shape similarity for 3d video sequences of people this paper presents a performance evaluation of shape similarity metrics for 3d video sequences of people with unknown temporal correspondence performance of similarity measures is compared by evaluating receiver operator characteristics for classification against ground truth for a comprehensive database of synthetic 3d video sequences comprising animations of fourteen people performing twenty eight motions static shape similarity metrics shape distribution spin image shape histogram and spherical harmonics are evaluated using optimal parameter settings for each approach shape histograms with volume sampling are found to consistently give the best performance for different people and motions static shape similarity is extended over time to eliminate the temporal ambiguity time filtering of the static shape similarity together with two novel shape flow descriptors are evaluated against temporal ground truth this evaluation demonstrates that shape flow with a multi frame alignment of motion sequences achieves the best performance is stable for different people and motions and overcome the ambiguity in static shape similarity time filtering of the static shape histogram similarity measure with a fixed window size achieves marginally lower performance for linear motions with the same computational cost as static shape descriptors performance of the temporal shape descriptors is validated for real 3d video sequence of nine actors performing a variety of movements time filtered shape histograms are shown to reliably identify frames from 3d video sequences with similar shape and motion for people with loose clothing and complex motion

the diameter of the first nodal line of a convex domains the main goal of this paper is to prove that the first nodal line for the dirichlet problem in a convex planar domain has diameter less than an absolute constant times the inradius of the domain more precisely we locate the nodal line to within a distance comparable to the inradius near the zero of an ordinary differential equation which is associated to the domain in a natural way we also derive estimates for the first and second eigenvalues in terms of the corresponding eigenvalues of the ordinary differential equation and construct an approximate first eigenfunction two examples a rectangle and a circular sector illustrate the two extreme possibilities for the location of the nodal line for the rectangle r x y o 1 we have the second eigenfunction

an efficient method for the analysis of a structure comprising an appendage attached to a planar surface of a conducting body a technique is presented to efficiently solve for the currents on an appendage e g antenna attached to a planar surface of a conducting body the appendage may be embedded in a homogeneous dielectric material the technique presented alleviates the complications associated with the point where the appendage is attached to the body to illustrate the method a wire antenna attached to an axisymmetric body is analyzed in detail a set of coupled integral equations are formulated appropriate quantities are expanded into fourier modes and coupled integral equations are derived for the fourier coefficients of the unknowns these equations are solved and the input admittance of the wire antenna is determined from the computed currents and is corroborated by measurements

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

the effect of spatial information characterization on 3d local feature descriptors designing local feature descriptors for 3d objects is a fundamental yet challenging task in 3d computer vision both geometry and spatial information descriptions are critical for a 3d local descriptor while most previous studies concentrate on the former one this paper investigates on how the characterization of spatial information would affect a 3d local descriptor in terms of descriptiveness robustness compactness and efficiency the evaluation process is deployed as follows first based on the analysis of representative spatial information characterization methods of existing local shape descriptors six typical characterization methods with different spatial dimensions and partition principles of spatial information are presented second three geometric attributes i e normal deviation local depth and shape index are respectively assigned to each point in the local surface for local geometry description creating a total of 18 different feature descriptors then a quantitative analysis of performance i e descriptiveness robustness compactness and efficiency for these descriptors is carried out on three benchmark datasets grounded on the experimental outcomes the traits merits and demerits of each spatial information encoding approach are eventually summarized this study reveals that different spatial information encoding approaches would bring significant effect on a local shape descriptor with respect to its discriminative power stability compactness and efficiency highlightsthe effect of spatial information encoding sie on 3d local descriptors is emphasized eighteen types of 3d local descriptors with different sie approaches are proposed quantitative evaluation of sie approaches is performed on three standard datasets the merits demerits and suitable applications of different sie ways are summarized instructive guidance is concluded for the design of a 3d local descriptor

rotational projection statistics for 3d local surface description and object recognition recognizing 3d objects in the presence of noise varying mesh resolution occlusion and clutter is a very challenging task this paper presents a novel method named rotational projection statistics rops it has three major modules local reference frame lrf definition rops feature description and 3d object recognition we propose a novel technique to define the lrf by calculating the scatter matrix of all points lying on the local surface rops feature descriptors are obtained by rotationally projecting the neighboring points of a feature point onto 2d planes and calculating a set of statistics including low order central moments and entropy of the distribution of these projected points using the proposed lrf and rops descriptor we present a hierarchical 3d object recognition algorithm the performance of the proposed lrf rops descriptor and object recognition algorithm was rigorously tested on a number of popular and publicly available datasets our proposed techniques exhibited superior performance compared to existing techniques we also showed that our method is robust with respect to noise and varying mesh resolution our rops based algorithm achieved recognition rates of 100 98 9 95 4 and 96 0 respectively when tested on the bologna uwa queen s and ca foscari venezia datasets

