cyclic homology comodules and mixed complexes relating cyclic and hochschild homology one can see that any formula for hc a a will not only involve hc a and hc a but also the periodicity operator s and the hochschild groups fortunately if the map s brings in some complications it also endows hc a with a comodule structure over the cyclic homology of the ground ring k actually the comodule structure exists already on the complex level a convenient complex on which s has the form of a canonical surjection is connes s double complex with differentials b and b now the idea is to view the cyclic homology of an algebra as a composite functor

transition thresholds and transition operators for binarization and edge detection the transition method for image binarization is based on the concept of t transition pixels a generalization of edge pixels and t transition sets we introduce a novel unsupervised thresholding for unimodal histograms to estimate the transition sets we also present dilation and incidence transition operators to refine the transition set afterward we propose the simple edge transition operator for detecting edges our experiments show that the new approach increases the effectiveness of ocr applications outperforming several top ranked binarization algorithms

3 d image denoising by local smoothing and nonparametric regression three dimensional 3 d images are becoming increasingly popular in image applications such as magnetic resonance imaging mri functional mri fmri and other image applications observed 3 d images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses in the literature most existing image denoising methods are for 2 d images their direct extensions to 3 d cases generally cannot handle 3 d images efficiently because the structure of 3 d images is often substantially more complicated than that of 2 d images for instance edge locations are surfaces in 3 d cases which are much more challenging to handle compared to edge curves in 2 d cases in this article we propose a novel 3 d image denoising procedure based on nonparametric estimation of a 3 d jump surface from noisy data one important feature of this method is its ability to preserve edges and major edge structures such as intersections of two edge surfaces pyramids pointed corn

cyclic homology of hopf crossed products abstract we obtain a mixed complex simpler than the canonical one given the hochschild cyclic negative and periodic homology of a crossed product e a f h where h is an arbitrary hopf algebra and f is a convolution invertible cocycle with values in a we actually work in the more general context of relative cyclic homology specifically we consider a subalgebra k of a which is stable under the action of h and we find a mixed complex computing the hochschild cyclic negative and periodic homology of e relative to k as an application we obtain two spectral sequences converging to the cyclic homology of e relative to k the first one works in the general setting and the second one which generalizes those previously found by several authors works when f takes its values in k

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

artistic edge and corner enhancing smoothing two important visual properties of paintings and painting like images are the absence of texture details and the increased sharpness of edges as compared to photographic images painting like artistic effects can be achieved from photographic images by filters that smooth out texture details while preserving or enhancing edges and corners however not all edge preserving smoothers are suitable for this purpose we present a simple nonlinear local operator that generalizes both the well known kuwahara filter and the more general class of filters known in the literature as ldquocriterion and value filter structure rdquo this class of operators suffers from intrinsic theoretical limitations which give rise to a dramatic instability in presence of noise especially on shadowed areas such limitations are discussed in the paper and overcome by the proposed operator a large variety of experimental results shows that the output of the proposed operator is visually similar to a painting comparisons with existing techniques on a large set of natural images highlight conditions on which traditional edge preserving smoothers fail whereas our approach produces good results in particular unlike many other well established approaches the proposed operator is robust to degradations of the input image such as blurring and noise contamination

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

a jbig based approach to the encoding of contour maps previously a new technique for the lossless encoding of contour maps was introduced based on the concept of transition points in this paper we show that by using a simple representation for the transition points i e the map of transition points the problem of encoding arbitrary contour maps can be easily converted into a problem of lossless image coding experimental results show that the joint bilevel image experts group jbig image coding standard can be used successfully for encoding maps of transition points outperforming in most cases differential chain coding moreover if we take into account that jbig codecs are available as off the shelf components then the effort required to implement the proposed method is small

a multiscale edge detection algorithm based on wavelet domain vector hidden markov tree model abstract the wavelet analysis is an efficient tool for the detection of image edges based on the wavelet analysis we present an unsupervised learning algorithm to detect image edges in this paper a wavelet domain vector hidden markov tree wd vhmt is employed in our algorithm to model the statistical properties of multiscale and multidirectional subband wavelet coefficients of an image with this model each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge the wd vhmt model can be learned by an expectation maximization algorithm after the model is learned we employ an extended viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation the experiment results of the edge detection for several images are provided to evaluate our algorithm

