practical reliable bayesian recognition of 2d and 3d objects using implicit polynomials and algebraic invariants we treat the use of more complex higher degree polynomial curves and surfaces of degree higher than 2 which have many desirable properties for object recognition and position estimation and attack the instability problem arising in their use with partial and noisy data the scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function stored in the database then given partial data from one of the objects we want to recognize the object or the object class or collect more data in order to get better parameter estimates for more reliable recognition two problems arising in this scenario are discussed 1 the problem of recognizing these polynomials by comparing them in terms of their coefficients and 2 the problem of where to collect data so as to improve the parameter estimates as quickly as possible we use an asymptotic bayesian approximation for solving the two problems the intrinsic dimensionality of polynomials and the use of the mahalanobis distance are discussed

on the sequential accumulation of evidence in this paper we introduce a method for sequentially accumulating evidence as it pertains to an active observer seeking to identify an object in a known environment we develop a probabilistic framework based on a generalized inverse theory where assertions are represented by conditional probability density functions this leads to a sequential recognition strategy in which evidence is accumulated over successive viewpoints using bayesian chaining until a definitive assertion can be made to illustrate the theory we show how the characteristics of belief distributions can be exploited in a model based recognition problem where the task is to identify an unknown model from a database of known objects on the basis of parameter estimates we illustrate the robustness of the algorithm through recognition experiments in two very different contexts 1 a highly structured recognition context where 3 d parametric models can be estimated directly from range data 2 a complex environment where the relationship between the data and the model is learned through an appearance based strategy specifically the flow fields computed through the object s motion are used as structural signatures for recognition

registering multiview range data to create 3d computer objects concerns the problem of range image registration for the purpose of building surface models of 3d objects the registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces an integrated surface representation of the object the registration task is expressed as an optimization problem we define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters this function computes a sum of euclidean distances from control points on one surfaces to corresponding points on the other the strength of this approach is in the method used to determine point correspondences it reverses the rangefinder calibration process resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3d space a stochastic optimization technique very fast simulated reannealing vfsr is used to minimize the cost function dual view registration experiments yielded excellent results in very reasonable time a multiview registration experiment took a long time a complete surface model was then constructed from the integration of multiple partial views the effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3d objects must be constructed

computing the aspect graph for line drawings of polyhedral objects an algorithm for computing the aspect graph for polyhedral objects is described the aspects graph is a representation of three dimensional objects by a set of two dimensional views the set of viewpoints on the gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same at the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes it is shown that for polyhedral objects there are two fundamental visual events 1 the projections of an edge and a vertex coincide and 2 the projections of three nonadjacent edges intersect at a point the geometry of the object is reflected in the locus of the accidental viewpoints the algorithm computes the partition together with a representative view for each region of the partition

stochastic simulation algorithms for solving a nonlinear system of drift diffusion poisson equations of semiconductors abstract stochastic simulation algorithms for solving transient nonlinear drift diffusion recombination transport equations are developed the governing system of equations includes two drift diffusion equations coupled with a poisson equation for the potential whose gradient forms the drift velocity a stochastic algorithm for solving nonlinear drift diffusion equations is proposed here for the first time in each time step the method calculates the solution on a cloud of points using a new global monte carlo random walk and cellular automata algorithms the poisson equation is solved by a global version of the random walk on spheres method which calculates both the solutions and the derivatives without using finite difference approximations the method is also able to calculate fluxes to any desired part of the boundary from arbitrary sources for transient drift diffusion equations we suggest a stochastic expansion from cell to cell algorithm for calculating the whole solution field all new global random walk algorithms developed in this paper are validated by comparing the simulation results with exact solutions application of the developed method to solve a system of 2d transport equations for electrons and holes in a semiconductor is given

a closed form expression of the positional uncertainty for 3d point clouds we present a novel closed form expression of positional uncertainty measured by a near monostatic and time of flight laser range finder with consideration of its measurement uncertainties an explicit form of the angular variance of the estimated surface normal vector is also derived this expression is useful for the precise estimation of the surface normal vector and the outlier detection for finding correspondence in order to register multiple three dimensional point clouds two practical algorithms using these expressions are presented a method for finding optimal local neighbourhood size which minimizes the variance of the estimated normal vector and a resampling method of point clouds