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

actions as space time shapes human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion we regard human actions as three dimensional shapes induced by the silhouettes in the space time volume we adopt a recent approach 14 for analyzing 2d shapes and generalize it to deal with volumetric space time action shapes our method utilizes properties of the solution to the poisson equation to extract space time features such as local space time saliency action dynamics shape structure and orientation we show that these features are useful for action recognition detection and clustering the method is fast does not require video alignment and is applicable in but not limited to many scenarios where the background is known moreover we demonstrate the robustness of our method to partial occlusions nonrigid deformations significant changes in scale and viewpoint high irregularities in the performance of an action and low quality video

geometric probing of dense range data a new method is presented for the efficient and reliable pose determination of 3d objects in dense range image data the method is based upon a minimalistic geometric probing strategy that hypothesizes the intersection of the object with some selected image point and searches for additional surface data at locations relative to that point the strategy is implemented in the discrete domain as a binary decision tree classifier the tree leaf nodes represent individual voxel templates of the model with one template per distinct model pose the internal nodes represent the union of the templates of their descendant leaf nodes the union of all leaf node templates is the complete template set of the model over its discrete pose space each internal node also encodes a single voxel which is the most common element of its child node templates traversing the free is equivalent to efficiently matching the large set of templates at a selected image seed location the method was implemented and extensive experiments were conducted for a variety of combinations of tree designs and traversals under isolated cluttered and occluded scene conditions the results demonstrated a tradeoff between efficiency and reliability it was concluded that there exist combinations of tree design and traversal which are both highly efficient and reliable

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

smoothing and matching of 3 d space curves we present a new approach to the problem of matching 3 d curves the approach has a low algorithmic complexity in the number of models and can operate in the presence of noise and partial occlusions our method builds upon the seminal work of kishon et al 1990 where curves are first smoothed using b splines with matching based on hashing using curvature and torsion measures however we introduce two enhancements we present experimental results using synthetic data and also using characteristic curves extracted from 3 d medical images an earlier version of this article was presented at the 2nd european conference on computer vision in italy

consensus strategy for clustering using rc images contrary to most of the existing 3d shape clustering methods in which all the objects in a dataset must be classified in clusters in this paper we tackle an incomplete but reliable unsupervised clustering solution the central idea lies in obtaining coherent 3d shape groups using a consensus between different similarity measures which are defined in a common 3d shape representation framework our goal therefore is to extract some consistent groups of objects considering the incomplete classification if this occurs as a natural result the weighted cone curvature wcc is defined as an overall feature which synthesizes a set of curvature levels on the nodes of a standard triangular mesh representation the wcc concept is used to define a master descriptor called an rc image on which up to eight similarity measures are defined a hierarchical clustering process is then carried out for all the measures and evaluated by means of a clustering confidence measure finally a consensus between the best measures is achieved to provide a coherent group of objects the proposed clustering approach has been tested on a set of mesh models belonging to a wide variety of free shape objects yielding promising results the results of our experiments demonstrate that both the 3d shape descriptor used and the clustering strategy proposed might be useful for future developments in the unsupervised grouping field this work eliminates the imposition of a unique metric and a complete clustering rc image is an original 3d shape descriptor which represents the whole object clustering consensus between several similarity metrics under a common framework consistent clusters understanding at the expense of an incomplete classification successful test on a set of mesh models of a wide variety of free shape objects

3d free form surface registration and object recognition a new technique to recognise 3d free form objects via registration is proposed this technique attempts to register a free form surface represented by a set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d sensed data points to the model surface represented by another set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d model data points without prior knowledge of correspondence or view points between the two point sets with an initial assumption that the sensed surface be part of a more complete model surface the algorithm begins by selecting three dispersed reliable points on the sensed surface to find the three corresponding model points the method uses the principal curvatures and the darboux frames to restrict the search over the model space invariably many possible model 3 typles will be found for each hypothesized model 3 tuple the transformation to match the sensed 3 tuple to the model 3 tuple can be determined a heuristic search is proposed to single out the optimal transformation in low order time for realistic object recognition or registration where the two range images are often extracted from different view points of the model the earlier assumption that the sensed surface be part of a more complete model surface cannot be relied on with this the sensed 3 tuple must be chosen such that the three sensed points lie on the common region visible to both the sensed and model views we propose an algorithm to select a minimal non redundant set of 3 tuples such that at least one of the 3 tuples will lie on the overlap applying the previous algorithm to each 3 tuple within this set the optimal transformation can be determined experiments using data obtained from a range finder have indicated fast registration for relatively complex test cases if the optimal registrations between the sensed data candidate and each of a set of model data are found then for 3d object recognition purposes the minimal best fit error can be used as the decision rule

eigenmodes of isospectral drums recently it was proved that there exist nonisometric planar regions that have identical laplace spectra that is one cannot hear the shape of a drum the simplest isospectral regions known are bounded by polygons with reentrant corners while the isospectrality can be proven mathematically analytical techniques are unable to produce the eigenvalues themselves furthermore standard numerical methods for computing the eigenvalues such as adaptive finite elements are highly inefficient physical experiments have been performed to measure the spectra but the accuracy and flexibility of this method are limited we describe an algorithm due to descloux and tolley comput methods appl mech engrg 39 1983 pp 37 53 that blends singular finite elements with domain decomposition and show that with a modification that doubles its accuracy this algorithm can be used to compute efficiently the eigenvalues for polygonal regions we present results accurate to 12 digits for the most famous pair of isospectral drums as well as results for another pair

