the singular set of solutions to non differentiable elliptic systems we estimate the hausdorff dimension of the singular set of solutions to elliptic systems of the type if the vector fields a and b are holder continuous with respect to the variable x with exponent then the hausdorff dimension of the singular set of any weak solution is at most n 2

dominant dimension and tilting modules we study which algebras have tilting modules that are both generated and cogenerated by projective injective modules crawley boevey and sauter have shown that auslander algebras have such tilting modules and for algebras of global dimension 2 auslander algebras are classified by the existence of such tilting modules in this paper we show that the existence of such a tilting module is equivalent to the algebra having dominant dimension at least 2 independent of its global dimension in general such a tilting module is not necessarily cotilting here we show that the algebras which have a tilting cotilting module generated cogenerated by projective injective modules are precisely 1 minimal auslander gorenstein algebras when considering such a tilting module without the assumption that it is cotilting we study the global dimension of its endomorphism algebra and discuss a connection with the finitistic dimension conjecture furthermore as special cases we show that triangular matrix algebras obtained from auslander algebras and certain injective modules have such a tilting module we also give a description of which nakayama algebras have such a tilting module

a generalized depth estimation algorithm with a single image a depth estimation algorithm proposed by a p pentland 1987 is generalized in the proposed algorithm the raw image data in the vicinity of the edge is used to estimate the depth from defocus since no differentiation operation on the image data is required before the optimization process the method is less sensitive to the noise disturbance of measurements furthermore the edge orientation that was critical in pentland s approach will not be required in the case this algorithm is then applied to synthetic images containing various amounts of noise to test its performance experimental results indicate that the depth estimation errors are kept within 5 of true values on the average when it is applied to real images

on the discrete representation of the laplacian of gaussian the laplacian of gaussian log is commonly employed as a second order edge detector in image processing and it is popular because of its attractive scaling properties however its application within a finite sampled domain is non trivial due to its infinite extent heuristics are often employed to determine the required mask size and they may lead to poor edge detection and location we derive an explicit relationship between the size of the log mask and the probability of edge detection error introduced by its approximation providing a strong basis for its stable implementation in addition we demonstrate the need for bias correction to correct the offset error introduced by truncation and derive strict bounds on the scales that may be employed by consideration of the aliasing error introduced by sampling to characterise edges a zero crossing detector is proposed which uses a bilinear surface to guarantee detection and closure of edges these issues are confirmed by experimental results which particularly emphasise the importance of bias correction as such we give a new basis for implementation of the log edge detector and show the advantages that such analysis can confer

a theory of automatic parameter selection for feature extraction with application to feature based multisensor image registration this paper generalizes the previously developed automated edge detection parameter selection algorithm of yitzhaky and peli we generalize the approach to arbitrary multidimensional continuous or discrete parameter spaces and feature spaces this generalization enables use of the parameter selection approach with more general image features for use in feature based multisensor image registration applications we investigate the problem of selecting a suitable parameter space sampling density in the automated parameter selection algorithm a real valued sensitivity measure is developed which characterizes the effect of parameter space sampling on feature set variability closed form solutions of the sensitivity measure for special feature set relationships are derived we conduct an analysis of the convergence properties of the sensitivity measure as a function of increasing parameter space sampling density for certain parameter space sampling sequence types closed form expressions for the sensitivity measure limit values are presented we discuss an approach to parameter space sampling density selection which uses the sensitivity measure convergence behavior we provide numerical results indicating the utility of the sensitivity measure for selecting suitable parameter values

a moment based unified approach to image feature detection in this paper a novel model based approach is proposed for generating a set of image feature maps or primal sketches for each type of feature a piecewise smooth parametric model is developed to characterize the local intensity function in an image projections of the intensity profile onto a set of orthogonal zernike moment generating polynomials are used to estimate model parameters and in turn generate the desired feature map a small set of moment based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images one main advantage of using parametric model based techniques is that it is possible to extract complete information i e model parameters about the underlying image feature which is desirable in many high level vision tasks experimental results are included to demonstrate the effectiveness of proposed feature detectors

