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

discriminant subspace analysis a fukunaga koontz approach the fisher linear discriminant fld is commonly used in pattern recognition it finds a linear subspace that maximally separates class patterns according to the fisher criterion several methods of computing the fld have been proposed in the literature most of which require the calculation of the so called scatter matrices in this paper we bring a fresh perspective to fld via the fukunaga koontz transform fkt we do this by decomposing the whole data space into four subspaces with different discriminabilities as measured by eigenvalue ratios by connecting the eigenvalue ratio with the generalized eigenvalue we show where the fisher criterion is maximally satisfied we prove the relationship between fld and fkt analytically and propose a unified framework to understanding some existing work furthermore we extend our theory to the multiple discriminant analysis mda this is done by transforming the data into intraclass and extraclass spaces followed by maximizing the bhattacharyya distance based on our fkt analysis we identify the discriminant subspaces of mda fkt and propose an efficient algorithm which works even when the scatter matrices are singular or too large to be formed our method is general and may be applied to different pattern recognition problems we validate our method by experimenting on synthetic and real data

recognizing faces prone to occlusions and common variations using optimal face subgraphs an intuitive graph optimization face recognition approach called harmony search oriented ebgm hso ebgm inspired by the classical elastic bunch graph matching ebgm graphical model is proposed in this contribution in the proposed hso ebgm a recent evolutionary approach called harmony search optimization is tailored to automatically determine optimal facial landmarks a novel notion of face subgraphs have been formulated with the aid of these automated landmarks that maximizes the similarity entailed by the subgraphs for experimental evaluation two sets of de facto databases i e ar and face recognition grand challenge frgc ver2 0 are used to validate and analyze the behavior of the proposed hso ebgm in terms of number of subgraphs varying occlusion sizes face images under controlled ideal conditions realistic partial occlusions expression variations and varying illumination conditions for a number of experiments results justify that the hso ebgm shows improved recognition performance when compared to recent state of the art face recognition approaches

maximum correntropy criterion for robust face recognition in this paper we present a sparse correntropy framework for computing robust sparse representations of face images for recognition compared with the state of the art l1norm based sparse representation classifier src which assumes that noise also has a sparse representation our sparse algorithm is developed based on the maximum correntropy criterion which is much more insensitive to outliers in order to develop a more tractable and practical approach we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state of the art methods in particular it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic roc curves while the computational cost is much lower than the src algorithms

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

template matching matched spatial filters and beyond template matching by means of cross correlation is common practice in pattern recognition however its sensitivity to deformations of the pattern and the broad and unsharp peaks it produces are significant drawbacks this paper reviews some results on how these shortcomings can be removed several techniques matched spatial filters synthetic discriminant functions principal components projections and reconstruction residuals are reviewed and compared on a common task locating eyes in a database of faces new variants are also proposed and compared least squares discriminant functions and the combined use of projections on eigenfunctions and the corresponding reconstruction residuals finally approximation networks are introduced in an attempt to improve filter design by the introduction of nonlinearity

fast computation of low rank matrix approximations given a matrix a it is often desirable to find a good approximation to a that has low rank we introduce a simple technique for accelerating the computation of such approximations when a has strong spectral features that is when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to a our technique amounts to independently sampling and or quantizing the entries of a thus speeding up computation by reducing the number of nonzero entries and or the length of their representation our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix n to a whose entries are independent random variables with zero mean and bounded variance since with high probability n has very weak spectral features we can prove that the effect of sampling and quantization nearly vanishes when a low rank approximation to a p n is computed we give high probability bounds on the quality of our approximation both in the frobenius and the 2 norm

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

fractional order singular value decomposition representation for face recognition face representation fr plays a typically important role in face recognition and methods such as principal component analysis pca and linear discriminant analysis lda have been received wide attention recently however despite of the achieved successes these fr methods will inevitably lead to poor classification performance in case of great facial variations such as expression lighting occlusion and so on due to the fact that the image gray value matrices on which they manipulate are very sensitive to these facial variations in this paper we take notice of the facts that every image matrix can always have the well known singular value decomposition svd and can be regarded as a composition of a set of base images generated by svd and we further point out that the leading base images those corresponding to large singular values on one hand are sensitive to the aforementioned facial variations and on the other hand dominate the composition of the face image then based on these observations we subtly deflate the weights of the facial variation sensitive base images by a parameter and propose a novel fractional order singular value decomposition representation fsvdr to alleviate facial variations for face recognition finally our experimental results show that fsvdr can 1 effectively alleviate facial variations and 2 form an intermediate representation for many fr methods such as pca and lda to significantly improve their classification performance in case of great facial variations

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

face recognition using kernel direct discriminant analysis algorithms techniques that can introduce low dimensional feature representation with enhanced discriminatory power is of paramount importance in face recognition fr systems it is well known that the distribution of face images under a perceivable variation in viewpoint illumination or facial expression is highly nonlinear and complex it is therefore not surprising that linear techniques such as those based on principle component analysis pca or linear discriminant analysis lda cannot provide reliable and robust solutions to those fr problems with complex face variations in this paper we propose a kernel machine based discriminant analysis method which deals with the nonlinearity of the face patterns distribution the proposed method also effectively solves the so called small sample size sss problem which exists in most fr tasks the new algorithm has been tested in terms of classification error rate performance on the multiview umist face database results indicate that the proposed methodology is able to achieve excellent performance with only a very small set of features being used and its error rate is approximately 34 and 48 of those of two other commonly used kernel fr approaches the kernel pca kpca and the generalized discriminant analysis gda respectively

gender classification from unaligned facial images using support subspaces rough face alignments result in suboptimal performance of face identification in this study we present an approach for identifying the gender based on facial images without proper face alignments instead of just using only the detected face patch for identification a set of patches is randomly cropped around the face detection region each patch set is represented by a linear subspace and compared with other linear subspaces by measuring their canonical correlations a similarity matrix comprised of the canonical correlations is then incorporated into an indefinite kernel support vector machine svm formulation the number of support vectors which we call support subspaces can be decided automatically hence we can avoid the dimension selection problem observed in our previous work our experimental results demonstrate that the proposed approach outperforms state of the art methods