geodesic mapping for dynamic surface alignment this paper presents a novel approach that achieves dynamic surface alignment by geodesing mapping the surfaces are 3d manifold meshes representing non rigid objects in motion e g humans which can be obtained by multiview stereo reconstruction the proposed framework consists of a geodesic mapping i e geodesic diffeomorphism between surfaces which carry a distance function namely the global geodesic distance and a geodesic based coordinate system namely the global geodesic coordinates defined similarly to generalized barycentric coordinates the coordinates are used to recursively choose correspondence points in non ambiguous regions using a coarse to fine strategy to reliably locate all surface points and define a discrete mapping complete point to point surface alignment with smooth mapping is then derived by optimizing a piecewise objective function within a probabilistic framework the proposed technique only relies on surface intrinsic geometrical properties and does not require prior knowledge on surface appearance e g color or texture shape e g topology or parameterization e g mesh connectivity or complexity the method can be used for numerous applications such as visual information e g texture transfer between surface models representing different objects dense motion flow estimation of 3d dynamic surfaces wide timeframe matching etc experiments show compelling results on challenging publicly available real world datasets

universal constraints on the location of extrema of eigenfunctions of non local schrodinger operators abstract we derive a lower bound on the location of global extrema of eigenfunctions for a large class of non local schrodinger operators in convex domains under dirichlet exterior conditions featuring the symbol of the kinetic term the strength of the potential and the corresponding eigenvalue and involving a new universal constant we show a number of probabilistic and spectral geometric implications and derive a faber krahn type inequality for non local operators our study also extends to potentials with compact support and we establish bounds on the location of extrema relative to the boundary edge of the support or level sets around minima of the potential

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

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

new algorithms for 2d and 3d point matching pose estimation and correspondence abstract a fundamental open problem in computer vision determining pose and correspondence between two sets of points in space is solved with a novel fast robust and easily implementable algorithm the technique works on noisy 2d or 3d point sets that may be of unequal sizes and may differ by non rigid transformations using a combination of optimization techniques such as deterministic annealing and the softassign which have recently emerged out of the recurrent neural network statistical physics framework analog objective functions describing the problems are minimized over thirty thousand experiments on randomly generated points sets with varying amounts of noise and missing and spurious points and on hand written character sets demonstrate the robustness of the algorithm

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

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

tracking by detection of 3d human shapes from surfaces to volumes 3d human shape tracking consists in fitting a template model to temporal sequences of visual observations it usually comprises an association step that finds correspondences between the model and the input data and a deformation step that fits the model to the observations given correspondences most current approaches follow the iterative closest point icp paradigm where the association step is carried out by searching for the nearest neighbors it fails when large deformations occur and errors in the association tend to propagate over time in this paper we propose a discriminative alternative for the association that leverages random forests to infer correspondences in one shot regardless the choice of shape parameterizations being surface or volumetric meshes we convert 3d shapes to volumetric distance fields and thereby design features to train the forest we investigate two ways to draw volumetric samples voxels of regular grids and cells from centroidal voronoi tessellation cvt while the former consumes considerable memory and in turn limits us to learn only subject specific correspondences the latter yields much less memory footprint by compactly tessellating the interior space of a shape with optimal discretization this facilitates the use of larger cross subject training databases generalizes to different human subjects and hence results in less overfitting and better detection the discriminative correspondences are successfully integrated to both surface and volumetric deformation frameworks that recover human shape poses which we refer to as tracking by detection of 3d human shapes it allows for large deformations and prevents tracking errors from being accumulated when combined with icp for refinement it proves to yield better accuracy in registration and more stability when tracking over time evaluations on existing datasets demonstrate the benefits with respect to the state of the art

robust real time periodic motion detection analysis and applications we describe new techniques to detect and analyze periodic motion as seen from both a static and a moving camera by tracking objects of interest we compute an object s self similarity as it evolves in time for periodic motion the self similarity measure is also periodic and we apply time frequency analysis to detect and characterize the periodic motion the periodicity is also analyzed robustly using the 2d lattice structures inherent in similarity matrices a real time system has been implemented to track and classify objects using periodicity examples of object classification people running dogs vehicles person counting and nonstationary periodicity are provided

a novel local surface feature for 3d object recognition under clutter and occlusion this paper presents a highly distinctive local surface feature called the trisi feature for recognizing 3d objects in the presence of clutter and occlusion for a feature point we first construct a unique and repeatable local reference frame lrf using the implicit geometrical information of neighboring triangular faces we then generate three signatures from the three orthogonal coordinate axes of the lrf these signatures are concatenated and then compressed into a trisi feature finally we propose an effective 3d object recognition algorithm based on hierarchical feature matching we tested our trisi feature on two popular datasets rigorous experimental results show that the trisi feature was highly descriptive and outperformed existing algorithms under all levels of gaussian noise laplacian noise shot noise varying mesh resolutions occlusion and clutter moreover we tested our trisi based 3d object recognition algorithm on four standard datasets the experimental results show that our algorithm achieved the best overall recognition results on these datasets

registration of surfaces minimizing error propagation for a one shot multi slit hand held scanner we propose an algorithm for the on line automatic registration of multiple 3d surfaces acquired in a sequence by a new hand held laser scanner the laser emitter is coupled with an optical lens that spreads the light forming 19 parallel slits that are projected to the scene and acquired with subpixel accuracy by a camera splines are used to interpolate the acquired profiles to increase the sample of points and delaunay triangulation is used to obtain the normal vectors at every point a point to plane pair wise registration method is proposed to align the surfaces in pairs while they are acquired conforming paths and eventually cycles that are minimized once detected the algorithm is specially designed for on line applications and can be classified as a closing the loop technique where there are not that many competing methods though it has been compared to the literature experiments providing qualitative and quantitative evaluation are shown by means of synthetic and real data and we demonstrated the reliability of our technique

