randomized clustering forests for image classification some of the most effective recent methods for content based image classification work by quantizing image descriptors and accumulating histograms of the resulting visual word codes large numbers of descriptors and large codebooks are required for good results and this becomes slow using k means we introduce extremely randomized clustering forests ensembles of randomly created clustering trees and show that they provide more accurate results much faster training and testing and good resistance to background clutter second an efficient image classification method is proposed it combines erc forests and saliency maps very closely with the extraction of image information for a given image a classifier builds a saliency map online and uses it to classify the image we show in several state of the art image classification tasks that this method can speed up the classification process enormously finally we show that the proposed erc forests can also be used very successfully for learning distance between images the distance computation algorithm consists of learning the characteristic differences between local descriptors sampled from pairs of same or different objects these differences are vector quantized by erc forests and the similarity measure is computed from this quantization the similarity measure has been evaluated on four very different datasets and always outperforms the state of the art competitive approaches

interest point detection using rank order log filter this paper proposes a novel nonlinear filter named rank order laplacian of gaussian rolg filter based on which a new interest point detector is developed the rolg filter is a weighted rank order filter it is used to detect the image local structures where a significant majority of pixels are brighter or darker than a significant majority of pixels in their corresponding surroundings compared to linear filter based detectors e g sift detector the proposed rank order filter based detector is more robust to abrupt variations of images caused by illumination and geometric changes experiments on the benchmark databases demonstrate that the proposed rolg detector achieves superior performance comparing to four state of the art detectors evaluation experiments are also conducted on face recognition problems the results on five face databases further demonstrate that the rolg detector significantly outperforms the other detectors

intelligent meshing technique for 2d resistivity inverse problems abstractin geophysical inverse problems an a priori structured mesh is often used for inversion and mesh refinement is applied if needed by the user after observation of inversion results we have developed a new intelligent self adaptive unstructured finite element meshing technique for electrical resistivity tomography inverse problems this new approach uses harris corner and edge detectors that are based on the local autocorrelation function of 2d distribution of pixels this meshing technique optimizes the size of the inverse problem by refining areas where variations in the physical property structure are sensed to be important the meshing technique also generates a more appropriate and optimum mesh for the inverse problem that is dependent on the problem itself tests on modeled data have demonstrated that the proposed intelligent meshing technique can reduce data misfit produce a better reconstruction of the true physical properties and minimize the size of the inverse problem the synthetic m

a model based approach to junction detection using radial energy a novel junction detector is presented that fits the neighborhood around a point to a junction model the junction model segments the neighborhood into wedges by determining a set of radial edges the radial edges are invariant to affine transforms creating an affine invariant junction detector the radial edges are evaluated based upon the pixels along the edge the angle between the pixel gradient and the vector to the potential junction point forms the initial basis for the measurement an initial set of radial edges is selected based upon identifying local maximums within a given arc distance an energy function is applied to the resulting radial segmentation and a greedy optimization routine is used to construct the minimal set of radial edges to identify the final junctions a second energy function is used that combines the components of the first energy function with the resulting change in standard deviation by separation into radial segments the junctions with the most energy in their local neighborhoods are selected as potential junctions the neighborhoods about the potential junctions are analyzed to determine if they represent a single line or multiple non parallel lines if the neighborhood represents multiple non parallel lines the point is classified as a junction point the junction detector is tested on several images including both synthetic and real images highlights of radially segmented junction points are displayed for the real images

the zak transform and sampling theorems for wavelet subspaces the zak transform is used for generalizing a sampling theorem of g waiter see ieee trans informat theory vol 38 p 881 884 1992 for wavelet subspaces cardinal series based on signal samples f a n n in z with a possibly unequal to 0 waiter s case are considered the condition number of the sampling operator and worst case aliasing errors are expressed in terms of zak transforms of scaling function and wavelet this shows that the stability of the resulting interpolation formula depends critically on a

unsupervised learning of human action categories using spatial temporal words we present a novel unsupervised learning method for human action categories a video sequence is represented as a collection of spatial temporal words by extracting space time interest points the algorithm automatically learns the probability distributions of the spatial temporal words and the intermediate topics corresponding to human action categories this is achieved by using latent topic models such as the probabilistic latent semantic analysis plsa model and latent dirichlet allocation lda our approach can handle noisy feature points arisen from dynamic background and moving cameras due to the application of the probabilistic models given a novel video sequence the algorithm can categorize and localize the human action s contained in the video we test our algorithm on three challenging datasets the kth human motion dataset the weizmann human action dataset and a recent dataset of figure skating actions our results reflect the promise of such a simple approach in addition our algorithm can recognize and localize multiple actions in long and complex video sequences containing multiple motions

