on the repeatability and quality of keypoints for local feature based 3d object retrieval from cluttered scenes 3d object recognition from local features is robust to occlusions and clutter however local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features we present an algorithm for the detection of such keypoints on 3d models and partial views of objects the keypoints are highly repeatable between partial views of an object and its complete 3d model we also propose a quality measure to rank the keypoints and select the best ones for extracting local features keypoints are identified at locations where a unique local 3d coordinate basis can be derived from the underlying surface in order to extract invariant features we also propose an automatic scale selection technique for extracting multi scale and scale invariant features to match objects at different unknown scales features are projected to a pca subspace and matched to find correspondences between a database and query object each pair of matching features gives a transformation that aligns the query and database object these transformations are clustered and the biggest cluster is used to identify the query object experiments on a public database revealed that the proposed quality measure relates correctly to the repeatability of keypoints and the multi scale features have a recognition rate of over 95 for up to 80 occluded objects

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

fast fourier transform and singular value decomposition formulations for patch nearfield acoustical holography nearfield acoustical holography nah requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface the latter generally coincident with a vibrator patch nah provides a major simplification by eliminating the need for complete surface pressure scans only a small area needs to be scanned to determine the normal velocity on the corresponding small area concentric patch on the vibrator the theory of patch nah is based on 1 an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and 2 a decomposition of the transfer function pressure to velocity and or pressure to pressure between the two surfaces using the singular value decomposition svd for general shapes and the fast fourier transform fft for planar surfaces inversion of the transfer function is stabilized using tikhonov regularization and the morozov discrepancy principle experimental results show that root mean square errors of the normal velocity reconstruction for a point driven vibrator over 200 2700 hz average less than 20 for two small concentric patch surfaces 0 4 cm apart reconstruction of the active normal acoustic intensity was also successful with less than 30 error over the frequency band

analytic pca construction for theoretical analysis of lighting variability in images of a lambertian object we analyze theoretically the subspace best approximating images of a convex lambertian object taken from the same viewpoint but under different distant illumination conditions we analytically construct the principal component analysis for images of a convex lambertian object explicitly taking attached shadows into account and find the principal eigenmodes and eigenvalues with respect to lighting variability our analysis makes use of an analytic formula for the irradiance in terms of spherical harmonic coefficients of the illumination and shows under appropriate assumptions that the principal components or eigenvectors are identical to the spherical harmonic basis functions evaluated at the surface normal vectors our main contribution is in extending these results to the single viewpoint case showing how the principal eigenmodes and eigenvalues are affected when only a limited subset the upper hemisphere of normals is available and the spherical harmonics are no longer orthonormal over the restricted domain our results are very close both qualitatively and quantitatively to previous empirical observations and represent the first essentially complete theoretical explanation of these observations

on the position uncertainty measure on the circle new position uncertainty delocalization measures for a particle on the circle are proposed and illustrated in several examples where the previous measures based on 2 periodic position operators appear to be unsatisfactory the new measures are suitably constructed using the standard multiplication angle operator variances they are shown to depend solely on the state of the particle and to obey uncertainty relations of the schrodinger robertson type

the relationship of singular value decomposition to wave vector filtering in sound radiation problems singular value decomposition svd has recently been suggested as a filtering tool to analyze acoustic radiation the relationship between this filtering technique and the more familiar wave vector filtering is examined for a geometry with a preferred axis the source modes are found to consist approximately of a single wave number and the accompanying radiation modes are thus beams some simple examples are worked out to illustrate the general behavior of the filtering and some of the properties of the beams are given

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

on three dimensional surface reconstruction methods a survey is presented of some of the surface reconstruction methods that can be found in the literature the focus is on a small recent and important subset of the published reconstruction techniques the techniques are classified based on the surface representation used implicit versus explicit functions a study is made of the important aspects of the surface reconstruction techniques one aspect is the viewpoint invariance of the methods this is an important property if object recognition is the ultimate objective the robustness of the various methods is examined it is determined whether the parameter estimates are biased and the sensitivity to obscuration is addressed the latter two aspects are particularly important for fitting functions in the implicit form a detailed description is given of a parametric reconstruction method for three dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations this technique is invariant to rigid motion in dimensional space

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

a structural approach to representation of curved objects abstract representation of complex curved objects is still a challenging and difficult problem in this paper we present a scheme for multi level structural qualitative representation of object surfaces the analysis begins with local face based descriptions of object surfaces surface primitive graphs and global high level structural and qualitative features are derived from these local descriptions the final descriptions global feature graphs are based on the quasi convexity concavity structures incorporating quantized directional features of closed boundaries of cross sections along several directions the global feature graphs have the following properties 1 they provide a characterization of global structural qualitative properties of the object 2 the graphs are composed of a few components nodes and edges with rich features and give compact descriptions of the objects 3 the global feature graph representations are robust and qualitative in that they are not affected by geometrical quantitative properties of the shape such as curvatures length and position 4 the representation has clear and rigorous properties furthermore we present some theoretical basis for object recognition using the global features graphs

state extended uncertainty relations a scheme for construction of uncertainty relations for n observables and m states is presented several lowest order inequalities are displayed and briefly discussed for two states and and canonical observables the entangled extension of the heisenberg relation reads p 2 q 2 p 2 q 2