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

kernel quadratic discriminant analysis for small sample size problem it is generally believed that quadratic discriminant analysis qda can better fit the data in practical pattern recognition applications compared to linear discriminant analysis lda method this is due to the fact that qda relaxes the assumption made by lda based methods that the covariance matrix for each class is identical however it still assumes that the class conditional distribution is gaussian which is usually not the case in many real world applications in this paper a novel kernel based qda method is proposed to further relax the gaussian assumption by using the kernel machine technique the proposed method solves the complex pattern recognition problem by combining the qda solution and the kernel machine technique and at the same time tackles the so called small sample size problem through a regularized estimation of the covariance matrix extensive experimental results indicate that the proposed method is a more sophisticated solution outperforming many traditional kernel based learning algorithms

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 recognition using an enhanced independent component analysis approach this paper is concerned with an enhanced independent component analysis ica and its application to face recognition typically face representations obtained by ica involve unsupervised learning and high order statistics in this paper we develop an enhancement of the generic ica by augmenting this method by the fisher linear discriminant analysis lda hence its abbreviation fica the fica is systematically developed and presented along with its underlying architecture a comparative analysis explores four distance metrics as well as classification with support vector machines svms we demonstrate that the fica approach leads to the formation of well separated classes in low dimension subspace and is endowed with a great deal of insensitivity to large variation in illumination and facial expression the comprehensive experiments are completed for the facial recognition technology feret face database a comparative analysis demonstrates that fica comes with improved classification rates when compared with some other conventional approaches such as eigenface fisherface and the ica itself

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

a new solution to one sample problem in face recognition using flda fisher linear discriminant analysis flda is a very popular method in face recognition but flda fails when one image per person is available this is due to the fact that the within class scatter matrices cannot be calculated an image decomposition method that uses qr decomposition with column pivoting qrcp is proposed in this paper to overcome one image per person problem at first the image and its two approximations that are evaluated using qrcp decomposition are all placed in the training set then 2d flda method becomes applicable with these new data the performance of the proposed image decomposition algorithm is tested on five different face databases namely orl feret yale umist and polyu nir using 2d flda our image decomposition algorithm performs better than the svd based method mentioned by gao et al 2008 1 in terms of recognition rate and training time in all of the above databases

worst case linear discriminant analysis as scalable semidefinite feasibility problems in this paper we propose an efficient semidefinite programming sdp approach to worst case linear discriminant analysis wlda compared with the traditional lda wlda considers the dimensionality reduction problem from the worst case viewpoint which is in general more robust for classification however the original problem of wlda is non convex and difficult to optimize in this paper we reformulate the optimization problem of wlda into a sequence of semidefinite feasibility problems to efficiently solve the semidefinite feasibility problems we design a new scalable optimization method with a quasi newton method and eigen decomposition being the core components the proposed method is orders of magnitude faster than standard interior point sdp solvers experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard lda our method is also much faster and more scalable than standard interior point sdp solvers based wlda the computational complexity for an sdp with m constraints and matrices of size d by d is roughly reduced from mathcal o m 3 md 3 m 2 d 2 to mathcal o d 3 m d in our case

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

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

maximal likelihood correspondence estimation for face recognition across pose due to the misalignment of image features the performance of many conventional face recognition methods degrades considerably in across pose scenario to address this problem many image matching based methods are proposed to estimate semantic correspondence between faces in different poses in this paper we aim to solve two critical problems in previous image matching based correspondence learning methods 1 fail to fully exploit face specific structure information in correspondence estimation and 2 fail to learn personalized correspondence for each probe image to this end we first build a model termed as morphable displacement field mdf to encode face specific structure information of semantic correspondence from a set of real samples of correspondences calculated from 3d face models then we propose a maximal likelihood correspondence estimation mlce method to learn personalized correspondence based on maximal likelihood frontal face assumption after obtaining the semantic correspondence encoded in the learned displacement we can synthesize virtual frontal images of the profile faces for subsequent recognition using linear discriminant analysis method with pixel intensity features state of the art performance is achieved on three multipose benchmarks i e cmu pie feret and multipie databases owe to the rational mdf regularization and the usage of novel maximal likelihood objective the proposed mlce method can reliably learn correspondence between faces in different poses even in complex wild environment i e labeled face in the wild database

space and time bounds on indexing 3d models from 2d images model based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses which are then verified in order to accelerate recognition considerably the model groups can be arranged in an index space hashed offline such that feasible matches are found by indexing into this space for the case of 2d images and 3d models consisting of point features bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated it is proved that even in the absence of image error each model must be represented by a 2d surface in the index space this places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined and an implementation of indexing for measuring this speedup empirically is presented it is found that indexing can produce only a minimal speedup on its own however when accompanied by a grouping operation indexing can provide significant speedups that grow exponentially with the number of features in the groups

recovery guarantees for exemplar based clustering for a certain class of distributions we prove that the linear programming relaxation of k medoids clustering a variant of k means clustering where means are replaced by exemplars from within the dataset distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn and the separation distance between any two balls are sufficiently large our results hold in the nontrivial regime where the separation distance is small enough that points drawn from different balls may be closer to each other than points drawn from the same ball in this case clustering by thresholding pairwise distances between points can fail we also exhibit numerical evidence of high probability recovery in a substantially more permissive regime

low rank latent pattern approximation with applications to robust image classification this paper develops a novel method to address the structural noise in samples for image classification recently regression related classification methods have shown promising results when facing the pixelwise noise however they become weak in coping with the structural noise due to ignoring of relationships between pixels of noise image meanwhile most of them need to implement the iterative process for computing representation coefficients which leads to the high time consumption to overcome these problems we exploit a latent pattern model called low rank latent pattern approximation llpa to reconstruct the test image having structural noise the rank function is applied to characterize the structure of the reconstruction residual between test image and the corresponding latent pattern simultaneously the error between the latent pattern and the reference image is constrained by frobenius norm to prevent overfitting llpa involves a closed form solution by the virtue of a singular value thresholding operator the provided theoretic analysis demonstrates that llpa indeed removes the structural noise during classification task additionally llpa is further extended to the form of matrix regression by connecting multiple training samples and alternating direction of multipliers method with gaussian back substitution algorithm is used to solve the extended llpa experimental results on several popular data sets validate that the proposed methods are more robust to image classification with occlusion and illumination changes as compared to some existing state of the art reconstruction based methods and one deep neural network based method

