subspace averaging and order determination for source enumeration in this paper we address the problem of subspace averaging with special emphasis placed on the question of estimating the dimension of the average the results suggest that the enumeration of sources in a multi sensor array which is a problem of estimating the dimension of the array manifold and as a consequence the number of radiating sources may be cast as a problem of averaging subspaces this point of view stands in contrast to conventional approaches which cast the problem as one of identifiying covariance models in a factor model we present a robust formulation of the proposed order fitting rule based on majorization minimization algorithms a key element of the proposed method is to construct a bootstrap procedure based on a newly proposed discrete distribution on the manifold of projection matrices for stochastically generating subspaces from a function of experimentally determined eigenvalues in this way the proposed subspace averaging sa technique determines the order based on the eigenvalues of an average projection matrix rather than on the likelihood of a covariance model penalized by functions of the model order by means of simulation examples we show that the proposed sa criterion is especially effective in high dimensional scenarios with low sample support

application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

three dimensional face shape by local fitting to a single reference model the authors present a simple method to estimate the three dimensional shape of a face from an input image using a single reference model based on least squares between the output of the linear nonlinear ln neuronal model applied to blocks from an intensity image and blocks from a depth reference model the authors present the results obtained by varying the ln model parameters and estimate their best values which provide an acceptable reconstruction of each subject s depth the authors show that increasing the light source angle over the horizontal plane in the input image produces slight increases in reconstruction error but increasing the ambient light proportion produces greater increases in reconstruction error the authors applied the method to predict each subject s unknown depth using different individual reference models and an average reference model which provides the best results as a noise reduction technique the authors perform a point by point weighted averaging with the average reference model with weights equal to the fractions of the squares of the laplacian of a gaussian applied to the prediction and to the reference depth over the sum of both finally the authors present acceptable visual results obtained from external images of faces under arbitrary illumination having performed an illumination estimation previously

range image registration using a photometric metric under unknown lighting based on the spherical harmonics representation of image formation we derive a new photometric metric for evaluating the correctness of a given rigid transformation aligning two overlapping range images captured under unknown distant and general illumination we estimate the surrounding illumination and albedo values of points of the two range images from the point correspondences induced by the input transformation we then synthesize the color of both range images using albedo values transferred using the point correspondences to compute the photometric reprojection error this way allows us to accurately register two range images by finding the transformation that minimizes the photometric reprojection error we also propose a practical method using the proposed photometric metric to register pairs of range images devoid of salient geometric features captured under unknown lighting our method uses a hypothesize and test strategy to search for the transformation that minimizes our photometric metric transformation candidates are efficiently generated by employing the spherical representation of each range image experimental results using both synthetic and real data demonstrate the usefulness of the proposed metric

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

shape estimation from shading defocus and correspondence using light field angular coherence light field cameras are quickly becoming commodity items with consumer and industrial applications they capture many nearby views simultaneously using a single image with a micro lens array thereby providing a wealth of cues for depth recovery defocus correspondence and shading in particular apart from conventional image shading one can refocus images after acquisition and shift one s viewpoint within the sub apertures of the main lens effectively obtaining multiple views we present a principled algorithm for dense depth estimation that combines defocus and correspondence metrics we then extend our analysis to the additional cue of shading using it to refine fine details in the shape by exploiting an all in focus image in which pixels are expected to exhibit angular coherence we define an optimization framework that integrates photo consistency depth consistency and shading consistency we show that combining all three sources of information defocus correspondence and shading outperforms state of the art light field depth estimation algorithms in multiple scenarios

a fast method for robot location determination abstract a fast single view method for determining the location of mobile robot in 3 d space is proposed in the method a tetragon mark is used as the reference target and no prerequisite condition is imposed in grabbing the image the method utilizes the 3 d vector analysis technique and simple algebraic computation to achieve the fast location determination error analysis on the effects of sensor resolution in different distances and elevation angles is included experimental results show that the location determination time is about 0 22 s in a 12 mhz ibm compatible pc at computer system and the location error is less than 2 in average

prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

robust regression for face recognition in this paper we address the problem of robust face recognition by formulating the pattern recognition task as a problem of robust estimation using a fundamental concept that in general patterns from a single object class lie on a linear subspace barsi and jacobs 2003 1 we develop a linear model representing a probe image as a linear combination of class specific galleries in the presence of noise the well conditioned inverse problem is solved using the robust huber estimation and the decision is ruled in favor of the class with the minimum reconstruction error the proposed robust linear regression classification rlrc algorithm is extensively evaluated for two important cases of robustness i e illumination variations and random pixel corruption illumination invariant face recognition is demonstrated on three standard databases under exemplary evaluation protocols reported in the literature comprehensive comparative analysis with the state of art illumination tolerant approaches indicates a comparable performance index for the proposed rlrc algorithm the efficiency of the proposed approach in the presence of severe random noise is validated under several exemplary noise models such as dead pixel problem salt and pepper noise speckle noise and additive white gaussian noise awgn the rlrc algorithm is found to be favorable compared with the benchmark generative approaches

linear regression for face recognition in this paper we present a novel approach of face identification by formulating the pattern recognition problem in terms of linear regression using a fundamental concept that patterns from a single object class lie on a linear subspace we develop a linear model representing a probe image as a linear combination of class specific galleries the inverse problem is solved using the least squares method and the decision is ruled in favor of the class with the minimum reconstruction error the proposed linear regression classification lrc algorithm falls in the category of nearest subspace classification the algorithm is extensively evaluated on several standard databases under a number of exemplary evaluation protocols reported in the face recognition literature a comparative study with state of the art algorithms clearly reflects the efficacy of the proposed approach for the problem of contiguous occlusion we propose a modular lrc approach introducing a novel distance based evidence fusion def algorithm the proposed methodology achieves the best results ever reported for the challenging problem of scarf occlusion

finding a sparse vector in a subspace linear sparsity using alternating directions is it possible to find the sparsest vector direction in a generic subspace mathcal s subseteq mathbb r p with text dim left mathcal s right n this problem can be considered a homogeneous variant of the sparse recovery problem and finds connections to sparse dictionary learning sparse pca and many other problems in signal processing and machine learning in this paper we focus on a planted sparse model for the subspace the target sparse vector is embedded in an otherwise random subspace simple convex heuristics for this planted recovery problem provably break down when the fraction of nonzero entries in the target sparse vector substantially exceeds o 1 sqrt n in contrast we exhibit a relatively simple nonconvex approach based on alternating directions which provably succeeds even when the fraction of nonzero entries is omega 1 to the best of our knowledge this is the first practical algorithm to achieve linear scaling under the planted sparse model empirically our proposed algorithm also succeeds in more challenging data models e g sparse dictionary learning

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

relations among some low rank subspace recovery models recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications in recent years a lot of work has modeled subspace recovery as low rank minimization problems we find that some representative models such as robust principal component analysis r pca robust low rank representation r lrr and robust latent low rank representation r latlrr are actually deeply connected more specifically we discover that once a solution to one of the models is obtained we can obtain the solutions to other models in closed form formulations since r pca is the simplest our discovery makes it the center of low rank subspace recovery models our work has two important implications first r pca has a solid theoretical foundation under certain conditions we could find globally optimal solutions to these low rank models at an overwhelming probability although these models are nonconvex second we can obtain significantly faster algorithms for these models by solving r pca first the computation cost can be further cut by applying low complexity randomized algorithms for example our novel filtering algorithm to r pca although for the moment the formal proof of our filtering algorithm is not yet available experiments verify the advantages of our algorithm over other state of the art methods based on the alternating direction method

the drift of a one dimensional self avoiding random walk we prove that a self avoiding random walk on the integers with bounded increments grows linearly we characterize its drift in terms of the frobenius eigenvalue of a certain one parameter family of primitive matrices as an important tool we express the local times as a two block functional of a certain markov chain which is of independent interest

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

color image segmentation using adaptive mean shift and statistical model based methods in this paper we propose an unsupervised segmentation algorithm for color images based on gaussian mixture models gmms the number of mixture components is determined automatically by adaptive mean shift in which local clusters are estimated by repeatedly searching for higher density points in feature vector space for the estimation of parameters of gmms the mean field annealing expectation maximization em is employed the mean field annealing em provides a global optimal solution to overcome the local maxima problem in a mixture model by combining the adaptive mean shift and the mean field annealing em natural color images are segmented automatically without over segmentation or isolated regions the experiments show that the proposed algorithm can produce satisfactory segmentation without any a priori information

