separability based multiscale basis selection and feature extraction for signal and image classification algorithms for multiscale basis selection and feature extraction for pattern classification problems are presented the basis selection algorithm is based on class separability measures rather than energy or entropy at each level the accumulated tree structured class separabilities obtained from the tree which includes a parent node and the one which includes its children are compared the decomposition of the node or subband is performed creating the children if it provides larger combined separability the suggested feature extraction algorithm focuses on dimensionality reduction of a multiscale feature space subject to maximum preservation of information useful for classification at each level of decomposition an optimal linear transform that preserves class separabilities and results in a reduced dimensional feature space is obtained classification and feature extraction is then performed at each scale and resulting soft decisions obtained for each area are integrated across scales the suggested algorithms have been tested for classification and segmentation of one dimensional 1 d radar signals and two dimensional 2 d texture and document images the same idea can be used for other tree structured local basis e g local trigonometric basis functions and even for nonorthogonal redundant and composite basis dictionaries

lorelogram a regression approach to exploring dependence in longitudinal categorical responses abstract we propose flexible regression estimators of the marginal pairwise log odds ratio measure of association for longitudinal categorical responses the function that we estimate is the log odds ratio analog of the correlogram hence we name the function the lorelogram measuring the association of categorical responses on the log odds scale allows ease of interpretation and allows pairwise association to remain unconstrained by the marginal means a feature not shared by correlations with binary or multinomial responses estimation of the function is achieved through the use of standard parametric estimating equations or through an extension of generalized additive models that allows nonparametric estimation of dependence functions for fixed smoothing parameters we apply the methodology to binary longitudinal data where scientific interest focuses on the dependence structure

color sparse representations for image processing review models and prospects sparse representations have been extended to deal with color images composed of three channels a review of dictionary learning based sparse representations for color images is made here detailing the differences between the models and comparing their results on the real and simulated data these models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering transformation of the color channels moreover this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix based color filtering which highlights the filtering implicitly applied through this model based on this reformulation the new color filtering model is introduced using unconstrained filters in this model spatial morphologies of color images are encoded by atoms and colors are encoded by color filters color variability is no longer captured in increasing the dictionary size but with color filters this gives an efficient color representation

rotation invariant texture classification using a complete space frequency model a method of rotation invariant texture classification based on a complete space frequency model is introduced a polar analytic form of a two dimensional 2 d gabor wavelet is developed and a multiresolution family of these wavelets is used to compute information conserving microfeatures from these microfeatures a micromodel which characterizes spatially localized amplitude frequency and directional behavior of the texture is formed the essential characteristics of a texture sample its macrofeatures are derived from the estimated selected parameters of the micromodel classification of texture samples is based on the macromodel derived from a rotation invariant subset of macrofeatures in experiments comparatively high correct classification rates were obtained using large sample sets

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

log polar wavelet energy signatures for rotation and scale invariant texture classification classification of texture images is important in image analysis and classification this paper proposes an effective scheme for rotation and scale invariant texture classification using log polar wavelet signatures the rotation and scale invariant feature extraction for a given image involves applying a log polar transform to eliminate the rotation and scale effects but at same time produce a row shifted log polar image which is then passed to an adaptive row shift invariant wavelet packet transform to eliminate the row shift effects so the output wavelet coefficients are rotation and scale invariant the adaptive row shift invariant wavelet packet transform is quite efficient with only o n spl middot log n complexity a feature vector of the most dominant log polar wavelet energy signatures extracted from each subband of wavelet coefficients is constructed for rotation and scale invariant texture classification in the experiments we employed a mahalanobis classifier to classify a set of 25 distinct natural textures selected from the brodatz album the experimental results based on different testing data sets for images with different orientations and scales show that the proposed classification scheme using log polar wavelet signatures outperforms two other texture classification methods its overall accuracy rate for joint rotation and scale invariance being 90 8 percent demonstrating that the extracted energy signatures are effective rotation and scale invariant features concerning its robustness to noise the classification scheme also performs better than the other methods

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

shape classification using the inner distance part structure and articulation are of fundamental importance in computer and human vision we propose using the inner distance to build shape descriptors that are robust to articulation and capture part structure the inner distance is defined as the length of the shortest path between landmark points within the shape silhouette we show that it is articulation insensitive and more effective at capturing part structures than the euclidean distance this suggests that the inner distance can be used as a replacement for the euclidean distance to build more accurate descriptors for complex shapes especially for those with articulated parts in addition texture information along the shortest path can be used to further improve shape classification with this idea we propose three approaches to using the inner distance the first method combines the inner distance and multidimensional scaling mds to build articulation invariant signatures for articulated shapes the second method uses the inner distance to build a new shape descriptor based on shape contexts the third one extends the second one by considering the texture information along shortest paths the proposed approaches have been tested on a variety of shape databases including an articulated shape data set mpeg7 ce shape 1 kimia silhouettes the eth 80 data set two leaf data sets and a human motion silhouette data set in all the experiments our methods demonstrate effective performance compared with other algorithms

