finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

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

representations of the quantum group suq 2 and the little q jacobi polynomials abstract in this paper we study the finite dimensional unitary representations of the quantum group suq 2 then we obtain the peter weyl theorem for suq 2 and the matrix elements of these unitary representations are explicitly expressed in terms of the little q jacobi polynomials which are known as q analogues of orthogonal polynomials using these expressions the orthogonality relations of these polynomials are obtained in terms of the haar measure on the quantum group suq 2

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

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

statistical properties of local extrema in two dimensional gaussian random fields this paper is concerned with the statistical properties of the local extrema and local maxima of two dimensional 2d gaussian random fields grfs a grf may be represented by a linear filtering operation on a white noise field the spatial properties of the grf are then determined by the shape of the filter kernel function new expressions are derived for the mean spatial density of local extrema and for the distribution of local extrema in a 2 d random field the work is motivated by the problem of detecting known structures in images using 2d matched filters the new results enable accurate performance predictions to be made of the reliability of such filters in the presence of noise case studies are presented for several well known 2 d filter kernel functions

matching point features with ordered geometric rigidity and disparity constraints this correspondence presents a matching algorithm for obtaining feature point correspondences across images containing rigid objects undergoing different motions first point features are detected using newly developed feature detectors then a variety of constraints are applied starting with simplest and following with more informed ones first an intensity based matching algorithm is applied to the feature points to obtain unique point correspondences this is followed by the application of a sequence of newly developed heuristic tests involving geometry rigidity and disparity the geometric tests match two dimensional geometrical relationships among the feature points the rigidity test enforces the three dimensional rigidity of the object and the disparity test ensures that no matched feature point in an image could be rematched with another feature if reassigned another disparity value associated with another matched pair or an assumed match on the epipolar line the computational complexity is proportional to the numbers of detected feature points in the two images experimental results with indoor and outdoor images are presented which show that the algorithm yields only correct matches for scenes containing rigid objects

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

universal t matrix representations of ospq 1 2 and little q jacobi polynomials we obtain a closed form expression of the universal t matrix encapsulating the duality between the quantum superalgebra uq osp 1 2 and the corresponding supergroup ospq 1 2 the classical q 1 limit of this universal t matrix yields the group element of the undeformed ospq 1 2 supergroup the finite dimensional representations of the quantum supergroup ospq 1 2 are readily constructed employing the above mentioned universal t matrix and the known finite dimensional representations of the dually related deformed uq osp 1 2 superalgebra proceeding further we derive the product law the recurrence relations and the orthogonality of the representations of the quantum supergroup ospq 1 2 it is shown that the entries of these representation matrices are expressed in terms of the little q jacobi polynomials with q q two mutually complementary singular maps of the universal t matrix on the universal r matrix are also presented

a sampling kaczmarz motzkin algorithm for linear feasibility we combine two iterative algorithms for solving large scale systems of linear inequalities the relaxation method of agmon motzkin et al and the randomized kaczmarz method we obtain a family of algorithms that generalize and extend both projection based techniques we prove several convergence results and our computational experiments show our algorithms often outperform the original methods

fast and scalable approximate spectral graph matching for correspondence problems establishing consistent correspondences between two sets of features is a fundamental problem in computer vision this problem can be well formulated as graph matching in which nodes and edges represent feature points and pairwise relationships between feature points respectively spectral matching 19 is the state of the art eigenvector based method for graph matching the spectral matching algorithm has been used successfully for small data but its heavy memory requirement limited the maximum data sizes and contexts it can be used in this paper we propose fasm a fast and scalable approximate spectral matching algorithm the main ideas are twofold first we exploit the redundancy in the data generation process to approximate the affinity matrix with the linear combination of kronecker products between bases and index matrices the bases and index matrices are highly compressed representation of the approximated affinity matrix requiring much smaller memory than in previous works which store the whole affinity matrix second we compute the eigenvector of the approximated affinity matrix using the small bases and index matrices without explicitly materializing the approximated matrix experimental results show that our proposed method is up to 33x faster requiring up to 645x smaller memory than the exact algorithm with little or no loss of accuracy