subpixel edge detection of color images by principal axis analysis and moment preserving principle this paper discusses a new approach for detecting edges with sub pixel accuracy in color images using the principal axis analysis and the moment preserving principle first the principal axis of the color vectors in a three dimensional space is obtained analytically for each image block based on the projection scores the direction of the line edge is obtained by analyzing the three dimensional principal axis of a color image block next by preserving some spatial color moments of the pixels of each square block analytic formulas are derived to extract the edge feature experiments on both synthetic and real images show that the accuracy of the proposed method is comparable to other color edge detectors the proposed algorithm can be performed very fast for real time applications with no need for special hardware

detecting the wheel pattern of a vehicle using stereo images abstract this paper presents a method for detecting the wheels of a vehicle in stereo image pairs the method consists of two steps i geometrical transformation and ii circle extraction the geometrical transformation uses the disparity values obtained from a stereo image pair to calculate the parameters of the plane containing wheels of the vehicle by using these parameters we transform any elliptical wheels contained in the plane to circular ones which can be extracted by the circle extraction algorithm the circle extraction algorithm consists of 1 template matching and 2 hough transform in order to save computation and improve the results in the hough transform we employ two constraints a the neighbor region edge connectivity and b the gradient direction of each edge point to eliminate non circular edge points experimental results show that these two constraints do eliminate non circular edge points and preserve any circle embedded in edges from the final results we can observe that our method can detect and locate the wheels of a vehicle successfully

relaxation labeling in stereo image matching this paper outlines a method for solving the global stereovision matching problem using edge segments as the primitives a relaxation scheme is the technique commonly used by existing methods to solve this problem these techniques generally impose the following competing constraints similarity smoothness ordering and uniqueness and assume a bound on the disparity range the smoothness constraint is basic in the relaxation process we have verified that the smoothness and ordering constraints can be violated by objects close to the cameras and that the setting of the disparity limit is a serious problem this problem also arises when repetitive structures appear in the scene i e complex images where the existing methods produce a high number of failures we develop our approach from a relaxation labeling method 1 w j christmas j kittler m petrou structural matching in computer vision using probabilistic relaxation ieee trans pattern anal mach intell 17 8 1995 749 764 which allows us to map the above constraints the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem produced by the required fixation of a disparity limit consequently we improve the stereovision matching process a better performance of the proposed method is illustrated by comparative analysis against some recent global matching methods

asymptotically regular problems i higher integrability abstract we consider weak solutions u of non linear systems of partial differential equations assuming that the system exhibits a certain kind of elliptic behavior near infinity we prove higher integrability results for the gradient du in particular we establish holder continuity of u in low dimensions moreover we obtain analogous results for vectorial minimizers of multi dimensional variational integrals finally we discuss an extension to minimizing sequences and applications to generalized minimizers

relaxation by hopfield network in stereo image matching abstract this paper outlines a relaxation approach using the hopfield neural network for solving the global stereovision matching problem the primitives used are edge segments the similarity smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem we combine two methods a optimization relaxation 1 and b relaxation merit 2 with the above three constraints mapped in an energy function the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit so we improve the stereovision matching process a better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method

3 d information derivation from a pair of binocular images abstract a new scheme using a pair of stereo images for 3 d information derivation about a scene is presented first we establish a triangulation geometry between two camera models and a point in 3 d scene in this scheme the successful implementation of a matching algorithm of features in images is considered as the key step of stereovision analysis after a brief discussion of feature extraction representation and internal implementation an efficient stereo feature matching algorithm is proposed finally some results obtained by applying the matching algorithm to several pairs of stereo images are shown in the paper

modeling edges at subpixel accuracy using the local energy approach in this paper we describe a new technique for id and 2d edge feature extraction to subpixel accuracy using edge models and the local energy approach a candidate edge is modeled as one of a number of parametric edge models and the fit is refined by a least squared error fitting technique

active tracking strategy for monocular depth inference over multiple frames the extraction of depth information from a sequence of images is investigated an algorithm that exploits the constraint imposed by active motion of the camera is described within this framework in order to facilitate measurement of the navigation parameters a constrained egomotion strategy was adopted in which the position of the fixation point is stabilized during the navigation in an anthropomorphic fashion this constraint reduces the dimensionality of the parameter space without increasing the complexity of the equations a further distinctive point is the use of two sampling rates the faster related to the computation of the instantaneous optical flow is fast enough to allow the local operator to sense the passing edge or in other words to allow the tracking of moving contour points while the slower used to perform the triangulation procedure necessary to derive depth is slow enough to provide a sufficiently large baseline for triangulation experimental results on real image sequences are presented