snapshots a novel local surface descriptor and matching algorithm for robust 3d surface alignment in this paper a novel local surface descriptor is proposed and applied to the problem of aligning partial views of a 3d object the descriptor is based on taking snapshots of the surface over each point using a virtual camera oriented perpendicularly to the surface this representation has the advantage of imposing minimal loss of information be robust to self occlusions and also be very efficient to compute then we describe an efficient search technique to deal with the rotation ambiguity of our representation and experimentally demonstrate the benefits of our approaches which are pronounced especially when we align views with small overlap

locating the first nodal set in higher dimensions we extend the two dimensional results of jerison 2000 on the location of the nodal set of the first neumann eigenfunction of a convex domain to higher dimensions if a convex domain in n is contained in a long and thin cylinder 0 n x b 0 with nonempty intersections with x 1 0 and x 1 n then the first nonzero eigenvalue is well approximated by the eigenvalue of an ordinary differential equation by a bound proportional to whose coefficients are expressed in terms of the volume of the cross sections of the domain also the first nodal set is located within a distance comparable to e near the zero of the corresponding ordinary differential equation

toldi an effective and robust approach for 3d local shape description abstract feature description for the 3d local shape in the presence of noise varying mesh resolutions clutter and occlusion is a quite challenging task in 3d computer vision this paper tackles the problem by proposing a new local reference frame lrf together with a novel triple orthogonal local depth images toldi representation forming the toldi method for local shape description compared with previous methods toldi manages to perform efficient distinctive and robust description for the 3d local surface simultaneously under various feature matching contexts the proposed lrf differs from many prior ones in its calculation of the z axis and x axis the z axis is calculated using the normal of the keypoint and the x axis is computed by aggregating the weighted projection vectors of the radius neighbors toldi feature descriptors are then obtained by concatenating three local depth images ldi captured from three orthogonal view planes in the lrf into feature vectors the performance of our toldi approach is rigorously evaluated on several public datasets which contain three major surface matching scenarios namely shape retrieval object recognition and 3d registration experimental results and comparisons with the state of the arts validate the effectiveness robustness high efficiency and overall superiority of our method our method is also applied to aligning 3d object and indoor scene point clouds obtained by different devices i e lidar and kinect the accurate outcomes further confirm the effectiveness of our method

point signatures a new representation for 3d object recognition few systems capable of recognizing complex objects with free form sculptured surfaces have been developed the apparent lack of success is mainly due to the lack of a competent modelling scheme for representing such complex objects in this paper a new form of point representation for describing 3d free form surfaces is proposed this representation which we call the point signature serves to describe the structural neighbourhood of a point in a more complete manner than just using the 3d coordinates of the point being invariant to rotation and translation the point signature can be used directly to hypothesize the correspondence to model points with similar signatures recognition is achieved by matching the signatures of data points representing the sensed surface to the signatures of data points representing the model surface the use of point signatures is not restricted to the recognition of a single object scene to a small library of models instead it can be extended naturally to the recognition of scenes containing multiple partially overlapping objects which may also be juxtaposed with each other against a large model library no preliminary phase of segmenting the scene into the component objects is required in searching for the appropriate candidate model recognition need not proceed in a linear order which can become prohibitive for a large model library for a given scene signatures are extracted at arbitrarily spaced seed points each of these signatures is used to vote for models that contain points having similar signatures inappropriate models with low votes can be rejected while the remaining candidate models are ordered according to the votes they received in this way efficient verification of the hypothesized candidates can proceed by testing the most likely model first experiments using real data obtained from a range finder have shown fast recognition from a library of fifteen models whose complexities vary from that of simple piecewise quadric shapes to complicated face masks results from the recognition of both single object and multiple object scenes are presented

locating the first nodal linein the neumann problem the location of the nodal line of the first nonconstant neumann eigenfunction of a convex planar domain is specified to within a distance comparable to the inradius this is used to prove that the eigenvalue of the partial differential equation is approximated well by the eigenvalue of an ordinary differential equation whose coefficients are expressed solely in terms of the width of the domain a variant of these estimates is given for domains that are thin strips and satisfy a lipschitz condition

the adiabatic limit of schrodinger operators on fibre bundles we consider schrodinger operators h delta g varepsilon v on a fibre bundle m mathop rightarrow limits pi b with compact fibres and a metric g varepsilon that blows up directions perpendicular to the fibres by a factor varepsilon 1 gg 1 we show that for an eigenvalue lambda of the fibre wise part of h satisfying a local gap condition and every n in mathbb n there exists a subspace of l 2 m that is invariant under h up to errors of order varepsilon n 1 the dynamical and spectral features of h on this subspace can be described by an effective operator on the fibre wise lambda eigenspace bundle mathcal e rightarrow b giving detailed asymptotics for h

