robust multitask multiview tracking in videos various sparse representation based methods have been proposed to solve tracking problems and most of them employ least squares lss criteria to learn the sparse representation in many tracking scenarios traditional ls based methods may not perform well owing to the presence of heavy tailed noise in this paper we present a tracking approach using an approximate least absolute deviation lad based multitask multiview sparse learning method to enjoy robustness of lad and take advantage of multiple types of visual features such as intensity color and texture the proposed method is integrated in a particle filter framework where learning the sparse representation for each view of the single particle is regarded as an individual task the underlying relationship between tasks across different views and different particles is jointly exploited in a unified robust multitask formulation based on lad in addition to capture the frequently emerging outlier tasks we decompose the representation matrix to two collaborative components that enable a more robust and accurate approximation we show that the proposed formulation can be effectively approximated by nesterov s smoothing method and efficiently solved using the accelerated proximal gradient method the presented tracker is implemented using four types of features and is tested on numerous synthetic sequences and real world video sequences including the cvpr2013 tracking benchmark and alov data set both the qualitative and quantitative results demonstrate the superior performance of the proposed approach compared with several state of the art trackers

object tracking via partial least squares analysis we propose an object tracking algorithm that learns a set of appearance models for adaptive discriminative object representation in this paper object tracking is posed as a binary classification problem in which the correlation of object appearance and class labels from foreground and background is modeled by partial least squares pls analysis for generating a low dimensional discriminative feature subspace as object appearance is temporally correlated and likely to repeat over time we learn and adapt multiple appearance models with pls analysis for robust tracking the proposed algorithm exploits both the ground truth appearance information of the target labeled in the first frame and the image observations obtained online thereby alleviating the tracking drift problem caused by model update experiments on numerous challenging sequences and comparisons to state of the art methods demonstrate favorable performance of the proposed tracking algorithm

differential invariants for quasi linear and semi linear wave type equations abstract in this paper we consider the class of wave type equations u tt f x t u u xx g x t u u x u t and two special cases of it we derive the equivalence transformations for these equations and using these transformations we obtain differential invariants and invariant equations we employ these invariants or and invariant equations to classify all equations of this general class that can be mapped into a simple linear hyperbolic or into an elliptic equation additional applications are presented

exact solutions via equivalence transformations of variable coefficient fifth order kdv equations abstract in this paper a family of variable coefficient fifth order kdv equations has been considered by using an infinitesimal method based on the determination of the equivalence group differential invariants and invariant equations are obtained invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations here differential invariants are applied to obtain exact solutions

random forests with ensemble of feature spaces random forests receive much attention from researchers because of their excellent performance as breiman suggested the performance of random forests depends on the strength of the weak learners in the forests and the diversity among them however in the literature many researchers only considered pre processing of the data or post processing of the random forests models in this paper we propose a new method to increase the diversity of each tree in the forests and thereby improve the overall accuracy during the training process of each individual tree in the forest different rotation spaces are concatenated into a higher space at the root node then the best split is exhaustively searched within this higher space the location where the best split lies decides which rotation method to be used for all subsequent nodes the performance of the proposed method here is evaluated on 42 benchmark data sets from various research fields and compared with the standard random forests the results show that the proposed method improves the performance of the random forests in most cases

the sine gordon equations complete and partial integrability the sine gordon equation in one space one time dimension is known to possess the painleve property and to be completely integrable it is shown how the method of singular manifold analysis obtains the backlund transform and the lax pair for this equation a connection with the sequence of higher order kdv equations is found the modified sine gordon equations are defined in terms of the singular manifold these equations are shown to be identically painleve also certain rational solutions are constructed iteratively the double sine gordon equation is shown not to possess the painleve property however if the singular manifold defines an affine minimal surface then the equation has integrable solutions this restriction is termed partial integrability the sine gordon equation in n 1 variables n space 1 time where n is greater than one is shown not to possess the painleve property the condition of partial integrability requires the singular manifold to be an einstein space with null scalar curvature the known integrable solutions satisfy this constraint in a trivial manner finally the coupled kdv or hirota satsuma equations possess the painleve property the associated modified equations are derived and from these the lax pair is found