finitistic dimension and igusa todorov algebras abstract the notion of igusa todorov algebras is introduced in connection with the little finitistic dimension conjecture and the conjecture is proved for those algebras such algebras contain many known classes of algebras over which the finitistic dimension conjecture holds e g algebras with the representation dimension at most 3 algebras with radical cube zero monomial algebras and left serial algebras etc it is an open question whether all artin algebras are igusa todorov we provide some methods to construct many new classes of 2 igusa todorov algebras and thus obtain many algebras such that the finitistic dimension conjecture holds in particular we show that the class of 2 igusa todorov algebras is closed under taking endomorphism algebras of projective modules hence if all quasi hereditary algebras are 2 igusa todorov then all artin algebras are 2 igusa todorov by v dlab c m ringel every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring proc amer math soc 107 1 1989 1 5 and have finite finitistic dimension

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

fuzzy cognitive maps for stereovision matching this paper outlines a method for solving the stereovision matching problem using edge segments as the primitives in stereovision matching the following constraints are commonly used epipolar similarity smoothness ordering and uniqueness we propose a new matching strategy under a fuzzy context in which such constraints are mapped the fuzzy context integrates both fuzzy clustering and fuzzy cognitive maps with such purpose a network of concepts nodes is designed each concept represents a pair of primitives to be matched each concept has associated a fuzzy value which determines the degree of the correspondence the goal is to achieve high performance in terms of correct matches the main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped initially each concept value is loaded via the fuzzy clustering and then updated by the fuzzy cognitive maps framework this updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved under this fuzzy approach we gain quantitative and qualitative matching correspondences this method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods

one pixel wide closed boundary identification an appropriate space of one pixel wide closed opwc boundary configurations is explicitly defined and an automatic algorithm to obtain opwc contour estimates from a segmented image is presented the motivation is to obtain a reasonable starting estimate for a markov chain monte carlo based mcmc based boundary optimization algorithm

the singular set of ω minima we consider minima open image in new window of convex variational integrals in the vectorial case n n 2 and we provide estimates for the hausdorff dimension of their singular sets

image smoothing and edge detection by hermite integration in the present paper we propose hermite polynomial integration method for gaussian and gaussian derivatives filtering in image smoothing and edge detection hermite integration method for one dimensional 1d gaussian filtering is at first introduced and its performance is analysed the hermite method is then generalized to gaussian derivative filtering and to multi dimensional cases application for edge detection with a subpixel precision is presented as well experimental results which confirm the theoretical analysis are reported

detection of intensity changes with subpixel accuracy using laplacian gaussian masks we present a system that takes a gray level image as input locates edges with subpixel accuracy and links them into lines edges are detected by finding zero crossings in the convolution of the image with laplacian of gaussian log masks the implementation differs markedly from m i t s as we decompose our masks exactly into a sum of two separable filters instead of the usual approximation by a difference of two gaussians dog subpixel accuracy is obtained through the use of the facet model 1 we also note that the zero crossings obtained from the full resolution image using a space constant for the gaussian and those obtained from the 1 n resolution image with 1 n pixel accuracy and a space constant of n for the gaussian are very similar but the processing times are very different finally these edges are grouped into lines using the technique described in 2

auslander gorenstein algebras and precluster tilting abstract we generalize the notions of n cluster tilting subcategories and selfinjective algebras into n precluster tilting subcategories and n selfinjective algebras where we show that a subcategory naturally associated to n precluster tilting subcategories has a higher auslander reiten theory furthermore we give a bijection between n precluster tilting subcategories and n minimal auslander gorenstein algebras which is a higher dimensional analog of auslander solberg correspondence 8 as well as a gorenstein analog of n auslander correspondence 22 the auslander reiten theory associated to an n precluster tilting subcategory is used to classify the n minimal auslander gorenstein algebras into four disjoint classes our method is based on relative homological algebra due to auslander solberg

on quiver grassmannians and orbit closures for representation finite algebras we show that auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective injective its endomorphism ring is called the projective quotient algebra for any representation finite algebra we use the projective quotient algebra to construct desingularizations of quiver grassmannians orbit closures in representation varieties and their desingularizations this generalizes results of cerulli irelli feigin and reineke