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

two stage image denoising by principal component analysis with local pixel grouping this paper presents an efficient image denoising scheme by using principal component analysis pca with local pixel grouping lpg for a better preservation of image local structures a pixel and its nearest neighbors are modeled as a vector variable whose training samples are selected from the local window by using block matching based lpg such an lpg procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for pca transform estimation so that the image local features can be well preserved after coefficient shrinkage in the pca domain to remove the noise the lpg pca denoising procedure is iterated one more time to further improve the denoising performance and the noise level is adaptively adjusted in the second stage experimental results on benchmark test images demonstrate that the lpg pca method achieves very competitive denoising performance especially in image fine structure preservation compared with state of the art denoising algorithms

what is the set of images of an object under all possible illumination conditions the appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated if the appearance of two objects is never identical for any pose or lighting conditions then in theory the objects can always be distinguished or recognized the question arises what is the set of images of an object under all lighting conditions and pose in this paper we consider only the set of images of an object under variable illumination including multiple extended light sources and shadows we prove that the set of n pixel images of a convex object with a lambertian reflectance function illuminated by an arbitrary number of point light sources at infinity forms a convex polyhedral cone in r n and that the dimension of this illumination cone equals the number of distinct surface normals furthermore the illumination cone can be constructed from as few as three images in addition the set of n pixel images of an object of any shape and with a more general reflectance function seen under all possible illumination conditions still forms a convex cone in r n extensions of these results to color images are presented these results immediately suggest certain approaches to object recognition throughout we present results demonstrating the illumination cone representation

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

degradation of turbid images based on the adaptive logarithmic algorithm turbidity such as fog mist haze and smoke progressively reduces image contrast and visibility with increasing distance in this paper we propose an algorithm to degrade the turbid degree from the turbid image the turbidity can be considered as a kind of noise the basic assumption of the proposed algorithm is that an image consists of a reference intensity level and a characteristic intensity level the reference intensity level is considered as general or background intensity level and it can be obtained by a low pass filter the characteristic intensity level can be calculated by subtracting the reference intensity level from the original intensity level in the given image the human eye has a logarithmic intensity response so the target intensity level will be created by the adaptive logarithmic function to approach the human vision the turbid image will be degraded by transforming the characteristic intensity level into the target intensity level according to the proportion of the reference intensity level to the chosen target intensity level the experimental results show the varied degraded turbid image as well as compared with other algorithms

polyhedron recognition using three view analysis abstract using three view analysis this paper proposes a new approach for single polyhedron recognition both the 3d surface data and 2d image projection patterns are used to find the exact corresponding model of an unknown input object the recognition process first applies a hypothesis generation verification process to match the 3d partial object of the unknown input which is reconstructed by applying the three view matching strategy chiou et al proc ics 88 pp 1516 1521 1988 and the polyhedron reconstruction process hung et al pattern recognition 22 231 246 1989 against the data based models for selecting the possible corresponding models candidates it then backprojects each candidate onto the three image planes and matches the outer boundaries of the three backprojections by a simple method for judging the exact corresponding model measurement error is also analyzed theoretically to give a bound of the threshold value so that it can be automatically chosen in each decision making process the approach is implemented on a pc level vision system experimental results show that the system is feasible and reliable even in a noisy environment

weak interaction limits for one dimensional random polymers in this paper we present a new and flexible method to show that in one dimension various self repellent random walks converge to self repellent brownian motion in the limit of weak interaction after appropriate space time scaling our method is based on cutting the path into pieces of an appropriately scaled length controlling the interaction between the different pieces and applying an invariance principle to the single pieces in this way we show that the self repellent random walk large deviation rate function for the empirical drift of the path converges to the self repellent brownian motion large deviation rate function after appropriate scaling with the interaction parameters the method is considerably simpler than the approach followed in our earlier work which was based on functional analytic arguments applied to variational representations and only worked in a very limited number of situations

self intersections of 1 dimensional random walks consider a random walk snon the integers where the steps i have mean 0 and variance 2 let t be the time of first self intersection of the random walk it is shown that as t grows at rate 2 3 more precisely t 2 3 has a non degenerate limit distribution which can be described in terms of brownian motion local time