minimal multi element stochastic collocation for uncertainty quantification of discontinuous functions we propose a multi element stochastic collocation method that can be applied in high dimensional parameter space for functions with discontinuities lying along manifolds of general geometries the key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized on each of the resulting elements the function is smooth and can be approximated using high order methods with fast convergence properties the decomposition strategy is in direct contrast to the traditional multi element approaches which define the sub domains by repeated splitting of the axes in the parameter space such methods are more prone to the curse of dimensionality because of the fast growth of the number of elements caused by the axis based splitting the present method is a two step approach firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth the detector uses an efficient combination of the high order polynomial annihilation technique along with adaptive sparse grids and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low dimensional after partitioning an adaptive technique based on the least orthogonal interpolant is used to construct a generalized polynomial chaos surrogate on each element the adaptive technique reuses all information from the partitioning and is variance suppressing we present numerous numerical examples that illustrate the accuracy efficiency and generality of the method when compared against standard locally adaptive sparse grid methods the present method uses many fewer number of collocation samples and is more accurate

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

residual analysis for feature detection it is shown that in a very simple form residual analysis achieves results that are at least as good as if not better than those obtained by other techniques there are many ways for extensions of the method for example moving average filters of regularization can be used to obtain the residual images also the strength of the correlation measured by d sub rr o can be used to eliminate noise weak edges etc a more ambitious extension is by considering smoothing filters that leave invariant the function representing the reflectance from smooth surfaces

image enhancement based on a nonlinear multiscale method an image enhancement method that reduces speckle noise and preserves edges is introduced the method is based on a new nonlinear multiscale reconstruction scheme that is obtained by successively combining each coarser scale image with the corresponding modified interscale image simulation results are included to demonstrate the performance of the proposed method

the 3d line motion matrix and alignment of line reconstructions we study the problem of aligning two 3d line reconstructions in projective affine metric or euclidean space we introduce the 6 6 3d line motion matrix that acts on plucker coordinates we characterize its algebraic properties and its relation to the usual 4 4 point motion matrix and propose various methods for estimating 3d motion from line correspondences based on cost functions defined in images or 3d space we assess the quality of the different estimation methods using simulated data and real images

an edge detection technique using genetic algorithm based optimization abstract in this paper we present a genetic algorithm based optimization technique for edge detection the problem of edge detection is formulated as one of choosing a minimum cost edge configuration the edge configurations are viewed as two dimensional chromosomes with fitness values inversely proportional to their costs the design of the crossover and the mutation operators in the context of the two dimensional chromosomal representation is described the knowledge augmented mutation operator which exploits knowledge of the local edge structure is shown to result in rapid convergence the incorporation of meta level operators and strategies such as the elitism strategy the engineered conditioning operator and adaptation of mutation and crossover rates in the context of edge detection are discussed and are shown to improve the convergence rate the genetic algorithm with various combinations of meta level operators is tested on synthetic and natural images the performance of the genetic algorithm based cost minimization technique is compared both qualitatively and quantitatively with local search based and simulated annealing based cost minimization approaches the genetic algorithm based technique is shown to perform very well in terms of robustness to noise rate of convergence and quality of the final edge image

3d object classification using multi object kohonen networks the problem of three dimensional planar faced opaque object recognition from one single perspective view is addressed in this paper a view parameterization based on hough transform is described classification is accomplished by multiple multi object kohonen networks a new object grouping criterion has been investigated to assign disjoint subsets of objects to each kohonen network of the system on the basis of input space topology recognition tests are presented on both synthetic and real world 3d objects even in the presence of partial occlusion

hopf cyclic homology and relative cyclic homology of hopf galois extensions let h be a hopf algebra and let mathcal m s h be the category of all left h modules and right h comodules satisfying appropriate compatibility relations an object in mathcal m s h will be called a stable anti yetter drinfeld module over h or a sayd module for short to each m in mathcal m s h we associate in a functorial way a cyclic object mathrm z ast h m we show that our construction can be used to compute the cyclic homology of the underlying algebra structure of h and the relative cyclic homology of h galois extensions let k be a hopf subalgebra of h for an arbitrary m in mathcal m s k we define a right h comodule structure on mathrm ind k h m h otimes k m so that mathrm ind k h m becomes an object in mathcal m s h under some assumptions on k and m we compute the cyclic homology of mathrm z ast h mathrm ind k h m as a direct application of this result we describe the relative cyclic homology of strongly graded algebras in particular we calculate the cyclic homology of group algebras and quantum tori finally when h is the enveloping algebra of a lie algebra mathfrak g we construct a spectral sequence that converges to the cyclic homology of h with coefficients in a given sayd module m we also show that the cyclic homology of almost symmetric algebras is isomorphic to the cyclic homology of h with coefficients in a certain sayd module

