lle score a new filter based unsupervised feature selection method based on nonlinear manifold embedding and its application to image recognition the task of feature selection is to find the most representative features from the original high dimensional data because of the absence of the information of class labels selecting the appropriate features in unsupervised learning scenarios is much harder than that in supervised scenarios in this paper we investigate the potential of locally linear embedding lle which is a popular manifold learning method in feature selection task it is straightforward to apply the idea of lle to the graph preserving feature selection framework however we find that this straightforward application suffers from some problems for example it fails when the elements in the feature are all equal it does not enjoy the property of scaling invariance and cannot capture the change of the graph efficiently to solve these problems we propose a new filter based feature selection method based on lle in this paper which is named as lle score the proposed criterion measures the difference between the local structure of each feature and that of the original data our experiments of classification task on two face image data sets an object image data set and a handwriting digits data set show that lle score outperforms state of the art methods including data variance laplacian score and sparsity score

the cauchy formula with s monogenic kernel and a functional calculus for noncommuting operators abstract the new notion of slice monogenic functions introduced in the paper f colombo i sabadini d c struppa slice monogenic functions israel j math 171 2009 385 403 led us to define a new functional calculus for an n tuple of not necessarily commuting operators see f colombo i sabadini d c struppa a new functional calculus for noncommuting operators j funct anal 254 2008 2255 2274 in this paper we prove a cauchy formula with slice monogenic kernel for the slice monogenic functions this new cauchy formula is the fundamental tool to prove that our functional calculus apply to a more general setting moreover we deduce some fundamental properties of the functional calculus for example some algebraic properties the spectral mapping theorem and the spectral radius theorem

super normal vector for human activity recognition with depth cameras the advent of cost effectiveness and easy operation depth cameras has facilitated a variety of visual recognition tasks including human activity recognition this paper presents a novel framework for recognizing human activities from video sequences captured by depth cameras we extend the surface normal to polynormal by assembling local neighboring hypersurface normals from a depth sequence to jointly characterize local motion and shape information we then propose a general scheme of super normal vector snv to aggregate the low level polynormals into a discriminative representation which can be viewed as a simplified version of the fisher kernel representation in order to globally capture the spatial layout and temporal order an adaptive spatio temporal pyramid is introduced to subdivide a depth video into a set of space time cells in the extensive experiments the proposed approach achieves superior performance to the state of the art methods on the four public benchmark datasets i e msraction3d msrdailyactivity3d msrgesture3d and msractionpairs3d

action recognition with dynamic image networks we introduce the concept of dynamic image a novel compact representation of videos useful for video analysis particularly in combination with convolutional neural networks cnns a dynamic image encodes temporal data such as rgb or optical flow videos by using the concept of rank pooling the idea is to learn a ranking machine that captures the temporal evolution of the data and to use the parameters of the latter as a representation we call the resulting representation dynamic image because it summarizes the video dynamics in addition to appearance this powerful idea allows to convert any video to an image so that existing cnn models pre trained with still images can be immediately extended to videos we also present an efficient approximate rank pooling operator that runs two orders of magnitude faster than the standard ones with any loss in ranking performance and can be formulated as a cnn layer to demonstrate the power of the representation we introduce a novel four stream cnn architecture which can learn from rgb and optical flow frames as well as from their dynamic image representations we show that the proposed network achieves state of the art performance 95 5 and 72 5 percent accuracy in the ucf101 and hmdb51 respectively

kernelized multiview projection for robust action recognition conventional action recognition algorithms adopt a single type of feature or a simple concatenation of multiple features in this paper we propose to better fuse and embed different feature representations for action recognition using a novel spectral coding algorithm called kernelized multiview projection kmp computing the kernel matrices from different features views via time sequential distance learning kmp can encode different features with different weights to achieve a low dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative more crucially kmp is linear for the reproducing kernel hilbert space which allows it to be competent for various practical applications we demonstrate kmp s performance for action recognition on five popular action datasets and the results are consistently superior to state of the art techniques