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

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

using angular dispersion of gradient direction for detecting edge ribbons edges in a scene generally project to smooth continuous curves nearly everywhere in the image which results in low angular deviation of the intensity gradients in small neighborhoods straddling edges angular deviation is shown to be a measure of snr a theoretical analysis of angular deviation arising due to independent and identically distributed n 0 sigma sup 2 random noise is presented angular deviation thresholds for neighborhood sizes from 3 3 to 11 11 pixels are determined both from this analysis and numerical examples the proposed gradient angular dispersion detection algorithm detects edge elements by comparing the measured angular deviation with values computed for the minimum acceptable snr low values of deviation violate the no edge hypothesis the algorithm is shown to make good use of the limited dynamic range of the imaging system the sensitivity and selectivity of the strategy are both shown to be high

segmenting multisensor aerial images in class scale space abstract we introduce a class scale space for automated segmentation of aerial images from diverse sensors we describe the performance of a segmentation algorithm operating in this space this algorithm is carried out by three processors in succession multiscale feature extractor multiclass pattern classifier and class scale logic the multiscale feature extractor extracts features at three levels of precision the multiclass pattern classifier is an array of neural classifiers one classifier for each class scale pair each classifier is optimized by genetic feature selectors and genetic weight initiators the array of neural classifiers produces an array of segmented images class scale logic operates on these images to produce a final segmented image that combines coarsely detected regions with finely detected curves and points we describe applications of these techniques to segmenting and matching sar ir and visible light images

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

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

inexact bayesian estimation abstract bayesian estimation has many applications in computer vision a frequent objection to bayesian estimation is that the probability density functions pdfs involved are usually not known exactly in fact exact knowledge of the pdfs is not important it often suffices to know the pdfs approximately furthermore it may even suffice if we have a family of pdfs one of which approximates the actual pdf provided we specify a second stage pdf on the family such that the approximation of the actual pdf has high probability

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

a sparse approximate inverse preconditioner for the conjugate gradient method a method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix a is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations it is proved that in exact arithmetic the preconditioner is well defined if a is an h matrix the results of numerical experiments are presented

crystal bases foruq osp 1 2r abstract we construct z 2 graded crystal bases for the quantized universal enveloping algebra of the lie superalgebraosp 1 2r we show that like the crystal bases in the lie algebra case these crystal bases carry a remarkable combinatorial structure

geometry and representations of the quantum supergroup ospq 1 2n the quantum supergroup ospq 1 2n is studied systematically a haar functional is constructed and an algebraic version of the peter weyl theory is extended to this quantum supergroup quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of connes theory parabolic induction is developed by employing the quantum homogeneous supervector bundles quantum frobenius reciprocity and a generalized borel weil theorem are established for the induced representations

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

randomized block kaczmarz method with projection for solving least squares abstract the kaczmarz method is an iterative method for solving overcomplete linear systems of equations a x b the randomized version of the kaczmarz method put forth by strohmer and vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix a and converges linearly 1 in expectation to the solution of a consistent system in this paper we analyze two block versions of the method each with a randomized projection designed to converge in expectation to the least squares solution often faster than the standard variants our approach utilizes both a row and column paving of the matrix a to guarantee linear convergence when the matrix has consistent row norms called nearly standardized and a single column paving when the row norms are unbounded the proposed methods are an extension of the block kaczmarz method analyzed by needell and tropp and the randomized extended kaczmarz method of zouzias and freris the contribution is thus two fold unlike the standard kaczmarz method our results demonstrate convergence to the least squares solution of inconsistent systems both methods in the nearly standardized case and the second method in other cases by using appropriate blocks of the matrix this convergence can be significantly accelerated as is demonstrated by numerical experiments

a direct projection method for sparse linear systems an oblique projection method is adapted to solve large sparse unstructured systems of linear equations this row projection technique is a direct method which can be interpreted as an oblique kaczmarz type algorithm and is also related to other standard solution methods when a sparsity preserving pivoting strategy is incorporated it is demonstrated that the technique can be superior in terms of both fill in and arithmetic complexity to more standard sparse algorithms based on gaussian elimination this is especially true for systems arising from stiff ordinary differential equations problems in chemical kinetics studies