adaptive backstepping control of uncertain linear systems under unknown actuator delay trajectory tracking of uncertain time delay linear systems by output feedback control is of theoretical importance and practical value in this paper concentrating on a class of linear plants whose relative degree equals to system dimension we develop a lyapunov based control scheme to achieve trajectory tracking despite some classic difficulties including unmeasurable system state unknown plant parameters and unknown input time delay a comprehensive approach combining adaptive backstepping output feedback with prediction based boundary control is employed in the design the stability analysis exhibits the global boundedness of all closed loop system signals and the tracking performance is also guaranteed

an adaptive smith controller for time delay systems with relative degree n 2 abstract this paper addresses the control of time delay systems whose relative degree does not exceed two an adaptive smith controller together with an adaptive law similar to the delay free case is proposed by using lyapunov krasovskii functionals for an appropriate model transformation of the original system semiglobal stability of the closed loop system and asymptotic convergence of the output error is established strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties robustness properties of the adaptive controller are briefly discussed

polymers as self avoiding walks a brief overview is presented of the relation of the properties of real polymers to the problem of self avoiding random walks the self consistent field method is discussed wherein the non markovian continuous self avoiding polymer is replaced by a self consistent markovian approximation an outline is presented of the method of solution of the resultant nonlinear integrodifferential equations a description is also presented of the scaling theories which provide a means for deducing some exponents in the asymptotic dependence of walk properties on the length of the walk in the limit of infinite length walks

numerical scheme for efficient colour image denoising in this paper we are interested by the enhancement of colour images where we present a numerical scheme to implement a non linear diffusion filter this scheme is developed to denoise colour images corrupted by additive noise the method is based on harmonic averaging that takes into account correlation between all colour components of the image by using a common gradient magnitude which can be computed by using the di zenzo idea and a marginal gradient magnitude in order to conserve the self behaviour of each colour component the proposed scheme is an efficient tool at image selective smoothing in presence of strong noise this analysis shows that our method performs better than some related works and particularly in avoiding colour artifacts

model driven domain adaptation on product manifolds for unconstrained face recognition many classification algorithms see a reduction in performance when tested on data with properties different from that used for training this problem arises very naturally in face recognition where images corresponding to the source domain gallery training data and the target domain probe testing data are acquired under varying degree of factors such as illumination expression blur and alignment in this paper we account for the domain shift by deriving a latent subspace or domain which jointly characterizes the multifactor variations using appropriate image formation models for each factor we formulate the latent domain as a product of grassmann manifolds based on the underlying geometry of the tensor space and perform recognition across domain shift using statistics consistent with the tensor geometry more specifically given a face image from the source or target domain we first synthesize multiple images of that subject under different illuminations blur conditions and 2d perturbations to form a tensor representation of the face the orthogonal matrices obtained from the decomposition of this tensor where each matrix corresponds to a factor variation are used to characterize the subject as a point on a product of grassmann manifolds for cases with only one image per subject in the source domain the identity of target domain faces is estimated using the geodesic distance on product manifolds when multiple images per subject are available an extension of kernel discriminant analysis is developed using a novel kernel based on the projection metric on product spaces furthermore a probabilistic approach to the problem of classifying image sets on product manifolds is introduced we demonstrate the effectiveness of our approach through comprehensive evaluations on constrained and unconstrained face datasets including still images and videos

the drift of a one dimensional self repellent random walk with bounded increments consider a one dimensional walk s k k having steps of bounded size and weight the probability of the path with some factor 1 0 1 for every single self intersection up to timen we prove thats n ss converges towards some deterministic number called the effective drift of the self repellent walk furthermore this drift is shown to tend to the basic drift as tends to 0 and as tends to 1 to the self avoiding walk s drift which is introduced in 10 the main tool of the present paper is a representation of the sequence of the local times as a functional of a certain markov process

globally stable adaptive controller for systems with delay we propose a globally stable finite spectrum assignment adaptive controller for systems with delay it is assumed that the process is minimum phase though not necessarily stable and the delay is known it is shown that the plant output asymptotically tracks a reference model output with all signals remaining bounded