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

multiobjective optimization for model selection in kernel methods in regression regression plays a major role in many scientific and engineering problems the goal of regression is to learn the unknown underlying function from a set of sample vectors with known outcomes in recent years kernel methods in regression have facilitated the estimation of nonlinear functions however two major interconnected problems remain open the first problem is given by the bias versus variance tradeoff if the model used to estimate the underlying function is too flexible i e high model complexity the variance will be very large if the model is fixed i e low complexity the bias will be large the second problem is to define an approach for selecting the appropriate parameters of the kernel function to address these two problems this paper derives a new smoothing kernel criterion which measures the roughness of the estimated function as a measure of model complexity then we use multiobjective optimization to derive a criterion for selecting the parameters of that kernel the goal of this criterion is to find a tradeoff between the bias and the variance of the learned function that is the goal is to increase the model fit while keeping the model complexity in check we provide extensive experimental evaluations using a variety of problems in machine learning pattern recognition and computer vision the results demonstrate that the proposed approach yields smaller estimation errors as compared with methods in the state of the art

towards robust discriminative projections learning via non greedy l2 1 norm minmax linear discriminant analysis lda is one of the most successful supervised dimensionality reduction methods and has been widely used in many real world applications however the l 2 norm is employed as the distance measure in objective of lda which is sensitive to outliers many previous works improve the robustness of lda by using l1 norm distance however the robustness against outliers is limited and the solver of l1 norm are mostly based on greedy search strategy which is time consuming and easy to get stuck in a local optimum in this paper we propose a novel robust lda measured by l 2 1 norm to learn robust discriminative projections since the proposed model needs to minimize and maximize minmax l 2 1 norm terms simultaneously it is challenging to solve as a result we first systematically derive an efficient iterative optimization algorithm to solve a general ratio minimization problem and rigorously prove its convergence more importantly an efficient non greedy iterative re weighted optimization algorithm is developed based on preceding approach for solving proposed l 2 1 norm minmax problem besides an optimal weighted mean mechanism is driven according to designed objective and solver which can be applied to other approach for robustness improvement extensive experimental results on several real world datasets show the effectiveness of proposed method

how should we represent faces for automatic recognition we describe results obtained from a testbed used to investigate different codings for automatic face recognition an eigenface coding of shape free faces using manually located landmarks was more effective than the corresponding coding of correctly shaped faces configuration also proved an effective method of recognition with rankings given to incorrect matches relatively uncorrelated with those from shape free faces both sets of information combine to improve significantly the performance of either system the addition of a system which directly correlated the intensity values of shape free images also significantly increased recognition suggesting extra information was still available the recognition advantage for shape free faces reflected and depended upon high quality representation of the natural facial variation via a disjoint ensemble of shape free faces if the ensemble comprised nonfaces a shape free disadvantage was induced manipulation within the shape free coding to emphasize distinctive features of the faces by caricaturing allowed further increases in performance this effect was only noticeable when the independent shape free and configuration coding was used taken together these results strongly support the suggestion that faces should be considered as lying in a high dimensional manifold which is locally linearly approximated by these shapes and textures possibly with a separate system for local features principal components analysis is then seen as a convenient tool in this local approximation

face recognition using flda with single training image per person fisher linear discriminant analysis flda has been widely used for feature extraction in face recognition however it cannot be used when each object has only one training sample because the intra class variations cannot be statistically measured in this case in this paper a novel method is proposed to solve this problem by evaluating the within class scatter matrix from the available single training image by using singular value decomposition svd we decompose the face image into two complementary parts a smooth general appearance image and a difference image the later is used to approximately evaluate the within class scatter matrix and thus the flda can be applied to extract the discriminant face features experimental results show that the proposed method is efficient and it can achieve higher recognition accuracy than many existing schemes

illumination invariant single face image recognition under heterogeneous lighting condition illumination problem is still a bottleneck of robust face recognition system which demands extracting illumination invariant features in this field existing works only consider the variations caused by lighting direction or magnitude denoted as homogeneous lighting but the effect of spectral wavelength is always ignored and thus existing illumination invariant descriptors have its limitation on processing face images under different spectral wavelengths denoted as heterogeneous lighting we propose a novel gradient based descriptor namely logarithm gradient histogram lgh which takes the illumination direction magnitude and the spectral wavelength together into consideration so that it can handle both homogeneous and heterogeneous lightings our proposal contributes in three folds 1 we incorporate lmsn log filter to eliminate the lighting effect of each image and extract two illumination invariant components namely logarithm gradient orientation lgo and logarithm gradient magnitude lgm 2 we propose an effective post processing strategy to make our model tolerant to noise and generate a histogram representation to integrate both lgo and lgm 3 we present solid theoretical analysis on the illumination invariant properties of our proposed descriptors extensive experimental results on cmu pie extended yaleb frgc and hfb databases are reported to verify the effectiveness of our proposed model highlightstwo illumination invariant components namely logarithm gradient orientation lgo and logarithm gradient magnitude lgm are extracted an effective post processing strategy is proposed to integrate both lgo and lgm generating the logarithm gradient histogram lgh solid theoretical analysis on the illumination invariant properties of the proposed descriptors is presented competitive results are reported both in homogeneous and heterogeneous lighting conditions

3d face discriminant analysis using gauss markov posterior marginals we present a markov random field model for the analysis of lattices e g images or 3d meshes in terms of the discriminative information of their vertices the proposed method provides a measure field that estimates the probability of each vertex being discriminative or nondiscriminative for a given classification task to illustrate the applicability and generality of our framework we use the estimated probabilities as feature scoring to define compact signatures for three different classification tasks 1 3d face recognition 2 3d facial expression recognition and 3 ethnicity based subject retrieval obtaining very competitive results the main contribution of this work lies in the development of a novel framework for feature selection in scenaria in which the most discriminative information is smoothly distributed along a lattice