on the location error of curved edges in low pass filtered 2 d and 3 d images the authors study the location error of curved edges in two and three dimensional images after analog and digital low pass filtering the zero crossing of a second derivative filter is a well known edge localization criterion the second derivative in gradient direction sdgd produces a predictable bias in edge location towards the centers of curvature while the linear laplace filter produces a shift in the opposite direction their sum called plus plus laplace sdgd leads to an edge detector that finds curved edges one order more accurately than its constituents this argument holds irrespective of the dimension the influence of commonly used low pass filters such as the psf originating from diffraction limited optics using incoherent light 2 d the gaussian filter with variable cutoff point d d and the isotropic uniform filter d d is studied

on achievable accuracy in edge localization edge localization occurs when an edge detector determines the location of an edge in an image the authors use statistical parameter estimation techniques to derive bounds on achievable accuracy in edge localization these bounds known as the cramer rao bounds reveal the effect on localization of factors such as signal to noise ratio snr extent of edge observed scale of smoothing filter and a priori uncertainty about edge intensity by using continuous values for both image coordinates and intensity the authors focus on the effect of these factors prior to sampling and quantization they also analyze the canny algorithm and show that for high snr its mean squared error is only a factor of two higher than the lower limit established by the cramer rao bound although this is very good the authors show that for high snr the maximum likelihood estimator which is also derived virtually achieves the lower bound

building surfaces of evolution the weaving wall this paper describes a three dimensional surface construction process designed for the analysis of image sequences named the weaving wall the process operates over images as they arrive from a sensor knitting together along a parallel frontier connected descriptions of images as they evolve over time although the weaving wall was developed to support a tracking mechanism for recovering the three dimensional structure of a scene being traversed other applications of the surface building process have since become apparent these include rendering and computation on tomographic medical data display of higher dimensional analytic functions edge detection on the scale space surface and display and analysis of material fracture data more generally the weaving wall may be of use in representing the evolution of any two dimensional imagery varying in a nearly continuous manner along a third dimension we are currently looking into extending the processing to higher dimensions

edge detection and linear feature extraction using a 2 d random field model the edge detection problem is posed as one of detecting step discontinuities in the observed correlated image using directional derivatives estimated with a random field model specifically the method consists of representing the pixels in a local window by a 2 d causal autoregressive ar model whose parameters are adaptively estimated using a recursive least squares algorithm the directional derivatives are functions of parameter estimates an edge is detected if the second derivative in the direction of the estimated maximum gradient is negatively sloped and the first directional derivative and a local estimate of variance satisfy some conditions because the ordered edge detector may not detect edges of all orientations well the image scanned in four different directions and the union of the four edge images is taken as the final output the performance of the edge detector is illustrated using synthetic and real images comparisons to other edge detectors are given a linear feature extractor that operates on the edges produced by the ar model is presented

a new learning strategy for stereo matching derived from a fuzzy clustering method this paper presents an approach to the local stereo correspondence problem the primitives or features used are groups of collinear connected edge points called segments each segment has several associated attributes or properties we have verified that the differences of the attributes for the true matches cluster in a cloud around a center then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center the correspondence is established in the basis of the minimum distance criterion similarity constraint we have designed an image understanding system to learn the best representative cluster center for such purpose a new learning method is derived from the fuzzy c means fcm algorithm where the dispersion of the true samples in the cluster is taken into account through the mahalanobis distance this is the main contribution of this paper a better performance of the proposed local stereo matching learning method is illustrated with a comparative analysis between classical local methods without learning

on the edge location error for local maximum and zero crossing edge detectors examines the localization criterion for edge detection and determine the probability density function describing the edge location error canny 1986 defines the measure of localization as the reciprocal of the root mean square edge location error and formulates an expression of this measure for local maximum detectors however tagare and defigueiredo 1990 point out that an incorrect assumption is made in the calculation the same procedure is used by sarkar and boyer 1991 for their localization measure for zero crossing detectors we modify the analysis and obtain a closed form solution of the probability density function of the edge location error examination of the density function indicates the variance of the edge location error does not exist and hence cannot be used directly as a measure of localization

subpixel measurements using a moment based edge operator recent results in precision measurements using computer vision are presented an edge operator based on two dimensional spatial moments is given the operator can be implemented for virtually any size of window and has been shown to locate edges in digitized images to a twentieth of a pixel this accuracy is unaffected by additive or multiplicative changes to the data values the precision is achieved by correcting for many of the deterministic errors caused by nonideal edge profiles using a lookup table to correct the original estimates of edge orientation and location this table is generated using a synthesized edge which is located at various subpixel locations and various orientations the operator is extended to accommodate nonideal edge profiles and rectangularly sampled pixels the technique is applied to the measurement of imaged machined metal parts theoretical and experimental noise analyses show that the operator has relatively small bias in the presence of noise

