roundoff noise analysis of signals represented using signed power of two terms it is a well known fact that the multiplication of a number by an integer power of two is a very simple process in binary arithmetic hence digital filters whose coefficient values are integer power of two are essentially multiplierless the design of digital filters with power of two coefficient values require time consuming optimization process and may not always be possible in some applications such as in adaptive filtering since hardware circuitry for real time conversion of a binary integer into a sum of a limited number of signed power of two spt terms is available if the signal is expressed in spt terms i e in digit code the filter is also multiplierless even though the coefficient values are not spt when each signal data is rounded to a limited number of spt terms a roundoff noise representing the roundoff error is introduced in the spt space the quantization step size is nonuniform and so the roundoff noise characteristic is different from that produced when the quantization step size is uniform this paper presents an analysis for the roundoff noise of signal represented using a limited number of spt terms the result is useful for determining the number of spt terms required to represent a signal subject to a given roundoff noise

dimension reduction and coefficient estimation in multivariate linear regression summary we introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model we argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions we continue to propose a new method that is more flexible and more generally applicable the method proposed can be formulated as a novel penalized least squares estimate the penalty that we employ is the coefficient matrix s ky fan norm such a penalty encourages the sparsity among singular values and at the same time gives shrinkage coefficient estimates and thus conducts dimension reduction and coefficient estimation simultaneously in the multivariate linear model we also propose a generalized cross validation type of criterion for the selection of the tuning parameter in the penalized least squares simulations and an application in financial econometrics demonstrate competitive performance of the new method an extension to the non parametric factor model is also discussed

a compact association of particle filtering and kernel based object tracking particle filtering pf and kernel based object tracking kbot algorithms have shown their promises in a wide range of visual tracking contexts this paper mainly addresses the association of pf and kbot unlike other related association approaches which usually directly use kbot to refine the position states of propagated particles for more accurate mode seeking we elucidate the problem of what kind of particles is suitable for employing kbot to refine their position states from a theoretical point of view in accordance with the theoretical analysis a two stage solution is also proposed to resample propagated particles that are suitable for invoking kbot from a computational perspective the incremental bhattacharyya dissimilarity ibd based stage is designed to consistently distinguish the particles located in the object region from the others placed in the background while the matrix condition number based stage is formulated to further eliminate the particles positioned at the ill posed conditions for running kbot once the appropriate particles are obtained constrained gradient based mean shift optimization enables us to efficiently refine the particles position states besides a state transition model embodying object scale oriented information and prior motion cues is presented to adapt to fast movement scenarios these ingredients lead to a new tracking algorithm experiments demonstrate that the proposed association approach is more robust to handle complex tracking conditions in comparison with related methods also a limited number of particles are used in our association algorithm to maintain multiple hypotheses

efficient evaluation of 1 d and 2 d polynomials at equispaced points an extension to the two dimensional case of a previously published fast algorithm for evaluating exponential functions and polynomials over periodically distributed points is generalized to evaluate two dimensional polynomials efficiently over general periodic parallelograms the problem of getting the initial values required for other fast algorithms is treated in a general manner fast algorithms are presented for computing initial values in both cases of one and two dimensional polynomials it is observed that the two dimensional recursion is not always advantageous compared with taking the one dimensional recursion for each variable separately

estimation of low rank high dimensional multivariate linear models for multi response data in this article we study low rank high dimensional multivariate linear models lrmlm for high dimensional multi response data we propose an intuitively appealing estimation approach and develop

optimal selection of reduced rank estimators of high dimensional matrices we introduce a new criterion the rank selection criterion rsc for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models the corresponding rsc estimator minimizes the frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model the rank of the rsc estimator provides a consistent estimator of the rank of the coefficient matrix in general the rank of our estimator is a consistent estimate of the effective rank which we define to be the number of singular values of the target matrix that are appropriately large the consistency results are valid not only in the classic asymptotic regime when n the number of responses and p the number of predictors stay bounded and m the number of observations grows but also when either or both n and p grow possibly much faster than m we establish minimax optimal bounds on the mean squared errors of our estimators our finite sample performance bounds for the rsc estimator show that it achieves the optimal balance between the approximation error and the penalty term furthermore our procedure has very low computational complexity linear in the number of candidate models making it particularly appealing for large scale problems we contrast our estimator with the nuclear norm penalized least squares nnp estimator which has an inherently higher computational complexity than rsc for multivariate regression models we show that nnp has estimation properties similar to those of rsc albeit under stronger conditions however it is not as parsimonious as rsc we offer a simple correction of the nnp estimator which leads to consistent rank estimation we verify and illustrate our theoretical findings via an extensive simulation study

orthonormal and biorthonormal filter banks as convolvers and convolutional coding gain convolution theorems for filter bank transformers are introduced both uniform and nonuniform decimation ratios are considered and orthonormal as well as biorthonormal cases are addressed all the theorems are such that the original convolution reduces to a sum of shorter decoupled convolutions in the subbands that is there is no need to have cross convolution between subbands for the orthonormal case expressions for optimal bit allocation and the optimized coding gain are derived the contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum with one of the convolved sequences taken to be the unit pulse function e coding gain expressions reduce to those for traditional subband and transform coding the filter bank convolver has about the same computational complexity as a traditional convolver if the analysis bank has small complexity compared to the convolution itself