a comparison between two kinds of equivalent currents to analyze conducting bodies with apertures using moment methods application to horns with symmetry of revolution a system of integral equations sie based on the unique hess theorem that uses only electric equivalent currents eec is formulated to analyze conducting bodies with apertures this sie is compared with an sie that uses both electric and magnetic equivalent currents emec in general to solve both sie s numerically difficult computations of cauchy principal value integrals with highly singular kernels are required these integrals appear when computing electric magnetic fields created by magnetic electric currents their evaluation can be avoided using the eec approach in many practical cases when the main interest is in the radiation patterns of aperture antennas the two sie s are compared by carrying out an analysis of rotationally symmetric horns using the moment method mm in its formulation for bodies of revolution numerical results of electric currents and radiation patterns are presented for small horns of various geometries these results compare quite well with measurements for both sie s however the central processing unit cpu time for the eec formulation is an order of magnitude smaller than for the emec formulation

dense 3d face correspondence we present an algorithm that automatically establishes dense correspondences between a large number of 3d faces starting from automatically detected sparse correspondences on the outer boundary of 3d faces the algorithm triangulates existing correspondences and expands them iteratively by matching points of distinctive surface curvature along the triangle edges after exhausting keypoint matches further correspondences are established by generating evenly distributed points within triangles by evolving level set geodesic curves from the centroids of large triangles a deformable model k3dm is constructed from the dense corresponded faces and an algorithm is proposed for morphing the k3dm to fit unseen faces this algorithm iterates between rigid alignment of an unseen face followed by regularized morphing of the deformable model we have extensively evaluated the proposed algorithms on synthetic data and real 3d faces from the frgcv2 bosphorus bu3dfe and und ear databases using quantitative and qualitative benchmarks our algorithm achieved dense correspondences with a mean localisation error of 1 28 mm on synthetic faces and detected 14 anthropometric landmarks on unseen real faces from the frgcv2 database with 3 mm precision furthermore our deformable model fitting algorithm achieved 98 5 percent face recognition accuracy on the frgcv2 and 98 6 percent on bosphorus database our dense model is also able to generalize to unseen datasets

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

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

pairwise matching of 3d fragments using cluster trees we propose a novel and efficient surface matching approach for reassembling broken solids as well as for matching assembly components using cluster trees of oriented points the method rapidly scans through the space of all possible contact poses of the fragments to be re assembled using a tree search strategy which neither relies on any surface features nor requires an initial solution the new method first decomposes each point set into a binary tree structure using a hierarchical clustering algorithm subsequently the fragments are matched pairwise by descending the cluster trees simultaneously in a depth first fashion in contrast to the reassemblage of pottery and thin walled artifacts this paper addresses the problem of matching broken 3d solids on the basis of their 2 5d fracture surfaces which are assumed to be reasonable large our proposed contact area maximization is a powerful common basis for most surface matching tasks which can be adapted to numerous special applications the suggested approach is very robust and offers an outstanding efficiency

a 3d scene registration method via covariance descriptors and an evolutionary stable strategy game theory solver in this paper we provide an integrated approach for matching patterns in scenes combining 3d and visual information for local definition of points we propose a descriptor based on the notion of covariance of features for fusion of shape and color information of 3d surfaces so called multi scale covariance descriptor mcov the intrinsic properties of this descriptor are many it is invariant to spatial rigid transformations and robust to noise and resolution changes it can also be used for characteristic point detection and lies on top of a manifold topology which allows the use of analytical metric properties this descriptor is complemented with a game theoretic approach for solving the matching correspondences under global geometric constraints this layer offers a comprehensive understanding of the scene and avoids possible mismatches due to repeated areas or symmetries which would be impossibly identified by the detector solely at a local level our solution is able to accurately match different views of a scene even under spatial transformations high noise levels and with small overlap between views outperforming state of the art approaches results are validated by comparing mcov against other state of the art 3d point descriptor methods and matching complex 3d and color scenes under several challenging conditions

registration of 3d points using geometric algebra and tensor voting we address the problem of finding the correspondences of two point sets in 3d undergoing a rigid transformation using these correspondences the motion between the two sets can be computed to perform registration our approach is based on the analysis of the rigid motion equations as expressed in the geometric algebra framework through this analysis it was apparent that this problem could be cast into a problem of finding a certain 3d plane in a different space that satisfies certain geometric constraints in order to find this plane in a robust way the tensor voting methodology was used unlike other common algorithms for point registration like the iterated closest points algorithm ours does not require an initialization works equally well with small and large transformations it cannot be trapped in local minima and works even in the presence of large amounts of outliers we also show that this algorithm is easily extended to account for multiple motions and certain non rigid or elastic transformations

shapes of drums with lowest base frequency under non isotropic perimeter constraints we study the minimizers of the sum of the principal dirichlet eigenvalue of the negative laplacian and the perimeter with respect to a general norm in the class of jordan domains in the plane this is equivalent modulo scaling to minimizing the said eigenvalue or the base frequency of a drum of this shape subject to a hard constraint on the perimeter we show that for all norms a minimizer exists is unique up to spatial translations and is convex but not necessarily smooth we give conditions on the norm that characterize the appearance of facets and corners we also demonstrate that near minimizers have to be close to the optimal ones in the hausdorff distance our motivation for considering this class of variational problems comes from a study of random walks in random environment interacting through the boundary of their support 1 main results the aim of this paper is to analyze the planar domains that minimize the principal harmonic frequency i e the lowest dirichlet eigenvalue of the negative laplacian or the base frequency of the drum of this shape subject to a hard constraint on the perimeter defined using a general norm let us introduce the problem and state our results on it first and leave the discussion of our motivation as well as connections to existing literature to a later section 1 1 the model and main theorems we will consider the following class of admissible domains u u r2 jordan domain 0 u 1 1 note that each u u is open bounded connected and simply connected with u being the trace of a simple closed curve the principal dirichlet eigenvalue of the negative laplacian is for any open u r2 given by u inf g 2 g c r2 supp g u g 2 1 1 2 where 2 denotes the l2 norm on r2 with respect to the lebesgue measure next fix a norm on r2 and denote by 0 1 r2 the curve constituting u where 0 1 then we c 2016 m biskup e b procaccia reproduction by any means of the entire article for non commercial purposes is permitted without charge