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

the segal bargmann transform on a symmetric space of compact type abstract we study the segal bargmann transform on a symmetric space x of compact type mapping l 2 x into holomorphic functions on the complexification x c we invert this transform by integrating against a dual heat kernel measure in the fibers of a natural fibration of x c over x we prove that the segal bargmann transform is an isometry from l 2 x onto the space of holomorphic functions on x c which are square integrable with respect to a natural measure these results extend those of b hall in the compact group case

3d face recognition with sparse spherical representations this paper addresses the problem of 3d face recognition using simultaneous sparse approximations on the sphere the 3d face point clouds are first aligned with a fully automated registration process they are then represented as signals on the 2 sphere in order to preserve depth and geometry information next we implement a dimensionality reduction process with simultaneous sparse approximations and subspace projection it permits to represent each 3d face by only a few spherical functions that are able to capture the salient facial characteristics and hence to preserve the discriminant facial information we eventually perform recognition by effective matching in the reduced space where linear discriminant analysis can be further activated for improved recognition performance the 3d face recognition algorithm is evaluated on the frgc v 1 0 data set where it is shown to outperform classical state of the art solutions that work with depth images

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

registration of partially overlapping surfaces by rejection of false point correspondences we present a new algorithm for the registration of three dimensional partially overlapping surfaces it is based on an efficient scheme for the rejection of false point correspondences correspondence outliers and does not require initial pose estimation or feature extraction an initial list of corresponding points is first derived using the regional properties of vertices on both surfaces from these point correspondences pairs of corresponding rigid triplets are formed the normal vectors at the vertices of each corresponding triplet are used to compute the candidate rotations by clustering the candidate rotation axes and candidate rotation angles separately a large number of false correspondences are eliminated and an approximate rotation is decided from which an approximate translation is also obtained finally the optimal transformation parameters are determined by further refining the estimated parameters in an iterative manner mathematical analysis and experimental results show that the registration process is fast and accurate even when the objects are regularly shaped and contain many regionally similar surface patches

integration of local and global geometrical cues for 3d face recognition we present a unified feature representation of 2 5d pointclouds and apply it to face recognition the representation integrates local and global geometrical cues in a single compact representation which makes matching a probe to a large database computationally efficient the global cues provide geometrical coherence for the local cues resulting in better descriptiveness of the unified representation multiple rank 0 tensors scalar features are computed at each point from its local neighborhood and from the global structure of the 2 5d pointcloud forming multiple rank 0 tensor fields the pointcloud is then represented by the multiple rank 0 tensor fields which are invariant to rigid transformations each local tensor field is integrated with every global field in a 2d histogram which is indexed by a local field in one dimension and a global field in the other dimension finally pca coefficients of the 2d histograms are concatenated into a single feature vector the representation was tested on frgc v2 0 data set and achieved 93 78 identification and 95 37 verification rate at 0 1 far

a spherical representation for recognition of free form surfaces introduces a new surface representation for recognizing curved objects the authors approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object the mesh is computed from the data by deforming a standard shaped mesh for example an ellipsoid until it fits the surface of the object the authors define local regularity constraints that the mesh must satisfy the authors then define a canonical mapping between the mesh describing the object and a standard spherical mesh a surface curvature index that is pose invariant is stored at every node of the mesh the authors use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene the authors show how the similarity between reference model and observed data can be evaluated and they show how the pose of the reference object in the observed scene can be easily computed using this representation the authors present results on real range images which show that this approach to modelling and recognizing 3d objects has three main advantages 1 it is applicable to complex curved surfaces that cannot be handled by conventional techniques 2 it reduces the recognition problem to the computation of similarity between spherical distributions in particular the recognition algorithm does not require any combinatorial search and 3 even though it is based on a spherical mapping the approach can handle occlusions and partial views

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

global shape invariants a solution for 3d free form object discrimination identification problem abstract a method for solving the 3d object recognition problem is described in this paper the method uses a new set of global features as discriminant parameters the general purpose of our approach is to achieve simplicity speed and efficiency by using global invariants for this two new global parameters are introduced which are invariant to rotation translation and scaling canonical length cl which provides an indirect measurement of object surface and weighted principal directions wpds corresponding to the meaningful normal directions of the object surface abundant experimentation has been conducted with a real world system in order to validate the method