active contours for tracking distributions a new approach to tracking using active contours is presented the class of objects to be tracked is assumed to be characterized by a probability distribution over some variable such as intensity color or texture the goal of the algorithm is to find the region within the current image such that the sample distribution of the interior of the region most closely matches the model distribution two separate criteria for matching distributions are examined and the curve evolution equations are derived in each case the flows are shown to perform well in experiments

finding waldo or focus of attention using local color information we present a method to locate an object in a color image or more precisely to select a set of likely locations for the object the model is assumed to be of known color distribution which permits the use color space processing a new method is presented which exploits more information than the previous backprojection algorithm of swain and ballard 1990 at a competitive complexity precisely the new algorithm is based on matching local histograms with the model instead of directly replacing pixels with a confidence that they belong to the object we prove that a simple version of this algorithm degenerates into backprojection in the worst case in addition we show how to estimate the scale of the model results are shown on pictures digitized from the famous where is waldo books issues concerning the optimal choice of a color space and its quantization are carefully considered and studied in this application we also propose to use co occurrence histograms to deal with cases where important color variations can be expected

a probabilistic graph based framework for plug and play multi cue visual tracking in this paper we propose a novel approach for integrating multiple tracking cues within a unified probabilistic graph based markov random fields mrfs representation we show how to integrate temporal and spatial cues encoded by unary and pairwise probabilistic potentials as the inference of such high order mrf models is known to be np hard we propose an efficient spectral relaxation based inference scheme the proposed scheme is exemplified by applying it to a mixture of five tracking cues and is shown to be applicable to wider sets of cues this paves the way for a modular plug and play tracking framework that can be easily adapted to diverse tracking scenarios the proposed scheme is experimentally shown to compare favorably with contemporary state of the art schemes and provides accurate tracking results

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

interactive image segmentation via kernel propagation abstract in this paper we propose a new approach to interactive image segmentation via kernel propagation kp called kp cut the key to success in interactive image segmentation is to preserve characteristics of the user s interactive input and maintain data coherence effectively to achieve this we employ kp which is very effective in propagating the given supervised information into the entire data set kp first learns a small size seed kernel matrix and then propagates it into a large size full kernel matrix it is based on a learned kernel and thus can fit the given data better than a predefined kernel based on kp we first generate a small size seed kernel matrix from the user s interactive input then the seed kernel matrix is propagated into the full kernel matrix of the entire image during the propagation foreground objects are effectively segmented from background experimental results demonstrate that kp cut effectively extracts foreground objects from background and outperforms the state of the art methods for interactive image segmentation

optical flow constraints on deformable models with applications to face tracking optical flow provides a constraint on the motion of a deformable model we derive and solve a dynamic system incorporating flow as a hard constraint producing a model based least squares optical flow solution our solution also ensures the constraint remains satisfied when combined with edge information which helps combat tracking error accumulation constraint enforcement can be relaxed using a kalman filter which permits controlled constraint violations based on the noise present in the optical flow information and enables optical flow and edge information to be combined more robustly and efficiently we apply this framework to the estimation of face shape and motion using a 3d deformable face model this model uses a small number of parameters to describe a rich variety of face shapes and facial expressions we present experiments in extracting the shape and motion of a face from image sequences which validate the accuracy of the method they also demonstrate that our treatment of optical flow as a hard constraint as well as our use of a kalman filter to reconcile these constraints with the uncertainty in the optical flow are vital for improving the performance of our system

convex regularization for high dimensional multiresponse tensor regression in this paper we present a general convex optimization approach for solving high dimensional multiple response tensor regression problems under low dimensional structural assumptions we consider using convex and weakly decomposable regularizers assuming that the underlying tensor lies in an unknown low dimensional subspace within our framework we derive general risk bounds of the resulting estimate under fairly general dependence structure among covariates our framework leads to upper bounds in terms of two very simple quantities the gaussian width of a convex set in tensor space and the intrinsic dimension of the low dimensional tensor subspace to the best of our knowledge this is the first general framework that applies to multiple response problems these general bounds provide useful upper bounds on rates of convergence for a number of fundamental statistical models of interest including multiresponse regression vector autoregressive models low rank tensor models and pairwise interaction models moreover in many of these settings we prove that the resulting estimates are minimax optimal we also provide a numerical study that both validates our theoretical guarantees and demonstrates the breadth of our framework

quantization and roundoff noises in fixed point fir digital filters the errors in a fixed point finite impulse response fir filter due to quantization analog to digital conversion and roundoff are considered expressions for the exact moments of the filter output noise are derived it is well known that when the input signal satisfies certain conditions the popular additive white noise model can be valid in describing the quantization noise the characteristics of multiplicative roundoff noises however differ from what this model predicts even under conditions where the roundoff noises are white hence the additive white noise model does not provide accurate results on the characteristics of the output error in an fir filter using the exact formulas for the moments the author computes the exact power spectrum of the filter output error these results agree well with those obtained from simulation

