wada basin boundaries and basin cells in dynamical systems examples are common in which two or more attractors coexist and in such cases the basin boundary is nonempty we consider a two dimensional diffeomorphism f that is f is an invertible map and both f and its inverse are differentiable with continuous derivatives which has at least three basins fractal basin boundaries contain infinitely many periodic points generally only finitely many of these periodic points are outermost on the basin boundary that is accessible from a basin for many systems all accessible points lie on stable manifolds of periodic points a point x on the basic boundary is a wada point if every open neighborhood of x has a nonempty intersection with at least three different basins we call the boundary of a basin a wada basin boundary if all its points are wada points our main goal is to have definitions and hypotheses for wada basin boundaries that can be verified by computer the basic notion basin cell will play a fundamental role in our results for numerical verifications assuming each accessible point on the boundary of a basin b is on the stable manifold of some periodic orbit we show that partial derivative b over bar is a wada basin boundary if the unstable manifold of each of its accessible periodic orbits intersects at least three basins in addition we find conditions for basins b 1 b 2 b n n greater than or equal to 3 to satisfy partial derivative b over bar 1 partial derivative b over bar 2 partial derivative b over bar n our results provide numerically verifiable conditions guaranteeing that the boundary of a basin is a wada basin boundary our examples make use of an existing numerical procedure for finding the accessible periodic points on the basin boundary and another procedure for plotting stable and unstable manifolds to verify the existence of wada basin boundaries

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

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

rotation numbers of periodic orbits in the henon map for invertible area contracting maps of the plane it is common for a basin of attraction to have a fractal basin boundary certain periodic orbits on the basin boundary are distinguished by being accessible by a path from the interior of the basin a numerical study is made of the accessible periodic orbits for the henon family of maps theoretical results on rotary homoclinic tangencies are given which describe the appearance of the accessible saddles and organize them in a natural way according to the continued fractions expansions of their rotation numbers

motivic cohomology over dedekind rings we study properties of bloch s higher chow groups on smooth varieties over dedekind rings we prove the vanishing of open image in new window for i n and the existence of a gersten resolution for open image in new window if the residue characteristic is p we also show that the bloch kato conjecture implies the beilinson lichtenbaum conjecture open image in new window an identification open image in new window for m invertible and a gersten resolution with arbitrary finite coefficients over a complete discrete valuation ring of mixed characteristic 0 p we construct a map from motivic cohomology to syntomic cohomology which is a quasi isomorphism provided the bloch kato conjecture holds

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

learning spectral descriptors for deformable shape correspondence informative and discriminative feature descriptors play a fundamental role in deformable shape analysis for example they have been successfully employed in correspondence registration and retrieval tasks in recent years significant attention has been devoted to descriptors obtained from the spectral decomposition of the laplace beltrami operator associated with the shape notable examples in this family are the heat kernel signature hks and the recently introduced wave kernel signature wks the laplacian based descriptors achieve state of the art performance in numerous shape analysis tasks they are computationally efficient isometry invariant by construction and can gracefully cope with a variety of transformations in this paper we formulate a generic family of parametric spectral descriptors we argue that to be optimized for a specific task the descriptor should take into account the statistics of the corpus of shapes to which it is applied the signal and those of the class of transformations to which it is made insensitive the noise while such statistics are hard to model axiomatically they can be learned from examples following the spirit of the wiener filter in signal processing we show a learning scheme for the construction of optimized spectral descriptors and relate it to mahalanobis metric learning the superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures we also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes

a novel 3d vorticity based approach for automatic registration of low resolution range images this paper tackles the problem of feature matching and range image registration our approach is based on a novel set of discriminating three dimensional 3d local features named 3d vor vorticity in contrast to conventional local feature representation techniques which use the vector field i e surface normals to just construct their local reference frames the proposed feature representation exploits the vorticity of the vector field computed at each point of the local surface to capture the distinctive characteristics at each point of the underlying 3d surface the 3d vor descriptors of two range images are then matched using a fully automatic feature matching algorithm which identifies correspondences between the two range images correspondences are verified in a local validation step of the proposed algorithm and used for the pairwise registration of the range images quantitative results on low resolution kinect 3d data washington rgb d dataset show that our proposed automatic registration algorithm is accurate and computationally efficient the performance evaluation of the proposed descriptor was also carried out on the challenging low resolution washington rgb d kinect object dataset for the tasks of automatic range image registration reported experimental results show that the proposed local surface descriptor is robust to resolution noise and more accurate than state of the art techniques it achieves 90 registration accuracy compared to 50 69 2 and 52 for spin image 3d surf and sisi ld sift descriptors respectively highlightsa novel local surface descriptor 3d vor is proposed for surface representation the proposed 3d vor exploits the vector field s vorticity a novel pairwise registration algorithm is also proposed 3d vor is tested on low resolution dataset for range image registration 3d vor based registration achieves 90 accuracy on low resolution data and outperforms state of the art techniques

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

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

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

a comprehensive performance evaluation of 3d local feature descriptors a number of 3d local feature descriptors have been proposed in the literature it is however unclear which descriptors are more appropriate for a particular application a good descriptor should be descriptive compact and robust to a set of nuisances this paper compares ten popular local feature descriptors in the contexts of 3d object recognition 3d shape retrieval and 3d modeling we first evaluate the descriptiveness of these descriptors on eight popular datasets which were acquired using different techniques we then analyze their compactness using the recall of feature matching per each float value in the descriptor we also test the robustness of the selected descriptors with respect to support radius variations gaussian noise shot noise varying mesh resolution distance to the mesh boundary keypoint localization error occlusion clutter and dataset size moreover we present the performance results of these descriptors when combined with different 3d keypoint detection methods we finally analyze the computational efficiency for generating each descriptor

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

metamorphoses sudden jumps in basin boundaries in some invertible maps of the plane that depend on a parameter boundaries of basins of attraction are extremely sensitive to small changes in the parameter a basin boundary can jump suddenly and as it does change from being smooth to fractal such changes are calledbasin boundary metamorphoses we prove under certain non degeneracy assumptions that a metamorphosis occurs when the stable and unstable manifolds of a periodic saddle on the boundary undergo a homoclinic tangency

jumping stable manifolds for dissipative maps of the plane abstract one of the more drastic changes in the nature of a chaotic dynamical system is a transformation of the basins of competing attractors in a two dimensional system the basin boundary is typically the stable manifold of a saddle point the transformation of the basin boundary from smooth to fractal is presaged by a homoclinic tangency for the saddle point as a varying parameter in a dissipative map of the plane forces a homoclinic tangency we show that the location of the stable manifold changes discontinuously this forces a basin boundary to change in a dramatic way which is often an immediate precursor of the collision between a strange attractor and its basin boundary finally we describe the application of our results to the behavior of the ikeda map from nonlinear optics

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

explosions of chaotic sets abstract large scale invariant sets such as chaotic attractors undergo bifurcations as a parameter is varied these bifurcations include sudden changes in the size and or type of the set an explosion is a bifurcation in which new recurrent points suddenly appear at a non zero distance from any pre existing recurrent points we discuss the following in a generic one parameter family of dissipative invertible maps of the plane there are only four known mechanisms through which an explosion can occur 1 a saddle node bifurcation isolated from other recurrent points 2 a saddle node bifurcation embedded in the set of recurrent points 3 outer homoclinic tangencies and 4 outer heteroclinic tangencies the term outer tangency refers to a particular configuration of the stable and unstable manifolds at tangency in particular we examine different types of tangencies of stable and unstable manifolds from orbits of pre existing invariant sets this leads to a general theory that unites phenomena such as crises basin boundary metamorphoses explosions of chaotic saddles etc we illustrate this theory with numerical examples

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

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

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

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