fast convolution with laplacian of gaussian masks we present a technique for computing the convolution of an image with log laplacian of gaussian masks it is well known that a log of variance a can be decomposed as a gaussian mask and a log of variance 1 we take advantage of the specific spectral characteristics of these filters in our computation the log is a bandpass filter we can therefore fold the spectrum of the image after low pass filtering without loss of information which is equivalent to reducing the resolution we present a complete evaluation of the parameters involved together with a complexity analysis that leads to the paradoxical result that the computation time decreases when increases we illustrate the method on two images

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

the singular set of minima of integral functionals in this paper we provide upper bounds for the hausdorff dimension of the singular set of minima of general variational integrals open image in new window where f is suitably convex with respect to dv and holder continuous with respect to x v in particular we prove that the hausdorff dimension of the singular set is always strictly less than n where open image in new window

directional analysis of images in scale space the authors propose a computational technique for the directional analysis of piecewise linear patterns in images based on the notion of zero crossings in gradient images a given image is preprocessed by a sequence of filters that are second derivatives of 2 d gaussian functions with different scales this gives a set of zero crossing maps the scale space from which a stability map is generated significant linear patterns are detected from measurements on the stability map information regarding orientation of the linear patterns in the image and the area covered by the patterns in specific directions is then computed the performance of the method is illustrated through applications to a simple test image made up of straight bar patterns as well as to scanning electron microscope images of collagen fibrils in rabbit ligaments the method has significant applications in quantitative analysis of ligament healing and in comparison of treatment methods for ligament injuries

fast computation of a contrast invariant image representation this paper sets out a new representation of an image which is contrast independent the image is decomposed into a tree of shapes based on connected components of level sets which provides a full and nonredundant representation of the image a fast algorithm to compute the tree the fast level lines transform fllt is explained in detail some simple and direct applications of this representation are shown

stereo correspondence by surface reconstruction an algorithm that solves the computational stereo correspondence and the surface reconstruction is presented the algorithm integrates the reconstruction process in the correspondence analysis by means of multipass attribute matching and disparity refinement in the matching process the requirement of attribute similarity is relaxed with the pass number while the requirement for agreement between the predicted and the measured disparity is tightened disparity discontinuities and occluded areas are detected by analyzing the partial derivatives of the reconstructed disparity surface results on synthetic and on real stereo image pairs are reported

estimation of optical flow based on higher order spatiotemporal derivatives in interlaced and non interlaced image sequences abstract this contribution 1 investigates local differential techniques for estimating optical flow and its derivatives based on the brightness change constraint by using the tensor calculus representation we build the taylor expansion of the gray value derivatives as well as of the optical flow in a spatiotemporal neighborhood such a formulation provides a unifying framework for all existing local differential approaches and allows to derive new systems of equations for the estimation of the optical flow and of its derivatives we also tested various optical flow estimation approaches on real image sequences recorded by a calibrated camera which was fixed on the arm of a robot by moving the arm of the robot along a precisely defined trajectory we can determine the true displacement rate of scene surface elements projected into the image plane and compare it quantitatively with the results of different optical flow estimators since the optical flow estimators are based on gray value derivatives of up to fourth order we were forced to develop modified gaussian derivative filters to obtain acceptable estimates for the derivatives further we show quantitatively that these filters contribute to a much more robust optical flow estimation in addition successive lines of tv cameras have an offset in time due to the interlace technique we demonstrate the adaptation of filter kernels for estimating higher order spatiotemporal derivatives in interlaced image sequences

a global sparse gradient based coupled system for image denoising abstract we consider a coupled system for image denoising which consists of an anisotropic diffusion equation and a global sparse gradient model gsg the global sparse gradient model is used to estimate the edge map from the noisy image accurately and robustly the anisotropic diffusion process is guided by the edge map furthermore we prove the existence and uniqueness of the solutions of the coupled system with dirichlet initial boundary value problem finally comparing with the edge indicators based on local methods experimental results demonstrate that our proposed method has the state of the art performance among the pde based anisotropic diffusion approaches both in objective measurement and visual evaluation