view invariant representation and recognition of actions analysis of human perception of motion shows that information for representing the motion is obtained from the dramatic changes in the speed and direction of the trajectory in this paper we present a computational representation of human action to capture these dramatic changes using spatio temporal curvature of 2 d trajectory this representation is compact view invariant and is capable of explaining an action in terms of meaningful action units called dynamic instants and intervals a dynamic instant is an instantaneous entity that occurs for only one frame and represents an important change in the motion characteristics an interval represents the time period between two dynamic instants during which the motion characteristics do not change starting without a model we use this representation for recognition and incremental learning of human actions the proposed method can discover instances of the same action performed by different people from different view points experiments on 47 actions performed by 7 individuals in an environment with no constraints shows the robustness of the proposed method

eigenvalue ratio test for the number of factors this paper proposes two new estimators for determining the number of factors r in static approximate factor models we exploit the well known fact that the r largest eigenvalues of the variance matrix of n response variables grow unboundedly as n increases while the other eigenvalues remain bounded the new estimators are obtained simply by maximizing the ratio of two adjacent eigenvalues our simulation results provide promising evidence for the two estimators

multiple object tracking with partial occlusion handling using salient feature points abstract handling occlusion has been a challenging task in object tracking in this paper we propose a multiple object tracking method in the presence of partial occlusion using salient feature points we first extract the prominent feature points from each target object and then use a particle filter based approach to track the feature points in image sequences based on various attributes such as location velocity and other descriptors we then detect and revise the feature points that have been tracked incorrectly the main idea is that even if some feature points are not successfully tracked due to occlusion or poor imaging condition the other correctly tracked features can collectively perform the corrections on their behalf finally we track the objects using the correctly tracked feature points through a hough like approach and the object bounding boxes are updated using the relative locations of these feature points experimental results demonstrate that our method is proficient in providing accurate human tracking as well as appropriate occlusion handling compared to the existing methods

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

online passive aggressive algorithms we present a family of margin based online learning algorithms for various prediction tasks in particular we derive and analyze algorithms for binary and multiclass categorization regression uniclass prediction and sequence prediction the update steps of our different algorithms are all based on analytical solutions to simple constrained optimization problems this unified view allows us to prove worst case loss bounds for the different algorithms and for the various decision problems based on a single lemma our bounds on the cumulative loss of the algorithms are relative to the smallest loss that can be attained by any fixed hypothesis and as such are applicable to both realizable and unrealizable settings we demonstrate some of the merits of the proposed algorithms in a series of experiments with synthetic and real data sets

fixed point roundoff error analysis of the exponentially windowed rls algorithm for time varying systems a fixed point roundoff error analysis of the exponentially windowed rls algorithm is presented it is shown that a tradeoff exists in the choice of the forgetting factor in order to reduce the sensitivity of the algorithm to additive noise must be chosen close to one on the other hand the roundoff error increases as lambda rightarrow 1 it is shown that the algorithm is stabilized with lambda rightarrow 1 to derive the theoretical results it is assumed that the input signal is a white gaussian random process finally simulations are presented which confirm the theoretical findings of the paper

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

learning with kernel smoothing models and low discrepancy sampling this brief presents an analysis of the performance of kernel smoothing models used to estimate an unknown target function addressing the case where the choice of the training set is part of the learning process in particular we consider a choice of the points at which the function is observed based on low discrepancy sequences which is a family of sampling methods commonly employed for efficient numerical integration we prove that under suitable regularity assumptions consistency of the empirical risk minimization is guaranteed with a good rate of convergence of the estimation error as well as the convergence of the approximation error simulation results confirm in practice the good theoretical properties given by the combination of kernel smoothing models with low discrepancy sampling

nonconcave penalized likelihood with a diverging number of parameters a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by fan and li to simultaneously estimate parameters and select important variables they demonstrated that this class of procedures has an oracle property when the number of parameters is finite however in most model selection problems the number of parameters should be large and grow with the sample size in this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators furthermore the consistency of the sandwich formula of the covariance matrix is demonstrated nonconcave penalized likelihood ratio statistics are discussed and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions the asymptotic results are augmented by a simulation study and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary

coupling deep correlation filter and online discriminative learning for visual object tracking advances in mathematical models and optimization introduce powerful tools for solving the visual object tracking problem but this fundamental problem remains unsolved due to various challenges such as illumination variation deformation and occlusion recent progress in correlation filter based models has provided an effective and efficient tracking solution this type of trackers exploits the property of convolution theorem to significantly speed up their computational processes however their scheme of training correlation filters restricts them to use only a few negative examples to train their model consequently lowers their performance therefore in this paper we propose to combine the fast calculation advantage of correlation filter with an online discriminative learning model which can fully exploit the negative examples in the context around the target the proposed tracker proceeds in a coarse to fine scheme the proposed tracker will first employ a correlation filter to generate a coarse estimation of the location of the target and then employ a translating model to refine its estimation and calculate the scale variation of the target via a scaling model both the translating model and the scaling model are formulated in the framework of our online discriminative model besides we also propose an effective offline representation learning method to generate robust image feature for our correlation filter extensive experiments on the online object tracking benchmark against the state of the art methods validate the effectiveness of the proposed tracker