probabilistic modeling and recognition of 3 d objects this paper introduces a uniform statistical framework for both 3 d and 2 d object recognition using intensity images as input data the theoretical part provides a mathematical tool for stochastic modeling the algorithmic part introduces methods for automatic model generation localization and recognition of objects 2 d images are used for learning the statistical appearance of 3 d objectss both the depth information and the matching between image and model features are missing for model generation the implied incomplete data estimation problem is solved by the expectation maximization algorithm this leads to a novel class of algorithms for automatic model generation from projections the estimation of pose parameters corresponds to a non linear maximum likelihood estimation problem which is solved by a global optimization procedure classification is done by the bayesian decision rule this work includes the experimental evaluation of the various facets of the presented approach an empirical evaluation of learning algorithms and the comparison of different pose estimation algorithms show the feasibility of the proposed probabilistic framework

an estimation based approach for range image segmentation on the reliability of primitive extraction this paper presents a new algorithm for estimation based range image segmentation aiming at surface primitive extraction from range data we focus on the reliability of the primitive representation in the process of region estimation we introduce an optimal description of surface primitives by which the uncertainty of a region estimate is explicitly represented with a covariance matrix then the reliability of an estimate is interpreted in terms of measure of uncertainty the segmentation approach follows the region growing scheme in which the regions are estimated in an iterative way with the probabilistic model proposed in this paper surface homogeneity is defined and tested by an optimal criterion a notable feature of the algorithm is that the order of merging is organized to lead the growth towards the most reliable representation of the merged region concerned with man made objects in the scene we restrict the class of surface primitives to be quadric or planar the proposed algorithm has been applied to real data and synthetic data and demonstrated with experimental results

computing exact aspect graphs of curved objects algebraic surfaces this article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface orthographic projection is assumed the algorithm is based on a catalog of visual events available from singularity theory it uses curve tracing cell decomposition homotopy continuation and ray tracing to construct the regions of the view sphere delineated by visual event curves the algorithm has been fully implemented and examples are presented

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

cellular automation model of reaction transport processes abstract the transport and chemical reactions of solutes are modelled as a cellular automation in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule the model describes advection and diffusion in a simple way and as no restriction is placed on the number of particles at a lattice site it is also able to describe a wide variety of chemical reactions assuming molecular chaos and a smooth density function we obtain the standard reaction transport equations in the continuum limit simulations on one an two dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations we discuss discrepancies which arise from correlations between molecules and how these disappear as the continuum limit is approached of particular interest are simulations displaying long time behaviour which depends on long wavelength statistical fluctuations not accounted for by the standard equations the model is applied to the reactions a b c and a b c with homogenous and inhomogenous initial conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration patterns

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

visibility occlusion and the aspect graph this chapter studies the ways in which the topology of the image of a polyhedron changes with changing viewpoint we catalog the ways that the topological appearance or aspect can change this enables us to find maximal regions of viewpoints of the same aspect we use these techniques to construct the viewpoint space partition vsp a partition of viewpoint space into maximal regions of constant aspect and its dual the aspect graph here we present tight bounds on the maximum size of the vsp and the aspect graph and give algorithms for their construction first in the convex case and then in the general case in particular we give bounds on the maximum size of n 2 and n 6 under an orthographic projection viewing model and of n 3 and n 9 under a perspective viewing model the algorithms make use of a new representation of the appearance of polyhedra from all viewpoints called the aspect representation or asp we believe that this representation is one of the significant contributions of this paper

a computational model of view degeneracy we quantify the observation by kender and freudenstein 1987 that degenerate views occupy a significant fraction of the viewing sphere surrounding an object for a perspective camera geometry we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object for a typical recognition system parameterization view degeneracies typically occur with probabilities of 20 percent and depending on the parameterization as high as 50 percent we discuss the impact of view degeneracy on the problem of object recognition and for a particular recognition framework relate the cost of object disambiguation to the probability of view degeneracy to reduce this cost we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view in order to validate both our view degeneracy model as well as our active focal length control model a set of experiments are reported using a real recognition system operating on real images