linear time subspace clustering via bipartite graph modeling we present a linear time subspace clustering approach that combines sparse representations and bipartite graph modeling the signals are modeled as drawn from a union of low dimensional subspaces and each signal is represented by a sparse combination of basis elements termed atoms which form the columns of a dictionary matrix the sparse representation coefficients are arranged in a sparse affinity matrix which defines a bipartite graph of two disjoint sets 1 atoms and 2 signals subspace clustering is obtained by applying low complexity spectral bipartite graph clustering that exploits the small number of atoms for complexity reduction the complexity of the proposed approach is linear in the number of signals thus it can rapidly cluster very large data collections performance evaluation of face clustering and temporal video segmentation demonstrates comparable clustering accuracies to state of the art at a significantly lower computational load

invariant feature extraction for 3d model retrieval an adaptive approach using euclidean and topological metrics with the fast development of 3d model construction and widespread popularity of 3d graphic engines more applications employ 3d geometric models to provide an interactive environment as the number of 3d models increases some 3d model retrieval systems have been proposed for indexing and matching these models an important issue in a retrieval system is feature extraction an efficient and invariant feature is a global shape distribution that collects some geometric properties of a model the d2 shape descriptor by osada et al is a one dimensional histogram of euclidean distances between two random points although the d2 is effective for some cases it changes when the model deforms we propose two shape descriptors in this paper gd which is the topological metric and asf which combines both euclidean and topological metrics the topological metric is an invariant deformation factor the two features are also robust against common geometric processing including scaling rotation resampling compression and remeshing in experiments we implement these methods and confirm their feasibility

prediction based control for lti systems with uncertain time varying delays and partial state knowledge abstractthe stability of a prediction based controller for linear time invariant lti systems is studied in the presence of time varying input and output delays the uncertain delay case is treated as well as the partial state knowledge case the reduction method is used in order to prove the convergence of the closed loop system including the state observer the predictor and the plant explicit conditions that guarantee the closed loop stability are given thanks to a lyapunov razumikhin analysis simulations illustrate the theoretical results

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

rank constraints for homographies over two views revisiting the rank four constraint it is well known that one can collect the coefficients of five or more homographies between two views into a large rank deficient matrix in principle this implies that one can refine the accuracy of the estimates of the homography coefficients by exploiting the rank constraint however the standard rank projection approach is impractical for two different reasons it requires many homographies to even score a modest gain and secondly correlations between the errors in the coefficients will lead to poor estimates in this paper we study these problems and provide solutions to each firstly we show that the matrices of the homography coefficients can be recast into two parts each consistent with ranks of only one this immediately establishes the prospect of realistically that is with as few as only three or four homographies exploiting the redundancies of the homographies over two views we also tackle the remaining issue correlated coefficients we compare our approach with the gold standard that is non linear bundle adjustment initialized from the ground truth estimate the ideal initialization the results confirm our theory and show one can implement rank constrained projection and come close to the gold standard in effectiveness indeed our algorithm by itself or our algorithm further refined by a bundle adjustment stage may be a practical algorithm providing generally better results than the standard dlt direct linear transformation algorithm and even better than the bundle adjustment result with the dlt result as the starting point our unoptimized version has roughly the same cost as bundle adjustment and yet can generally produce close to the gold standard estimate as illustrated by comparison with bundle adjustment initialized from the ground truth independent of the merits or otherwise of our algorithm we have illuminated why the naive approach of direct rank projection is relatively doomed to failure moreover in revealing that there are further rank constraints not previously known we have added to the understanding of these issues and this may pave the way for further improvements

a novel color detection method based on hsl color space for robotic soccer competition in a robotic soccer competition the locations of the ball and the robot are recognized through the vision system in a strong dynamic environment therefore the robot and the computer need to identify the object in real time and accurately through the vision system due to the influence of the game ball under different brightnesses the color clusters of glossy materials will produce a nonlinear behavior and will cause difficulty of recognition thus we propose a novel color detection method based on hue saturation and lightness hsl color space in this paper firstly by utilizing the hue histogram the hue and saturation hs plane and the hue and lightness hl plane can be obtained respectively in addition based on the obtained information from two planes the databases can be built for decreasing the running time and increasing the recognition success rate of identifying object moreover a novel algorithm is presented for the game ball in the robotic soccer competition finally some examples under different brightnesses are illustrated to demonstrate the preciseness and the accuracy of the proposed method are better than the traditional method

