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

netscal a network scaling algorithm for nonsymmetric proximity data a simple property of networks is used as the basis for a scaling algorithm that represents nonsymmetric proximities as network distances the algorithm determines which vertices are directly connected by an arc and estimates the length of each arc network distance defined as the minimum pathlength between vertices is assumed to be a generalized power function of the data the derived network structure however is invariant across monotonic transformations of the data a monte carlo simulation and applications to eight sets of proximity data support the practical utility of the algorithm

minimax length links of a dissimilarity matrix and minimum spanning trees a theorem is proved stating that the set of all minimax links defined as links minimizing over paths the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph comprise the union of all minimum spanning trees of that graph this theorem is related to methods of fitting network models to dissimilarity data particularly a method called pathfinder due to schvaneveldt and his colleagues as well as to single linkage clustering and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees

joint hypergraph learning and sparse regression for feature selection abstract in this paper we propose a unified framework for improved structure estimation and feature selection most existing graph based feature selection methods utilize a static representation of the structure of the available data based on the laplacian matrix of a simple graph here on the other hand we perform data structure learning and feature selection simultaneously to improve the estimation of the manifold representing the structure of the selected features we use a higher order description of the neighborhood structures present in the available data using hypergraph learning this allows those features which participate in the most significant higher order relations to be selected and the remainder discarded through a sparsification process we formulate a single objective function to capture and regularize the hypergraph weight estimation and feature selection processes finally we present an optimization algorithm to recover the hypergraph weights and a sparse set of feature selection indicators this process offers a number of advantages first by adjusting the hypergraph weights we preserve high order neighborhood relations reflected in the original data which cannot be modeled by a simple graph moreover our objective function captures the global discriminative structure of the features in the data comprehensive experiments on 9 benchmark datasets show that our method achieves statistically significant improvement over state of art feature selection methods supporting the effectiveness of the proposed method

extended similarity trees proximity data can be represented by an extended tree which generalizes traditional trees by including marked segments that correspond to overlapping clusters an extended tree is a graphical representation of the distinctive features model a computer program extree that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data

color face image enhancement using adaptive singular value decomposition in fourier domain for face recognition face recognition is still a challenging problem because of large intra class variability small inter class variability and the presence of lighting variation to deal with these difficulties an illumination compensation method adaptive singular value decomposition in the two dimensional discrete fourier domain asvdf and an efficient brightness detector for lighting detection for face image enhancement are proposed in this paper the proposed enhancement algorithm involves three steps in the first step uniform lighting is rapidly distinguished from lateral lighting in the image by using the brightness detector which is based on the percentage ratio of pixels among the three rgb color channels asvdf is then globally performed for the uniform lighting image whereas asvdf is applied block by block for the lateral lighting image in addition to reduce computing time a region based asvdf method is introduced the asvdf method is applied to four regions of the face image experimental results for the cmu pie color feret and fei face databases show that the method considerably improves the quality of face images even lateral lighting thereby improving the accuracy of face recognition substantially adaptive singular value decomposition in the fourier domain is proposed for face recognition self adapted illumination compensation is devised to overcome lighting variation experimental results are demonstrated on cmu feret and fei databases to verify the effectiveness

enhanced local texture feature sets for face recognition under difficult lighting conditions making recognition more reliable under uncontrolled lighting conditions is one of the most important challenges for practical face recognition systems we tackle this by combining the strengths of robust illumination normalization local texture based face representations distance transform based matching kernel based feature extraction and multiple feature fusion specifically we make three main contributions 1 we present a simple and efficient preprocessing chain that eliminates most of the effects of changing illumination while still preserving the essential appearance details that are needed for recognition 2 we introduce local ternary patterns ltp a generalization of the local binary pattern lbp local texture descriptor that is more discriminant and less sensitive to noise in uniform regions and we show that replacing comparisons based on local spatial histograms with a distance transform based similarity metric further improves the performance of lbp ltp based face recognition and 3 we further improve robustness by adding kernel principal component analysis pca feature extraction and incorporating rich local appearance cues from two complementary sources gabor wavelets and lbp showing that the combination is considerably more accurate than either feature set alone the resulting method provides state of the art performance on three data sets that are widely used for testing recognition under difficult illumination conditions extended yale b cas peal r1 and face recognition grand challenge version 2 experiment 4 frgc 204 for example on the challenging frgc 204 data set it halves the error rate relative to previously published methods achieving a face verification rate of 88 1 at 0 1 false accept rate further experiments show that our preprocessing method outperforms several existing preprocessors for a range of feature sets data sets and lighting conditions