action recognition based on overcomplete independent components analysis existing works on action recognition rely on two separate stages 1 designing hand designed features or learning features from video data 2 classifying features using a classifier such as svm or adaboost motivated by two observations 1 independent component analysis ica is capable of encoding intrinsic features underlying video data and 2 videos of different actions can be easily distinguished by their intrinsic features we propose a simple but effective action recognition framework based on the recently proposed overcomplete ica model after a set of overcomplete ica basis functions are learned from the densely sampled 3d patches from training videos for each action a test video is classified as the class whose basis functions can reconstruct the sampled 3d patches from the test video with the smallest reconstruction error the experimental results on five benchmark datasets demonstrate that the proposed approach outperforms several state of the art works

robust optical flow integration we analyze the problem of how to correctly construct dense point trajectories from optical flow fields first we show that simple euler integration is unavoidably inaccurate no matter how good is the optical flow estimator then an inverse integration scheme is analyzed which is more robust to bias and input noise and shows better stability properties our contribution is threefold 1 a theoretical analysis that demonstrates why and in what sense inverse integration is more accurate 2 a rich experimental validation both on synthetic and real image data and 3 an algorithm for approximate online inverse integration this new technique is precious whether one is trying to propagate information densely available on a reference frame to the other frames in the sequence or conversely to assign information densely over each frame by pulling it from the reference

a discriminative representation for human action recognition action recognition has been standing as an active research topic over the past years many efforts have been made and many methods have been proposed however there are still some challenges such as illumination condition viewpoint camera motion and cluttered background in order to tackle these challenges a discriminative representation is proposed by discovering key information of the input data this task can be addressed by improvements of two major components parameterized representation and discriminative classifier the representation is parameterized with hidden variables and can be learned from training data and the classifier can be trained to recognize actions based on the proposed representation the contributions of this paper are as follows 1 a novel probabilistic representation is utilized to capture the relative significant information of low level features 2 a novel framework is proposed by combining the parameterized representation and discriminative classifier 3 an alternating strategy is favorable to improve the performance of action recognition by updating the representation and the classifier alternatively experimental results on five well known datasets demonstrate that the proposed method significantly improves the performance in action recognition highlightsa discriminative representation is proposed by discovering key information of the input data the representation is parameterized with hidden variables and can be learned from training data human action is recognized by combining the parameterized representation and discriminative classifier the performance of action recognition is improved by updating the representation and the classifier alternatively

highly articulated kinematic structure estimation combining motion and skeleton information in this paper we present a novel framework for unsupervised kinematic structure learning of complex articulated objects from a single view 2d image sequence in contrast to prior motion based methods which estimate relatively simple articulations our method can generate arbitrarily complex kinematic structures with skeletal topology via a successive iterative merging strategy the iterative merge process is guided by a density weighted skeleton map which is generated from a novel object boundary generation method from sparse 2d feature points our main contributions can be summarised as follows i an unsupervised complex articulated kinematic structure estimation method that combines motion segments with skeleton information ii an iterative fine to coarse merging strategy for adaptive motion segmentation and structural topology embedding iii a skeleton estimation method based on a novel silhouette boundary generation from sparse feature points using an adaptive model selection method iv a new highly articulated object dataset with ground truth annotation we have verified the effectiveness of our proposed method in terms of computational time and estimation accuracy through rigorous experiments with multiple datasets our experiments show that the proposed method outperforms state of the art methods both quantitatively and qualitatively

a robust and efficient video representation for action recognition this paper introduces a state of the art video representation and applies it to efficient action recognition and detection we first propose to improve the popular dense trajectory features by explicit camera motion estimation more specifically we extract feature point matches between frames using surf descriptors and dense optical flow the matches are used to estimate a homography with ransac to improve the robustness of homography estimation a human detector is employed to remove outlier matches from the human body as human motion is not constrained by the camera trajectories consistent with the homography are considered as due to camera motion and thus removed we also use the homography to cancel out camera motion from the optical flow this results in significant improvement on motion based hof and mbh descriptors we further explore the recent fisher vector as an alternative feature encoding approach to the standard bag of words bow histogram and consider different ways to include spatial layout information in these encodings we present a large and varied set of evaluations considering i classification of short basic actions on six datasets ii localization of such actions in feature length movies and iii large scale recognition of complex events we find that our improved trajectory features significantly outperform previous dense trajectories and that fisher vectors are superior to bow encodings for video recognition tasks in all three tasks we show substantial improvements over the state of the art results