real time object recognition in sparse range images using error surface embedding a novel object recognition algorithm is introduced to identify objects and recover their pose from sparse range data the method is based upon comparing the 7 d error surfaces of objects in various poses which result from the registration error function between two convolved surfaces the objects and their pose values are encoded by a small set of feature vectors extracted from the minima of the error surfaces the problem of object recognition is thus reduced to comparing these feature vectors to find the corresponding error surfaces between the runtime data and a preprocessed database the algorithm called potential well space embedding pwse has been implemented and tested on both simulated and real data the experimental results show the technique to be both effective and efficient executing at 122 frames per second on standard hardware and with recognition rates exceeding 97 for a database of 60 objects the performance of pwse on the large size database was also evaluated on the princeton shape benchmark containing 1 814 objects in addition it functions well with very sparse data possibly comprising only hundreds of points per image and is shown to be robust to measurement error and outliers with some small modifications we applied pwse to the problem of object class recognition in experiments with the princeton shape benchmark pwse is able to provides better classification rates than the previous methods in terms of nearest neighbour classification

electromagnetic radiation from structures consisting of combined body of revolution and arbitrary surfaces a formulation is developed to treat radiation from structures consisting of a body of revolution bor in the presence of multiple arbitrarily shaped three dimensional objects an electric field integral equation is set up on the surface of the combined structure the resulting integro differential equation is solved using the method of moments on the bor harmonic entire domain expansion functions are used for the circumferential dependence while overlapping subdomain functions are used to model the axial curvature the arbitrarily shaped portions of the structure are modeled using triangular surface patches the resulting system matrix has a partial block diagonal nature which provides a more economical solution for structures that have some rational symmetry numerical results are presented and compared to measurements of a unique cavity backed patch fed antenna

global non rigid alignment of surface sequences this paper presents a general approach based on the shape similarity tree for non sequential alignment across databases of multiple unstructured mesh sequences from non rigid surface capture the optimal shape similarity tree for non rigid alignment is defined as the minimum spanning tree in shape similarity space non sequential alignment based on the shape similarity tree minimises the total non rigid deformation required to register all frames in a database into a consistent mesh structure with surfaces in correspondence this allows alignment across multiple sequences of different motions reduces drift in sequential alignment and is robust to rapid non rigid motion evaluation is performed on three benchmark databases of 3d mesh sequences with a variety of complex human and cloth motion comparison with sequential alignment demonstrates reduced errors due to drift and improved robustness to large non rigid deformation together with global alignment across multiple sequences which is not possible with previous sequential approaches

the h path distribution of the lifetime of conditioned brownian motion for non smooth domains consider the h paths of doob and let d be the lifetime of brownian motion killed at d where d is a bounded lipschitz or nta domain in n then log p x h tau d t sim lambda d t as t to infty where d is the first positive eigenvalue of 1 2 on d

an efficient multimodal 2d 3d hybrid approach to automatic face recognition we present a fully automatic face recognition algorithm and demonstrate its performance on the frgc v2 0 data our algorithm is multimodal 2d and 3d and performs hybrid feature based and holistic matching in order to achieve efficiency and robustness to facial expressions the pose of a 3d face along with its texture is automatically corrected using a novel approach based on a single automatically detected point and the hotelling transform a novel 3d spherical face representation sfr is used in conjunction with the scale invariant feature transform sift descriptor to form a rejection classifier which quickly eliminates a large number of candidate faces at an early stage for efficient recognition in case of large galleries the remaining faces are then verified using a novel region based matching approach which is robust to facial expressions this approach automatically segments the eyes forehead and the nose regions which are relatively less sensitive to expressions and matches them separately using a modified iterative closest point icp algorithm the results of all the matching engines are fused at the metric level to achieve higher accuracy we use the frgc benchmark to compare our results to other algorithms that used the same database our multimodal hybrid algorithm performed better than others by achieving 99 74 percent and 98 31 percent verification rates at a 0 001 false acceptance rate far and identification rates of 99 02 percent and 95 37 percent for probes with a neutral and a nonneutral expression respectively