image watermarking based on invariant regions of scale space representation this paper proposes a novel content based image watermarking method based on invariant regions of an image the invariant regions are self adaptive image patches that deform with geometric transformations three different invariant region detection methods based on the scale space representation of an image were considered for watermarking at each invariant region the watermark is embedded after geometric normalization according to the shape of the region by binding watermarking with invariant regions resilience against geometric transformations can be readily obtained experimental results show that the proposed method is robust against various image processing steps including geometric transformations cropping filtering and jpeg compression

generalized sampling stability and performance analysis generalized sampling provides a general mechanism for recovering an unknown input function f x spl epsiv spl hscr from the samples of the responses of m linear shift invariant systems sampled at 1 mth the reconstruction rate the system can be designed to perform a projection of f x onto the reconstruction subspace v spl phi span spl phi x k sub k spl epsiv z for example the family of bandlimited signals with spl phi x sinc x this implies that the reconstruction will be perfect when the input signal is included in v spl phi the traditional framework of papoulis 1977 generalized sampling theory otherwise one recovers a signal approximation f x spl epsiv v spl phi that is consistent with f x in the sense that it produces the same measurements to characterize the stability of the algorithm we prove that the dual synthesis functions that appear in the generalized sampling reconstruction formula constitute a riesz basis of v spl phi and we use the corresponding riesz bounds to define the condition number of the system we then use these results to analyze the stability of various instances of interlaced and derivative sampling next we consider the issue of performance which becomes pertinent once we have extended the applicability of the method to arbitrary input functions that is when spl hscr is considerably larger than v spl phi and the reconstruction is no longer exact we show that the generalized sampling solution is essentially equivalent to the optimal minimum error approximation we then perform a detailed analysis for the case in which the analysis filters are in l sub 2 and determine all relevant bound constants explicitly finally we use an interlaced sampling example to illustrate these various calculations

multiplicative lidskii s inequalities and optimal perturbations of frames abstract in this paper we study two design problems in frame theory on the one hand given a fixed finite frame f f j j i n for c d we compute those dual frames g of f that are optimal perturbations of the canonical dual frame for f under certain restrictions on the norms of the elements of g on the other hand we compute those v f v f j j i n for invertible operators v which are close to the identity that are optimal perturbations of f that is we compute the optimal perturbations of f among frames g g j j i n that have the same linear relations as f in both cases optimality is measured with respect to submajorization of the eigenvalues of the frame operators hence our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error the key tool for these results is a multiplicative analogue of lidskii s inequality in terms of log majorization and a characterization of the case of equality

principal angles between subspaces in an a based scalar product algorithms and perturbation estimates computation of principal angles between subspaces is important in many applications e g in statistics and information retrieval in statistics the angles are closely related to measures of dependency and covariance of random variables when applied to column spaces of matrices the principal angles describe canonical correlations of a matrix pair we highlight that all popular software codes for canonical correlations compute only cosine of principal angles thus making impossible because of round off errors finding small angles accurately we review a combination of sine and cosine based algorithms that provide accurate results for all angles we generalize the method to the computation of principal angles in an a based scalar product for a symmetric and positive definite matrix a we provide a comprehensive overview of interesting properties of principal angles we prove basic perturbation theorems for absolute errors for sine and cosine of principal angles with improved constants numerical examples and a detailed description of our code are given

reductibilite d un systeme differentiel lineaire dans la resolution des systemes differentiels lineaires au voisinage d un point singulier nous sommes amenes ame etudier la nature de cette singularite on presente dans cet article un moyen pratique par application du critere de j moser permettant de reconnaitre sur un systeme si la singlarite est reguliere on donne par le meme moyen un algorithme programmable en langage de calcul formel reduce permettat de reduire en un nombre fini de pas le systeme differentiel considere sous foe forme irreductible in solving linear differential systems in the neighbourhood of a singular point we are led to study the nature of this singularity in this paper we give a practical method based on the j moser criterion that allows to recognize on a system if a singularity is regular in the same manner we give an algorithm implementable in a computer algebra system which reduces in a finite number of steps the differential system on an irreducible form