slice segal bargmann transform the segal bargmann transform is a unitary map between the schrodinger and fock space which is used for example to show the integrability of quantum rabi models slice monogenic functions provide the framework in which functional calculus for quaternionic quantum mechanics can be developed in this paper a generalisation of the segal bargmann transform to the context of slice monogenic functions is constructed and studied in detail it is shown to interact appropriately with the recently constructed slice fourier transform this leads furthermore to a construction of a slice fock space which is shown to be a reproducing kernel space

variational method for joint optical flow estimation and edge aware image restoration the most popular optical flow algorithms rely on optimizing the energy function that integrates a data term and a smoothness term in contrast to this traditional framework we derive a new objective function that couples optical flow estimation and image restoration our method is inspired by the recent successes of edge aware constraints eac in preserving edges in general gradient domain image filtering by incorporating an eac image fidelity term ift in the conventional variational model the new energy function can simultaneously estimate optical flow and restore images with preserved edges in a bidirectional manner for the energy minimization we rewrite the eac into gradient form and optimize the ift with euler lagrange equations we can thus apply the image restoration by analytically solving a system of linear equations our eac combined ift is easy to implement and can be seamlessly integrated into various optical flow functions suggested in literature extensive experiments on public optical flow benchmarks demonstrate that our method outperforms the current state of the art in optical flow estimation and image restoration highlightsincorporating an eac added ift to the variational model to form a new energy function which can estimate optical flow and restore images jointly the eac can be rewritten into the first order gradient form and is beneficial for preserving edges and minimization input images can be fast restored by optimizing the euler lagrange equations of the eac integrated ift

domain generalization and adaptation using low rank exemplar svms domain adaptation between diverse source and target domains is challenging especially in the real world visual recognition tasks where the images and videos consist of significant variations in viewpoints illuminations qualities etc in this paper we propose a new approach for domain generalization and domain adaptation based on exemplar svms specifically we decompose the source domain into many subdomains each of which contains only one positive training sample and all negative samples each subdomain is relatively less diverse and is expected to have a simpler distribution by training one exemplar svm for each subdomain we obtain a set of exemplar svms to further exploit the inherent structure of source domain we introduce a nuclear norm based regularizer into the objective function in order to enforce the exemplar svms to produce a low rank output on training samples in the prediction process the confident exemplar svm classifiers are selected and reweigted according to the distribution mismatch between each subdomain and the test sample in the target domain we formulate our approach based on the logistic regression and least square svm algorithms which are referred to as low rank exemplar svms lre svms and low rank exemplar least square svms lre lssvms respectively a fast algorithm is also developed for accelerating the training of lre lssvms we further extend domain adaptation machine dam to learn an optimal target classifier for domain adaptation and show that our approach can also be applied to domain adaptation with evolving target domain where the target data distribution is gradually changing the comprehensive experiments for object recognition and action recognition demonstrate the effectiveness of our approach for domain generalization and domain adaptation with fixed and evolving target domains

julia theory for slice regular functions the theory of slice regular functions is nowadays widely studied and has found elegant applications to functional calculus for quaternionic linear operators and schur analysis however much less is known about their boundary behaviors in this paper we initiate the study of julia theory for slice regular functions more precisely we establish the quaternionic versions of the julia lemma the julia caratheodory theorem the boundary schwarz lemma the hopf lemma and the burns krantz rigidity theorem for slice regular self mappings of the open unit ball b h and of the right half space h we provide an explicit example to show that in quaternionic hopf lemma the slice derivative of a slice regular function f at the boundary fixed point may not be real in contrast to the complex version our result implies that the commonly believed version of the hopf lemma turns out to be totally wrong this new quaternionic version of the hopf lemma also improves osserman estimate even in the complex setting and is essentially the first significant theorem belonging to the theory of quaternions itself other than the theory of complex analysis since the result involves the lie brackets which reflect the non commutative feature of quaternions