visual tracking via boolean map representations abstract in this paper we present a simple yet effective boolean map based representation that exploits connectivity cues for visual tracking we describe a target object with histogram of oriented gradients and raw color features of which each one is characterized by a set of boolean maps generated by uniformly thresholding their values the boolean maps effectively encode multi scale connectivity cues of the target with different granularities the fine grained boolean maps capture spatially structural details that are effective for precise target localization while the coarse grained ones encode global shape information that are robust to large target appearance variations finally all the boolean maps form together a robust representation that can be approximated by an explicit feature map of the intersection kernel which is fed into a logistic regression classifier with online update and the target location is estimated within a particle filter framework the proposed representation scheme is computationally efficient and facilitates achieving favorable performance in terms of accuracy and robustness against the state of the art tracking methods on the otb50 and vot2016 benchmark datasets

robust visual tracking via co trained kernelized correlation filters abstract recent advances in visual tracking have witnessed the importance of discriminative classifiers tasked with distinguishing the target from the background however a single classifier may fail to cope with complex surrounding environment and large appearance variations of the target motivated by multi view learning we equip a basic framework to train a pool of discriminative classifiers jointly in a closed form fashion in this paper it poses an extra regularization term in ridge regression which interacts with other base models in the ensemble through a simple realization of this approach we show co trained kernelized correlation filters cokcf which consist of two kcf trackers are able to outperform the kcf tracker by a larger margin and perform favorably against other state of the art trackers on 63 benchmark video sequences

second order differential invariants of a family of diffusion equations an equivalence transformation algebra for a class of nonlinear diffusion equations is found after having obtained the second order differential invariants with respect to we get some results which allow us to linearize a subclass of the equations considered

ensemble tracking we consider tracking as a binary classification problem where an ensemble of weak classifiers is trained online to distinguish between the object and the background the ensemble of weak classifiers is combined into a strong classifier using adaboost the strong classifier is then used to label pixels in the next frame as either belonging to the object or the background giving a confidence map the peak of the map and hence the new position of the object is found using mean shift temporal coherence is maintained by updating the ensemble with new weak classifiers that are trained online during tracking we show a realization of this method and demonstrate it on several video sequences

preliminary group classification of equations vtt f x vx vxx g x vx a classification is given of equations vtt f v vx vxx g x vx admitting an extension by one of the principal lie algebra of the equation under consideration the paper is one of few applications of a new algebraic approach to the problem of group classification the method of preliminary group classification the result of the work is a wide class of equations summarized in table ii

singular invariant equation for the 1 1 fokker planck equation semi invariants for the linear parabolic equations with two independent variables time variable t and space variable x and one dependent variable u are derived under the transformation of the independent variables by using the infinitesimal method we also obtain the joint invariant equation for the above mentioned equation under equivalence transformation in fact we prove a necessary and sufficient condition for a 1 1 parabolic equation to be reducible via a local equivalence transformation to the one dimensional classical heat equation this result provides practical criteria for reduction finally examples of 1 1 fokker planck equations from applications are given to verify the results obtained

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

arcing classifier with discussion and a rejoinder by the author recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error one of the more effective is bagging here modified training sets are formed by resampling from the original training set classifiers constructed using these training sets and then combined by voting freund and schapire propose an algorithm the basis of which is to adaptively resample and combine hence the acronym arcing so that the weights in the resampling are increased for those cases most often misclassified and the combining is done by weighted voting arcing is more successful than bagging in test set error reduction we explore two arcing algorithms compare them to each other and to bagging and try to understand how arcing works we introduce the definitions of bias and variance for a classifier as components of the test set error unstable classifiers can have low bias on a large range of data sets their problem is high variance combining multiple versions either through bagging or arcing reduces variance significantly