visual events identification of solids of revolution from perspective views abstract an algorithm is presented for identifying the visual events of solids of revolution from a perspective point of view the object representation model comprises of these different visual events or aspects which can be applied for object identification algorithms have been developed to handle general polyhedral objects from either orthographic or perspective views or to compute the aspect graph of solids of revolution using the orthographic projection the orthographic view aims to find the aspects of the solid of revolution which are purely object oriented the theory of differential geometry can be applied sufficiently to find the aspects without referring to the distance of the viewer in the real case the distance effect that may influence the aspect dramatically when the viewer is close to the object has to be considered for instance to generate the same aspect the viewer may have to change his viewing directions when he is at a different distance from the object firstly this paper uses the constraint of contour generator to identify the aspects of solids of revolution under perspective projection the difference between our approach and the others is the distance effect the present method combines the object oriented and viewer oriented aspect finding secondly a method is developed to find the limb termination point of the non transparent object from a certain perspective viewpoint many aspect finding methods are developed for transparent objects i e objects made of glass of which the projection contour limb is continuous for non transparent objects the self occlusion may induce the limb termination phenomena

uncertainty minimization in the localization of polyhedral objects a straightforward method is presented for the determination of the optimal sensor exploration in the localization of a polyhedral object whose geometry is known optimality is intended in the sense of the a posteriori covariance matrix of the object position and orientation parameters the method consists in decomposing the problem into simpler subproblems each one relative to a single planar face of the object it requires reasonable processing time i e comparable with the sensor activation time

three dimensional weak visibility complexity and applications abstract in this paper we study the complexity of 3d weak visibility we obtain an o n 8 time and n 6 space algorithm to compute the weakly visible region of a triangle f from another triangle g among general scenes which are a set of n disjoint triangles we also consider the cases when the scenes are rectilinear objects and polyhedral terrains we show that in these special situations the weakly visible regions can be computed much faster in o n 6 time and o n 4 space with these results we obtain the first known polynomial time algorithm to decide whether or not a simple polyhedron is weakly internally or externally visible

choice and value flexibility jointly contribute to the capacity of a subsampled quadratic classifier biophysical modeling studies have suggested that neurons with active dendrites can be viewed as linear units augmented by product terms that arise from interactions between synaptic inputs within the same dendritic subregions however the degree to which local nonlinear synaptic interactions could augment the memory capacity of a neuron is not known in a quantitative sense to approach this question we have studied the family of subsampled quadratic classifiers linear classifiers augmented by the best k terms from the set of k d2 d 2 second order product terms available in d dimensions we developed an expression for the total parameter entropy whose form shows that the capacity of an sq classifier does not reside solely in its conventional weight values the explicit memory used to store constant linear and higher order coefficients rather we identify a second type of parameter flexibility that jointly contributes to an sq classifier s capacity the choice as to which product terms are included in the model and which are not we validate the form of the entropy expression using empirical studies of relative capacity within families of geometrically isomorphic sq classifiers our results have direct implications for neurobiological and other hardware learning systems where in the limit of high dimensional input spaces and low resolution synaptic weight values this relatively little explored form of choice flexibility could constitute a major source of trainable model capacity

a comparison of fuzzy shell clustering methods for the detection of ellipses in this paper we introduce a shell clustering algorithm for ellipsoidal clusters based on the so called radial distance which can be easily extended to superquadric clusters we compare our algorithm with other algorithms in the literature that are based on the algebraic distance the approximate distance the normalized radial distance and the exact distance we evaluate the performance of each algorithm on two dimensional data sets containing scattered ellipses partial ellipses outliers and ellipses of disparate sizes and summarize the relative strengths and weaknesses of each algorithm

vc dimension of an integrate and fire neuron model we compute the vc dimension of a leaky integrate and fire neuron model the vc dimension quantifies the ability of a function class to partition an input pattern space and can be considered a measure of computational capacity in this case the function class is the class of integrate and fire models generated by varying the integration time constant t and the threshold the input space they partition is the space of continuous time signals and the binary partition is specified by whether or not the model reaches threshold at some specified time we show that the vc dimension diverges only logarithmically with the input signal bandwidth n we also extend this approach to arbitrary passive dendritic trees the main contributions of this work are 1 it offers a novel treatment of computational capacity of this class of dynamic system and 2 it provides a framework for analyzing the computational capabilities of the dynamic systems defined by networks of spiking neurons