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

efficient and robust feature extraction by maximum margin criterion in pattern recognition feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information principal component analysis pca and linear discriminant analysis lda are the two most popular linear dimensionality reduction methods however pca is not very effective for the extraction of the most discriminant features and lda is not stable due to the small sample size problem in this paper we propose some new linear and nonlinear feature extractors based on maximum margin criterion mmc geometrically feature extractors based on mmc maximize the average margin between classes after dimensionality reduction it is shown that mmc can represent class separability better than pca as a connection to lda we may also derive lda from mmc by incorporating some constraints by using some other constraints we establish a new linear feature extractor that does not suffer from the small sample size problem which is known to cause serious stability problems for lda the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper our extensive experiments demonstrate that the new feature extractors are effective stable and efficient

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

hybrid output feedback for attitude tracking on mathbb so 3 we present two solutions to the global exponential attitude tacking control problem using only attitude information on mathbb so 3 the first approach is based on a combined hybrid observer hybrid controller structure we derive a hybrid angular velocity observer for rigid body systems designed directly on mathbb so 3 times mathbb r 3 guaranteeing global exponential stability of the zero estimation error thereafter we propose an observer based attitude tracking control scheme guaranteeing global exponential stability the second approach consists of introducing an auxiliary dynamical system that generates the necessary damping in the absence of the velocity we prove that the proposed auxiliary system based hybrid controller guarantees global exponential stability as well

gender discriminating models from facial surface normals in this paper we show how to use facial shape information to construct discriminating models for gender classification we represent facial shapes using 2 5d fields of facial surface normals and investigate three different methods to improve the gender discriminating capacity of the model constructed using the standard eigenspace method the three methods are novel variants of principal geodesic analysis pga namely a weighted pga b supervised weighted pga and c supervised pga our starting point is to define a weight map over the facial surface that indicates the importance of different locations in discriminating gender we show how to compute the relevant weights and how to incorporate the weights into the 2 5d model construction we evaluate the performance of the alternative methods using facial surface normals extracted from 3d range images or recovered from brightness images experimental results demonstrate the effectiveness of our methods moreover the classification accuracy which is as high as 97 demonstrates the effectiveness of using facial shape information for gender classification

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

enhanced fisher discriminant criterion for image recognition many previous studies have shown that image recognition can be significantly improved by fisher linear discriminant analysis flda technique however flda ignores the variation of data points from the same class which characterizes the most important modes of variability of patterns and helps to improve the generalization capability of flda thus the performance of flda on testing data is not good enough in this paper we propose an enhanced fisher discriminant criterion efdc efdc explicitly considers the intra class variation and incorporates the intra class variation into the fisher discriminant criterion to build a robust and efficient dimensionality reduction function efdc obtains a subspace which best detects the discriminant structure and simultaneously preserves the modes of variability of patterns which will result in stable intraclass representation experimental results on four image database show a clear improvement over the results of flda based methods

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

analysing images of curved surfaces a reflectance map makes the relationship between image intensity and surface orientation explicit trade offs between image intensity and surface orientation emerge which cannot be resolved locally in a single view existing methods for determining surface orientation from a single view embody assumptions about surface curvature the hessian matrix is introduced to represent surface curvature properties of surface curvature are expressed as properties of the hessian matrix for several classes of surface image analysis simplifies this result has already been established for planar surfaces forming trihedral corners similar simplification is demonstrated for developable surfaces and for the subclass of surfaces known as generalized cones these studies help to delineate shape information that can be determined from geometric measurements at object boundaries and shape information that can be determined from intensity measurements over sections of smoothly curved surface a novel technique called photometric stereo is discussed the idea of stereo is to obtain multiple images in order to determine the underlying scene precisely in photometric stereo the viewing direction is constant multiple images are obtained by varying the incident illumination it is shown that this provides sufficient information to determine surface orientation at each image point

interest point detection using rank order log filter this paper proposes a novel nonlinear filter named rank order laplacian of gaussian rolg filter based on which a new interest point detector is developed the rolg filter is a weighted rank order filter it is used to detect the image local structures where a significant majority of pixels are brighter or darker than a significant majority of pixels in their corresponding surroundings compared to linear filter based detectors e g sift detector the proposed rank order filter based detector is more robust to abrupt variations of images caused by illumination and geometric changes experiments on the benchmark databases demonstrate that the proposed rolg detector achieves superior performance comparing to four state of the art detectors evaluation experiments are also conducted on face recognition problems the results on five face databases further demonstrate that the rolg detector significantly outperforms the other detectors

improved discriminate analysis for high dimensional data and its application to face recognition many pattern recognition applications involve the treatment of high dimensional data and the small sample size problem principal component analysis pca is a common used dimension reduction technique linear discriminate analysis lda is often employed for classification pca plus lda is a famous framework for discriminant analysis in high dimensional space and singular cases in this paper we examine the theory of this framework and find out that even if there is no small sample size problem the pca dimension reduction cannot guarantee the subsequent successful application of lda we thus develop an improved discriminate analysis method by introducing an inverse fisher criterion and adding a constrain in pca procedure so that the singularity phenomenon will not occur experiment results on face recognition suggest that this new approach works well and can be applied even when the number of training samples is one per class

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

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

a topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon we show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium this result is directly applicable to mechanical systems having rotational degrees of freedom in particular the result applies to the attitude motion of a rigid body in light of this result we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

pose and expression independent facial landmark localization using dense surf and the hausdorff distance we present an approach to automatic localization of facial feature points which deals with pose expression and identity variations combining 3d shape models with local image patch classification the latter is performed by means of densely extracted surf like features which we call du surf while the former is based on a multiclass version of the hausdorff distance to address local classification errors and nonvisible points the final system is able to localize facial points in real world scenarios dealing with out of plane head rotations expression changes and different lighting conditions extensive experimentation with the proposed method has been carried out showing the superiority of our approach with respect to other state of the art systems finally du surf features have been compared with other modern features and we experimentally demonstrate their competitive classification accuracy and computational efficiency

a new face recognition method based on svd perturbation for single example image per person at present there are many methods for frontal view face recognition however few of them can work well when only one example image per class is available in this paper we present a new method based on svd perturbation to deal with the one example image problem and two generalized eigenface algorithms are proposed in the first algorithm the original image is linearly combined with its derived image gotten by perturbing the image matrix s singular values and then principal component analysis pca is performed on the joined images in the second algorithm the derived images are regarded as independent images that could augment training image set and then pca is performed on all the training images available including the original ones and the derived ones the proposed algorithms are compared with both the standard eigenface algorithm and the pc 2a algorithm which is proposed for addressing the one example image problem on the well known feret database with three different image resolutions experimental results show that the generalized eigenface algorithms are more accurate and use far fewer eigenfaces than both the standard eigenface algorithm and the pc 2a algorithm