discriminative video pattern search for efficient action detection actions are spatiotemporal patterns similar to the sliding window based object detection action detection finds the reoccurrences of such spatiotemporal patterns through pattern matching by handling cluttered and dynamic backgrounds and other types of action variations we address two critical issues in pattern matching based action detection 1 the intrapattern variations in actions and 2 the computational efficiency in performing action pattern search in cluttered scenes first we propose a discriminative pattern matching criterion for action classification called naive bayes mutual information maximization nbmim each action is characterized by a collection of spatiotemporal invariant features and we match it with an action class by measuring the mutual information between them based on this matching criterion action detection is to localize a subvolume in the volumetric video space that has the maximum mutual information toward a specific action class a novel spatiotemporal branch and bound stbb search algorithm is designed to efficiently find the optimal solution our proposed action detection method does not rely on the results of human detection tracking or background subtraction it can handle action variations such as performing speed and style variations as well as scale changes well it is also insensitive to dynamic and cluttered backgrounds and even to partial occlusions the cross data set experiments on action detection including kth cmu action data sets and another new msr action data set demonstrate the effectiveness and efficiency of the proposed multiclass multiple instance action detection method

activity representation with motion hierarchies complex activities e g pole vaulting are composed of a variable number of sub events connected by complex spatio temporal relations whereas simple actions can be represented as sequences of short temporal parts in this paper we learn hierarchical representations of activity videos in an unsupervised manner these hierarchies of mid level motion components are data driven decompositions specific to each video we introduce a spectral divisive clustering algorithm to efficiently extract a hierarchy over a large number of tracklets i e local trajectories we use this structure to represent a video as an unordered binary tree we model this tree using nested histograms of local motion features we provide an efficient positive definite kernel that computes the structural and visual similarity of two hierarchical decompositions by relying on models of their parent child relations we present experimental results on four recent challenging benchmarks the high five dataset patron perez et al high five recognising human interactions in tv shows 2010 the olympics sports dataset niebles et al modeling temporal structure of decomposable motion segments for activity classification 2010 the hollywood 2 dataset marszalek et al actions in context 2009 and the hmdb dataset kuehne et al hmdb a large video database for human motion recognition 2011 we show that per video hierarchies provide additional information for activity recognition our approach improves over unstructured activity models baselines using other motion decomposition algorithms and the state of the art

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

dense trajectories and motion boundary descriptors for action recognition this paper introduces a video representation based on dense trajectories and motion boundary descriptors trajectories capture the local motion information of the video a dense representation guarantees a good coverage of foreground motion as well as of the surrounding context a state of the art optical flow algorithm enables a robust and efficient extraction of dense trajectories as descriptors we extract features aligned with the trajectories to characterize shape point coordinates appearance histograms of oriented gradients and motion histograms of optical flow additionally we introduce a descriptor based on motion boundary histograms mbh which rely on differential optical flow the mbh descriptor shows to consistently outperform other state of the art descriptors in particular on real world videos that contain a significant amount of camera motion we evaluate our video representation in the context of action classification on nine datasets namely kth youtube hollywood2 ucf sports ixmas uiuc olympic sports ucf50 and hmdb51 on all datasets our approach outperforms current state of the art results

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

multiview alignment hashing for efficient image search hashing is a popular and efficient method for nearest neighbor search in large scale data spaces by embedding high dimensional feature descriptors into a similarity preserving hamming space with a low dimension for most hashing methods the performance of retrieval heavily depends on the choice of the high dimensional feature descriptor furthermore a single type of feature cannot be descriptive enough for different images when it is used for hashing thus how to combine multiple representations for learning effective hashing functions is an imminent task in this paper we present a novel unsupervised multiview alignment hashing approach based on regularized kernel nonnegative matrix factorization which can find a compact representation uncovering the hidden semantics and simultaneously respecting the joint probability distribution of data in particular we aim to seek a matrix factorization to effectively fuse the multiple information sources meanwhile discarding the feature redundancy since the raised problem is regarded as nonconvex and discrete our objective function is then optimized via an alternate way with relaxation and converges to a locally optimal solution after finding the low dimensional representation the hashing functions are finally obtained through multivariable logistic regression the proposed method is systematically evaluated on three data sets 1 caltech 256 2 cifar 10 and 3 cifar 20 and the results show that our method significantly outperforms the state of the art multiview hashing techniques