a probabilistic exclusion principle for tracking multiple objects tracking multiple targets is a challenging problem especially when the targets are identical in the sense that the same model is used to describe each target in this case simply instantiating several independent 1 body trackers is not an adequate solution because the independent trackers tend to coalesce onto the best fitting target this paper presents an observation density for tracking which solves this problem by exhibiting a probabilistic exclusion principle exclusion arises naturally from a systematic derivation of the observation density without relying on heuristics another important contribution of the paper is the presentation of partitioned sampling a new sampling method for multiple object tracking partitioned sampling avoids the high computational load associated with fully coupled trackers while retaining the desirable properties of coupling

registration of longitudinal brain image sequences with implicit template and spatial temporal heuristics abstract accurate measurement of longitudinal changes of brain structures and functions is very important but challenging in many clinical studies also across subject comparison of longitudinal changes is critical in identifying disease related changes in this paper we propose a novel method to meet these two requirements by simultaneously registering sets of longitudinal image sequences of different subjects to the common space without assuming any explicit template specifically our goal is to 1 consistently measure the longitudinal changes from a longitudinal image sequence of each subject and 2 jointly align all image sequences of different subjects to a hidden common space to achieve these two goals we first introduce a set of temporal fiber bundles to explore the spatial temporal behavior of anatomical changes in each longitudinal image sequence then a probabilistic model is built upon the temporal fibers to characterize both spatial smoothness and temporal continuity finally the transformation fields that connect each time point image of each subject to the common space are simultaneously estimated by the expectation maximization em approach via the maximum a posterior map estimation of the probabilistic models promising results have been obtained in quantitative measurement of longitudinal brain changes i e hippocampus volume changes showing better performance than those obtained by either the pairwise or the groupwise only registration methods

an efficient implementation of reid s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking an efficient implementation of reid s multiple hypothesis tracking mht algorithm is presented in which the k best hypotheses are determined in polynomial time using an algorithm due to murly 1968 the mht algorithm is then applied to several motion sequences the mht capabilities of track initiation termination and continuation are demonstrated together with the latter s capability to provide low level support of temporary occlusion of tracks between 50 and 150 corner features are simultaneously tracked in the image plane over a sequence of up to 51 frames each corner is tracked using a simple linear kalman filter and any data association uncertainty is resolved by the mht kalman filter parameter estimation is discussed and experimental results show that the algorithm is robust to errors in the motion model an investigation of the performance of the algorithm as a function of look ahead tree depth indicates that high accuracy can be obtained for tree depths as shallow as three experimental results suggest that a real time mht solution to the motion correspondence problem is possible for certain classes of scenes

anomaly detection in images with smooth background via smooth sparse decomposition in various manufacturing applications such as steel composites and textile production anomaly detection in noisy images is of special importance although there are several methods for image den

how to compare noisy patches patch similarity beyond gaussian noise many tasks in computer vision require to match image parts while higher level methods consider image features such as edges or robust descriptors low level approaches so called image based compare groups of pixels patches and provide dense matching patch similarity is a key ingredient to many techniques for image registration stereo vision change detection or denoising recent progress in natural image modeling also makes intensive use of patch comparison a fundamental difficulty when comparing two patches from real data is to decide whether the differences should be ascribed to noise or intrinsic dissimilarity gaussian noise assumption leads to the classical definition of patch similarity based on the squared differences of intensities for the case where noise departs from the gaussian distribution several similarity criteria have been proposed in the literature of image processing detection theory and machine learning by expressing patch dis similarity as a detection test under a given noise model we introduce these criteria with a new one and discuss their properties we then assess their performance for different tasks patch discrimination image denoising stereo matching and motion tracking under gamma and poisson noises the proposed criterion based on the generalized likelihood ratio is shown to be both easy to derive and powerful in these diverse applications

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

neighborhood rough filter and intuitionistic entropy in unsupervised tracking this paper aims at developing a novel methodology for unsupervised video tracking by exploring the merits of neighborhood rough sets a neighborhood rough filter is designed in this process for initial labeling of continuous moving object s even in the presence of several variations in different feature spaces the locations and color models of the object s are estimated using their lower upper approximations in spatio color neighborhood granular space velocity neighborhood granules and acceleration neighborhood granules are then defined over this estimation to predict the object location in the next frame and to speed up the tracking process a novel concept namely intuitionsistic entropy is introduced here which consists of two new measures neighborhood rough entropy and neighborhood probabilistic entropy to deal with the ambiguities that arise due to occurrence of overlapping occlusion in a video sequence the unsupervised method of tracking is equally good even when compared with some of the state of the art partially supervised methods while showing superior performance during total occlusion

probabilistic detection and tracking of motion boundaries we propose a bayesian framework for representing and recognizing local image motion in terms of two basic models translational motion and motion boundaries motion boundaries are represented using a non linear generative model that explicitly encodes the orientation of the boundary the velocities on either side the motion of the occluding edge over time and the appearance disappearance of pixels at the boundary we represent the posterior probability distribution over the model parameters given the image data using discrete samples this distribution is propagated over time using a particle filtering algorithm to efficiently represent such a high dimensional space we initialize samples using the responses of a low level motion discontinuity detector the formulation and computational model provide a general probabilistic framework for motion estimation with multiple non linear models