neither global nor local regularized patch based representation for single sample per person face recognition this paper presents a regularized patch based representation for single sample per person face recognition we represent each image by a collection of patches and seek their sparse representations under the gallery images patches and intra class variance dictionaries at the same time for the reconstruction coefficients of all the patches from the same image by imposing a group sparsity constraint on the reconstruction coefficients corresponding to the patches from the gallery images and by imposing a sparsity constraint on the reconstruction coefficients corresponding to the intra class variance dictionaries our formulation harvests the advantages of both patch based image representation and global image representation i e our method overcomes the side effect of those patches which are severely corrupted by the variances in face recognition while enforcing those less discriminative patches to be constructed by the gallery patches from the right person moreover instead of using the manually designed intra class variance dictionaries we propose to learn the intra class variance dictionaries which not only greatly accelerate the prediction of the probe images but also improve the face recognition accuracy in the single sample per person scenario experimental results on the ar extended yale b cmu pie and lfw datasets show that our method outperforms sparse coding related face recognition methods as well as some other specially designed single sample per person face representation methods and achieves the best performance these encouraging results demonstrate the effectiveness of regularized patch based face representation for single sample per person face recognition

two stage nonnegative sparse representation for large scale face recognition this paper proposes a novel nonnegative sparse representation approach called two stage sparse representation tsr for robust face recognition on a large scale database based on the divide and conquer strategy tsr decomposes the procedure of robust face recognition into outlier detection stage and recognition stage in the first stage we propose a general multisubspace framework to learn a robust metric in which noise and outliers in image pixels are detected potential loss functions including l1 l2 1 and correntropy are studied in the second stage based on the learned metric and collaborative representation we propose an efficient nonnegative sparse representation algorithm to find an approximation solution of sparse representation according to the l1 ball theory in sparse representation the approximated solution is unique and can be optimized efficiently then a filtering strategy is developed to avoid the computation of the sparse representation on the whole large scale dataset moreover theoretical analysis also gives the necessary condition for nonnegative least squares technique to find a sparse solution extensive experiments on several public databases have demonstrated that the proposed tsr approach in general achieves better classification accuracy than the state of the art sparse representation methods more importantly a significant reduction of computational costs is reached in comparison with sparse representation classifier this enables the tsr to be more suitable for robust face recognition on a large scale dataset

robust and efficient ridge based palmprint matching during the past decade many efforts have been made to use palmprints as a biometric modality however most of the existing palmprint recognition systems are based on encoding and matching creases which are not as reliable as ridges this affects the use of palmprints in large scale person identification applications where the biometric modality needs to be distinctive as well as insensitive to changes in age and skin conditions recently several ridge based palmprint matching algorithms have been proposed to fill the gap major contributions of these systems include reliable orientation field estimation in the presence of creases and the use of multiple features in matching while the matching algorithms adopted in these systems simply follow the matching algorithms for fingerprints however palmprints differ from fingerprints in several aspects 1 palmprints are much larger and thus contain a large number of minutiae 2 palms are more deformable than fingertips and 3 the quality and discrimination power of different regions in palmprints vary significantly as a result these matchers are unable to appropriately handle the distortion and noise despite heavy computational cost motivated by the matching strategies of human palmprint experts we developed a novel palmprint recognition system the main contributions are as follows 1 statistics of major features in palmprints are quantitatively studied 2 a segment based matching and fusion algorithm is proposed to deal with the skin distortion and the varying discrimination power of different palmprint regions and 3 to reduce the computational complexity an orientation field based registration algorithm is designed for registering the palmprints into the same coordinate system before matching and a cascade filter is built to reject the nonmated gallery palmprints in early stage the proposed matcher is tested by matching 840 query palmprints against a gallery set of 13 736 palmprints experimental results show that the proposed matcher outperforms the existing matchers a lot both in matching accuracy and speed

face recognition a convolutional neural network approach we present a hybrid neural network for human face recognition which compares favourably with other methods the system combines local image sampling a self organizing map som neural network and a convolutional neural network the som provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space thereby providing dimensionality reduction and invariance to minor changes in the image sample and the convolutional neural network provides partial invariance to translation rotation scale and deformation the convolutional network extracts successively larger features in a hierarchical set of layers we present results using the karhunen loeve transform in place of the som and a multilayer perceptron mlp in place of the convolutional network for comparison we use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression pose and facial details we analyze the computational complexity and discuss how new classes could be added to the trained recognizer

contrast invariant interest point detection by zero norm log filter the laplacian of gaussian log filter is widely used in interest point detection however low contrast image structures though stable and significant are often submerged by the high contrast ones in the response image of the log filter and hence are difficult to be detected to solve this problem we derive a generalized log filter and propose a zero norm log filter the response of the zero norm log filter is proportional to the weighted number of bright dark pixels in a local region which makes this filter be invariant to the image contrast based on the zero norm log filter we develop an interest point detector to extract local structures from images compared with the contrast dependent detectors such as the popular scale invariant feature transform detector the proposed detector is robust to illumination changes and abrupt variations of images experiments on benchmark databases demonstrate the superior performance of the proposed zero norm log detector in terms of the repeatability and matching score of the detected points as well as the image recognition rate under different conditions