geometric characterization of strongly normal extensions this paper continues previous work in which we developed the galois theory of strongly normal extensions using differential schemes in the present paper we derive two main results first we show that an extension is strongly normal if and only if a certain differential scheme splits i e is obtained by base extension of a scheme over constants this gives a geometric characterization to the notion of strongly normal second we show that picard vessiot extensions are characterized by their galois group being affine our proofs are elementary and do not use group chunks or cohomology we end by recalling some important results about strongly normal extensions with the hope of spurring future research

an analysis of linear subspace approaches for computer vision and pattern recognition linear subspace analysis lsa has become rather ubiquitous in a wide range of problems arising in pattern recognition and computer vision the essence of these approaches is that certain structures are intrinsically or approximately low dimensional for example the factorization approach to the problem of structure from motion sfm and principal component analysis pca based approach to face recognition in lsa the singular value decomposition svd is usually the basic mathematical tool however analysis of the performance in the presence of noise has been lacking we present such an analysis here first the denoising capacity of the svd is analysed specifically given a rank r matrix corrupted by noise how much noise remains in the rank r projected version of that corrupted matrix second we study the learning capacity of the lsa based recognition system in a noise corrupted environment specifically lsa systems that attempt to capture a data class as belonging to a rank r column space will be affected by noise in both the training samples measurement noise will mean the learning samples will not produce the true subspace and the test sample which will also have measurement noise on top of the ideal clean sample belonging to the true subspace these results should help one to predict aspects of performance and to design more optimal systems in computer vision particularly in tasks such as sfm and face recognition our analysis agrees with certain observed phenomenon and these observations together with our simulations verify the correctness of our theory

illumination recovery from image with cast shadows via sparse representation in this paper we propose using sparse representation for recovering the illumination of a scene from a single image with cast shadows given the geometry of the scene the images with cast shadows can be quite complex and therefore cannot be well approximated by low dimensional linear subspaces however it can be shown that the set of images produced by a lambertian scene with cast shadows can be efficiently represented by a sparse set of images generated by directional light sources we first model an image with cast shadows composed of a diffusive part without cast shadows and a residual part that captures cast shadows then we express the problem in an l1 regularized least squares formulation with nonnegativity constraints as light has to be non negative at any point in space this sparse representation enjoys an effective and fast solution thanks to recent advances in compressive sensing in experiments on synthetic and real data our approach performs favorably in comparison with several previously proposed methods

ordinal network representation representing proximities by graphs ordinal network representations are graph theoretic representations of proximity data they seek to provide parsimonious representations of the ordinal nonmetric information in observed proximity data by means of the minimum path length distance of a connected and weighted graph in contrast to traditional tree based graph theoretic approaches ordinal network representation is not limited to but includes the representation by trees asymmetry in the proximity data and violations of zero minimality are allowed for the paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations a simple strategy for handling the problem of errors in the data is described and illustrated

a constructive algorithm for realizing a distance matrix the natural metric of a weighted graph is the length of the shortest paths between all pairs of vertices the investigated problem consists in a representation of a given metric by a graph such that the total length of the graph is minimized for that purpose we give a constructive algorithm based on a technique of reduction fusion and deletion we then show some results on a set of various distance matrices whose optimal realization is known

pairwise partitioning a nonmetric algorithm for identifying feature based similarity structures pairwise partitioning is a nonmetric divisive algorithm for identifying feature structures based on pairwise similarities for errorless data this algorithm is shown to identify only and sometimes all valid features for certain hierarchical and multidimensional feature structures unfortunately the algorithm is also extremely sensitive to error in the data fortunately several modifications of the algorithm are shown to compensate significantly for this deficiency the algorithm is illustrated with simulations and analyses of three sets of similarity data the results suggest that this algorithm will be most useful a as an exploratory tool for generating a relatively large set of potential features that can be reduced using other criteria either statistical or substantive and b as a source of confirmatory or disconfirmatory evidence

reconstructing 3d face model with associated expression deformation from a single face image via constructing a low dimensional expression deformation manifold facial expression modeling is central to facial expression recognition and expression synthesis for facial animation in this work we propose a manifold based 3d face reconstruction approach to estimating the 3d face model and the associated expression deformation from a single face image with the proposed robust weighted feature map rwf we can obtain the dense correspondences between 3d face models and build a nonlinear 3d expression manifold from a large set of 3d facial expression models then a gaussian mixture model in this manifold is learned to represent the distribution of expression deformation by combining the merits of morphable neutral face model and the low dimensional expression manifold a novel algorithm is developed to reconstruct the 3d face geometry as well as the facial deformation from a single face image in an energy minimization framework experimental results on simulated and real images are shown to validate the effectiveness and accuracy of the proposed algorithm