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

quantization noise fixed point multiplicative roundoff noise and dithering the author considers the characteristics of the error resulting when a continuous amplitude signal x sub n is quantized and then multiplied by a constant multiplier a under fixed point roundoff arithmetic it is shown that the overall error of such an operation can be decomposed into two terms one being a scaled version of the error due to the quantization of x sub n and the other due to rounding off the product aq x sub n exact first and second order moments are derived for the quantization error the roundoff error and the overall error as a function of the multiplier a and the distribution of x sub n sufficient conditions are given for the quantization error and the roundoff error to be individually uniformly distributed and white up to the first and second order moments and also for them to be mutually uncorrelated it is also shown that regardless of the probability distribution of the input signal x sub n it is always possible to add a suitable dither signal to the input of the system so that both the quantization error and the roundoff error are uniformly distributed white and mutually uncorrelated for gaussian inputs the sufficient conditions given are not satisfied

on the statistics of fixed point roundoff error roundoff error after fixed point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal this paper presents a statistical analysis of fixed point roundoff error that identifies the conditions under which this model is valid and examines the statistical behavior of roundoff error when these conditions are not satisfied the results show that if the multiplier coefficient is expressed as a n m where m is a positive integral power of two and n is an odd integer then the errors generated by roundoff after multiplication can generally be modeled as uniformly distributed white and uncorrelated with the signal if the signal has sufficiently wide bandwidth and has a dynamic range that extends over approximately m quantum steps for narrow band low level signals the roundoff error statistics can differ significantly from the uniform white uncorrelated model in addition these results show that statistical behavior of roundoff error can differ significantly from that of the quantization error that is generated when a continuous random variable is quantized

robust control based object tracking this correspondence presents a video tracking framework using control based observer design it unifies several kernel based approaches into a consistent theoretical framework by modeling tracking as a recursive inverse problem the framework relies on observability theory to handle the ldquosingularityrdquo problem and provides explicit criteria for kernel design and dynamics evaluation

sequential monte carlo methods for multiple target tracking and data fusion the classical particle filter deals with the estimation of one state process conditioned on a realization of one observation process we extend it here to the estimation of multiple state processes given realizations of several kinds of observation processes the new algorithm is used to track with success multiple targets in a bearings only context whereas a jpdaf diverges making use of the ability of the particle filter to mix different types of observations we then investigate how to join passive and active measurements for improved tracking

tracking by affine kernel transformations using color and boundary cues kernel based trackers aggregate image features within the support of a kernel a mask regardless of their spatial structure these trackers spatially fit the kernel usually in location and in scale such that a function of the aggregate is optimized we propose a kernel based visual tracker that exploits the constancy of color and the presence of color edges along the target boundary the tracker estimates the best affinity of a spatially aligned pair of kernels one of which is color related and the other of which is object boundary related in a sense this work extends previous kernel based trackers by incorporating the object boundary cue into the tracking process and by allowing the kernels to be affinely transformed instead of only translated and isotropically scaled these two extensions make for more precise target localization a more accurately localized target also facilitates safer updating of its reference color model further enhancing the tracker s robustness the improved tracking is demonstrated for several challenging image sequences

a novel approach for stabilizing recursive least squares filters a novel approach for stabilizing recursive least squares rls filters is presented the approach relies on a detailed fixed point analysis which provides two important benefits the analysis reveals a bias in the error propagation mechanism providing an analytical basis for instability problems the analysis then indicates which specific roundoff errors are causing instability these roundoff errors are then biased in such a way that the overall filter is biased towards stable performance experimental results indicate that stability can be achieved with negligible loss in least squares performance

distortion aware correlation tracking recently correlation filter cf based tracking methods have attracted considerable attention because of their high speed performance however distortion which refers to the phenomenon that the correlation outputs of cf based trackers are distorted remains a major obstacle for these methods in this paper we propose a distortion aware correlation filter framework which can detect distortions and recover from tracking failures our framework employs a simple yet effective feature termed normed correlation response to detect distortions meanwhile we introduce a competition mechanism to handle distortions in which we build a specialized graph to formulate and handle tracking under distortion as a maximum multi clique problem furthermore a global local context model is exploited to alleviate underlying distortions during the tracking process extensive experiments on the online tracking benchmark show that our tracker can find the optimal target trajectory during the distortion period and retrieve the possibly missing target consequently outperforms the state of the art methods and improves the performance of cf based trackers favorably