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

face recognition using elasticfaces though principle component analysis pca and locality preserving projections lpps are two of the most popular linear methods for face recognition pca can only see the euclidean structure of the training set and lpp preserves the nonlinear submanifold structure hidden in the training set in this paper we propose the elastic preserving projections epps which by incorporating the merits of the local geometry and the global information of the training set epp outputs a sample subspace which simultaneously preserves the local geometrical structure and exploits the global information of the training set different from some other linear dimensionality reduction methods epp can be deemed as learning both the coordinates and the affinities between sample points furthermore the effectiveness of our proposed algorithm is analyzed theoretically and confirmed by some experiments on several well known face databases the obtained results indicate that epp significantly outperforms its other rival algorithms

approximate orthogonal sparse embedding for dimensionality reduction locally linear embedding lle is one of the most well known manifold learning methods as the representative linear extension of lle orthogonal neighborhood preserving projection onpp has attracted widespread attention in the field of dimensionality reduction in this paper a unified sparse learning framework is proposed by introducing the sparsity or l 1 norm learning which further extends the lle based methods to sparse cases theoretical connections between the onpp and the proposed sparse linear embedding are discovered the optimal sparse embeddings derived from the proposed framework can be computed by iterating the modified elastic net and singular value decomposition we also show that the proposed model can be viewed as a general model for sparse linear and nonlinear kernel subspace learning based on this general model sparse kernel embedding is also proposed for nonlinear sparse feature extraction extensive experiments on five databases demonstrate that the proposed sparse learning framework performs better than the existing subspace learning algorithm particularly in the cases of small sample sizes

equidistant prototypes embedding for single sample based face recognition with generic learning and incremental learning abstract we develop a parameter free face recognition algorithm which is insensitive to large variations in lighting expression occlusion and age using a single gallery sample per subject we take advantage of the observation that equidistant prototypes embedding is an optimal embedding that maximizes the minimum one against the rest margin between the classes rather than preserving the global or the local structure of the training data our method called linear regression analysis lra applies a least square regression technique to map gallery samples to the equally distant locations regardless of the true structure of training data further a novel generic learning method which maps the intraclass facial differences of the generic faces to the zero vectors is incorporated to enhance the generalization capability of lra using this novel method learning based on only a handful of generic classes can largely improve the face recognition performance even when the generic data are collected from a different database and camera set up the incremental learning based on the greville algorithm makes the mapping matrix efficiently updated from the newly coming gallery classes training samples or generic variations although it is fairly simple and parameter free lra combined with commonly used local descriptors such as gabor representation and local binary patterns outperforms the state of the art methods for several standard experiments on the extended yale b cmu pie ar and feret databases

double linear regressions for single labeled image per person face recognition recently the underlying sparse representation structure in high dimensional data has received considerable attention in pattern recognition and computer vision in this paper we propose a novel semi supervised dimensionality reduction sdr method named double linear regressions dlr to tackle the single labeled image per person slip face recognition problem dlr simultaneously seeks the best discriminating subspace and preserves the sparse representation structure specifically a subspace assumption based label propagation salp method which is accomplished using linear regressions lr is first presented to propagate the label information to the unlabeled data then based on the propagated labeled dataset a sparse representation regularization term is constructed via linear regressions lr finally dlr takes into account both the discriminating efficiency and the sparse representation structure by using the learned sparse representation regularization term as a regularization term of linear discriminant analysis lda the extensive and encouraging experimental results on three publicly available face databases cmu pie extended yale b and ar demonstrate the effectiveness of the proposed method

kernel self optimization learning for kernel based feature extraction and recognition kernel learning is becoming an important research topic in the area of machine learning and it has wide applications in pattern recognition computer vision image and signal processing kernel learning provides a promising solution to nonlinear problems including nonlinear feature extraction classification and clustering however in kernel based systems the problem of the kernel function and its parameters remains to be solved methods of choosing parameters from a discrete set of values have been presented in previous studies but these methods do not change the data distribution structure in the kernel based mapping space accordingly performance is not improved because the current kernel optimization does not change the data distribution based on this problem this paper presents a uniform framework for kernel self optimization with the ability to adjust the data structure the data dependent kernel is extended and applied to kernel learning and optimization equations with two criteria for measuring data discrimination are used to solve the optimal parameter values some experiments are performed to evaluate the performance in popular kernel learning methods including kernel principal components analysis kpca kernel discriminant analysis kda and kernel locality preserving projection klpp these evaluations show that the framework of kernel self optimization is feasible for enhancing kernel based learning methods

mode kn factor analysis for image ensembles in this corespondence we study the extra factor estimation problem with the assumption that the training image ensemble is expressed as an nth order tensor with the nth dimension characterizing all features for an image and other dimensions for different extra factors such as illuminations poses and identities to overcome the local minimum issue of conventional algorithms designed for this problem we present a novel statistical learning framework called mode kn factor analysis for obtaining a closed form solution to estimating the extra factors of any test image in the learning stage for the kth k ne n dimension of the data tensor the mode kn patterns are constructed by concatenating the feature dimension and the kth extra factor dimension and then a mode kn factor analysis model is learnt based on the mode kn patterns unfolded from the original data tensor in the inference stage for a test image the mode classification of the kth dimension is performed within a probabilistic framework the advantages of mode kn factor analysis over conventional tensor analysis algorithms are twofold 1 a closed form solution instead of iterative sub optimal solution as conventionally is derived for estimating the extra factor mode of any test image and 2 the classification capability is enhanced by interacting with the process of synthesizing data of all other modes in the k th dimension experiments on the pointing 04 and cmu pie databases for pose and illumination estimation both validate the superiority of the proposed algorithm over conventional algorithms for extra factor estimation

quadratic projection based feature extraction with its application to biometric recognition this paper presents a novel quadratic projection based feature extraction framework where a set of quadratic matrices is learned to distinguish each class from all other classes we formulate quadratic matrix learning qml as a standard semidefinite programming sdp problem however the conventional interior point sdp solvers do not scale well to the problem of qml for high dimensional data to solve the scalability of qml we develop an efficient algorithm termed dualqml based on the lagrange duality theory to extract nonlinear features to evaluate the feasibility and effectiveness of the proposed framework we conduct extensive experiments on biometric recognition experimental results on three representative biometric recognition tasks including face palmprint and ear recognition demonstrate the superiority of the dualqml based feature extraction algorithm compared to the current state of the art algorithms highlightsa novel quadratic projection based feature extraction framework is developed a set of quadratic matrices is learnt to distinguish each class from other classes quadratic matrix learning qml is formulated as an sdp problem an efficient algorithm is developed to solve qml based on lagrange duality theory experiments on biometric recognition show the effectiveness of our algorithm