spatial versus tree representations of proximity data in this paper we investigated two of the most common representations of proximities two dimensional euclidean planes and additive trees our purpose was to develop guidelines for comparing these representations and to discover properties that could help diagnose which representation is more appropriate for a given set of data in a simulation study artificial data generated either by a plane or by a tree were scaled using procedures for fitting either a plane kyst or a tree addtree as expected the appropriate model fit the data better than the inappropriate model for all noise levels furthermore the two models were roughly comparable for all noise levels kyst accounted for plane data about as well as addtree accounted for tree data two properties of the data proved useful in distinguishing between the models the skewness of the distribution of distances and the proportion of elongated triangles which measures departures from the ultrametric inequality applications of kyst and addtree to some twenty sets of real data collected by other investigators showed that most of these data could be classified clearly as favoring either a tree or a two dimensional representation

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

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

latent features in similarity judgments a nonparametric bayesian approach one of the central problems in cognitive science is determining the mental representations that underlie human inferences solutions to this problem often rely on the analysis of subjective similarity judgments on the assumption that recognizing likenesses between people objects and events is crucial to everyday inference one such solution is provided by the additive clustering model which is widely used to infer the features of a set of stimuli from their similarities on the assumption that similarity is a weighted linear function of common features existing approaches for implementing additive clustering often lack a complete framework for statistical inference particularly with respect to choosing the number of features to address these problems this article develops a fully bayesian formulation of the additive clustering model using methods from nonparametric bayesian statistics to allow the number of features to vary we use this to explore several approaches to parameter estimation showing that the nonparametric bayesian approach provides a straightforward way to obtain estimates of both the number of features and their importance

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

an intrinsic characterization of picard vessiot extensions abstract we present a characterization of differential picard vessiot extensions which is analogous to the field theoretic characterization of galois extensions in classical galois theory

principal angles separate subject illumination spaces in ydb and cmu pie the theory of illumination subspaces is well developed and has been tested extensively on the yale face database b ydb and cmu pie pie data sets this paper shows that if face recognition under varying illumination is cast as a problem of matching sets of images to sets of images then the minimal principal angle between subspaces is sufficient to perfectly separate matching pairs of image sets from nonmatching pairs of image sets sampled from ydb and pie this is true even for subspaces estimated from as few as six images and when one of the subspaces is estimated from as few as three images if the second subspace is estimated from a larger set 10 or more this suggests that variation under illumination may be thought of as useful discriminating information rather than unwanted noise

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

the differential galois theory of strongly normal extensions differential galois theory the theory of strongly normal extensions has unfortunately languished this may be due to its reliance on kolchin s elegant but not widely adopted axiomatization of the theory of algebraic groups this paper attempts to revive the theory using a differential scheme in place of those axioms we also avoid using a universal differential field instead relying on a certain tensor product we identify automorphisms of a strongly normal extension with maximal differential ideals of this tensor product thus identifying the galois group with the closed points of an affine differential scheme moreover the tensor product has a natural coring structure which translates into the galois group operation composition of automorphisms this affine differential scheme splits i e is obtained by base extension from a not differential not necessarily affine group scheme as a consequence the galois group is canonically isomorphic to the closed or rational points of a group scheme defined over constants we obtain the fundamental theorem of differential galois theory giving a bijective correspondence between subgroup schemes and intermediate differential fields on the way to this result we study certain aspects of differential algebraic geometry e g closed immersions products local ringed space of constants and split differential schemes

tscale a new multidimensional scaling procedure based on tversky s contrast model tversky s contrast model of proximity was initially formulated to account for the observed violations of the metric axioms often found in empirical proximity data this set theoretic approach models the similarity dissimilarity between any two stimuli as a linear or ratio combination of measures of the common and distinctive features of the two stimuli this paper proposes a new spatial multidimensional scaling mds procedure called tscale based on tversky s linear contrast model for the analysis of generally asymmetric three way two mode proximity data we first review the basic structure of tversky s conceptual contrast model a brief discussion of alternative mds procedures to accommodate asymmetric proximity data is also provided the technical details of the tscale procedure are given as well as the program options that allow for the estimation of a number of different model specifications the nonlinear estimation framework is discussed as are the results of a modest monte carlo analysis two consumer psychology applications are provided one involving perceptions of fast food restaurants and the other regarding perceptions of various competitive brands of cola soft drinks finally other applications and directions for future research are mentioned