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

robust visual tracking via consistent low rank sparse learning object tracking is the process of determining the states of a target in consecutive video frames based on properties of motion and appearance consistency in this paper we propose a consistent low rank sparse tracker clrst that builds upon the particle filter framework for tracking by exploiting temporal consistency the proposed clrst algorithm adaptively prunes and selects candidate particles by using linear sparse combinations of dictionary templates the proposed method learns the sparse representations of image regions corresponding to candidate particles jointly by exploiting the underlying low rank constraints in addition the proposed clrst algorithm is computationally attractive since temporal consistency property helps prune particles and the low rank minimization problem for learning joint sparse representations can be efficiently solved by a sequence of closed form update operations we evaluate the proposed clrst algorithm against 14 14 state of the art tracking methods on a set of 25 25 challenging image sequences experimental results show that the clrst algorithm performs favorably against state of the art tracking methods in terms of accuracy and execution time

optimal finite wordlength linear quadratic regulation the authors consider the design of an lqg regulator implemented in fixed point arithmetic which is optimized with respect to its state wordlength and structure the approach extends previous design methods so that arithmetic errors are directly included the optimal finite controller gains are computed as a function of the arithmetic wordlength subject to an l sub 2 scaling constant on the controller states the design method used permits the cost for the near optimal structure to be developed so that this can then be used as a basis for comparison to other less complex structures

model selection via multifold cross validation a natural extension of the simple leave one out cross validation cv method is to allow the deletion of more than one observations in this article several notions of the multifold cross validation mcv method have been discussed in the context of variable selection under a linear regression model we show that the delete d mcv criterion is asymptotically equivalent to the well known fpe criterion two computationally more feasible methods the r fold cross validation and the repeated learning testing criterion are also studied the performance of these criteria are compared with the simple leave one out cross validation method simulation results are obtained to gain some understanding on the small sample properties of these methods

piecewise affine kernel tracking for non planar targets since the multiple kernel representation opened in tracking the possibility of representing several features of the target in the same model tracking multiple features using kernel based methods has received a great attention in spite of these efforts the formulation has been reduced to tracking planar targets or targets rotating inside a plane parallel to the image plane the aim of this paper is to extend the multi kernel tracking to cope with situations different to those to this end we consider the triangular mesh described by the centers of the kernels and we develop the estimation of a set of affine transforms one at each mesh triangle subject to the constraints that each affine transform of a triangle must be compatible with the affine transforms coming from contiguous triangles the method is applied to sequences including face and car tracking results show an outperformance respect to previous kernel tracking methods which generally work with a too restricted set of movements

quantization noise spectra several results describing the behavior of quantization noise in a unified and simplified manner are discussed exact formulas for quantizer noise spectra are developed they are applied to a variety of systems and inputs including scalar quantization pcm dithered pcm sigma delta modulation dithered sigma delta modulation two stage sigma delta modulation and second order sigma delta modulation

the mean shift algorithm and its relation to kernel regression we investigate the connection between the asymptotic bias of the well known nadaraya watson kernel regression and the mean shift ms vector with the gaussian kernel we first show that the asymptotic bias for the univariate nadaraya watson kernel regression can be estimated using the ms scalar then we investigate the general d dimensional case d 1 and derive a formula for the asymptotic bias as a function of the ms vector we show that when the regression function is a linear function of its entries then the asymptotic bias can be represented as a linear function of the ms vector the ms algorithm for the univariate and the linear cases can be used to find points where the nadaraya watson kernel regression gives an unbiased estimate furthermore this connection suggests that exploiting the theoretical properties of the asymptotic bias of the nadaraya watson kernel regression may be helpful to show the convergence of the ms algorithm through the simulations we show that how the given theoretical results can be used to estimate the bias of the estimated clean signal by just observing the noisy signal having access to the bias of the estimator enables us to evaluate the accuracy of the estimated clean data which later will be used to design a quantizer

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

properties of mean shift we study properties of the mean shift ms type algorithms for estimating modes of probability density functions pdfs via regarding these algorithms as gradient ascent on estimated pdfs with adaptive step sizes we rigorously prove convergence of mode estimate sequences generated by the ms type algorithms under the assumption that an analytic kernel function is used moreover our analysis on the ms function finds several new properties of mode estimate sequences and corresponding density estimate sequences including the result that in the ms type algorithm using a gaussian kernel the density estimate monotonically increases between two consecutive mode estimates this implies that in the one dimensional case the mode estimate sequence monotonically converges to the stationary point nearest to an initial point without jumping over any stationary point

divergence measures based on the shannon entropy a novel class of information theoretic divergence measures based on the shannon entropy is introduced unlike the well known kullback divergences the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved more importantly their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds these bounds are crucial in many applications of divergence measures the measures are also well characterized by the properties of nonnegativity finiteness semiboundedness and boundedness

bittracker a bitmap tracker for visual tracking under very general conditions this paper addresses the problem of visual tracking under very general conditions a possibly non rigid target whose appearance may drastically change over time general camera motion a 3d scene and no a priori information except initialization this is in contrast to the vast majority of trackers which rely on some limited model in which for example the target s appearance is known a priori or restricted the scene is planar or a pan tilt zoom camera is used their goal is to achieve speed and robustness but their limited context may cause them to fail in the more general case the proposed tracker works by approximating in each frame a pdf probability distribution function of the target s bitmap and then estimating the maximum a posteriori bitmap the pdf is marginalized over all possible motions per pixel thus avoiding the stage in which optical flow is determined this is an advantage over other general context trackers that do not use the motion cue at all or rely on the error prone calculation of optical flow using a gibbs distribution with respect to the first order neighborhood system yields a bitmap pdf whose maximization may be transformed into that of a quadratic pseudo boolean function the maximum of which is approximated via a reduction to a maximum flow problem many experiments were conducted to demonstrate that the tracker is able to track under the aforementioned general context