from uncertainty to visual exploration the authors attempt to determine what can be inferred from ambiguity in processes of visual interpretation they discuss this question in a specific context the interpretation of scene geometry in the form of parametrized volumetric models ambiguity is described as a local probabilistic property of the misfit error surface in the parameter space of superellipsoid models namely as an ellipsoid of confidence in which there is a given probability that the true parameters can be found the authors show how to project the ellipsoid of confidence back into 3d space to obtain the shell in which the true 3d surface most probably lies and introduce what they call the uncertainty as a local property of the fitted model s surface they propose a technique that can use this information to plan a new direction of view that minimizes the ambiguity of subsequent interpretation

global surface reconstruction by purposive control of observer motion abstract what viewpoint control strategies are important for performing global visual exploration tasks such as searching for specific surface markings building a global model of an arbitrary object or recognizing an object in this paper we consider the task of purposefully controlling the motion of an active monocular observer in order to recover a global description of a smooth arbitrarily shaped object we formulate global surface reconstruction as the task of controlling the motion of the observer so that the visible rim slides over the maximal connected reconstructible surface regions intersecting the visible rim at the initial viewpoint we show that these regions are bounded by a subset of the visual event curves defined on the surface by studying the epipolar parameterization we develop two basic strategies that allow reconstruction of a surface region around any point in a reconstructible surface region these strategies control viewpoint to achieve and maintain a well defined geometric relationship with the object s surface rely only on information extracted directly from images e g tangents to the occluding contour and are simple enough to be performed in real time we then show how global surface reconstruction can be provably achieved by 1 appropriately integrating these strategies to iteratively grow the reconstructed regions and 2 obeying four simple rules

uncertainty propagation in model based recognition robust recognition systems require a careful understanding of the effects of error in sensed features in model based recognition matches between model features and sensed image features typically are used to compute a model pose and then project the unmatched model features into the image the error in the image features results in uncertainty in the projected model features we first show how error propagates when poses are based on three pairs of 3d model and 2d image points in particular we show how to simply and efficiently compute the distributed region in the image where an unmatched model point might appear for both gaussian and bounded error in the detection of image points and for both scaled orthographic and perspective projection models next we provide geometric and experimental analyses to indicate when this linear approximation will succeed and when it will fail then based on the linear approximation we show how we can utilize linear programming to compute bounded propagated error regions for any number of initial matches finally we use these results to extend from two dimensional to three dimensional objects robust implementations of alignment interpretation tree search and transformation clustering

nonlinear population codes theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information however recent theoretical studies have investigated the effect of crosscorrelations in the trial to trial fluctuations of the neuronal responses on the accuracy of the representation assuming that only the first order statistics of the neuronal responses are tuned to the stimulus these studies have shown that in the presence of correlations similar to those observed experimentally in cortical ensembles of neurons the amount of information in the population is limited yielding nonzero error levels even in the limit of infinitely large populations of neurons in this letter we study correlated neuronal populations whose higher order statistics and in particular response variances are also modulated by the stimulus we ask two questions does the correlated noise limit the accuracy of the neuronal representation of the stimulus and how can a biological mechanism extract most of the information embedded in the higher order statistics of the neuronal responses specifically we address these questions in the context of a population of neurons coding an angular variable we show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise this information cannot be extracted by linear readout schemes including the linear population vector instead we propose a bilinear readout scheme that involves spatial decorrelation quadratic non linearity and population vector summation we show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters with an efficiency that grows linearly with the population size this code can be implemented using biologically plausible neurons

generalized random walk algorithm for the numerical modeling of complex diffusion processes a generalized form of the random walk algorithm to simulate diffusion processes is introduced unlike the usual approach at a given time all the particles from a grid node are simultaneously scattered using the bernoulli repartition this procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations we prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles as an example simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested 2003 elsevier science b v all rights reserved

recovery of parametric models from range images the case for superquadrics with global deformations a method for recovery of compact volumetric models for shape representation of single part objects in computer vision is introduced the models are superquadrics with parametric deformations bending tapering and cavity deformation the input for the model recovery is three dimensional range points model recovery is formulated as a least squares minimization of a cost function for all range points belonging to a single part during an iterative gradient descent minimization process all model parameters are adjusted simultaneously recovery position orientation size and shape of the model such that most of the given range points lie close to the model s surface a specific solution among several acceptable solutions where are all minima in the parameter space can be reached by constraining the search to a part of the parameter space the many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization results using real range data show that the recovered models are stable and that the recovery procedure is fast