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

bayesian wavelet method for multivariate model assessment of dynamic systems abstract in this paper an energy based bayesian wavelet method is presented for validation assessment of multivariate predictive models under uncertainty using time series data collected from a dynamic system time history data are decomposed into multiple time frequency resolutions using a discrete wavelet packet transform method as a signal feature wavelet packet component energy is computed in terms of the decomposed coefficients the effectiveness of the selected feature is assessed using both cross correlation and cross coherence metrics a generalized likelihood ratio is derived as a quantitative validation metric based on bayes theorem and gaussian distribution assumption of errors of the wavelet packet component energy between validation data and model prediction the multivariate model is then assessed based on the bayesian point and interval hypothesis testing approaches the probability density function of the likelihood ratio is constructed using the statistics of multiple response quantities and monte carlo simulation the proposed methodology is implemented in the validation of a structural dynamics problem using multivariate time series data sets sensitivity analysis is also performed to investigate the effect of parameter selection on the model validation decision

design of efficient m band coders with linear phase and perfect reconstruction properties this paper presents a new design technique for obtaining m band orthogonal coders where m 2 sup i the structures obtained using the proposed technique have the perfect reconstruction property furthermore all filters that constitute the subband coder are linear phase fir type filters in contrast with conventional design techniques that attempt to find a unitary alias component matrix in the frequency domain we carry out the design in the time domain based on time domain orthonormality constraints that the filters must satisfy the m band design problem is reduced to the problem of finding a suitable lowpass filter h sub 0 n once a suitable lowpass filter is found the remaining m 1 filters of the coder are obtained through the use of shuffling operators on the lowpass filter this approach leads to a set of filters that use the same numerical coefficient values in different shift positions allowing very efficient numerical implementation of the subband coder in addition by imposing further constraints on the lowpass branch impulse response h sub 0 n we are able to construct continuous bases of m channel wavelets with good regularity properties design examples are presented for four eight and 16 band coders along with examples of continuous wavelet bases that they generate

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

multidirectional and multiscale edge detection via m band wavelet transform in this correspondence the problem of directional and multiscale edge detection is considered orthogonal and linear phase m band wavelet transform is used to decompose the image into m spl times m channels these channels are then combined such that each combination which we refer to as decomposition filter results in zero crossings at the locations of edges corresponding to different directions and resolutions and inherently performs regularization against noise by applying a zero crossing detector on the outputs of the decomposition filters edge maps of desired resolution and direction are obtained in addition with the application of the teager s energy operator at the analysis stage it is possible to obtain a reduction in unwanted zero crossings final edge maps of images are obtained through simple combinations of directional edge maps

calculation of the taylor series expansion coefficients of the jacobian elliptic function introduction not much is known about the taylor series expansion coefficients of the jacobian elliptic functions sn x k cn x k and dn x k in handbooks only the first four or five terms are given see for instance abramowitz and stegun 1 p 575 hancock s book on elliptic functions 4 p 252 and p 486 or gradshteyn and ryshik 5 recently however alois schett gave a combinatorial expression of the coefficients of the taylor series expansion of sn x k and evaluated explicitly the first eight nontrivial terms see 6 p 146 his results were extended by dominique dumont 3 who gave a new combinatorial interpretation of the coefficients of sn x k it is often said that no recurrence formulae exist for these coefficients 1 p 575 or 6 p 143 what is meant by that is probably that no simple recurrence formulae exist using differential and other equations one can deduce a number of useful recurrence relations and with the help of the burmann lagrange theorem even a definite although hard to handle expression of the coefficients in question

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

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

cyclic homology of brzezinski s crossed products and of braided hopf crossed products abstract let k be a field a a unitary associative k algebra and v a k vector space endowed with a distinguished element 1 v we obtain a mixed complex simpler than the canonical one that gives the hochschild cyclic negative and periodic homologies of a crossed product e a f v in the sense of brzezinski we actually work in the more general context of relative cyclic homology specifically we consider a subalgebra k of a that satisfies suitable hypothesis and we find a mixed complex computing the hochschild cyclic negative and periodic homologies of e relative to k then when e is a cleft braided hopf crossed product we obtain a simpler mixed complex that also gives the hochschild cyclic negative and periodic homologies of e