inverse rendering of lambertian surfaces using subspace methods we propose a vector space approach for inverse rendering of a lambertian convex object with distant light sources in this problem the texture of the object and arbitrary lightings are both to be recovered from multiple images of the object and its 3d model our work is motivated by the observation that all possible images of a lambertian object lie around a low dimensional linear subspace spanned by the first few spherical harmonics the inverse rendering can therefore be formulated as a matrix factorization in which the basis of the subspace is encoded in a spherical harmonic matrix s associated with the object s geometry a necessary and sufficient condition on s for unique factorization is derived with an introduction to a new notion of matrix rank called nonseparable full rank a singular value decomposition based algorithm for exact factorization in the noiseless case is introduced in the presence of noise two algorithms namely alternating and optimization based are proposed to deal with two different types of noise a random sample consensus based algorithm is introduced to reduce the size of the optimization problem which is equal to the number of pixels in each image implementations of the proposed algorithms are done on a real data set

combined affine geometric transformations and spatially dependent radiometric deformations a decoupled linear estimation framework this paper considers the problem of registering two observations of the same object where the observations differ due to a combined effect of an affine geometric transformation and nonuniform illumination changes the problem of deriving new representations of the observations that are both invariant to geometric transformations and linear in the illumination model is analyzed in this framework we present a novel method for linear estimation of illumination changes in an affine invariant manner thus decoupling the original problem into two simpler ones the computational complexity of the method is low as it requires no more than solving a linear set of equations the prior step of illumination estimation is shown to improve the accuracy of state of the art registration techniques by a factor of two

what are textons textons refer to fundamental micro structures in natural images and videos and are considered as the atoms of pre attentive human visual perception julesz 1981 unfortunately the word texton remains a vague concept in the literature for lack of a good mathematical model in this article we first present a three level generative image model for learning textons from texture images in this model an image is a superposition of a number of image bases selected from an over complete dictionary including various gabor and laplacian of gaussian functions at various locations scales and orientations these image bases are in turn generated by a smaller number of texton elements selected from a dictionary of textons by analogy to the waveform phoneme word hierarchy in speech the pixel base texton hierarchy presents an increasingly abstract visual description and leads to dimension reduction and variable decoupling by fitting the generative model to observed images we can learn the texton dictionary as parameters of the generative model then the paper proceeds to study the geometric dynamic and photometric structures of the texton representation by further extending the generative model to account for motion and illumination variations 1 for the geometric structures a texton consists of a number of image bases with deformable spatial configurations the geometric structures are learned from static texture images 2 for the dynamic structures the motion of a texton is characterized by a markov chain model in time which sometimes can switch geometric configurations during the movement we call the moving textons as motons the dynamic models are learned using the trajectories of the textons inferred from video sequence 3 for photometric structures a texton represents the set of images of a 3d surface element under varying illuminations and is called a lighton in this paper we adopt an illumination cone representation where a lighton is a texton triplet for a given light source a lighton image is generated as a linear sum of the three texton bases we present a sequence of experiments for learning the geometric dynamic and photometric structures from images and videos and we also present some comparison studies with k mean clustering sparse coding independent component analysis and transformed component analysis we shall discuss how general textons can be learned from generic natural images

appearance characterization of linear lambertian objects generalized photometric stereo and illumination invariant face recognition traditional photometric stereo algorithms employ a lambertian reflectance model with a varying albedo field and involve the appearance of only one object in this paper we generalize photometric stereo algorithms to handle all appearances of all objects in a class in particular the human face class by making use of the linear lambertian property a linear lambertian object is one which is linearly spanned by a set of basis objects and has a lambertian surface the linear property leads to a rank constraint and consequently a factorization of an observation matrix that consists of exemplar images of different objects e g faces of different subjects under different unknown illuminations integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account the effectiveness of the linear lambertian property is further investigated by using it for the problem of illumination invariant face recognition using just one image attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in lambert s law this enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources experimental results using standard data sets are presented

active appearance models revisited active appearance models aams and the closely related concepts of morphable models and active blobs are generative models of a certain visual phenomenon although linear in both shape and appearance overall aams are nonlinear parametric models in terms of the pixel intensities fitting an aam to an image consists of minimising the error between the input image and the closest model instances i e solving a nonlinear optimisation problem we propose an efficient fitting algorithm for aams based on the inverse compositional image alignment algorithm we show that the effects of appearance variation during fitting can be precomputed projected out using this algorithm and how it can be extended to include a global shape normalising warp typically a 2d similarity transformation we evaluate our algorithm to determine which of its novel aspects improve aam fitting performance