efficiently computing and representing aspect graphs of polyhedral objects an efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented the aspect graph is an approach to representing 3 d objects by a set of 2 d views for the purpose of object recognition in this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change the viewing data of an object is the partition of the viewpoint space together with a representative view in each region the algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection

combination of the meshless finite difference approach with the monte carlo random walk technique for solution of elliptic problems abstract this paper proposes a stochastic approach for the fast and effective numerical analysis of the second order elliptic differential equations it is based upon the well known monte carlo mc method with a random walk rw technique carried out on the grid of points this method allows for accurate estimation of the solution of the differential equation at selected point s of the domain and or its boundary it extends the standard formulation of the monte carlo random walk mc rw approach by means of its appropriate combination with the meshless version of the finite difference method in this manner the proposed approach may deal with elliptic equations in more general non homogeneous form as well as boundary conditions of both essential and natural types moreover arbitrarily irregular clouds of nodes may be used with no a priori imposed nodes structure therefore the meshless mc rw approach may be applied to the significantly wider class of problems with more complex geometry this concept was examined on variety of 2d boundary value problems selected numerical results are presented and discussed a simple matlab code is included as well

aspect graph generation for non convex polyhedra from perspective projection view abstract the aspect graph is basically a multiple view representation of the designated three dimensional 3d object in this paper a complete algorithm is presented for constructing the aspect graph of general polyhedral objects from the perspective point of view the aspect graph generation is based on a so called visual event these visual events will completely capture the way the appearance of an edge or a face can be occluded by other faces and edges in the model all the visual events can be found for polyhedra as facial ee and eee events the facial event indicates the visibility transition of the faces the ee event indicates the possible visibility variation of the occlusion of two edges and the eee event represents another visibility change the consecutive occlusion among three edges the system consists of the following five stages 1 find the viewing cell for each planar face ee event and eee event and then create the parcellation graph 2 employ the parcellation graph to create a face level enumeration array and edge level enumeration array 3 generate test points 4 examine plausible cells that enclose a volume of viewing space and 5 generate an explicit aspect graph structure finally nine non convex polyhedra are obtained in the experiments the aspect graphs of these non regular shaped objects can be easily generated by this system

spectral embedding of graphs in this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern space we adopt a graph spectral approach we use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix for each eigenmode we compute vectors of spectral properties these include the eigenmode perimeter eigenmode volume cheeger number inter mode adjacency matrices and intermode edge distance we embed these vectors in a pattern space using two contrasting approaches the first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors the second approach involves performing multidimensional scaling on the l2 norm for pairs of pattern vectors we illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2d images of 3d polyhedral objects two problems are investigated the first of these is the clustering of graphs representing distinct objects viewed from different directions the second is the identification of characteristic views of single objects these two studies reveal that both embedding methods result in well structured view spaces for graph data extracted from 2d views of 3d objects

a robust approach to image enhancement based on fuzzy logic in this paper we propose a robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement i removing impulse noise ii smoothing out nonimpulse noise and iii enhancing or preserving edges and certain other salient structures we derive three different filters for each of the above three tasks using the weighted or fuzzy least squares ls method and define the criteria for selecting each of the three filters the criteria are based on the local context and they constitute the antecedent clauses of the fuzzy rules the overall result of the fuzzy rule based system is the combination of the results of the individual filters where each result contributes to the degree that the corresponding antecedent clause is satisfied this approach gives us a powerful and flexible image enhancement paradigm results of the proposed method on several types of images are compared with those of other standard techniques

describing complicated objects by implicit polynomials this paper introduces and focuses on two problems first is the representation power of closed implicit polynomials of modest degree for curves in 2 d images and surfaces in 3 d range data super quadrics are a small subset of object boundaries that are well fitted by these polynomials the second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces the attractive features of these polynomials for vision is discussed

vc dimension and uniform learnability of sparse polynomials and rational functions the authors prove upper and lower bounds on the vc dimension of sparse univariate polynomials over reals and apply these results to prove uniform learnability of sparse polynomials and rational functions as an application the solution to the open problem of vapnik in estimation of dependences based on empirical data springer verlag berlin 1982 on computational approximation of the regression in a class of polynomials used in the theory of empirical data dependences is given