modified principal component analysis an integration of multiple similarity subspace models we modify the conventional principal component analysis pca and propose a novel subspace learning framework modified pca mpca using multiple similarity measurements mpca computes three similarity matrices exploiting the similarity measurements 1 mutual information 2 angle information and 3 gaussian kernel similarity we employ the eigenvectors of similarity matrices to produce new subspaces referred to as similarity subspaces a new integrated similarity subspace is then generated using a novel feature selection approach this approach needs to construct a kind of vector set termed weak machine cell wmc which contains an appropriate number of the eigenvectors spanning the similarity subspaces combining the wrapper method and the forward selection scheme mpca selects a wmc at a time that has a powerful discriminative capability to classify samples mpca is very suitable for the application scenarios in which the number of the training samples is less than the data dimensionality mpca outperforms the other state of the art pca based methods in terms of both classification accuracy and clustering result in addition mpca can be applied to face image reconstruction mpca can use other types of similarity measurements extensive experiments on many popular real world data sets such as face databases show that mpca achieves desirable classification results as well as has a powerful capability to represent data

probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

exact solutions to a class of feedback systems on so n this paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on so n the closed loop systems are solved exactly for the rotation matrices as explicit functions of time the initial conditions and the gain parameters of the control laws the exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix applications of these results are found in model predictive control problems where detailed insight into the transient attitude dynamics is utilized to approximately complete a task of secondary importance knowledge of the future trajectory of the states can also be used as an alternative to the zero order hold in systems where the attitude is sampled at discrete time instances

compound rank k projections for bilinear analysis in many real world applications data are represented by matrices or high order tensors despite the promising performance the existing 2 d discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection making the model less flexible in this paper we propose a novel compound rank k projection crp algorithm for bilinear analysis the crp deals with matrices directly without transforming them into vectors and it therefore preserves the correlations within the matrix and decreases the computation complexity different from the existing 2 d discriminant analysis algorithms objective function values of crp increase monotonically in addition the crp utilizes multiple rank k projection models to enable a larger search space in which the optimal solution can be found in this way the discriminant ability is enhanced we have tested our approach on five data sets including uuim cvl pointing 04 usps and coil20 experimental results show that the performance of our proposed crp performs better than other algorithms in terms of classification accuracy

a new discriminant subspace analysis approach for multi class problems fukunaga koontz transform fkt is a famous feature extraction method in statistical pattern recognition which aims to find a set of vectors that have the best representative power for one class while the poorest representative power for the other class li and savvides 1 propose a one against all strategy to deal with multi class problems in which the two class fkt method can be directly applied to find the presentative vectors of each class motivated by the fkt method in this paper we propose a new discriminant subspace analysis dsa method for the multi class feature extraction problems to solve dsa we propose an iterative algorithm for the joint diagonalization jd problem finally we generalize the linear dsa method to handle nonlinear feature extraction problems via the kernel trick to demonstrate the effectiveness of the proposed method for pattern recognition problems we conduct extensive experiments on real data sets and show that the proposed method outperforms most commonly used feature extraction methods

eigenfeature regularization and extraction in face recognition this work proposes a subspace approach that regularizes and extracts eigenfeatures from the face image eigenspace of the within class scatter matrix is decomposed into three subspaces a reliable subspace spanned mainly by the facial variation an unstable subspace due to noise and finite number of training samples and a null subspace eigenfeatures are regularized differently in these three subspaces based on an eigenspectrum model to alleviate problems of instability overfitting or poor generalization this also enables the discriminant evaluation performed in the whole space feature extraction or dimensionality reduction occurs only at the final stage after the discriminant assessment these efforts facilitate a discriminative and a stable low dimensional feature representation of the face image experiments comparing the proposed approach with some other popular subspace methods on the feret orl ar and gt databases show that our method consistently outperforms others

domain adaptation and sample bias correction theory and algorithm for regression we present a series of new theoretical algorithmic and empirical results for domain adaptation and sample bias correction in regression we prove that the discrepancy is a distance for the squared loss when the hypothesis set is the reproducing kernel hilbert space induced by a universal kernel such as the gaussian kernel we give new pointwise loss guarantees based on the discrepancy of the empirical source and target distributions for the general class of kernel based regularization algorithms these bounds have a simpler form than previous results and hold for a broader class of convex loss functions not necessarily differentiable including l q losses and the hinge loss we also give finer bounds based on the discrepancy and a weighted feature discrepancy parameter we extend the discrepancy minimization adaptation algorithm to the more significant case where kernels are used and show that the problem can be cast as an sdp similar to the one in the feature space we also show that techniques from smooth optimization can be used to derive an efficient algorithm for solving such sdps even for very high dimensional feature spaces and large samples we have implemented this algorithm and report the results of experiments both with artificial and real world data sets demonstrating its benefits both for general scenario of adaptation and the more specific scenario of sample bias correction our results show that it can scale to large data sets of tens of thousands or more points and demonstrate its performance improvement benefits

a least squares framework for component analysis over the last century component analysis ca methods such as principal component analysis pca linear discriminant analysis lda canonical correlation analysis cca locality preserving projections lpp and spectral clustering sc have been extensively used as a feature extraction step for modeling classification visualization and clustering ca techniques are appealing because many can be formulated as eigen problems offering great potential for learning linear and nonlinear representations of data in closed form however the eigen formulation often conceals important analytic and computational drawbacks of ca techniques such as solving generalized eigen problems with rank deficient matrices e g small sample size problem lacking intuitive interpretation of normalization factors and understanding commonalities and differences between ca methods this paper proposes a unified least squares framework to formulate many ca methods we show how pca lda cca lpp sc and its kernel and regularized extensions correspond to a particular instance of least squares weighted kernel reduced rank regression ls wkrrr the ls wkrrr formulation of ca methods has several benefits 1 provides a clean connection between many ca techniques and an intuitive framework to understand normalization factors 2 yields efficient numerical schemes to solve ca techniques 3 overcomes the small sample size problem 4 provides a framework to easily extend ca methods we derive weighted generalizations of pca lda sc and cca and several new ca techniques