an edge detection technique using the facet model and parameterized relaxation labeling we present a method for detecting and labeling the edge structures in digital gray scale images in two distinct stages first a variant of the cubic facet model is applied to detect the location orientation and curvature of the putative edge points next a relaxation labeling network is used to reinforce meaningful edge structures and suppress noisy edges each node label of this network is a 3d vector parameterizing the orientation and curvature information of the corresponding edge point a hysteresis step in the relaxation process maximizes connected contours for certain types of images prefiltering by adaptive smoothing improves robustness against noise and spatial blurring

subpixel edge location in binary images using dithering this paper concerns the problem of obtaining subpixel estimates of the locations of straight edges in binary digital images using dithering by adding uniformly distributed independent random noise it is shown that estimation bias may be removed and that the estimation variance is inversely proportional to the length of the line segment the sensitivity to incorrect dither amplitude is calculated and implementation is discussed

upper bounds for the dominant dimension of nakayama and related algebras abstract optimal upper bounds are provided for the dominant dimensions of nakayama algebras and more general algebras a with an idempotent e such that there is a minimal faithful injective projective module ea and such that eae is a nakayama algebra this answers a question of abrar and proves a conjecture of yamagata for monomial algebras

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

higher auslander algebras admitting trivial maximal orthogonal subcategories abstract in this paper we prove that is an n 1 auslander artinian algebra with gl dim n 2 admitting a trivial maximal n 1 orthogonal subcategory of mod if and only if it is morita equivalent to a finite product of f and f f 0 0 0 0 f f 0 0 0 0 f 0 0 0 0 0 f f 0 0 0 0 f n 1 n 1 where f is a division algebra in addition we obtain a necessary condition for an auslander artinian algebra admitting a non trivial maximal 1 orthogonal subcategory

optimally isotropic laplacian operator laplacian operators used in the literature for digital image processing are not rotationally invariant we examine the anisotropy of 3 spl times 3 laplacian operators for images quantized in square pixels and find the operator which has the minimum overall anisotropy

lower bounds for auslander s representation dimension the notion of representation dimension of a finite dimensional algebra has been introduced by auslander he has shown that an algebra is of finite representation type if and only if its representation dimension is at most two he has expected that the representation dimension of a representation infinite algebra should measure how far this algebra is from being representation finite in many cases and thanks to iyama also in general upper bounds for the representation dimension are known however there are non trivial lower bounds only for two similarly constructed series of algebras in this thesis new lower bounds for auslander s representation dimension are constructed and more general methods are developed first we consider group algebras of elementary abelian groups we show that their representation dimension is greater than the rank of the group this leads to a proof of a conjecture of benson concerning the loewy length of blocks of group algebras then a notion of dimension of a module category is introduced this notion enables us to find better lower bounds for the representation dimension in particular it allows us for the first time to determine the value of the representation dimension of non self injective algebras of representation dimension greater than three finally we give a general criterion for finding lower bounds for auslander s representation dimension suppose there is a family of modules such that sufficiently many members of the family have certain d extensions then the representation dimension of the algebra is at least d 2 we illustrate how this criterion is applied on some interesting families of algebras it turns out that the lower bound is often the precise value of the representation dimension

tracking a smooth fault line in a response surface we suggest a sequential or tracking algorithm for estimating a smooth fault line in a response surface the method starts with an approximation to a point on the line and from there the line is tracked as it meanders through the plane the technique differs from recent approaches in that it does not require a large part of the plane to be searched for evidence of a fault line this offers potential computational savings and produces a method that is invariant under rotations of coordinate axes except insofar as a rotation might affect the estimated starting point and the relative orientation of the grid on which calculations are done that feature is important if design points are not located on a regular grid we investigate properties of the method under very general conditions on the design allowing poisson cluster processes jiggled grid processes and deterministic regular lattices uniform rates of convergence are derived in all these settings for the case of noisy data and shown to be within logarithmic factors of optimal pointwise convergence rates in the no noise setting