aliasing and oblique dual pair designs for consistent sampling abstract in this paper we study some aspects of oblique duality between finite sequences of vectors f and g lying in finite dimensional subspaces w and v respectively we compute the possible eigenvalue lists of the frame operators of oblique duals to f lying in v we compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for f with norm restrictions as an application we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible among oblique duals with norm restrictions we obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces v and w has in oblique duality we apply this analysis to compute those rigid rotations u for w such that the canonical oblique dual of u f minimize every convex potential we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations u for w such that the canonical oblique dual pair associated to u f minimize the aliasing we point out that these two last problems are intrinsic to oblique duality within the context of consistent sampling

fast learning adaptive subspace self organizing map an application to saliency based invariant image feature construction the adaptive subspace self organizing map assom is useful for invariant feature generation and visualization however the learning procedure of the assom is slow in this paper two fast implementations of the assom are proposed to boost assom learning based on insightful discussions of the basis rotation operator of assom we investigate the objective function approximately maximized by the classical rotation operator we then explore a sequence of two schemes to apply the proposed assom implementations to saliency based invariant feature construction for image classification in the first scheme a cumulative activity map computed from a single assom is used as descriptor of the input image in the second scheme we use one assom for each image category and a joint cumulative activity map is calculated as the descriptor both schemes are evaluated on a subset of the corel photo database with ten classes the multi assom scheme is favored it is also applied to adult image filtering and shows promising results

sparsity and spectral properties of dual frames we study sparsity and spectral properties of dual frames of a given finite frame we show that any finite frame has a dual with no more than n 2 non vanishing entries where n denotes the ambient dimension and that for most frames no sparser dual is possible moreover we derive an expression for the exact sparsity level of the sparsest dual for any given finite frame using a general ized notion of spark we then study the spectral properties of dual frames in terms of singular values of the synthesis operator we provide a complete characteriza tion for which spectral patterns of dual frames are possible for a fixed frame for many cases we provide simple explicit constructions for dual frames with a given spectrum in particular if the constraint on the dual is that it be tight

learning to match deriving optimal template matching algorithms from probabilistic image models finding correspondences between images by template matching is a common problem in image understanding although a variety of solutions have been proposed most of them rely on the arbitrary choice of a template and a matching function often different cost functions lead to different results and the choice of a good cost for a specific application remains an art statistical models on the other hand allow us to derive optimal learning and matching algorithms from modeling assumptions using likelihood maximization principles the key contribution of this paper is the development of a statistical framework for learning what function to optimize from training examples we present a family of statistical models for grayscale images which allow us to derive optimal template matching algorithms the intensity at each pixel is described by a random variable whose distribution is encoded by a deformable template firstly we assume the intensity distribution to be gaussian and derive an intensity matching algorithm which is a generalization of the classical sum of squared differences then we introduce a hidden segmentation variable in the probabilistic model and derive a segmentation matching algorithm that can handle photometric variations both models are exemplified on the automatic detection of anatomical landmarks in brain magnetic resonance images

properties of oblique dual frames in shift invariant systems abstract gramian analysis is used to study properties of a shift invariant system x b k k z n where b is an invertible n n matrix and a finite or countable subset of l 2 r n under the assumption that the system forms a frame for the closed subspace m of l 2 r n in particular the relationship between various features of such system such as being a frame for the whole space l 2 r n being a riesz sequence and having a unique shift generated dual of type i or ii is discussed in details several interesting examples are presented

robust image corner detection through curvature scale space this paper describes a novel method for image corner detection based on the curvature scale space css representation the first step is to extract edges from the original image using a canny detector 1986 the corner points of an image are defined as points where image edges have their maxima of absolute curvature the corner points are detected at a high scale of the css and tracked through multiple lower scales to improve localization this method is very robust to noise and we believe that it performs better than the existing corner detectors an improvement to canny edge detector s response to 45 spl deg and 135 spl deg edges is also proposed furthermore the css detector can provide additional point features curvature zero crossings of image edge contours in addition to the traditional corners