detection and classification of areca nuts with machine vision in this study we present an application of neural networks and image processing techniques for detecting and classifying the quality of areca nuts defects with diseases or insects of areca nuts were segmented by a detection line dl method six geometric features i e the principle axis length the secondary axis length axis number area perimeter and compactness of the areca nut image 3 color features i e the mean gray level of an areca nut image on the r g and b bands and defects area were used in the classification procedure a back propagation neural network classifier was employed to sort the quality of areca nuts the methodology presented herein effectively works for classifying areca nuts to an accuracy of 90 9

efficient object identification and localization for image retrieval using query by region localizing an object within an image is a common task in the field of computer vision and represents the first step towards the solution of the recognition problem this paper presents an efficient approach to object localization for image retrieval using query by region the new algorithm utilizes correlogram back projection in the ycbcr chromaticity components to handle the problem of subregion querying utilizing similar spatial color information enables users to detect and locate primary location and candidate regions accurately without the need for further information about the number of objects comparing this new approach to existing methods an improvement of 21 was observed in experimental trials these results reveal that color correlograms are markedly more effective than color histograms for this task

particle filter with a mode tracker for visual tracking across illumination changes in this correspondence our goal is to develop a visual tracking algorithm that is able to track moving objects in the presence of illumination variations in the scene and that is robust to occlusions we treat the illumination and motion x y translation and scale parameters as the unknown state sequence the observation is the entire image and the observation model allows for occasional occlusions modeled as outliers the nonlinearity and multimodality of the observation model necessitate the use of a particle filter pf due to the inclusion of illumination parameters the state dimension increases thus making regular pfs impractically expensive we show that the recently proposed approach using a pf with a mode tracker can be used here since even in most occlusion cases the posterior of illumination conditioned on motion and the previous state is unimodal and quite narrow the key idea is to importance sample on the motion states while approximating importance sampling by posterior mode tracking for estimating illumination experiments demonstrate the advantage of the proposed algorithm over existing pf based approaches for various face and vehicle tracking we are also able to detect illumination model changes e g those due to transition from shadow to sunlight or vice versa by using the generalized expected log likelihood statistics and successfully compensate for it without ever loosing track

determining generative models of objects under varying illumination shape and albedo from multiple images using svdand integrability we describe a method of learning generative models of objects from a set of images of the object under different and unknown illumination such a model allows us to approximate the objects appearance under a range of lighting conditions this work is closely related to photometric stereo with unknown light sources and in particular to the use of singular value decomposition svd to estimate shape and albedo from multiple images up to a linear transformation hayakawa 1994 firstly we analyze and extend the svd approach to this problem we demonstrate that it applies to objects for which the dominant imaging effects are lambertian reflectance with a distant light source and a background ambient term to determine that this is a reasonable approximation we calculate the eigenvectors of the svd on a set of real objects under varying lighting conditions and demonstrate that the first few eigenvectors account for most of the data in agreement with our predictions we then analyze the linear ambiguities in the svd approach and demonstrate that previous methods proposed to resolve them hayakawa 1994 are only valid under certain conditions we discuss alternative possibilities and in particular demonstrate that knowledge of the object class is sufficient to resolve this problem secondly we describe the use of surface consistency for putting constraints on the possible solutions we prove that this constraint reduces the ambiguities to a subspace called the generalized bas relief ambiguity gbr which is inherent in the lambertian reflectance function and which can be shown to exist even if attached and cast shadows are present belhumeur et al 1997 we demonstrate the use of surface consistency to solve for the shape and albedo up to a gbr and describe and implement a variety of additional assumptions to resolve the gbr thirdly we demonstrate an iterative algorithm that can detect and remove some attached shadows from the objects thereby increasing the accuracy of the reconstructed shape and albedo