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

linearization of third order ordinary differential equations by point and contact transformations we present here the solution of the problem on linearization of third order ordinary differential equations by means of point and contact transformations we provide in explicit forms the necessary and sufficient conditions for linearization the equations for determining the linearizing point and contact transformations as well as the coefficients of the resulting linear equations

on invariance properties of the wave equation a complete group classification is given of both the wave equation c2 x uxx utt 0 i and its equivalent system vt ux c2 x vx ut ii when the wave speed c x const equations i and ii admit either a two or four parameter group for the exceptional case c x ax b 2 equation i admits an infinite group equations i and ii do not always admit the same group for a given c x the group for i can have more parameters or fewer parameters than that for ii moreover the groups can be different with the same number of parameters separately for i and ii all possible c x that admit a four parameter group are found explicitly the corresponding invariant similarity solutions are considered some of these wave speeds have realistic physical properties c x varies monotonically from one positive constant to another positive constant as x goes from to

interacting multiview tracker a robust algorithm is proposed for tracking a target object in dynamic conditions including motion blurs illumination changes pose variations and occlusions to cope with these challenging factors multiple trackers based on different feature representations are integrated within a probabilistic framework each view of the proposed multiview multi channel feature learning algorithm is concerned with one particular feature representation of a target object from which a tracker is developed with different levels of reliability with the multiple trackers the proposed algorithm exploits tracker interaction and selection for robust tracking performance in the tracker interaction a transition probability matrix is used to estimate dependencies between trackers multiple trackers communicate with each other by sharing information of sample distributions the tracker selection process determines the most reliable tracker with the highest probability to account for object appearance changes the transition probability matrix and tracker probability are updated in a recursive bayesian framework by reflecting the tracker reliability measured by a robust tracker likelihood function that learns to account for both transient and stable appearance changes experimental results on benchmark datasets demonstrate that the proposed interacting multiview algorithm performs robustly and favorably against state of the art methods in terms of several quantitative metrics

high speed tracking with kernelized correlation filters the core component of most modern trackers is a discriminative classifier tasked with distinguishing between the target and the surrounding environment to cope with natural image changes this classifier is typically trained with translated and scaled sample patches such sets of samples are riddled with redundancies any overlapping pixels are constrained to be the same based on this simple observation we propose an analytic model for datasets of thousands of translated patches by showing that the resulting data matrix is circulant we can diagonalize it with the discrete fourier transform reducing both storage and computation by several orders of magnitude interestingly for linear regression our formulation is equivalent to a correlation filter used by some of the fastest competitive trackers for kernel regression however we derive a new kernelized correlation filter kcf that unlike other kernel algorithms has the exact same complexity as its linear counterpart building on it we also propose a fast multi channel extension of linear correlation filters via a linear kernel which we call dual correlation filter dcf both kcf and dcf outperform top ranking trackers such as struck or tld on a 50 videos benchmark despite running at hundreds of frames per second and being implemented in a few lines of code algorithm 1 to encourage further developments our tracking framework was made open source

quasi self adjoint nonlinear wave equations in this paper we generalize the classification of self adjoint second order linear partial differential equation to a family of nonlinear wave equations with two independent variables we find a class of quasi self adjoint nonlinear equations which includes the self adjoint linear equations as a particular case the property of a differential equation to be quasi self adjoint is important e g for constructing conservation laws associated with symmetries of the differential equation

acyclic and star coloring of p4 reducible and p4 sparse graphs an acyclic coloring of a graph g is a proper vertex coloring such that g contains no bicolored cycles the more restricted notion of star coloring of g is an acyclic coloring in which each path of length 3 is not bicolored in this paper we mainly study on the acyclic and star coloring of p4 reducible and p4 sparse graphs moreover we list polynomial time algorithms for giving an optimal acyclic or star coloring of a p4 reducible or p4 sparse graph

multiple kernel learning algorithms in recent years several methods have been proposed to combine multiple kernels instead of using a single one these different kernels may correspond to using different notions of similarity or may be using information coming from multiple sources different representations or different feature subsets in trying to organize and highlight the similarities and differences between them we give a taxonomy of and review several multiple kernel learning algorithms we perform experiments on real data sets for better illustration and comparison of existing algorithms we see that though there may not be large differences in terms of accuracy there is difference between them in complexity as given by the number of stored support vectors the sparsity of the solution as given by the number of used kernels and training time complexity we see that overall using multiple kernels instead of a single one is useful and believe that combining kernels in a nonlinear or data dependent way seems more promising than linear combination in fusing information provided by simple linear kernels whereas linear methods are more reasonable when combining complex gaussian kernels