a new functional calculus for noncommuting operators abstract in this paper we use the notion of slice monogenic functions f colombo i sabadini d c struppa slice monogenic functions israel j math in press to define a new functional calculus for an n tuple t of not necessarily commuting operators this calculus is different from the one discussed in b jefferies spectral properties of noncommuting operators lecture notes in math vol 1843 springer verlag berlin 2004 and it allows the explicit construction of the eigenvalue equation for the n tuple t based on a new notion of spectrum for t our functional calculus is consistent with the riesz dunford calculus in the case of a single operator

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

a priori error estimates for mixed finite element approximations of the acoustic wave equation in this paper we derive optimal a priori l infty l 2 error estimates for mixed finite element displacement formulations of the acoustic wave equation the computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure however the displacement formulations with the physical variables of interest displacement and pressure requires less regularity on the displacement

large displacement optical flow descriptor matching in variational motion estimation optical flow estimation is classically marked by the requirement of dense sampling in time while coarse to fine warping schemes have somehow relaxed this constraint there is an inherent dependency between the scale of structures and the velocity that can be estimated this particularly renders the estimation of detailed human motion problematic as small body parts can move very fast in this paper we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting this way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

graph embedded one class classifiers for media data classification this paper introduces the graph embedded one class support vector machine and graph embedded support vector data description methods these methods constitute novel extensions of the one class support vectors machines and support vector data description incorporating generic graph structures that express geometric data relationships of interest in their optimization process local or global relationships between the training patterns can be expressed with single graphs or combinations of fully connected and knn graphs we show that the adoption of generic geometric class information acts as a regularizer to the solution of the original methods moreover we prove that the regularized solutions for both one class support vector machine and support vector data description are equivalent to applying the original methods in a transformed and shared feature space qualitative and quantitative evaluation of the proposed methods shows that they compare favorably to the standard oc svm and svdd classifiers respectively highlightsintroducing the graph embedded one class svm and graph embedded svdd methods exploiting data relationships in the optimization process adopting generic geometric class information acts as a regularizer the regularized solutions for both proposed methods are equivalent they compare favorably to the standard oc svm and svdd classifiers

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

the h functional calculus based on the s spectrum for quaternionic operators and for n tuples of noncommuting operators abstract in this paper we extend the h functional calculus to quaternionic operators and to n tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus called s functional calculus the s functional calculus has two versions one for quaternionic valued functions and one for clifford algebra valued functions and can be considered the riesz dunford functional calculus based on slice hyperholomorphicity because it shares with it the most important properties the s functional calculus is based on the notion of s spectrum which in the case of quaternionic normal operators on a hilbert space is also the notion of spectrum that appears in the quaternionic spectral theorem the main purpose of this paper is to construct the h functional calculus based on the notion of s spectrum for both quaternionic operators and for n tuples of noncommuting operators we remark that the h functional calculus for n 1 tuples of operators applies in particular to the dirac operator

space time tree ensemble for action recognition and localization human actions are inherently structured patterns of body movements we explore ensembles of hierarchical spatio temporal trees discovered directly from training data to model these structures for action recognition and spatial localization discovery of frequent and discriminative tree structures is challenging due to the exponential search space particularly if one allows partial matching we address this by first building a concise action word vocabulary via discriminative clustering of the hierarchical space time segments which is a two level video representation that captures both static and non static relevant space time segments of the video using this vocabulary we then utilize tree mining with subsequent tree clustering and ranking to select a compact set of discriminative tree patterns our experiments show that these tree patterns alone or in combination with shorter patterns action words and pairwise patterns achieve promising performance on three challenging datasets ucf sports highfive and hollywood3d moreover we perform cross dataset validation using trees learned on highfive to recognize the same actions in hollywood3d and using trees learned on ucf sports to recognize and localize the similar actions in jhmdb the results demonstrate the potential for cross dataset generalization of the trees our approach discovers

a new theory of regular functions of a quaternionic variable abstract in this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable the theory we describe follows a classical idea of cullen but we use a more geometric formulation to show that it is possible to build a rather complete theory our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series

