proper intrinsic scales for a posteriori multiscale error estimation recently the multiscale a posteriori error estimator has been introduced showing excellent robustness for fluid mechanics problems in this paper a theoretical analysis for element edge exact solutions is conducted in which case the error constant is the norm of a green s function or a residual free bubble this finds application when the solution is computed with a stabilized method one of the features of the technique is that it gives the proper scales for a posteriori error estimation in any norm of interest such as the l2 h1 energy and l norms for fluid transport problems it is shown that the constant for predicting the error in the h1 seminorm is unbounded as the element peclet number tends to infinity making lp norms more suitable for this type of problems furthermore it is shown that the flow intrinsic time scale parameter represents the l1 norm of the error as a function of the l norm of the residual when these scales are employed for one dimensional nodally exact solutions piecewise linear finite element spaces and piecewise constant residuals the multiscale error estimator is shown to be exact

subspace learning from image gradient orientations we introduce the notion of subspace learning from image gradient orientations for appearance based object recognition as image data are typically noisy and noise is substantially different from gaussian traditional subspace learning from pixel intensities very often fails to estimate reliably the low dimensional subspace of a given data population we show that replacing pixel intensities with gradient orientations and the l2 norm with a cosine based distance measure offers to some extend a remedy to this problem within this framework which we coin image gradient orientations igo subspace learning we first formulate and study the properties of principal component analysis of image gradient orientations igo pca we then show its connection to previously proposed robust pca techniques both theoretically and experimentally finally we derive a number of other popular subspace learning techniques namely linear discriminant analysis lda locally linear embedding lle and laplacian eigenmaps le experimental results show that our algorithms significantly outperform popular methods such as gabor features and local binary patterns and achieve state of the art performance for difficult problems such as illumination and occlusion robust face recognition in addition to this the proposed igo methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding l2 norm intensity based counterparts matlab code for the methods presented in this paper can be found at http ibug doc ic ac uk resources

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

learning linear discriminant projections for dimensionality reduction of image descriptors in this paper we present linear discriminant projections ldp for reducing dimensionality and improving discriminability of local image descriptors we place ldp into the context of state of the art discriminant projections and analyze its properties ldp requires a large set of training data with point to point correspondence ground truth we demonstrate that training data produced by a simulation of image transformations leads to nearly the same results as the real data with correspondence ground truth this makes it possible to apply ldp as well as other discriminant projection approaches to the problems where the correspondence ground truth is not available such as image categorization we perform an extensive experimental evaluation on standard data sets in the context of image matching and categorization we demonstrate that ldp enables significant dimensionality reduction of local descriptors and performance increases in different applications the results improve upon the state of the art recognition performance with simultaneous dimensionality reduction from 128 to 30

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

variational multiscale a posteriori error estimation for multi dimensional transport problems this paper presents an explicit a posteriori error estimator for the multi dimensional transport equation based on an approximation to the variational multiscale theory the technique is adequate for methods with a local error distribution such as stabilized methods yielding efficiencies close to one for both the hyperbolic and diffusive limit regarding the hyperbolic limit previous work is extended to multi dimensions adequate norms are proposed for the computation of the error and proper error intrinsic time scales are calculated for the bilinear quadrilateral and the linear triangle furthermore the model considers the element interface error along the element edges enabling the error prediction in the diffusive limit the success of the method can be explained by the fact that in stabilized methods the element local problem captures most of the error and the proposed error intrinsic time scales are an approximation to the solution of the dual problem the proposed technology which can be implemented straightforwardly in existing codes is extremely economical because it is a simple explicit postprocessing

variational multiscale error estimators for solid mechanics adaptive simulations an orthogonal subgrid scale approach abstract in this work we present a general error estimator for the finite element solution of solid mechanics problems based on the variational multiscale method the main idea is to consider a rich model for the subgrid scales as an error estimator the subscales are considered to belong to a space orthogonal to the finite element space orthogonal subgrid scales and we take into account their contribution both in the element interiors and on the element boundaries subscales on the element boundaries a simple analysis shows that the upper bound for the obtained error estimator is sharper than in other error estimators based on the variational multiscale method numerical examples show that the proposed error estimator is an accurate approximation for the energy norm error and can be used both in simple linear constitutive models and in more complex non linear cases