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

three dimensional face recognition using shapes of facial curves we study shapes of facial surfaces for the purpose of face recognition the main idea is to 1 represent surfaces by unions of level curves called facial curves of the depth function and 2 compare shapes of surfaces implicitly using shapes of facial curves the latter is performed using a differential geometric approach that computes geodesic lengths between closed curves on a shape manifold these ideas are demonstrated using a nearest neighbor classifier on two 3d face databases florida state university and notre dame highlighting a good recognition performance

coherent states on spheres we describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d dimensional sphere sd the coherent states are labeled by points in the associated phase space t sd these coherent states are not of perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators we describe as well the segal bargmann representation for the system the associated unitary segal bargmann transform and a natural inversion formula although many of these results are in principle special cases of the results of hall and stenzel we give here a substantially different description based on ideas of thiemann and of kowalski and rembielinski all of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space we focus on the sphere case in order to carry out the calculations in a self contained and explicit way

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

interior sound field control using generalized singular value decomposition in the frequency domain the problem of controlling a sound field inside a region surrounded by acoustic control sources is considered inspired by the kirchhoff helmholtz integral the use of double layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers however the practical implementation of the kirchhoff helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions the present study investigates the potential of the generalized singular value decomposition gsvd to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields respectively a proper truncation of the singular basis provided by the gsvd factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial nyquist freq

three dimensional model based object recognition and segmentation in cluttered scenes viewpoint independent recognition of free form objects and their segmentation in the presence of clutter and occlusions is a challenging task we present a novel 3d model based algorithm which performs this task automatically and efficiently a 3d model of an object is automatically constructed offline from its multiple unordered range images views these views are converted into multidimensional table representations which we refer to as tensors correspondences are automatically established between these views by simultaneously matching the tensors of a view with those of the remaining views using a hash table based voting scheme this results in a graph of relative transformations used to register the views before they are integrated into a seamless 3d model these models and their tensor representations constitute the model library during online recognition a tensor from the scene is simultaneously matched with those in the library by casting votes similarity measures are calculated for the model tensors which receive the most votes the model with the highest similarity is transformed to the scene and if it aligns accurately with an object in the scene that object is declared as recognized and is segmented this process is repeated until the scene is completely segmented experiments were performed on real and synthetic data comprised of 55 models and 610 scenes and an overall recognition rate of 95 percent was achieved comparison with the spin images revealed that our algorithm is superior in terms of recognition rate and efficiency

capitalize on dimensionality increasing techniques for improving face recognition grand challenge performance this paper presents a novel pattern recognition framework by capitalizing on dimensionality increasing techniques in particular the framework integrates gabor image representation a novel multiclass kernel fisher analysis kfa method and fractional power polynomial models for improving pattern recognition performance gabor image representation which increases dimensionality by incorporating gabor filters with different scales and orientations is characterized by spatial frequency spatial locality and orientational selectivity for coping with image variabilities such as illumination variations the kfa method first performs nonlinear mapping from the input space to a high dimensional feature space and then implements the multiclass fisher discriminant analysis in the feature space the significance of the nonlinear mapping is that it increases the discriminating power of the kfa method which is linear in the feature space but nonlinear in the input space the novelty of the kfa method comes from the fact that 1 it extends the two class kernel fisher methods by addressing multiclass pattern classification problems and 2 it improves upon the traditional generalized discriminant analysis gda method by deriving a unique solution compared to the gda solution which is not unique the fractional power polynomial models further improve performance of the proposed pattern recognition framework experiments on face recognition using both the feret database and the frgc face recognition grand challenge databases show the feasibility of the proposed framework in particular experimental results using the feret database show that the kfa method performs better than the gda method and the fractional power polynomial models help both the kfa method and the gda method improve their face recognition performance experimental results using the frgc databases show that the proposed pattern recognition framework improves face recognition performance upon the bee baseline algorithm and the lda based baseline algorithm by large margins

similarity measures for convex polyhedra based on minkowski addition abstract in this paper we introduce and investigate similarity measures for convex polyhedra based on minkowski addition and inequalities for the mixed volume and volume related to the brunn minkowski theory all measures considered are invariant under translations furthermore some of them are also invariant under subgroups of the affine transformation group for the case of rotation and scale invariance we prove that to obtain the measures based on mixed volume it is sufficient to compute certain functionals only for a finite number of critical rotations the paper presents a theoretical framework for comparing convex shapes and contains a complexity analysis of the solution numerical implementations of the proposed approach are not discussed

automatic registration for 3d shapes using hybrid dimensionality reduction shape descriptions automatic registration for 3d shapes is an attractive problem in computer vision various registration algorithms based on different surface representations have been developed for this topic however most of the existing algorithms suffer from some limitations mainly related to discriminating similarity metric partially overlapping data and the robustness to resolution noise and occlusion in this research hybrid dimensionality reduction shape descriptions drsd are proposed for pair wise registration which aims to overcome these limitations based on recently emerging angle preserving parameterization techniques such as harmonic maps and abf 3d shapes are described in low dimension space with both local and global considerations therefore searching for correspondences verifying overlapping regions and calculating registration error all can be implemented in low dimension space moreover a large number of experiments using both real and synthetic images have been carried out to show the accuracy efficiency and robustness of the hybrid drsd algorithm