recognizing imprecisely localized partially occluded and expression variant faces from a single sample per class the classical way of attempting to solve the face or object recognition problem is by using large and representative data sets in many applications though only one sample per class is available to the system in this contribution we describe a probabilistic approach that is able to compensate for imprecisely localized partially occluded and expression variant faces even when only one single training sample per class is available to the system to solve the localization problem we find the subspace within the feature space e g eigenspace that represents this error for each of the training images to resolve the occlusion problem each face is divided into k local regions which are analyzed in isolation in contrast with other approaches where a simple voting space is used we present a probabilistic method that analyzes how good a local match is to make the recognition system less sensitive to the differences between the facial expression displayed on the training and the testing images we weight the results obtained on each local area on the basis of how much of this local area is affected by the expression displayed on the current test image

segmented linear subspaces for illumination robust face recognition all images of a convex lambertian surface captured with a fixed pose under varying illumination are known to lie in a convex cone in the image space that is called the illumination cone since this cone model is too complex to be built in practice researchers have attempted to approximate it with simpler models in this paper we propose a segmented linear subspace model to approximate the cone our idea of segmentation is based on the fact that the success of low dimensional linear subspace approximations of the illumination cone increases if the directions of the surface normals get close to each other hence we propose to cluster the image pixels according to their surface normal directions and to approximate the cone with a linear subspace for each of these clusters separately we perform statistical performance evaluation experiments to compare our system to other popular systems and demonstrate that the performance increase we obtain is statistically significant

face recognition from a single training image under arbitrary unknown lighting using spherical harmonics in this paper we propose two novel methods for face recognition under arbitrary unknown lighting by using spherical harmonics illumination representation which require only one training image per subject and no 3d shape information our methods are based on the result which demonstrated that 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 we provide two methods to estimate the spherical harmonic basis images spanning this space from just one image our first method builds the statistical model based on a collection of 2d basis images we demonstrate that by using the learned statistics we can estimate the spherical harmonic basis images from just one image taken under arbitrary illumination conditions if there is no pose variation compared to the first method the second method builds the statistical models directly in 3d spaces by combining the spherical harmonic illumination representation and a 3d morphable model of human faces to recover basis images from images across both poses and illuminations after estimating the basis images we use the same recognition scheme for both methods we recognize the face for which there exists a weighted combination of basis images that is the closest to the test face image we provide a series of experiments that achieve high recognition rates under a wide range of illumination conditions including multiple sources of illumination our methods achieve comparable levels of accuracy with methods that have much more onerous training data requirements comparison of the two methods is also provided

a flag representation for finite collections of subspaces of mixed dimensions abstract given a finite set of subspaces of r n perhaps of differing dimensions we describe a flag of vector spaces i e a nested sequence of vector spaces that best represents the collection based on a natural optimization criterion and we present an algorithm for its computation the utility of this flag representation lies in its ability to represent a collection of subspaces of differing dimensions when the set of subspaces all have the same dimension d the flag mean is related to several commonly used subspace representations for instance the d dimensional subspace in the flag corresponds to the extrinsic manifold mean when the set of subspaces is both well clustered and equidimensional of dimension d then the d dimensional component of the flag provides an approximation to the karcher mean an intermediate matrix used to construct the flag can also be used to recover the canonical components at the heart of multiset canonical correlation analysis two examples utilizing the carnegie mellon university pose illumination and expression database cmu pie serve as visual illustrations of the algorithm

compact mixed integer linear programming models to the minimum weighted tree reconstruction problem the minimum weighted tree reconstruction mwtr problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes this problem has applications in several areas namely the inference of phylogenetic trees the modeling of traffic networks and the analysis of internet infrastructures in this paper we investigate the mwtr problem and we present two compact mixed integer linear programming models to solve the problem computational results using two different sets of instances one from the phylogenetic area and another from the telecommunications area show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes

a parametric procedure for ultrametric tree estimation from conditional rank order proximity data the psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models e g hierarchical or ultrametric trees for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures i e procedures which optimize a stress based criteria of fit and whose solutions are invariant under a monotone transformation of the input data this paper proposes a new parametric maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data we present the technical aspects of the model and the estimation algorithm some preliminary monte carlo results are discussed a consumer psychology application is provided examining the similarity of fifteen types of snack breakfast items finally some directions for future research are provided