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

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

using computer algebra to diagonalize some kane matrices in semiconductor theory applying the kp method to the monodimensional schrodinger equation leads to a symmetric perturbed eigenvalue problem kane e o 1967 the kp method semiconductors and semimetals new york academic p 75 i e to the diagonalization of a matrix a depending on a small parameter symmetric the eigenelements of a admit expansions in fractional powers of puiseux series usually physicists solve this problem by using schrodinger perturbation formulae under some restrictive conditions which make perturbed eigenvector symbolic approximation impossible this is illustrated by the modified kane matrix fishman g 1997 quasi cube et wurtzite application au gan montpellier ecole thematique du cnrs to solve this problem completely from a symbolic computing point of view we consider the symmetric perturbed eigenvalue problem in the case of analytic perturbations baumgartel h 1985 analytic perturbation theory for matrices and operators basle birkhauser kato t 1980 perturbation theory for linear operators berlin springer we first review the classical characteristic polynomial approach showing why it may be not optimal we also present a direct matricial algorithm jeannerod c p and pflugel e 1999 int symp on symbolic and algebraic computation vancouver canada july 1999 new york acm pp 121 8 transforming the analytic matrix a into its so called q reduced form allows to recover the information we need for the eigenvalues this alternative method as well as the classical one can be described in terms of the newton polygon however our approach uses only a finite number of terms of a and is more suitable for large matrices and a low approximation order besides we show that the q reduction process can simultaneously provide symbolic approximations of both the perturbed eigenvalues and eigenvectors the implementation of this algorithm in maple is used to diagonalize the modified kane matrix up to a given order

optimal frames for erasures we study frames from the viewpoint of coding theory we introduce a numerical measure of how well a frame reconstructs vectors when some of the frame coefficients of a vector are lost and then attempt to find and classify the frames that are optimal in this setting

duality in reconstruction systems we consider the notion of finite dimensional reconstructions systems rs s which includes the fusion frames as projective rs s we study erasures some geometrical properties of these spaces the spectral picture of the set of all dual systems of a fixed rs the spectral picture of the set of rs operators for the projective systems with fixed weights and the structure of the minimizers of the joint potential in this setting we give several examples

frame representations and parseval duals with applications to gabor frames let x n be a frame for a hilbert space h we investigate the conditions under which there exists a dual frame for x n which is also a parseval or tight frame we show that the existence of a parseval dual is equivalent to the problem whether x n can be dilated to an orthonormal basis under an oblique projection a necessary and sufficient condition for the existence of parseval duals is obtained in terms of the frame excess for a frame g g g induced by a projective unitary representation of a group g it is possible that g g g can have a parseval dual but does not have a parseval dual of the same type the primary aim of this paper is to present a complete characterization for all the projective unitary representations such that every frame g g g with a necessary lower frame bound condition has a parseval dual of the same type as an application of this characterization together with a result about lattice tiling we prove that every gabor frame g g l k again with the same necessary lower frame bound condition has a parseval dual of the same type if and only if the volume of the fundamental domain of l k is less than or equal to 1 2

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 computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

hierarchical segmentation using tree based shape spaces current trends in image segmentation are to compute a hierarchy of image segmentations from fine to coarse a classical approach to obtain a single meaningful image partition from a given hierarchy is to cut it in an optimal way following the seminal approach of the scale set theory while interesting in many cases the resulting segmentation being a non horizontal cut is limited by the structure of the hierarchy in this paper we propose a novel approach that acts by transforming an input hierarchy into a new saliency map it relies on the notion of shape space a graph representation of a set of regions extracted from the image each region is characterized with an attribute describing it we weigh the boundaries of a subset of meaningful regions local minima in the shape space by extinction values based on the attribute this extinction based saliency map represents a new hierarchy of segmentations highlighting regions having some specific characteristics each threshold of this map represents a segmentation which is generally different from any cut of the original hierarchy this new approach thus enlarges the set of possible partition results that can be extracted from a given hierarchy qualitative and quantitative illustrations demonstrate the usefulness of the proposed method

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

calcul des invariants de malgrange et de gerard levelt d un systeme differentiel lineaire en un point singulier irregulier we consider a system of ordinary differential equations y x a x y x where a x is a matrix with a pole of the order q at x 0 for this system b malgrange has introduced the quantity i d which can be computed with the cyclic vector method the present paper treats the practical evaluation of i d and the invariants 1 2 q 1 of gerard and levelt without using a cyclic vector first we shall give a survey of the algorithm given in hilali and wazner numer math 50 1987 429 449 by which a system is reduced to a super irreducible form we show that these invariants follows directly from this form

variable length signature for near duplicate image matching we propose a variable length signature for near duplicate image matching in this paper an image is represented by a signature the length of which varies with respect to the number of patches in the image a new visual descriptor viz probabilistic center symmetric local binary pattern is proposed to characterize the appearance of each image patch beyond each individual patch the spatial relationships among the patches are captured in order to compute the similarity between two images we utilize the earth mover s distance which is good at handling variable length signatures the proposed image signature is evaluated in two different applications i e near duplicate document image retrieval and near duplicate natural image detection the promising experimental results demonstrate the validity and effectiveness of the proposed variable length signature