slice regular functions on real alternative algebras in this paper we develop a theory of slice regular functions on a real alternative algebra a our approach is based on a well known fueter s construction two recent function theories can be included in our general theory the one of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a clifford variable our approach permits to extend the range of these function theories and to obtain new results in particular we get a strong form of the fundamental theorem of algebra for an ample class of polynomials with coefficients in a and we prove a cauchy integral formula for slice functions of class c 1

fast coding of feature vectors using neighbor to neighbor search searching for matches to high dimensional vectors using hard soft vector quantization is the most computationally expensive part of various computer vision algorithms including the bag of visual word bow this paper proposes a fast computation method neighbor to neighbor ntn search 1 which skips some calculations based on the similarity of input vectors for example in image classification using dense sift descriptors the ntn search seeks similar descriptors from a point on a grid to an adjacent point applications of the ntn search to vector quantization a gaussian mixture model sparse coding and a kernel codebook for extracting image or video representation are presented in this paper we evaluated the proposed method on image and video benchmarks the pascal voc 2007 classification challenge and the trecvid 2010 semantic indexing task ntn vq reduced the coding cost by 77 4 percent and ntn gmm reduced it by 89 3 percent without any significant degradation in classification performance

supervised matrix factorization hashing for cross modal retrieval the target of cross modal hashing is to embed heterogeneous multimedia data into a common low dimensional hamming space which plays a pivotal part in multimedia retrieval due to the emergence of big multimodal data recently matrix factorization has achieved great success in cross modal hashing however how to effectively use label information and local geometric structure is still a challenging problem for these approaches to address this issue we propose a cross modal hashing method based on collective matrix factorization which considers both the label consistency across different modalities and the local geometric consistency in each modality these two elements are formulated as a graph laplacian term in the objective function leading to a substantial improvement on the discriminative power of latent semantic features obtained by collective matrix factorization moreover the proposed method learns unified hash codes for different modalities of an instance to facilitate cross modal search and the objective function is solved using an iterative strategy the experimental results on two benchmark data sets show the effectiveness of the proposed method and its superiority over state of the art cross modal hashing methods

human action recognition with graph based multiple instance learning a new approach to human action recognition from realistic videos is presented in this paper first an affine motion model is utilized to compensate background motion for the purpose of extracting dense foreground trajectories then a trajectory spectral embedding is introduced to split up foreground action into multiple spatio temporal action parts for constructing a mid level representation to deal with over segmentation a novel density discontinuity detector is proposed for the sake of generating semantically salient action parts finally to handle the ambiguity in the training set action classification is formulated within the multiple instance learning framework which a spatio temporal graph model is incorporated into extensive experiments show that the proposed approach achieves competitive results to state of the art on ucf sports kisses slaps youtube and hollywood datasets a motion compensation approach based on affine model is introduced a density discontinuity detector is proposed to deal with over segmentation the bag of histograms is presented to develop the bag of features a graph based multiple instance learning method is proposed to handle ambiguity

two grid methods for maxwell eigenvalue problems two new two grid algorithms are proposed for solving the maxwell eigenvalue problem the new methods are based on the two grid methodology recently proposed by xu and zhou math comp 70 2001 pp 17 25 and further developed by hu and cheng math comp 80 2011 pp 1287 1301 for elliptic eigenvalue problems the new two grid schemes reduce the solution of the maxwell eigenvalue problem on a fine grid to one linear indefinite maxwell equation on the same fine grid and an original eigenvalue problem on a much coarser grid the new schemes therefore save total computational cost the error estimates reveals that the two grid methods maintain asymptotically optimal accuracy and the numerical experiments presented confirm the theoretical results