fast global kernel density mode seeking applications to localization and tracking tracking objects in video using the mean shift ms technique has been the subject of considerable attention in this work we aim to remedy one of its shortcomings ms like other gradient ascent optimization methods is designed to find local modes in many situations however we seek the global mode of a density function the standard ms tracker assumes that the initialization point falls within the basin of attraction of the desired mode when tracking objects in video this assumption may not hold particularly when the target s displacement between successive frames is large in this case the local and global modes do not correspond and the tracker is likely to fail a novel multibandwidth ms procedure is proposed which converges to the global mode of the density function regardless of the initialization point we term the procedure annealed ms as it shares similarities with the annealed importance sampling procedure the bandwidth of the procedure plays the same role as the temperature in conventional annealing we observe that an over smoothed density function with a sufficiently large bandwidth is unimodal using a continuation principle the influence of the global peak in the density function is introduced gradually in this way the global maximum is more reliably located since it is imperative that the computational complexity is minimal for real time applications such as visual tracking we also propose an accelerated version of the algorithm this significantly decreases the number of iterations required to achieve convergence we show on various data sets that the proposed algorithm offers considerable promise in reliably and rapidly finding the true object location when initialized from a distant point

occlusion aware fragment based tracking with spatial temporal consistency in this paper we present a robust tracking method by exploiting a fragment based appearance model with consideration of both temporal continuity and discontinuity information from the perspective of probability theory the proposed tracking algorithm can be viewed as a two stage optimization problem in the first stage by adopting the estimated occlusion state as a prior the optimal state of the tracked object can be obtained by solving an optimization problem where the objective function is designed based on the classification score occlusion prior and temporal continuity information in the second stage we propose a discriminative occlusion model which exploits both foreground and background information to detect the possible occlusion and also models the consistency of occlusion labels among different frames in addition a simple yet effective training strategy is introduced during the model training and updating process with which the effects of spatial temporal consistency are properly weighted the proposed tracker is evaluated by using the recent benchmark data set on which the results demonstrate that our tracker performs favorably against other state of the art tracking algorithms

on fixed point roundoff error analysis the author points out the existence of work published by the author us dept of commerce tech rep ad a086826 57 pp apr 1980 prior to the appearance of the paper by barnes et al ibid vol assp 33 p 595 606 june 1985 covering the same subject

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

finite precision error analysis of qrd rls and star rls adaptive filters the qr decomposition based recursive least squares rls adaptive filtering qrd rls algorithm is suitable for vlsi implementation since it has good numerical properties and can be mapped onto a systolic array a new fine grain pipelinable star rls algorithm was developed the pipelined star rls algorithm pstar rls is useful for high speed applications the stability of qrd rls star rls and pstar rls has been proved but the performance of these algorithms in finite precision arithmetic has not yet been analyzed the authors determine expressions for the degradation in the performance of these algorithms due to finite precision by exploiting the steady state properties of these algorithms simple expressions are obtained that depend only on known parameters this analysis can be used to compare the algorithms and to decide the wordlength to be used in an implementation since floating or fixed point arithmetic representations may be used in practice both representations are considered the results show that the three algorithms have about the same finite precision performance with pstar rls performing better than star rls which does better than qrd rls these algorithms can be implemented with as few as 8 bits for the fractional part depending on the filter size and the forgetting factor used the theoretical expressions are found to be in good agreement with the simulation results

probability density function estimation with the frequency polygon transform a probability density function estimator is proposed which is based on frequency polygons its convergence to the true density is formally proved a mode finding algorithm is also proposed as an alternative to mean shift our approach outperforms histogram and kernel based estimators in synthetic and real datasets our proposal is shown to be suitable to object tracking in video sequences most current nonparametric approaches to probability density function estimation are based on the kernel density estimator also known as the parzen window estimator a usual alternative is the multivariate histogram which features a low computational complexity multivariate frequency polygons have often been neglected even though they share many of the advantages of the histograms while they are continuous unlike the histograms here we build on our previous work on histograms in order to propose a new probability density estimator which is based on averaging multivariate frequency polygons the convergence of the estimator is formally proved experiments are carried out with synthetic and real machine learning datasets finally image denoising and object tracking applications are also considered

robust tracking with discriminative ranking lists in this paper we propose a novel tracking algorithm i e the discriminative ranking list based tracker drltracker the drltracker models the target object and its local background by using ranking lists of patches of different scales within object bounding boxes the ranking list of each of such patches is its k nearest neighbors patches of the same scale with ranking lists of high purity values meaning high probabilities to be on the target object and some confusable background patches constitute the object model under that scale a pair of object models of two different scales collaborate to determine which patches may belong to the target object in the next frame the drltracker can effectively alleviate the distraction problem and its superior ability over several representative and state of the art trackers is demonstrated through extensive experiments