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

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

adaptively merging large scale range data with reflectance properties in this paper we tackle the problem of geometric and photometric modeling of large intricately shaped objects typical target objects we consider are cultural heritage objects when constructing models of such objects we are faced with several important issues that have not been addressed in the past issues that mainly arise due to the large amount of data that has to be handled we propose two novel approaches to efficiently handle such large amounts of data a highly adaptive algorithm for merging range images and an adaptive nearest neighbor search to be used with the algorithm we construct an integrated mesh model of the target object in adaptive resolution taking into account the geometric and or photometric attributes associated with the range images we use surface curvature for the geometric attributes and laser reflectance values for the photometric attributes this adaptive merging framework leads to a significant reduction in the necessary amount of computational resources furthermore the resulting adaptive mesh models can be of great use for applications such as texture mapping as we will briefly demonstrate additionally we propose an additional test for the k d tree nearest neighbor search algorithm our approach successfully omits back tracking which is controlled adaptively depending on the distance to the nearest neighbor since the main consumption of computational cost lies in the nearest neighbor search the proposed algorithm leads to a significant speed up of the whole merging process in this paper we present the theories and algorithms of our approaches with pseudo code and apply them to several real objects including large scale cultural assets

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

robust image watermarking based on multiband wavelets and empirical mode decomposition in this paper we propose a blind image watermarking algorithm based on the multiband wavelet transformation and the empirical mode decomposition unlike the watermark algorithms based on the traditional two band wavelet transform where the watermark bits are embedded directly on the wavelet coefficients in the proposed scheme we embed the watermark bits in the mean trend of some middle frequency subimages in the wavelet domain we further select appropriate dilation factor and filters in the multiband wavelet transform to achieve better performance in terms of perceptually invisibility and the robustness of the watermark the experimental results show that the proposed blind watermarking scheme is robust against jpeg compression gaussian noise salt and pepper noise median filtering and con vfilter attacks the comparison analysis demonstrate that our scheme has better performance than the watermarking schemes reported recently

the cyclic homology of crossed product algebras in their article 9 on cyclic homology feigin and tsygan have given a spectral sequence for the cyclic homology of a crossed product algebra generalizing burghelea s calculation 4 of the cyclic homology of a group algebra for an analogous spectral sequence for the hochschild homology of a crossed product algebra see brylinski 2 3 in this article we give a new derivation of this spectral sequence and generalize it to negative and periodic cyclic homology hc a and hp a the method of proof is itself of interest since it involves a natural generalization of the notion of a cyclic module in which the condition that the morphism n n is cyclic of order n 1 is relaxed to the condition that it be invertible we call this category the paracyclic category given a paracyclic module p we can define a chain complex c p with differentials b and b which respectively lower and raise degree the condition that the module p is paracyclic translates to the condition on c p that 1 bb bb is invertible our main result is to show that there is an analogue of the eilenberg zilber theorem for bi paracyclic modules it is then easy to obtain a new expression for the cyclic homology of a crossed product algebra which leads immediately to the spectral sequence of feigin and tsygan if m is a module over a commutative ring k we will denote by m k the iterated tensor product defined by m 0 k and m k 1 m k m if m and n are graded modules we will denote by m n their graded tensor product we would like to thank j block j l brylinski and c kassel for a number of interesting discussions on the results presented here

edge and line feature extraction based on covariance models image segmentation based on contour extraction usually involves three stages of image operations feature extraction edge detection and edge linking this paper is devoted to the first stage a method to design feature extractors used to detect edges from noisy and or blurred images the method relies on a model that describes the existence of image discontinuities e g edges in terms of covariance functions the feature extractor transforms the input image into a log likelihood ratio image such an image is a good starting point of the edge detection stage since it represents a balanced trade off between signal to noise ratio and the ability to resolve detailed structures for 1 d signals the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called average risk measure the results are compared with the performances of 1 d edge detectors known from literature generalizations to 2 d operators are given applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors finally it is shown that the covariance model can be coupled to a mrf model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