junctions detection classification and reconstruction junctions are important features for image analysis and form a critical aspect of image understanding tasks such as object recognition we present a unified approach to detecting classifying and reconstructing junctions in images our main contribution is a modeling of the junction which is complex enough to handle all these issues and yet simple enough to admit an effective dynamic programming solution we use a template deformation framework along with a gradient criterium to detect radial partitions of the template we use the minimum description length principle to obtain the optimal number of partitions that best describes the junction the kona detector presented by parida et al 1997 is an implementation of this model we demonstrate the stability and robustness of the detector by analyzing its behavior in the presence of noise using synthetic controlled apparatus we also present a qualitative study of its behavior on real images

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

an information fusion framework for robust shape tracking existing methods for incorporating subspace model constraints in shape tracking use only partial information from the measurements and model distribution we propose a unified framework for robust shape tracking optimally fusing heteroscedastic uncertainties or noise from measurement system dynamics and a subspace model the resulting nonorthogonal subspace projection and fusion are natural extensions of the traditional model constraint using orthogonal projection we present two motion measurement algorithms and introduce alternative solutions for measurement uncertainty estimation we build shape models offline from training data and exploit information from the ground truth initialization online through a strong model adaptation our framework is applied for tracking in echocardiograms where the motion estimation errors are heteroscedastic in nature each heart has a distinct shape and the relative motions of epicardial and endocardial borders reveal crucial diagnostic features the proposed method significantly outperforms the existing shape space constrained tracking algorithm due to the complete treatment of heteroscedastic uncertainties the strong model adaptation and the coupled tracking of double contours robust performance is observed even on the most challenging cases

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

antiextensive connected operators for image and sequence processing this paper deals with a class of morphological operators called connected operators these operators filter the signal by merging its flat zones as a result they do not create any new contours and are very attractive for filtering tasks where the contour information has to be preserved this paper shows that connected operators work implicitly on a structured representation of the image made of flat zones the max tree is proposed as a suitable and efficient structure to deal with the processing steps involved in antiextensive connected operators a formal definition of the various processing steps involved in the operator is proposed and as a result several lines of generalization are developed first the notion of connectivity and its definition are analyzed several modifications of the traditional approach are presented they lead to connected operators that are able to deal with texture they also allow the definition of connected operators with less leakage than the classical ones second a set of simplification criteria are proposed and discussed they lead to simplicity entropy and motion oriented operators the problem of using a nonincreasing criterion is analyzed its solution is formulated as an optimization problem that can be very efficiently solved by a viterbi 1979 algorithm finally several implementation issues are discussed showing that these operators can be very efficiently implemented

image stitching by line guided local warping with global similarity constraint abstract low textured image stitching remains a challenging problem it is difficult to achieve good alignment of images and it is easy to break images structures are often broken due to insufficient and unreliable point correspondences moreover because of the viewpoint variations between multiple images the stitched images suffer from projective distortions to solve these problems this paper presents a line guided local warping method with a global similarity constraint for image stitching line features which serve well for geometric descriptions and scene constraints are employed to guide image stitching accurately on one hand the line features are integrated into a local warping model through a designed weight function on the other hand line features are adopted to impose strong geometric constraints including line correspondence and line colinearity to improve the stitching performance through mesh optimization to mitigate projective distortions we adopt a global similarity constraint which is integrated with the projective warps via a designed weight strategy this constraint causes the final warp to slowly change from a projective to a similarity transformation across the image finally the images undergo a two stage alignment scheme that provides accurate alignment and reduces projective distortion we evaluate our method on a series of images and compare it with several other methods the experimental results demonstrate that the proposed method provides a convincing stitching performance and that it outperforms other state of the art methods

mtos a tree of shapes for multivariate images the topographic map of a gray level image also called tree of shapes provides a high level hierarchical representation of the image contents this representation invariant to contrast changes and to contrast inversion has been proved very useful to achieve many image processing and pattern recognition tasks its definition relies on the total ordering of pixel values so this representation does not exist for color images or more generally multivariate images common workarounds such as marginal processing or imposing a total order on data are not satisfactory and yield many problems this paper presents a method to build a tree based representation of multivariate images which features marginally the same properties of the gray level tree of shapes briefly put we do not impose an arbitrary ordering on values but we only rely on the inclusion relationship between shapes in the image definition domain the interest of having a contrast invariant and self dual representation of multivariate image is illustrated through several applications filtering segmentation and object recognition on different types of data color natural images document images satellite hyperspectral imaging multimodal medical imaging and videos

a probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix the perspective projections of n physical points on two views stereovision are constrained as soon as n 8 however to prove in practice the existence of a rigid motion between two images more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches in this paper we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points n and the accuracy of the matches this criterion yields an objective way to compare say precise matches of a few points and approximate matches of a lot of points it gives a yes no answer to the question could this rigid points correspondence have occurred by chance since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired it also yields absolute accuracy requirements for rigidity detection in the case of non matched points and optimal values of n depending on the expected accuracy of the matches and on the proportion of outliers we use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90 of outliers which outperforms the best currently known methods like m estimators lmeds classical ransac and tensor voting

singular value estimates of oblique projections abstract let w and m be two finite dimensional subspaces of a hilbert space h such that h w m and let p w m denote the oblique projection with range w and nullspace m in this article we get the following formula for the singular values of p w m 2 s k p w m 1 min f h x w m 2 where the minimum is taken over the set of all operator pairs f h on h such that r f w r h m and fh p w m and k 1 dim w we also characterize all the pairs where the minimum is attained

formes super irreductibles des systemes differentiels lineaires dans cet article nous donnons une generalisation du critere de j moser une suite d invariants associes a un system differentiel est definie ainsi qu un algorithme permettant de reduire le systeme differentiel sous une formesuper irreductible le calcul de ces invariants est alors immediat nous obtenons ainsi une classification plus generale de la singularite cf 11 ou on etudie le lien entre cette forme et le polygone de newton d un systeme differentiel lineaire l algorithme donne est programme dans un langage de calcul formel reduce

contrast invariant interest point detection by zero norm log filter the laplacian of gaussian log filter is widely used in interest point detection however low contrast image structures though stable and significant are often submerged by the high contrast ones in the response image of the log filter and hence are difficult to be detected to solve this problem we derive a generalized log filter and propose a zero norm log filter the response of the zero norm log filter is proportional to the weighted number of bright dark pixels in a local region which makes this filter be invariant to the image contrast based on the zero norm log filter we develop an interest point detector to extract local structures from images compared with the contrast dependent detectors such as the popular scale invariant feature transform detector the proposed detector is robust to illumination changes and abrupt variations of images experiments on benchmark databases demonstrate the superior performance of the proposed zero norm log detector in terms of the repeatability and matching score of the detected points as well as the image recognition rate under different conditions

extremal regions detection guided by maxima of gradient magnitude a problem of computer vision applications is to detect regions of interest under different imaging conditions the state of the art maximally stable extremal regions msers detects affine covariant regions by applying all possible thresholds on the input image and through three main steps including 1 making a component tree of extremal regions evolution 2 obtaining region stability criterion and 3 cleaning up the mser performs very well but it does not consider any information about the boundaries of the regions which are important for detecting repeatable extremal regions we have shown in this paper that employing prior information about boundaries of regions results in a novel region detector algorithm that not only outperforms mser but avoids the mser s rather complicated steps of enumeration and the cleaning up to employ the information about the region boundaries we introduce maxima of gradient magnitudes mgms which are shown to be points that are mostly around the boundaries of the regions having found the mgms the method obtains a global criterion for each level of the input image which is used to find extremum levels els the found els are then used to detect extremal regions the proposed algorithm which is called extremal regions of extremum levels erel has been tested on the public benchmark data set of mikolajczyk the obtained experimental results show that the inclusion of region boundaries through mgms results in a detector that detects regions with high repeatability scores and is more robust against noise compared with mser

a discrete expression of canny s criteria for step edge detector performances evaluation optimal filters for edge detection are usually developed in the continuous domain and then transposed by sampling to the discrete domain simpler filters are directly defined in the discrete domain we define criteria to compare filter performances in the discrete domain canny has defined 1983 1986 three criteria to derive the equation of an optimal filter for step edge detection good detection good localization and low responses multiplicity these criteria seem to be good candidates for filter comparison unfortunately they have been developed in the continuous domain and their analytical expressions cannot be used in the discrete domain we establish three criteria with the same meaning as canny s some comparisons with experimental results confirm the validity of our approach this study highlights the existence of two classes of derivative operators that are distinguished by whether or not the impulse response of the filter in continuous space domain is continuous on its center these classes exhibit very different properties for the second and third criteria we extend the use of the first and third criteria to the smoothing filters we also define an optimal continuous filter according to the continuous third criterion and an optimal discrete filter according to the discrete third criterion we compare the performances of the sampled version of the continuous filter to those of the optimal discrete filter