low rank structure learning via nonconvex heuristic recovery in this paper we propose a nonconvex framework to learn the essential low rank structure from corrupted data different from traditional approaches which directly utilizes convex norms to measure the sparseness our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low rank structure and the sparse corruptions we will respectively introduce how to combine the widely used lp norm 0 p 1 and log sum term into the framework of low rank structure learning although the proposed optimization is no longer convex it still can be effectively solved by a majorization minimization mm type algorithm with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches we prove that the mm type algorithm can converge to a stationary point after successive iterations the proposed model is applied to solve two typical problems robust principal component analysis and low rank representation experimental results on low rank structure learning demonstrate that our nonconvex heuristic methods especially the log sum heuristic recovery algorithm generally perform much better than the convex norm based method 0 p 1 for both data with higher rank and with denser corruptions

variational multiscale a posteriori error estimation for systems application to linear elasticity abstract this paper presents an explicit residual based a posteriori error estimator for linear elasticity the method is derived from the variational multiscale theory where the subgrid scales and the constants of the method are calculated explicitly from fine scale green s functions several numerical examples are presented showing satisfactory local and global efficiencies when the h 1 seminorm is employed the formulation which is applied to plane stress problems can be easily extended to other elasticity problems

the multiscale approach to error estimation and adaptivity abstract a new explicit a posteriori error estimator is investigated which emanates from the variational multiscale theory the error estimator uses an approximation of the green s function which propagates the error according to the dual problem the technique predicts the error in the l2 norm from element residuals both interior and inter element jumps therefore leading to a very economical procedure finally the methodology is applied to fluid flow transport showing that for convection dominated flows the efficiency index is independent of the diffusion coefficient

real time enhancement of dynamic depth videos with non rigid deformations we propose a novel approach for enhancing depth videos containing non rigidly deforming objects depth sensors are capable of capturing depth maps in real time but suffer from high noise levels and low spatial resolutions while solutions for reconstructing 3d details in static scenes or scenes with rigid global motions have been recently proposed handling unconstrained non rigid deformations in relative complex scenes remains a challenge our solution consists in a recursive dynamic multi frame super resolution algorithm where the relative local 3d motions between consecutive frames are directly accounted for we rely on the assumption that these 3d motions can be decoupled into lateral motions and radial displacements this allows to perform a simple local per pixel tracking where both depth measurements and deformations are dynamically optimized the geometric smoothness is subsequently added using a multi level l 1 minimization with a bilateral total variation regularization the performance of this method is thoroughly evaluated on both real and synthetic data as compared to alternative approaches the results show a clear improvement in reconstruction accuracy and in robustness to noise to relative large non rigid deformations and to topological changes moreover the proposed approach implemented on a cpu is shown to be computationally efficient and working in real time

descriptor learning via supervised manifold regularization for multioutput regression multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis however due to the huge image variability and ambiguity it is fundamentally challenging to handle the highly complex input target relationship of multioutput regression especially with indiscriminate high dimensional representations in this paper we propose a novel supervised descriptor learning sdl algorithm for multioutput regression which can establish discriminative and compact feature representations to improve the multivariate estimation performance the sdl is formulated as generalized low rank approximations of matrices with a supervised manifold regularization the sdl is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low dimensional space aligned to targets the achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression which enables more accurate and efficient multivariate estimation we conduct extensive evaluation of the proposed sdl on both synthetic data and real world multioutput regression tasks for both computer vision and medical image analysis experimental results have shown that the proposed sdl can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts our method establishes a novel sdl framework for multioutput regression which can be widely used to boost the performance in different applications

time dependent subscales in the stabilized finite element approximation of incompressible flow problems abstract in this paper we analyze a stabilized finite element approximation for the incompressible navier stokes equations based on the subgrid scale concept the essential point is that we explore the properties of the discrete formulation that results allowing the subgrid scales to depend on time this apparently natural idea avoids several inconsistencies of previous formulations and also opens the door to generalizations

local feature discriminant projection in this paper we propose a novel subspace learning algorithm called local feature discriminant projection lfdp for supervised dimensionality reduction of local features lfdp is able to efficiently seek a subspace to improve the discriminability of local features for classification we make three novel contributions first the proposed lfdp is a general supervised subspace learning algorithm which provides an efficient way for dimensionality reduction of large scale local feature descriptors second we introduce the differential scatter discriminant criterion dsdc to the subspace learning of local feature descriptors which avoids the matrix singularity problem third we propose a generalized orthogonalization method to impose on projections leading to a more compact and less redundant subspace extensive experimental validation on three benchmark datasets including uiuc sports scene 15 and mit indoor demonstrates that the proposed lfdp outperforms other dimensionality reduction methods and achieves state of the art performance for image classification