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

a geometric analysis of subspace clustering with outliers this paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes as is common in computer vision or unsupervised learning applications we do not know in advance how many subspaces there are nor do we have any information about their dimensions we develop a novel geometric analysis of an algorithm named sparse subspace clustering ssc 11 which signicantly broadens the range of problems where it is provably eective for instance we show that ssc can recover multiple subspaces each of dimension comparable to the ambient dimension we also prove that ssc can correctly cluster data points even when the subspaces of interest intersect further we develop an extension of ssc that succeeds when the data set is corrupted with possibly overwhelmingly many outliers underlying our analysis are clear geometric insights which may bear on other sparse recovery problems a numerical study complements our theoretical analysis and demonstrates the eectiveness of these methods

on the refinement of cauchy s theorem and pellet s theorem using the relationship of a polynomial and its associated polynomial we derived a necessary and sufficient condition for determining all roots of a given polynomial on the circumference of a circle defined by its associated polynomial by employing the technology of analytic inequality and the theory of distribution of zeros of meromorphic function we refine two classical results of cauchy and pellet about bounds of modules of polynomial zeros sufficient conditions are obtained for the polynomial whose cauchy s bound and pellet s bounds are strict bounds the characteristics is given for the polynomial whose cauchy s bound or pellet s bounds can be achieved by the modules of zeros of the polynomial

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

radon transform orientation estimation for rotation invariant texture analysis this paper presents a new approach to rotation invariant texture classification the proposed approach benefits from the fact that most of the texture patterns either have directionality anisotropic textures or are not with a specific direction isotropic textures the wavelet energy features of the directional textures change significantly when the image is rotated however for the isotropic images the wavelet features are not sensitive to rotation therefore for the directional textures it is essential to calculate the wavelet features along a specific direction in the proposed approach the radon transform is first employed to detect the principal direction of the texture then the texture is rotated to place its principal direction at 0 degrees a wavelet transform is applied to the rotated image to extract texture features this approach provides a features space with small intraclass variability and therefore good separation between different classes the performance of the method is evaluated using three texture sets experimental results show the superiority of the proposed approach compared with some existing methods

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

estimating treatment efficacy over time a logistic regression model for binary longitudinal outcomes this paper presents a case study in longitudinal data analysis where the goal is to estimate the efficacy of a new drug for treatment of a severe chronic constipation data consist of long sequences of binary outcomes relief no relief on each of a large number of patients randomized to treatment low and high dose or placebo data characteristics indicate 1 the treatment effects vary non linearly with time 2 there is substantial heterogeneity across subjects in their responses to treatment and 3 there is a high proportion of subjects who never experience any relief the non responders to overcome these challenges we develop a hierarchical model for binary longitudinal data with a mixture distribution on the probability of response to account for the high frequency of non responders while the model is specified conditionally on subject specific latent variables we also draw inferences on key population average parameters for the assessment of the treatments efficacy in a population in addition we employ a model checking method to compare the goodness of fit for our model against simpler modelling approaches for aggregated counts such as the zero inflated poisson and zero inflated negative binomial models we estimate subject specific and population average rate ratios of relief for the treatment with respect to the placebo as functions of time rr t and compare them with the rate ratios estimated from the models for aggregated counts we find that 1 the treatment is effective with respect to the placebo with higher efficacy at the beginning of the study 2 the estimated rate ratios from the models for aggregated counts appear to be similar to the average across time of the population average rate ratios estimated under our model and 3 model checking suggests that the hierarchical and zero inflated negative binomial model fit the data best if we are mainly interested to establish the overall efficacy or safety of a new drug it is appropriate to aggregate the longitudinal data over time and analyse the count data by use of standard statistical methods however the models for aggregated counts cannot capture time trend of treatment such as the initial treatment benefit or the development of tolerance during the early stage of the treatment which may be important information to physicians to predict the treatment effects for their patients

shift 2d rotation invariant sparse coding for multivariate signals classical dictionary learning algorithms dla allow unicomponent signals to be processed due to our interest in two dimensional 2d motion signals we wanted to mix the two components to provide rotation invariance so multicomponent frameworks are examined here in contrast to the well known multichannel framework a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure within this multivariate framework we then present sparse coding methods multivariate orthogonal matching pursuit m omp which provides sparse approximation for multivariate signals and multivariate dla m dla which empirically learns the characteristic patterns or features that are associated to a multivariate signals set and combines shift invariance and online learning once the multivariate dictionary is learned any signal of this considered set can be approximated sparsely this multivariate framework is introduced to simply present the 2d rotation invariant 2dri case by studying 2d motions that are acquired in bivariate real signals we want the decompositions to be independent of the orientation of the movement execution in the 2d space the methods are thus specified for the 2dri case to be robust to any rotation 2dri omp and 2dri dla shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition as validation our methods are applied to 2d handwritten data to extract the elementary features of this signals set and to provide rotation invariant decomposition