robust photometric invariant features from the color tensor luminance based features are widely used as low level input for computer vision applications even when color data is available the extension of feature detection to the color domain prevents information loss due to isoluminance and allows us to exploit the photometric information to fully exploit the extra information in the color data the vector nature of color data has to be taken into account and a sound framework is needed to combine feature and photometric invariance theory in this paper we focus on the structure tensor or color tensor which adequately handles the vector nature of color images further we combine the features based on the color tensor with photometric invariant derivatives to arrive at photometric invariant features we circumvent the drawback of unstable photometric invariants by deriving an uncertainty measure to accompany the photometric invariant derivatives the uncertainty is incorporated in the color tensor hereby allowing the computation of robust photometric invariant features the combination of the photometric invariance theory and tensor based features allows for detection of a variety of features such as photometric invariant edges corners optical flow and curvature the proposed features are tested for noise characteristics and robustness to photometric changes experiments show that the proposed features are robust to scene incidental events and that the proposed uncertainty measure improves the applicability of full invariants

detection localization and sex classification of faces from arbitrary viewpoints and under occlusion this paper presents a novel framework for detecting localizing and classifying faces in terms of visual traits e g sex or age from arbitrary viewpoints and in the presence of occlusion all three tasks are embedded in a general viewpoint invariant model of object class appearance derived from local scale invariant features where features are probabilistically quantified in terms of their occurrence appearance geometry and association with visual traits of interest an appearance model is first learned for the object class after which a bayesian classifier is trained to identify the model features indicative of visual traits the framework can be applied in realistic scenarios in the presence of viewpoint changes and partial occlusion unlike other techniques assuming data that are single viewpoint upright prealigned and cropped from background distraction experimentation establishes the first result for sex classification from arbitrary viewpoints an equal error rate of 16 3 percent based on the color feret database the method is also shown to work robustly on faces in cluttered imagery from the cmu profile database a comparison with the geometry free bag of words model shows that geometrical information provided by our framework improves classification a comparison with support vector machines demonstrates that bayesian classification results in superior performance

using simple decomposition for smoothing and feature point detection of noisy digital curves this correspondence presents an algorithm for smoothed polygonal approximation of noisy digital planar curves and feature point detection the resulting smoothed polygonal representation preserves the signs of the curvature function of the curve the algorithm is based on a simple decomposition of noisy digital curves into a minimal number of convex and concave sections the location of each separation point is optimized yielding the minimal possible distance between the smoothed approximation and the original curve curve points within a convex concave section are discarded if their angle signs do not agree with the section sign and if the resulted deviations from the curve are less than a threshold spl epsi which is derived automatically inflection points are curve points between pairs of convex concave sections and cusps are curve points between pairs of convex convex or concave concave sections corners and points of local minimal curvature are detected by applying the algorithm to respective total curvature graphs the detection of the feature points is based on properties of pairs of sections that are determined in an adaptive manner rather than on properties of single points that are based on a fixed size neighborhood the detection is therefore reliable and robust complexity analysis and experimental results are presented

polar decomposition of oblique projections the partial isometries and the positive semidefinite operators which appear as factors of polar decompositions of bounded linear idempotent operators in a hilbert space are characterized

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

tree based morse regions a topological approach to local feature detection this paper introduces a topological approach to local invariant feature detection motivated by morse theory we use the critical points of the graph of the intensity image revealing directly the topology information as initial interest points critical points are selected from what we call a tree based shape space in particular they are selected from both the connected components of the upper level sets of the image the max tree and those of the lower level sets the min tree they correspond to specific nodes on those two trees 1 to the leaves extrema and 2 to the nodes having bifurcation saddle points we then associate to each critical point the largest region that contains it and is topologically equivalent in its tree we call such largest regions the tree based morse regions tbmrs the tbmr can be seen as a variant of maximally stable extremal region mser which are contrasted regions contrarily to mser tbmr relies only on topological information and thus fully inherit the invariance properties of the space of shapes e g invariance to affine contrast changes and covariance to continuous transformations in particular tbmr extracts the regions independently of the contrast which makes it truly contrast invariant furthermore it is quasi parameter free tbmr extraction is fast having the same complexity as mser experimentally tbmr achieves a repeatability on par with state of the art methods but obtains a significantly higher number of features both the accuracy and robustness of tbmr are demonstrated by applications to image registration and 3d reconstruction