a central limit theorem for a one dimensional polymer measure let s n n n 0 be a random walk on the integers having bounded steps the self repellent resp self avoiding walk is a sequence of transformed path measures which discourage resp forbid self intersections this is used as a model for polymers previously we proved a law of large numbers that is we showed the convergence of s n n toward a positive number under the polymer measure the present paper proves a classical central limit theorem for the self repellent and self avoiding walks that is we prove the asymptotic normality of s n n n for large n the proof refines and continues results and techniques developed previously

discrimination on the grassmann manifold fundamental limits of subspace classifiers we derive fundamental limits on the reliable classification of linear and affine subspaces from noisy linear features drawing an analogy between discrimination among subspaces and communication over vector wireless channels we define two shannon inspired characterizations of asymptotic classifier performance first we define the classification capacity which characterizes the necessary and sufficient conditions for vanishing misclassification probability as the signal dimension the number of features and the number of subspaces to be discriminated all approach infinity second we define the diversity discrimination tradeoff which by analogy with the diversity multiplexing tradeoff of fading vector channels characterizes relationships between the number of discernible subspaces and the misclassification probability as the feature noise power approaches zero we derive upper and lower bounds on these quantities which are tight in many regimes numerical results including a face recognition application validate the results in practice

face recognition the problem of compensating for changes in illumination direction a face recognition system must recognize a face from a novel image despite the variations between images of the same face a common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations examples of such representations are edge maps image intensity derivatives and images convolved with 2d gabor like filters here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination as well as viewpoint and facial expression our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination similar results were obtained for changes due to viewpoint and expression image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination however systems based only on such representations failed to recognize up to 20 percent of the faces in our database humans performed considerably better under the same conditions we discuss possible reasons for this superiority and alternative methods for overcoming illumination effects in recognition

on self repellent one dimensional random walks we consider an ordinary one dimensional recurrent random walk on a self repellent random walk is defined by changing the ordinary law of the random walk in the following way a path gets a new relative weight by multiplying the old one with a factor 1 for every self intersection of the path 0 1 is a parameter

a survey of one dimensional random polymers in the last decade there has been an enormous progress in the mathematical understanding of one dimensional polymer measures which are path measures that suppress self intersections we are currently in the situation that many interesting questions have either been answered or that essential new ideas are needed in this survey paper we discuss the most relevant results open questions and heuristics

extrinsic methods for coding and dictionary learning on grassmann manifolds sparsity based representations have recently led to notable results in various visual recognition tasks in a separate line of research riemannian manifolds have been shown useful for dealing with features and models that do not lie in euclidean spaces with the aim of building a bridge between the two realms we address the problem of sparse coding and dictionary learning in grassmann manifolds i e the space of linear subspaces to this end we propose to embed grassmann manifolds into the space of symmetric matrices by an isometric mapping this in turn enables us to extend two sparse coding schemes to grassmann manifolds furthermore we propose an algorithm for learning a grassmann dictionary atom by atom lastly to handle non linearity in data we extend the proposed grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional hilbert spaces experiments on several classification tasks gender recognition gesture classification scene analysis face recognition action recognition and dynamic texture classification show that the proposed approaches achieve considerable improvements in discrimination accuracy in comparison to state of the art methods such as kernelized affine hull method and graph embedding grassmann discriminant analysis

the generic bilinear calibration estimation problem we identify a very general recurring pattern in a number of well known problems in biological and machine vision many problems are of a peculiar double sided nature one attempts to estimate certain properties of the environment using a certain type of equipment and simultaneously one attempts to calibrate the same equipment on the structure of the environment at first sight this appears the kind of the chicken and the egg problem that might well prove to be insoluble however due to basic constraints that universally apply e g the world is only three dimensional a solution up to a certain class of ambiguity transformations often exists the more complicated the problem is the less important the remaining ambiguity will be at least in a relative sense many well known problems are special in that they can be cast in bilinear form sometimes after transformation or the introduction of dummy variables instances include photometric stereo photometric estimations e g of lightness local differential image operators a variety of photogrammetric problems etc it turns out that many of these problems and together these make up a large fraction of the generic problems in machine vision today can be cast in a simple universal framework this framework enables one to handle arbitrarily large that is not minimal consistent configurations noisy thus inconsistent date sets automatically the level at which prior information either of a deterministic or a statistical nature is used assumptions such as constant albedo rigidity uniform distributions etc is clearly separated as an additional typically nonlinear stage

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