cumulative attribute space regression for head pose estimation and color constancy abstract two stage cumulative attribute ca regression has been found effective in regression problems of computer vision such as facial age and crowd density estimation the first stage regression maps input features to cumulative attributes that encode correlations between target values the previous works have dealt with single output regression in this work we propose cumulative attribute spaces for 2 and 3 output multivariate regression we show how the original ca space can be generalized to multiple output by the cartesian product cartca however for target spaces with more than two outputs the cartca becomes computationally infeasible and therefore we propose an approximate solution multi view ca mvca where cartca is applied to output pairs we experimentally verify improved performance of the cartca and mvca spaces in 2d and 3d face pose estimation and three output rgb illuminant estimation for color constancy

a general framework for regularized similarity based image restoration any image can be represented as a function defined on a weighted graph in which the underlying structure of the image is encoded in kernel similarity and associated laplacian matrices in this paper we develop an iterative graph based framework for image restoration based on a new definition of the normalized graph laplacian we propose a cost function which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph laplacian the normalizing coefficients used in the definition of the laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing this results in some desired spectral properties for the normalized laplacian such as being symmetric positive semidefinite and returning zero vector when applied to a constant image our algorithm comprises of outer and inner iterations where in each outer iteration the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations this procedure improves the performance of the algorithm for image deblurring where we do not have access to a good initial estimate of the underlying image in addition the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations in addition the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems including deblurring denoising and sharpening experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples

learning discriminant face descriptor local feature descriptor is an important module for face recognition and those like gabor and local binary patterns lbp have proven effective face descriptors traditionally the form of such local descriptors is predefined in a handcrafted way in this paper we propose a method to learn a discriminant face descriptor dfd in a data driven way the idea is to learn the most discriminant local features that minimize the difference of the features between images of the same person and maximize that between images from different people in particular we propose to enhance the discriminative ability of face representation in three aspects first the discriminant image filters are learned second the optimal neighborhood sampling strategy is soft determined third the dominant patterns are statistically constructed discriminative learning is incorporated to extract effective and robust features we further apply the proposed method to the heterogeneous cross modality face recognition problem and learn dfd in a coupled way coupled dfd or c dfd to reduce the gap between features of heterogeneous face images to improve the performance of this challenging problem extensive experiments on feret cas peal r1 lfw and hfb face databases validate the effectiveness of the proposed dfd learning on both homogeneous and heterogeneous face recognition problems the dfd improves poem and lqp by about 4 5 percent on lfw database and the c dfd enhances the heterogeneous face recognition performance of lbp by over 25 percent

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

direct estimation of range flow on deformable shape from a video rate range camera a method of estimating range flow space displacement vector field on nonrigid as well as rigid objects from a sequence of range images is described this method can directly estimate the deformable motion parameters by solving a system of linear equations that are obtained from substituting a linear transformation of nonrigid objects expressed by the jacobian matrix into motion constraints based on an extension of the conventional scheme used in intensity image sequences the range flow is directly computed by substituting these estimated motion parameters into the linear transformation the algorithm is supported by experimental estimations of range flow on a sheet of paper a piece of cloth human skin and a rubber balloon being inflated using real range image sequences acquired by a video rate range camera

variational multiscale a posteriori error estimation for systems the euler and navier stokes equations this paper extends explicit a posteriori error estimators based on the variational multiscale theory to systems of equations in particular the emphasis is placed on flow problems the euler and navier stokes equations three error estimators are proposed the standard the naive and the upper bound numerical results show that with a very economical algorithm the attained global and local efficiencies for the naive approach are reasonably close to unity whereas the standard and upper bound approaches give respectively approximate lower and higher error estimates

localization of elliptic multiscale problems this paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients the basis functions are solutions of local problems on vertex patches the error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches hence on a uniform mesh of size h patches of diameter h log 1 h are sufficient to preserve a linear rate of convergence in h without pre asymptotic or resonance effects the analysis does not rely on regularity of the solution or scale separation in the coefficient this result motivates new and justifies old classes of variational multiscale methods see more at http www ams org journals mcom 2014 83 290 s0025 5718 2014 02868 8 sthash z2ccfxig dpuf