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

deformable kernels for early vision early vision algorithms often have a first stage of linear filtering that extracts from the image information at multiple scales of resolution and multiple orientations a common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs a technique is presented that allows 1 computing the best approximation of a given family using linear combinations of a small number of basis functions and 2 describing all finite dimensional families i e the families of filters for which a finite dimensional representation is possible with no error the technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations the relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi scale 2d edge detection kernels the implementation issues are also discussed

early jump out corner detectors the authors present two new corner detectors one works by using dissimilarity along the contour direction to detect curves in the image contour and the other estimates image curvature along the contour direction these operators are fast robust to noise and require no subjective thresholding

building the component tree in quasi linear time the level sets of a map are the sets of points with level above a given threshold the connected components of the level sets thanks to the inclusion relation can be organized in a tree structure that is called the component tree this tree under several variations has been used in numerous applications various algorithms have been proposed in the literature for computing the component tree the fastest ones considering the worst case complexity have been proven to run in o nln n in this paper we propose a simple to implement quasi linear algorithm for computing the component tree on symmetric graphs based on tarjan s union find procedure we also propose an algorithm that computes the n most significant lobes of a map

on super irreducible forms of linear differential systems with rational function coefficients consider a system of n linear first order differential equations d dx y a x y in which a x is an n n matrix of rational functions over a subfield f of the field c of complex numbers and let 1 d c be a set of conjugate singularities of this system i e poles of a x which are roots in c of some irreducible polynomial p x in f x we propose an algorithm for transforming the given system into an equivalent system over f x which is super irreducible in each element this algorithm does not require working in the algebraic extension f that appears when one applies hilali wazner s algorithm numer math 50 1987 429 successively with the individual singularities 1 d the transformation matrix as well as the resulting system have their coefficients in f x and all the computations are performed in f x p instead of the splitting field of p

frames of translates with prescribed fine structure in shift invariant spaces abstract for a given finitely generated shift invariant fsi subspace w l 2 r k we obtain a simple criterion for the existence of shift generated sg bessel sequences e f induced by finite sequences of vectors f w n that have a prescribed fine structure i e such that the norms of the vectors in f and the spectra of s e f are prescribed in each fiber of spec w t k we complement this result by developing an analogue of the so called sequences of eigensteps from finite frame theory in the context of sg bessel sequences that allows for a detailed description of all sequences with prescribed fine structure then given 1 n 0 we characterize the finite sequences f w n such that f i 2 i for 1 i n and such that the fine spectral structure of the shift generated bessel sequences e f has minimal spread i e we show the existence of optimal sg bessel sequences with prescribed norms in this context the spread of the spectra is measured in terms of the convex potential p w induced by w and an arbitrary convex function r r

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

focus of attention from local color symmetries in this paper a continuous valued measure for local color symmetry is introduced the new algorithm is an extension of the successful gray value based symmetry map proposed by reisfeld et al the use of color facilitates the detection of focus points fps on objects that are difficult to detect using gray value contrast only the detection of fps is aimed at guiding the attention of an object recognition system therefore fps have to fulfill three major requirements stability distinctiveness and usability the proposed algorithm is evaluated for these criteria and compared with the gray value based symmetry measure and two other methods from the literature stability is tested against noise object rotation and variations of lighting as a measure for the distinctiveness of fps the principal components of fp centered windows are compared with those of windows at randomly chosen points on a large database of natural images finally usability is evaluated in the context of an object recognition task

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

a novel image representation via local frequency analysis for illumination invariant stereo matching in this paper we propose a novel image representation approach to tackle illumination variations in stereo matching problems images are mapped using their fourier transforms which are convolved with a set of monogenic filters frequency analysis is carried out at different scales to account for most image content the phase congruency and the local weighted mean phase angle are then computed over all the scales the original image is transformed into a new representation using these two mappings this representation is invariant to illumination and contrast variations more importantly it is generic and can be used with most sparse as well as dense stereo matching algorithms in addition sequential feature matching or tracking can also benefit from our approach in varying radiometric conditions we demonstrate the improvements introduced with our image mappings on well established data sets in the literature as well as on our own experimental scenarios that include high dynamic range imagery the experiments include both dense and sparse stereo and sequential matching algorithms where the latter is considered in the very challenging visual odometry framework