deterministic compressed sensing matrices construction via euler squares and applications in compressed sensing the matrices that satisfy the restricted isometry property rip play an important role to date however very few results for designing such matrices are available for applications such as multiplier less data compression binary sensing matrices are of interest the present paper constructs deterministic and binary sensing matrices using euler squares in particular given a positive integer m different from p p 2 for a prime p we show that it is possible to construct a binary sensing matrix of size mtimes c mmu 2 where mu is the coherence parameter of the matrix and cin 1 2 the matrices that we construct have small density that is percentage of nonzero entries in the matrix is small with no function evaluation in their construction which support algorithms with low computational complexity through experimental work we show that our binary sensing matrices can be used for such applications as content based image retrieval our simulation results demonstrate that the euler square based cs matrices give better performance than their gaussian counterparts

salient views and view dependent dictionaries for object recognition a sparse representation based approach is proposed to determine the salient views of 3d objects the salient views are categorized into two groups the first are boundary representative views that have several visible sides and object surfaces that may be attractive to humans the second are side representative views that best represent views from sides of an approximating convex shape the side representative views are class specific and possess the most representative power compared to other within class views using the concept of characteristic view class we first present a sparse representation based approach for estimating the boundary representative views with the estimated boundaries we determine the side representative views based on a minimum reconstruction error criterion furthermore to evaluate our method we introduce the notion of view dependent dictionaries built from salient views for applications in 3d object recognition and retrieval the proposed view dependent dictionaries encode information on geometry across views and representation of the object through a series of experiments on four publicly available 3d object datasets we demonstrate the effectiveness of our approach compared to two existing state of the art algorithms and one baseline method highlightsa sparse representation based approach is proposed to determine the salient views of 3d objects the salient views are categorized into boundary representative and side representative views we present a sparse representation based approach for estimating the boundary representative views we determine the side representative views based on a minimum reconstruction error criterion we introduce view dependent dictionaries for applications in 3d object recognition and retrieval

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

in plane rotation and scale invariant clustering using dictionaries in this paper we present an approach that simultaneously clusters images and learns dictionaries from the clusters the method learns dictionaries and clusters images in the radon transform domain the main feature of the proposed approach is that it provides both in plane rotation and scale invariant clustering which is useful in numerous applications including content based image retrieval cbir we demonstrate the effectiveness of our rotation and scale invariant clustering method on a series of cbir experiments experiments are performed on the smithsonian isolated leaf kimia shape and brodatz texture datasets our method provides both good retrieval performance and greater robustness compared to standard gabor based and three state of the art shape based methods that have similar objectives

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

matching pursuit filters applied to face identification we present a face identification algorithm that automatically processes an unknown image by locating and identifying the face the heart of the algorithm is the use of pursuit filters a matching pursuit filter is an adapted wavelet expansion where the expansion is adapted to both the data and the pattern recognition problem being addressed for identification the filters find the features that differentiate among faces whereas for detection the filters encode the similarities among faces the filters are designed though a simultaneous decomposition of a training set into a two dimensional 2 d wavelet expansion this yields a representation that is explicitly 2 d and encodes information locally the algorithm uses coarse to fine processing to locate a small set of key facial features which are restricted to the nose and eye regions of the face the result is an algorithm that is robust to variations in facial expression hair style and the surrounding environment based on the locations of the facial features the identification module searches the data base for the identity of the unknown face using matching pursuit filters to make the identification the algorithm was demonstrated on three sets of images the first set was images from the feret data base the second set was infrared and visible images of the same people this demonstration was done to compare performance on infrared and visible images individually and on fusing the results from both modalities the third set was mugshot data from a law enforcement application

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

evaluation of interest point detectors many different low level feature detectors exist and it is widely agreed that the evaluation of detectors is important in this paper we introduce two evaluation criteria for interest points repeatability rate and information content repeatability rate evaluates the geometric stability under different transformations information content measures the distinctiveness of features different interest point detectors are compared using these two criteria we determine which detector gives the best results and show that it satisfies the criteria well

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

zeros of certain sums of two polynomials abstract in this paper we investigate the zero distribution of various sums of polynomials of the form a b or a tb 0 t t a and b monic polynomials of the same degree more precisely we study generalizations and analogues of x 1 n x 1 n and their factorizations