dual diversified dynamical gaussian process latent variable model for video repairing in this paper we propose a dual diversified dynamical gaussian process latent variable model text d 3 gplvm to tackle the video repairing issue for preservation purposes videos have to be conserved on media however storing on media such as films and hard disks can suffer from unexpected data loss for instance physical damage so repairing of missing or damaged pixels is essential for better video maintenance most methods seek to fill in missing holes by synthesizing similar textures from local patches the neighboring pixels consecutive frames or the whole video however these can introduce incorrect contexts especially when the missing hole or number of damaged frames is large furthermore simple texture synthesis can introduce artifacts in undamaged and recovered areas to address aforementioned problems we introduce two diversity encouraging priors to both of inducing points and latent variables for considering the variety in existing videos in text d 3 gplvm the inducing points constitute a smaller subset of observed data while latent variables are a low dimensional representation of observed data since they have a strong correlation with the observed data it is essential that both of them can capture distinct aspects of and fully represent the observed data the dual diversity encouraging priors ensure that the trained inducing points and latent variables are more diverse and resistant for context aware and artifacts free based video repairing the defined objective function in our proposed model is initially not analytically tractable and must be solved by variational inference finally experimental testing results illustrate the robustness and effectiveness of our method for damaged video repairing

superconvergence analysis of a two grid method for nonlinear hyperbolic equations abstract in this paper the superconvergence analysis of a second order fully discrete scheme with two grid method tgm is studied for the two dimensional nonlinear hyperbolic equations by the bilinear finite element the existence and uniqueness of the solution for the scheme are proved rigorously by use of the combination technique of the interpolation and ritz projection the superclose results in h 1 norm are obtained and the global superconvergence is derived through the interpolated postprocessing approach finally some numerical results are provided to verify the theoretical predictions and show the efficiency of the proposed tgm

fourier analysis on starlike lipschitz surfaces a theory of a class of singular integrals on starlike lipschitz surfaces in rn is established the class of singular integrals forms an operator algebra identical to the class of bounded holomorphic fourier multipliers as well as to the cauchy dunford bounded holomorphic functional calculus of the spherical dirac operator the study proposes a new method inducing clifford holomorphic functions from holomorphic functions of one complex variable by means of which problems on the sphere are reduced to those on the unit circle

a two grid method for expanded mixed finite element solution of semilinear reaction diffusion equations we present a scheme for solving two dimensional semilinear reaction diffusion equations using an expanded mixed finite element method to linearize the mixed method equations we use a two grid algorithm based on the newton iteration method the solution of a non linear system on the fine space is reduced to the solution of two small one linear and one non linear systems on the coarse space and a linear system on the fine space it is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h o h1 3 as a result solving such a large class of non linear equation will not be much more difficult than solving one single linearized equation copyright 2003 john wiley sons ltd

uniformly superconvergent analysis of an efficient two grid method for nonlinear bi wave singular perturbation problem abstract the main aim of this paper is to present a two grid method for the fourth order nonlinear bi wave singular perturbation problem with low order nonconforming finite element based on the ciarlet raviart scheme the existence and uniqueness of the approximation solution are demonstrated through the brouwer fixed point theorem and the uniform superconvergent estimates in the broken h 1 norm and l 2 norm are obtained which are independent of the perturbation parameter some numerical results indicate that the proposed method is indeed an efficient algorithm

structure preserving binary representations for rgb d action recognition in this paper we propose a novel binary local representation for rgb d video data fusion with a structure preserving projection our contribution consists of two aspects toacquire a general feature for the video data we convert the problem to describing the gradient fields of rgb and depth information of video sequences with the local fluxes of the gradient fields which include the orientation and the magnitude of the neighborhood of each point a new kind of continuous local descriptor called local flux feature lff is obtained then the lffs from rgb and depth channels are fused into a hamming space via the structure preserving projection spp specifically an orthogonal projection matrix is applied to preserve the pairwise structure with a shape constraint to avoid the collapse of data structure in the projected space furthermore a bipartite graph structure of data is taken into consideration which is regarded as a higher level connection between samples and classes than the pairwise structure of local features theextensive experiments show not only the high efficiency of binary codes and the effectiveness of combining lffs from rgb d channels via spp on various action recognition benchmarks of rgb d data but also the potential power of lff for general action recognition

ldahash improved matching with smaller descriptors sift like local feature descriptors are ubiquitously employed in computer vision applications such as content based retrieval video analysis copy detection object recognition photo tourism and 3d reconstruction feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations in particular affine and intensity scale transformations however real transformations that an image can undergo can only be approximately modeled in this way and thus most descriptors are only approximately invariant in practice second descriptors are usually high dimensional e g sift is represented as a 128 dimensional vector in large scale retrieval and matching problems this can pose challenges in storing and retrieving descriptor data we map the descriptor vectors into the hamming space in which the hamming metric is used to compare the resulting representations this way we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples we show extensive experimental validation demonstrating the advantage of the proposed approach