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

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

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

manifold manifold distance and its application to face recognition with image sets in this paper we address the problem of classifying image sets for face recognition where each set contains images belonging to the same subject and typically covering large variations by modeling each image set as a manifold we formulate the problem as the computation of the distance between two manifolds called manifold manifold distance mmd since an image set can come in three pattern levels point subspace and manifold we systematically study the distance among the three levels and formulate them in a general multilevel mmd framework specifically we express a manifold by a collection of local linear models each depicted by a subspace mmd is then converted to integrate the distances between pairs of subspaces from one of the involved manifolds we theoretically and experimentally study several configurations of the ingredients of mmd the proposed method is applied to the task of face recognition with image sets where identification is achieved by seeking the minimum mmd from the probe to the gallery of image sets our experiments demonstrate that as a general set similarity measure mmd consistently outperforms other competing nondiscriminative methods and is also promisingly comparable to the state of the art discriminative methods

face relighting from a single image under arbitrary unknown lighting conditions in this paper we present a new method to modify the appearance of a face image by manipulating the illumination condition when the face geometry and albedo information is unknown this problem is particularly difficult when there is only a single image of the subject available recent research demonstrates that 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 using a spherical harmonic representation moreover morphable models are statistical ensembles of facial properties such as shape and texture in this paper we integrate spherical harmonics into the morphable model framework by proposing a 3d spherical harmonic basis morphable model shbmm the proposed method can represent a face under arbitrary unknown lighting and pose simply by three low dimensional vectors i e shape parameters spherical harmonic basis parameters and illumination coefficients which are called the shbmm parameters however when the image was taken under an extreme lighting condition the approximation error can be large thus making it difficult to recover albedo information in order to address this problem we propose a subregion based framework that uses a markov random field to model the statistical distribution and spatial coherence of face texture which makes our approach not only robust to extreme lighting conditions but also insensitive to partial occlusions the performance of our framework is demonstrated through various experimental results including the improved rates for face recognition under extreme lighting conditions

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

mixtures of constrained ultrametric trees this paper presents a new methodology concerned with the estimation of ultrametric trees calibrated on subjects pairwise proximity judgments of stimuli capturing subject heterogeneity using a finite mixture formulation we assume that a number of unobserved classes of subjects exist each having a different ultrametric tree structure underlying the pairwise proximity judgments a new likelihood based estimation methodology is presented for those finite mixtures of ultrametric trees that accommodates ultrametric as well as other external constraints various assumptions on the correlation of the error of the dissimilarities are accommodated the performance of the method to recover known ultrametric tree structures is investigated on synthetic data an empirical application to published data from schiffman reynolds and young 1981 is provided the ability to deal with external constraints on the tree topology is demonstrated and a comparison with an alternative clustering based method is made

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

exploring the set theoretical structure of objects by additive trees arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects are shown to generate identical sets of set symmetric distances the set symmetric distances for these feature arrangements can be represented by path lengths in an additive linear tree imperfect versions of these feature arrangements are proposed which also are indistinguishable by the set symmetric distance model the distances for the imperfect versions can be represented by path lengths in an additive imperfectly linear tree when dissimilarities are defined by the more general contrast model and a constant may be added to proximity data then for both the perfect and imperfect arrangements an additive tree analysis obtains a perfect fit with an imperfectly linear tree however in the case of the contrast model also the distinction between the perfect and imperfect arrangements disappears in that also for the perfect arrangements the resulting tree need no longer be linear

hallucinating optimal high dimensional subspaces abstract linear subspace representations of appearance variation are pervasive in computer vision this paper addresses the problem of robustly matching such subspaces computing the similarity between them when they are used to describe the scope of variations within sets of images of different possibly greatly so scales a naive solution of projecting the low scale subspace into the high scale image space is described first and subsequently shown to be inadequate especially at large scale discrepancies a successful approach is proposed instead it consists of i an interpolated projection of the low scale subspace into the high scale space which is followed by ii a rotation of this initial estimate within the bounds of the imposed downsampling constraint the optimal rotation is found in the closed form which best aligns the high scale reconstruction of the low scale subspace with the reference it is compared to the method is evaluated on the problem of matching sets of i face appearances under varying illumination and ii object appearances under varying viewpoint using two large data sets in comparison to the naive matching the proposed algorithm is shown to greatly increase the separation of between class and within class similarities as well as produce far more meaningful modes of common appearance on which the match score is based