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

joint induction of shape features and tree classifiers we introduce a very large family of binary features for two dimensional shapes the salient ones for separating particular shapes are determined by inductive learning during the construction of classification trees there is a feature for every possible geometric arrangement of local topographic codes the arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial affine and nonlinear deformations they are also partially ordered which makes it possible to narrow the search for informative ones at each node of the tree different trees correspond to different aspects of shape they are statistically and weakly dependent due to randomization and are aggregated in a simple way adapting the algorithm to a shape family is then fully automatic once training samples are provided as an illustration we classified handwritten digits from the nist database the error rate was 0 7 percent

a fast and robust local descriptor for 3d point cloud registration this paper proposes a novel local feature descriptor called a local feature statistics histogram lfsh for efficient 3d point cloud registration an lfsh forms a comprehensive description of local shape geometries by encoding their statistical properties on local depth point density and angles between normals the sub features in the lfsh descriptor are low dimensional and quite efficient to compute in addition an optimized sample consensus osac algorithm is developed to iteratively estimate the optimum transformation from point correspondences osac can handle the challenging cases of matching highly self similar models based on the proposed lfsh and osac a coarse to fine algorithm can be formed for 3d point cloud registration experiments and comparisons with the state of the art descriptors demonstrate that lfsh is highly discriminative robust and significantly faster than other descriptors meanwhile the proposed coarse to fine registration algorithm is demonstrated to be robust to common nuisances including noise and varying point cloud resolutions and can achieve high accuracy on both model data and scene data

shape matching and object recognition using shape contexts 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 nearest neighbor 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 data set

critical points of solutions to a quasilinear elliptic equation with nonhomogeneous dirichlet boundary conditions abstract in this paper we mainly investigate the critical points associated to solutions u of a quasilinear elliptic equation with nonhomogeneous dirichlet boundary conditions in a connected domain in r 2 based on the fine analysis about the distribution of connected components of a super level set x u x t for any min u x t max u x we obtain the geometric structure of interior critical points of u precisely when is simply connected we develop a new method to prove i 1 k m i 1 n where m 1 m k are the respective multiplicities of interior critical points x 1 x k of u and n is the number of global maximal points of u on when is an annular domain with the interior boundary i and the external boundary e where u i h u e x and x has n local global maximal points on e for the case x h or x h or min e x h max e x we show that i 1 k m i n either i 1 k m i n or i 1 k m i 1 n

where best to hold a drum fast if we are allowed to fasten say one half of a drum s boundary which half produces the lowest or highest bass note the answer is a natural limit of solutions to a family of extremal robin problems for the least eigenvalue of the laplacian we produce explicit extremizers when the drum is a disk while for general shapes we establish existence and necessary conditions and we build and test a pair of numerical methods

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

on bending invariant signatures for surfaces isometric surfaces share the same geometric structure also known as the first fundamental form for example all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric we present a method to construct a bending invariant signature for such surfaces this invariant representation is an embedding of the geometric structure of the surface in a small dimensional euclidean space in which geodesic distances are approximated by euclidean ones the bending invariant representation is constructed by first measuring the intergeodesic distances between uniformly distributed points on the surface next a multidimensional scaling technique is applied to extract coordinates in a finite dimensional euclidean space in which geodesic distances are replaced by euclidean ones applying this transform to various surfaces with similar geodesic structures first fundamental form maps them into similar signature surfaces we thereby translate the problem of matching nonrigid objects in various postures into a simpler problem of matching rigid objects as an example we show a simple surface classification method that uses our bending invariant signatures

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

multi view ensemble manifold regularization for 3d object recognition view based methods are popular in 3d object recognition however current methods with traditional classifiers are usually based on one to one view matching and fail to capture the structure information of multiple views some multi view based methods take different views into consideration but they still treat views separately in this paper we propose a novel 3d object recognizing method based on multi view data fusion called multi view ensemble manifold regularization memr in this method we model image features with a regularization term for svm to train this modified svm multi view learning is achieved with alternating optimization hypergraph construction is used to better capture the connectivity among views experimental results show that the accuracy rate has been improved by 20 25 which demonstrates the effectiveness of the proposed method

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

view based recognition using an eigenspace approximation to the hausdorff measure view based recognition methods such as those using eigenspace techniques have been successful for a number of recognition tasks such approaches however are somewhat limited in their ability to recognize objects that are partly hidden from view or occur against cluttered backgrounds in order to address these limitations we have developed a view matching technique based on an eigenspace approximation to the generalized hausdorff measure this method achieves compact storage and fast indexing that are the main advantages of eigenspace view matching techniques while also being tolerant of partial occlusion and background clutter the method applies to binary feature maps such as intensity edges rather than directly to intensity images

some comparison theorems for sturm liouville eigenvalue problems abstract we give some comparison theorems about the location of the peak of the first dirichlet sturm liouville eigenfunction by means of the variational method

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

input impedance of wire antennas attached on axis to conducting bodies of revolution moment method calculations are presented for the input impedance of wire antennas attached on axis to a conducting body of revolution bor of arbitrary geometry the study of the wire antenna is carried out using integral equations of both reduced and exact kernel the analysis of the bor takes advantage of the symmetry of revolution that allows the expansion of the current in fourier series which takes advantage of the mode orthogonality and reduces the computer time required results for current distribution and input impedance are obtained for several structures such as vertical and nonvertical monopoles over circular ground planes and conical bodies measurements of impedance are presented to check numerical results these are also compared with results of other methods