an evolutionary particle filter with the immune genetic algorithm for intelligent video target tracking particle filter algorithm is widely used for target tracking using video sequences which is of great importance for intelligent surveillance applications however there is still much room for improvement e g the so called sample impoverishment it is brought by re sampling which aims to avoid particle degradation and thus becomes the inherent shortcoming of the particle filter in order to solve the problem of sample impoverishment increase the number of meaningful particles and ensure the diversity of the particle set an evolutionary particle filter with the immune genetic algorithm iga for target tracking is proposed by adding iga in front of the re sampling process to increase particle diversity particles are regarded as the antibodies of the immune system and the state of target being tracked is regarded as the external invading antigen with the crossover and mutation process the immune system produces a large number of new antibodies particles and thus the new particles can better approximate the true state by exploiting new areas regulatory mechanisms of antibodies such as promotion and suppression ensure the diversity of the particle set in the proposed algorithm the particle set optimized by iga can better express the true state of the target and the number of meaningful particles can be increased significantly the effectiveness and robustness of the proposed particle filter are verified by target tracking experiments simulation results show that the proposed particle filter is better than the standard one in particle diversity and efficiency the proposed algorithm can easily be extended to multiple objects tracking problems with occlusions

information theoretic measure for visual target distinctness it is of great benefit to have advance knowledge of human visual target acquisition performance for targets or other relevant objects however search performance inherently shows a large variance and depends strongly on prior knowledge of the perceived scene a typical search experiment therefore requires a large number of observers to obtain statistically reliable data moreover measuring target acquisition performance in field situations is usually impractical and often very costly or even dangerous the paper presents a method for characterizing information of a target relative to its background the resultant computational measures are then applied to quantify the visual distinctness of targets in complex natural backgrounds from digital imagery a generalization of the kullback leibler joint information gain of various random variables is shown to correlate strongly with visual target distinctness as estimated by human observers bootstrap methods for assessing statistical accuracy were used to produce this inference

differential earth mover s distance with its applications to visual tracking the earth mover s distance emd is a similarity measure that captures perceptual difference between two distributions its computational complexity however prevents a direct use in many applications this paper proposes a novel differential emd demd algorithm based on the sensitivity analysis of the simplex method and offers a speedup at orders of magnitude compared with its brute force counterparts the demd algorithm is discussed and empirically verified in the visual tracking context the deformations of the distributions for objects at different time instances are accommodated well by the emd and the differential algorithm makes the use of emd in real time tracking possible to further reduce the computation signatures i e variable size descriptions of distributions are employed as an object representation the new algorithm models and estimates local background scenes as well as foreground objects to handle scale changes in a principled way extensive quantitative evaluation of the proposed algorithm has been carried out using benchmark sequences and the improvement over the standard mean shift tracker is demonstrated

interaction pursuit in high dimensional multi response regression via distance correlation feature interactions can contribute to a large proportion of variation in many prediction models in the era of big data the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions in this paper we suggest a two stage interaction identification method called the interaction pursuit via distance correlation ipdc in the setting of high dimensional multi response interaction models that exploits feature screening applied to transformed variables with distance correlation followed by feature selection such a procedure is computationally efficient generally applicable beyond the heredity assumption and effective even when the number of responses diverges with the sample size under mild regularity conditions we show that this method enjoys nice theoretical properties including the sure screening property support union recovery and oracle inequalities in prediction and estimation for both interactions and main effects the advantages of our method are supported by several simulation studies and real data analysis

mean shift trackers with cross bin metrics cross bin metrics have been shown to be more suitable than bin by bin metrics for measuring the distance between histograms in various applications in particular a visual tracker that minimizes the earth mover s distance emd between the candidate and reference feature histograms has recently been proposed this tracker was shown to be more robust than the mean shift tracker which employs a bin by bin metric in each frame the former tracker iteratively shifts the candidate location by one pixel in the direction opposite to the emd s gradient until no improvement is made this optimization process involves the clustering of the candidate feature density in feature space as well as the computation of the emd between the candidate and reference feature histograms after each shift of the candidate location in this paper alternative trackers that employ cross bin metrics as well but that are based on mean shift ms iterations are derived the proposed trackers are simpler and faster due to 1 the use of ms based optimization which is not restricted to single pixel shifts 2 abstention from any clustering of feature densities and 3 abstention from emd computations in multidimensional spaces

the quality of training sample estimates of the bhattacharyya coefficient the quality in terms of the bias and variance of estimates of the bhattacharyya coefficient based on n training samples from two classes described by multivariate gaussian distributions is considered the case where the classes are described by a common covariance matrix as well as the case where each class is described by a different covariance matrix is analyzed expressions for the bias and the variance of estimates of the bhattacharyya coefficient are derived and numerical examples are used to show the relationship between these parameters the number of training samples and the dimensionality of the observation space

multiple collaborative kernel tracking those motion parameters that cannot be recovered from image measurements are unobservable in the visual dynamic system this paper studies this important issue of singularity in the context of kernel based tracking and presents a novel approach that is based on a motion field representation which employs redundant but sparsely correlated local motion parameters instead of compact but uncorrelated global ones this approach makes it easy to design fully observable kernel based motion estimators this paper shows that these high dimensional motion fields can be estimated efficiently by the collaboration among a set of simpler local kernel based motion estimators which makes the new approach very practical