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

a shearlet approach to edge analysis and detection it is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges in this paper we propose a novel approach based on the shearlet transform a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges indeed unlike traditional wavelets shearlets are theoretically optimal in representing images with edges and in particular have the ability to fully capture directional and other geometrical features numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges and outperforms methods based on wavelets as well as other standard methods furthermore the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions

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

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

group cohomology and the cyclic cohomology of crossed products definite results are obtained in the conditions the group g is torsion free and the class h of the extension 0 zh g h n h 0 in h2 nh k is niipotent here gh for h g stands for the centralizer of h the cyclic homology groups hc a g decompose naturally as a direct sum of two subgroups called the homogeneous and the inhomogeneous parts ofhc a g the homogeneous part can be obtained from a spectral sequence converging to it with e2 q hp g hcq a the inhomogeneous part vanishes after inverting s for g z and in the topological situation we thus reobtain the result of nest 17 for general g but a k and trivial action thus for group rings k g we reobtain results of burghelea 4 the free groups satisfy our conditions see 10 for other classes of groups satisfying these conditions in this case our results are compatible with the results of pimsner and voiculescu 18 19 and suggest that for a large class of groups the part of ktor a r d g is obtained from a convergent spectral sequence with e q hp g k here r176 denotes the topological k theory functors see 2 a is a c algebra and a d g the reduced crossed product c algebra is a suitable completion of a g kasparov 13 succeeded to prove this for groups having a special manifold as classifying space we expect that our spectral sequence will give more insight in kasparov s spectral sequence we also mention

a method to detect and characterize ellipses using the hough transform we describe a new technique for detecting and characterizing ellipsoidal shapes automatically from any type of image this technique is a single pass algorithm which can extract any group of ellipse parameters or characteristics which can be computed from those parameters without having to detect all five parameters for each ellipsoidal shape moreover the method can explicitly incorporate any a priori knowledge the user may have concerning ellipse parameters the method is based on techniques from projective geometry and on the hough transform this technique can significantly reduce interpretation and computation time by automatically extracting only those features or geometric parameters of interest from images and making exact use of a priori information

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

a level set method based on the bayesian risk for medical image segmentation this paper proposes an alternative criterion derived from the bayesian risk classification error for image segmentation the proposed model introduces a region based force determined through the difference of the posterior image densities for the different classes a term based on the prior probability derived from kullback leibler information number and a regularity term adopted to avoid the generation of excessively irregular and small segmented regions compared with other level set methods the proposed approach relies on the optimum decision of pixel classification and the estimates of prior probabilities thus the approach has more reliability in theory and practice experiments show that the proposed approach is able to extract the complicated shapes of targets and robust for various types of medical images moreover the algorithm can be easily extendable for multiphase segmentation

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

deblurring of bilevel waveforms an algorithm for processing closely spaced edges and accurately restoring their locations is presented the convolution distortion model is based on interacting edges the restoration algorithm takes three edges as input and forces the effects of two of them to cancel each other thus the third edge appears to be isolated and is located using a traditional edge detector experiments on bar code waveforms reveal that this approach outperforms the current commercial bar code readers

graph spectral image smoothing using the heat kernel a new method for smoothing both gray scale and color images is presented that relies on the heat diffusion equation on a graph we represent the image pixel lattice using a weighted undirected graph the edge weights of the graph are determined by the gaussian weighted distances between local neighboring windows we then compute the associated laplacian matrix the degree matrix minus the adjacency matrix anisotropic diffusion across this weighted graph structure with time is captured by the heat equation and the solution i e the heat kernel is found by exponentiating the laplacian eigensystem with time image smoothing is accomplished by convolving the heat kernel with the image and its numerical implementation is realized by using the krylov subspace technique the method has the effect of smoothing within regions but does not blur region boundaries we also demonstrate the relationship between our method standard diffusion based pdes fourier domain signal processing and spectral clustering experiments and comparisons on standard images illustrate the effectiveness of the method

one dimensional regularization with discontinuities regularization is equivalent to fitting smoothing splines to the data so that efficient and reliable numerical algorithms exist for finding solutions however the results exhibit poor performance along edges and boundaries to cope with such anomalies a more general class of smoothing splines that preserve corners and discontinuities is studied cubic splines are investigated in detail since they are easy to implement and produce smooth curves near all data points except those marked as discontinuities or creases a discrete regularization method is introduced to locate corners and discontinuities in the data points before the continuous regularization is applied