unified detection of skewed rotation reflection and translation symmetries from affine invariant contour features symmetry detection is significant for object detection and recognition since symmetries are salient cues for distinguishing geometrical structures from cluttered backgrounds this paper proposes a unified framework to detect rotation reflection and translation symmetries simultaneously on unsegmented real world images the detection is performed based on affine invariant contour features and is applicable under skewed imaging with distortions contours on a natural image are first matched to each other to find affine invariant matching pairs which are then classified into three groups using a sign change criterion corresponding to the three types of symmetries the three groups are used to vote for the corresponding symmetries the voting for rotation utilizes a scheme of short line segments the voting for reflection is based on a parameterization of axis equation and the voting for translation uses a cascade like approach experimental results of real world images are provided with quantitative evaluations validating that the proposed framework achieves desired performance

some defects in finite difference edge finders this work illustrates and explains various artifacts in the output of five finite difference edge finders those of j f canny 1983 1986 r a boie et al 1986 and r a boie and i j cox 1987 and three variations on that of d marr and e c hildreth 1980 reimplemented with a common output format and method of noise suppression these artifacts include gaps in boundaries spurious boundaries and deformation of region shape

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

1 auslander gorenstein algebras which are tilted abstract let be a 1 auslander gorenstein algebra we give a necessary and sufficient condition for to be a tilted algebra

a refined algorithm for multisensor image registration based on pixel migration multimodality image registration via pixel migration is a powerful approach however it suffers from a serious problem the global maximum on the sum of squared gradient magnitude ssg surface does not correspond to the correct solution of registration to solve the problem we partition the search space into feasible and infeasible regions the genetic algorithm global optimizer is used to obtain a good initial estimate of registration parameters and followed by a fast refining with powell s approach local optimizer the experimental results demonstrate that the use of this modified pixel migration algorithm on multisensor image registration is very effective

the position orientation masking approach to parametric search for template matching a new search method over x y spl theta called position orientation masking is introduced it is applied to vertices that are allowed to be separated into different bands of acuteness position orientation masking yields exactly one spl theta value for each x y that it considers to be the location of a possible occurrence of an object detailed matching of edge segments is performed at only these candidate x y spl theta to determine if objects actually do occur there template matching is accelerated dramatically since the candidates comprise only a small fraction of all x y spl theta position orientation masking eliminates the need for exhaustive search when deriving the candidate x y spl theta search is guided by correlations between template vertices and distance transforms of image vertices when a poor correlation is encountered at a particular position and orientation nearby positions at that orientation and nearby orientations at that position are masked out position and orientation traversal are by quadrant and binary decomposition

robust and fast computation of edge characteristics in image sequences in this paper we consider a non parametric analytical model of the intensity for a curved edge and derive the relations between the image data and some local characteristics of the edge in the discrete case in order to identify this model we also study how to develop high order non biased spatial derivative operators with subpixel accuracy in fact this discrete approach corresponds to the notion of spatio temporal surfaces in the continuous case and provides a way to obtain some of the spatio temporal parameters from an image sequence an implementation is proposed and experimental data are provided

dominant dimension and idempotent ideals abstract let a be a finite dimensional algebra over a field k in this paper we study dominant dimension from the point of view of the idempotent ideals the canonical a bimodule v hom a d a a was studied in 8 11 9 where d hom k k under certain condition we give a new understanding that d a a v is isomorphic to an idempotent ideal tensor product itself as a bimodules and show that the double dual functor is defined by d a a v we also give a characterization of dominant dimension for a in terms of vanishing of certain extension groups over a which just uses a and da as ingredients and generalizes the corresponding characterizations given in 8 9 moreover we show that a is a motita algebra if and only if there is a natural isomorphism 1 on a mod where is the nakayama functor

non lipschitz minimizers of smooth uniformly convex functionals we construct non lipschitz minimizers of smooth uniformly convex functionals of type i u f du x dx our method is based on the use of null lagrangians

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

multiple widths yield reliable finite differences computer vision a finite difference edge finder in which the finite difference is computed at a range of widths i e a range of distances between data points is introduced wide operators report low amplitude responses more reliably than narrow operators so if wide operators are used to fill gaps in narrow operator responses each operator can be restricted to report only statistically reliable responses without losing many real features this sharply reduces the noise in the final output theoretical bounds on spurious responses in the finite difference outputs given only weak assumptions about the signal and noise are presented the expected response of the edge finder to an ideal straight step edge is also analyzed these performance measures are compared with those of a standard algorithm based on gaussian smoothing and those of a second algorithm that also considers the spatial structure of noise the algorithms prove equally good at suppressing noise but are better able to detect faint or blurred features these predictions are confirmed by empirical tests on real images