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

3d geometric scale variability in range images features and descriptors despite their ubiquitous presence little has been investigated about the scale variability the relative variations in the spatial extents of local structures of 3d geometric data in this paper we present a comprehensive framework for exploiting this 3d geometric scale variability in range images that provides rich information for characterizing the overall geometry we derive a sound scale space representation which we refer to as the geometric scale space that faithfully encodes the scale variability of the surface geometry and derive novel detectors to extract prominent features and identify their natural scales the result is a hierarchical set of features of different scales which we refer to as scale dependent geometric features we then derive novel local shape descriptors that represent the surface structures that give rise to those features by carving out and encoding the local surface that fall within the support regions of the features this leads to scale dependent or scale invariant local shape descriptors that convey significant discriminative information of the object geometry we demonstrate the effectiveness of geometric scale analysis on range images and show that it enables novel applications in particular fully automatic registration of multiple objects from a mixed set of range images and 3d object recognition in highly cluttered range image scenes

fast and accurate surface alignment through an isometry enforcing game surface registration is often performed as a two step process a feature matching scheme is first adopted to find a coarse initial alignment between two meshes subsequently a refinement step which usually operates in the space of rigid motions is applied to reach an optimal registration with respect to pointwise distances between overlapping areas in this paper we propose a novel technique that allows to obtain an accurate surface registration in a single step without the need for an initial motion estimation the main idea of our approach is to cast the selection of correspondences between points on the surfaces in a game theoretic framework where a natural selection process allows matching points that satisfy a mutual rigidity constraint to thrive eliminating all the other correspondences this process yields a very robust inlier selection scheme that does not depend on any particular technique for selecting the initial strategies as it relies only on the global geometric compatibility between correspondences the practical effectiveness of the approach is confirmed by an extensive set of experiments and comparisons with state of the art techniques highlightswe introduce a novel pipeline for rigid surface alignment based on game theory the method allows to obtain accurate solutions without requiring an initial estimate we propose simple descriptors designed to be fast and effective within our pipeline we establish a relation between evolutionary stable states and optimal alignments the technique is efficient and outperforms the state of the art

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

from 3d point clouds to pose normalised depth maps we consider the problem of generating either pairwise aligned or pose normalised depth maps from noisy 3d point clouds in a relatively unrestricted poses our system is deployed in a 3d face alignment application and consists of the following four stages i data filtering ii nose tip identification and sub vertex localisation iii computation of the relative face orientation iv generation of either a pose aligned or a pose normalised depth map we generate an implicit radial basis function rbf model of the facial surface and this is employed within all four stages of the process for example in stage ii construction of novel invariant features is based on sampling this rbf over a set of concentric spheres to give a spherically sampled rbf ssr shape histogram in stage iii a second novel descriptor called an isoradius contour curvature signal is defined which allows rotational alignment to be determined using a simple process of 1d correlation we test our system on both the university of york uoy 3d face dataset and the face recognition grand challenge frgc 3d data for the more challenging uoy data our ssr descriptors significantly outperform three variants of spin images successfully identifying nose vertices at a rate of 99 6 nose localisation performance on the higher quality frgc data which has only small pose variations is 99 9 our best system successfully normalises the pose of 3d faces at rates of 99 1 uoy data and 99 6 frgc data

a novel representation and feature matching algorithm for automatic pairwise registration of range images automatic registration of range images is a fundamental problem in 3d modeling of free from objects various feature matching algorithms have been proposed for this purpose however these algorithms suffer from various limitations mainly related to their applicability efficiency robustness to resolution and the discriminating capability of the used feature representation we present a novel feature matching algorithm for automatic pairwise registration of range images which overcomes these limitations our algorithm uses a novel tensor representation which represents semi local 3d surface patches of a range image by third order tensors multiple tensors are used to represent each range image tensors of two range images are matched to identify correspondences between them correspondences are verified and then used for pairwise registration of the range images experimental results show that our algorithm is accurate and efficient moreover it is robust to the resolution of the range images the number of tensors per view the required amount of overlap and noise comparisons with the spin image representation revealed that our representation has more discriminating capabilities and performs better at a low resolution of the range images

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

the size of the first eigenfunction of a convex planar domain the goal of this paper is to estimate the size of the first eigenfunction u uniformly for all convex domains in particular we will locate the place where u achieves its maximum to within a distance comparable to the inradius uniformly for arbitrarily large diameter in addition we will estimate the location of other level sets of u by showing that u is well approximated by the first eigenfunction of a naturally associated ordinary differential schrodinger operator we intend to show in a separate paper that the estimates here are best possible in order of magnitude the present paper depends on the ideas and results of our earlier work j and gj where detailed estimates for the zero set of the second eigenfunction or first nodal line are obtained the paper j also contains some estimates for the first eigenfunction and lowest eigenvalue but the techniques of gj and new techniques introduced here are essential to the best possible estimates for the first eigenfunction presented here the maximum of the first eigenfunction occurs at the point of largest displacement of a vibrating drum with fixed edges when it vibrates at its fundamental or first resonant frequency the first nodal line is the stationary curve of the drum at the second resonant frequency the maximum is harder to find experimentally than the nodal line because it is a single point its location has less influence on the eigenvalue or dirichlet integral so it is also harder to locate mathematically another way to describe the difficulty is as follows to find the maximum of the first eigenfunction we will need to estimate its first directional derivative derivatives of the first eigenfunction are roughly speaking analogous to the second eigenfunction because they are solutions to an eigenfunction equation moreover convexity properties of the first eigenfunction imply that the zero set of the derivative divides the region into two connected components but the derivatives are harder to estimate than a second eigenfunction because they do not vanish at the boundary