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

action recognition using nonnegative action component representation and sparse basis selection in this paper we propose using high level action units to represent human actions in videos and based on such units a novel sparse model is developed for human action recognition there are three interconnected components in our approach first we propose a new context aware spatial temporal descriptor named locally weighted word context to improve the discriminability of the traditionally used local spatial temporal descriptors second from the statistics of the context aware descriptors we learn action units using the graph regularized nonnegative matrix factorization which leads to a part based representation and encodes the geometrical information these units effectively bridge the semantic gap in action recognition third we propose a sparse model based on a joint l2 1 norm to preserve the representative items and suppress noise in the action units intuitively when learning the dictionary for action representation the sparse model captures the fact that actions from the same class share similar units the proposed approach is evaluated on several publicly available data sets the experimental results and analysis clearly demonstrate the effectiveness of the proposed approach

two grid mixed finite element method for nonlinear hyperbolic equations abstract in this paper a combination method of mixed finite element method and two grid scheme is constructed for solving numerically the two dimensional nonlinear hyperbolic equations in this approach the nonlinear system is solved on a coarse mesh with width h and the linear system is solved on a fine mesh with width h h it is proved that the coarse grid can be much coarser than the fine grid the two grid methods achieve asymptotically optimal approximation as long as the mesh sizes h o h 1 2 in the first algorithm and h o h 1 4 in the second algorithm respectively error estimates are derived in detail finally two numerical examples are carried out to verify the accuracy and efficiency of the presented method

fusing mathcal r r features and local features with context aware kernels for action recognition the performance of action recognition in video sequences depends significantly on the representation of actions and the similarity measurement between the representations in this paper we combine two kinds of features extracted from the spatio temporal interest points with context aware kernels for action recognition for the action representation local cuboid features extracted around interest points are very popular using a bag of visual words bovw model such representations however ignore potentially valuable information about the global spatio temporal distribution of interest points we propose a new global feature to capture the detailed geometrical distribution of interest points it is calculated by using the 3d mathcal r r transform which is defined as an extended 3d discrete radon transform followed by the application of a two directional two dimensional principal component analysis for the similarity measurement we model a video set as an optimized probabilistic hypergraph and propose a context aware kernel to measure high order relationships among videos the context aware kernel is more robust to the noise and outliers in the data than the traditional context free kernel which just considers the pairwise relationships between videos the hyperedges of the hypergraph are constructed based on a learnt mahalanobis distance metric any disturbing information from other classes is excluded from each hyperedge finally a multiple kernel learning algorithm is designed by integrating the l 2 l2 norm regularization into a linear svm classifier to fuse the mathcal r r feature and the bovw representation for action recognition experimental results on several datasets demonstrate the effectiveness of the proposed approach for action recognition

mofap a multi level representation for action recognition this paper proposes a multi level video representation by stacking the activations of motion features atoms and phrases mofap motion features refer to those low level local descriptors while motion atoms and phrases can be viewed as mid level temporal parts motion atom is defined as an atomic part of action and captures the motion information of video in a short temporal scale motion phrase is a temporal composite of multiple motion atoms defined with an and or structure it further enhances the discriminative capacity of motion atoms by incorporating temporal structure in a longer temporal scale specifically we first design a discriminative clustering method to automatically discover a set of representative motion atoms then we mine effective motion phrases with high discriminative and representative capacity in a bottom up manner based on these basic units of motion features atoms and phrases we construct a mofap network by stacking them layer by layer this mofap network enables us to extract the effective representation of video data from different levels and scales the separate representations from motion features motion atoms and motion phrases are concatenated as a whole one called activation of mofap the effectiveness of this representation is demonstrated on four challenging datasets olympic sports ucf50 hmdb51 and ucf101 experimental results show that our representation achieves the state of the art performance on these datasets