local manifold distance based on neighborhood graph reordering in this paper we consider the problem of estimating pair wise signals dissimilarities through the comparison of the underlying local manifold structures aiming to confront with issues such as high geometrical complexity and significant overlap that characterize local manifold structures we propose a novel dissimilarity measure which is based on the reordering of a neighborhood graph using a permutation of its nodes in order to quantify the diversity between two manifolds the dissimilarity function utilizes a measure of reordering efficiency computed on each of the corresponding neighborhood graphs using a permutation derived from the solution of an optimization problem on the opposite graph we study the properties of the proposed measure demonstrating its efficiency in a variety of applications using both 1d and 2d signals additionally by exploiting the links to previous findings from the field of random graphs we introduce a generalization of the above measure based on the notion of multi dimensional ordering finally we perform a thorough evaluation on the problem of face recognition under various challenging conditions obtaining state of the art recognition accuracy with a competitive computational load pair wise dissimilarity between signals is addressed as a manifold to manifold distance diversity between two manifolds is estimated using a measure of reordering efficiency of the corresponding neighborhood graphs multi dimensional ordering of nodes proves to be even more discriminative we demonstrate the efficiency of the proposed measure in a variety of 1d and 2d signals state of the art performance is achieved in face recognition under challenging scenarios

discriminative multimanifold analysis for face recognition from a single training sample per person conventional appearance based face recognition methods usually assume that there are multiple samples per person mspp available for discriminative feature extraction during the training phase in many practical face recognition applications such as law enhancement e passport and id card identification this assumption however may not hold as there is only a single sample per person sspp enrolled or recorded in these systems many popular face recognition methods fail to work well in this scenario because there are not enough samples for discriminant learning to address this problem we propose in this paper a novel discriminative multimanifold analysis dmma method by learning discriminative features from image patches first we partition each enrolled face image into several nonoverlapping patches to form an image set for each sample per person then we formulate the sspp face recognition as a manifold manifold matching problem and learn multiple dmma feature spaces to maximize the manifold margins of different persons finally we present a reconstruction based manifold manifold distance to identify the unlabeled subjects experimental results on three widely used face databases are presented to demonstrate the efficacy of the proposed approach

automatic classification of single facial images we propose a method for automatically classifying facial images based on labeled elastic graph matching a 2d gabor wavelet representation and linear discriminant analysis results of tests with three image sets are presented for the classification of sex race and expression a visual interpretation of the discriminant vectors is provided

inexact implementation using krylov subspace methods for large scale exponential discriminant analysis with applications to high dimensionality reduction problems abstract exponential discriminant analysis eda is a generalized discriminant analysis method based on matrix exponential it can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear discriminant analysis lda however for data with high dimensionality one has to solve a large matrix exponential eigenproblem in this method and the time complexity is dominated by the computation of exponential of large matrices in this paper we propose two inexact krylov subspace algorithms for solving the large matrix exponential eigenproblem efficiently the contribution of this work is threefold first we consider how to compute matrix exponential vector products efficiently which is the key step in the krylov subspace method second we compare the discriminant analysis criterion of eda and that of lda from a theoretical point of view third we establish the relationship between the accuracy of the approximate eigenvectors and the distance to nearest neighbor classifier and show why the matrix exponential eigenproblem can be solved approximately in practice numerical experiments on some real world databases show the superiority of our new algorithms over their original counterpart for face recognition

enhanced shift and scale tolerance for rotation invariant polar matching with dual tree wavelets polar matching is a recently developed shift and rotation invariant object detection method that is based upon dual tree complex wavelet transforms or equivalent multiscale directional filterbanks it can be used to facilitate both keypoint matching neighborhood search detection or detection and tracking with particle filters the theory is extended here to incorporate an allowance for local spatial and dilation perturbations with experiments we demonstrate that the robustness of the polar matching method is strengthened at modest computational cost

face recognition using ipca ica algorithm in this paper a fast incremental principal non gaussian directions analysis algorithm called ipca ica is introduced this algorithm computes the principal components of a sequence of image vectors incrementally without estimating the covariance matrix so covariance free and at the same time transforming these principal components to the independent directions that maximize the non gaussianity of the source two major techniques are used sequentially in a real time fashion in order to obtain the most efficient and independent components that describe a whole set of human faces database this procedure is done by merging the runs of two algorithms based on principal component analysis pca and independent component analysis ica running sequentially this algorithm is applied to face recognition problem simulation results on different databases showed high average success rate of this algorithm compared to others

formulating robust linear regression estimation as a one class lda criterion discriminative hat matrix linear discriminant analysis such as fisher s criterion is a statistical learning tool traditionally devoted to separating a training dataset into two or even several classes by the way of linear decision boundaries in this paper we show that this tool can formalize the robust linear regression problem as a robust estimator will do more precisely we develop a one class fischer s criterion in which the maximization provides both the regression parameters and the separation of the data in two classes typical data and atypical data or outliers this new criterion is built on the statistical properties of the subspace decomposition of the hat matrix from this angle we improve the discriminative properties of the hat matrix which is traditionally used as outlier diagnostic measure in linear regression naturally we call this new approach discriminative hat matrix the proposed algorithm is fully nonsupervised and needs only the initialization of one parameter synthetic and real datasets are used to study the performance both in terms of regression and classification of the proposed approach we also illustrate its potential application to image recognition and fundamental matrix estimation in computer vision

formulating face verification with semidefinite programming this paper presents a unified solution to three unsolved problems existing in face verification with subspace learning techniques selection of verification threshold automatic determination of subspace dimension and deducing feature fusing weights in contrast to previous algorithms which search for the projection matrix directly our new algorithm investigates a similarity metric matrix smm with a certain verification threshold this matrix is learned by a semidefinite programming approach along with the constraints of the kindred pairs with similarity larger than the threshold and inhomogeneous pairs with similarity smaller than the threshold then the subspace dimension and the feature fusing weights are simultaneously inferred from the singular value decomposition of the derived smm in addition the weighted and tensor extensions are proposed to further improve the algorithmic effectiveness and efficiency respectively essentially the verification is conducted within an affine subspace in this new algorithm and is hence called the affine subspace for verification asv extensive experiments show that the asv can achieve encouraging face verification accuracy in comparison to other subspace algorithms even without the need to explore any parameters

detectability uniqueness and reliability of eigen windows for stable verification of partially occluded objects this paper describes a method for recognizing partially occluded objects for bin picking tasks using eigenspace analysis referred to as the eigen window method that stores multiple partial appearances of an object in an eigenspace such partial appearances require a large amount of memory space three measurements detectability uniqueness and reliability on windows are developed to eliminate redundant windows and thereby reduce memory requirements using a pose clustering technique the method determines the pose of an object and the object type itself we have implemented the method and verified its validity