learning local feature descriptors using convex optimisation the objective of this work is to learn descriptors suitable for the sparse feature detectors used in viewpoint invariant matching we make a number of novel contributions towards this goal first it is shown that learning the pooling regions for the descriptor can be formulated as a convex optimisation problem selecting the regions using sparsity second it is shown that descriptor dimensionality reduction can also be formulated as a convex optimisation problem using mahalanobis matrix nuclear norm regularisation both formulations are based on discriminative large margin learning constraints as the third contribution we evaluate the performance of the compressed descriptors obtained from the learnt real valued descriptors by binarisation finally we propose an extension of our learning formulations to a weakly supervised case which allows us to learn the descriptors from unannotated image collections it is demonstrated that the new learning methods improve over the state of the art in descriptor learning on the annotated local patches data set of brown et al and unannotated photo collections of philbin et al

adaptive variational multiscale methods based on a posteriori error estimation energy norm estimates for elliptic problems we develop a new adaptive multiscale finite element method using the variational multiscale framework together with a systematic technique for approximation of the fine scale part of the solution the fine scale is approximated by a sum of solutions to decoupled localized problems which are solved numerically on a fine grid partition of a patch of coarse grid elements the sizes of the patches of elements may be increased to control the error caused by localization we derive an a posteriori error estimate in the energy norm which captures the dependency of the crucial discretization parameters the coarse grid mesh size the fine grid mesh size and the sizes of the patches based on the a posteriori error estimate we present an adaptive algorithm that automatically tunes these parameters finally we show how the method works in practice by presenting various numerical examples

uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning this paper proposes an uncorrelated multilinear principal component analysis umpca algorithm for unsupervised subspace learning of tensorial data it should be viewed as a multilinear extension of the classical principal component analysis pca framework through successive variance maximization umpca seeks a tensor to vector projection tvp that captures most of the variation in the original tensorial input while producing uncorrelated features the solution consists of sequential iterative steps based on the alternating projection method in addition to deriving the umpca framework this work offers a way to systematically determine the maximum number of uncorrelated multilinear features that can be extracted by the method umpca is compared against the baseline pca solution and its five state of the art multilinear extensions namely two dimensional pca 2dpca concurrent subspaces analysis csa tensor rank one decomposition trod generalized pca gpca and multilinear pca mpca on the tasks of unsupervised face and gait recognition experimental results included in this paper suggest that umpca is particularly effective in determining the low dimensional projection space needed in such recognition tasks

structure constrained low rank representation benefiting from its effectiveness in subspace segmentation low rank representation lrr and its variations have many applications in computer vision and pattern recognition such as motion segmentation image segmentation saliency detection and semisupervised learning it is known that the standard lrr can only work well under the assumption that all the subspaces are independent however this assumption cannot be guaranteed in real world problems this paper addresses this problem and provides an extension of lrr named structure constrained lrr sc lrr to analyze the structure of multiple disjoint subspaces which is more general for real vision data we prove that the relationship of multiple linear disjoint subspaces can be exactly revealed by sc lrr with a predefined weight matrix as a nontrivial byproduct we also illustrate that sc lrr can be applied for semisupervised learning the experimental results on different types of vision problems demonstrate the effectiveness of our proposed method

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

stabilization of incompressibility and convection through orthogonal sub scales in finite element methods two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper the first of them is the stabilization through the pressure gradient projection which consists of adding a certain least squares form of the difference between the pressure gradient and its l2 projection onto the discrete velocity space in the variational equations of the problem the second is a sub grid scale method whose stabilization effect is very similar to that of the galerkin least squares gls method for the stokes problem it is shown here that the first method can also be recast in the framework of sub grid scale methods with a particular choice for the space of sub scales this leads to a new stabilization procedure whose applicability to stabilize convection is also studied in this paper

multi output regression on the output manifold multi output regression aims at learning a mapping from an input feature space to a multivariate output space previous algorithms define the loss functions using a fixed global coordinate of the output space which is equivalent to assuming that the output space is a whole euclidean space with a dimension equal to the number of the outputs so the underlying structure of the output space is completely ignored in this paper we consider the output space as a riemannian submanifold to incorporate its geometric structure into the regression process to this end we propose a novel mechanism called locally linear transformation llt to define the loss functions on the output manifold in this way currently existing regression algorithms can be improved in particular we propose an algorithm under the support vector regression framework our experimental results on synthetic and real life data are satisfactory