on kaczmarz s projection iteration as a direct solver for linear least squares problems abstract in this paper we construct and theoretically analyze a class of direct projection algorithms for the numerical solution of linear least squares problems these algorithms are obtained by adding supplementary directions for projection constructed as linear combinations of the initial system rows and columns in kaczmarz and extended kaczmarz iterative methods the above ideas are extended to the block row and column versions of the previously mentioned methods the developed algorithms are then compared with other direct projection based methods by the application to problems arising in multibody elasticity

invariants and orthogonal q polynomials associated with cq osp 1 2 abstract the spaces of invariants and the zonal spherical functions associated with quantum super 2 spheres defined by c q osp 1 2 are discussed connection between the zonal spherical functions and orthogonal q polynomials from the askey wilson scheme is investigated

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

mosaic models for images i geometric properties of components in cell structure mosaics abstract this paper deals with digital patterns generated by a class of random geometric processes proposed as models for images it derives expressions for the expected area and width of a connected component the expected number of components and the expected total perimeter in such patterns experiments conducted to verify some of the results are reported these results can be used for fitting the models to a given ensemble of images

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

camera calibration from surfaces of revolution this paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution camera calibration is the process of determining the intrinsic or internal parameters i e aspect ratio focal length and principal point of a camera and it is important for both motion estimation and metric reconstruction of 3d models in this paper a novel and simple calibration technique is introduced which is based on exploiting the symmetry of images of surfaces of revolution traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern such as a calibration grid the use of surfaces of revolution which are commonly found in daily life e g bowls and vases makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects in this paper it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio focal length and principal point of a camera with fixed intrinsic parameters the algorithms presented in this paper have been implemented and tested with both synthetic and real data experimental results show that the camera calibration method presented is both practical and accurate

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

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

combining spatial and scale space techniques for edge detection to provide a spatially adaptive wavelet based noise filtering algorithm new methods for detecting edges in an image using spatial and scale space domains are proposed a priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge an improved double thresholding technique is introduced for spatial domain filtering probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes gradient phases and edge connectivity the scale space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales a probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale space domain methods decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale these matched filters permit significant reduction in image noise without contributing to edge distortion the spatially adaptive wavelet noise filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images

a fuzzy approach to the evaluation of image complexity the inherently multidimensional problem of evaluating the complexity of an image is of a certain relevance in both computer science and cognitive psychology computer scientists usually analyze spatial dimensions in order to deal with automatic vision problems such as feature extraction psychologists seem more interested in the temporal dimension of complexity as a means to explore attentional models is it possible to define by merging both approaches a more general index of visual complexity the aim of this paper is the definition of objective measures of image complexity that fits with the so named perceived time towards the end we have defined a fuzzy mathematical model of visual complexity based on fuzzy measures of entropy the results obtained by applying this model to a set of pictorial images present a strong correlation with the outcomes of an experiment with human subjects based on variation of subjective temporal estimations associated with changes in visual attentional load which is also described herein

qualitative bayesian estimation of digital signals and images abstract bayesian estimation of digital signals is ordinarily concerned with the problem of estimating an ideal signal given a noisy signal the problem of partial or qualitative bayesian description is considered rather than complete estimation of the ideal signal only the case of a piecewise constant signal is considered instead of estimating the value of the ideal signal only a piecewise symbolic description of the signal is sought e g is the value high or low where these descriptors are defined by probability densities on the possible signal values this task is computationally less costly than that of complete bayesian estimation of the signal moreover it is found that the descriptions can be estimated robustly this approach is illustrated both for digital signals and for a simple class of digital images

a new approach to recognition of deformed patterns abstract by introducing a distance between original and deformed patterns and an adequate cost function we derive a gradient dynamics for transformation functions that transform one pattern into another one in its simplest form the cost function is lent from an elastic medium but in further improvements the corresponding lame constants are chosen pattern dependent in the case of line patterns a smearing out by means of a gaussian distribution is introduced and made time dependent the numerical simulations show the feasibility of the present approach for instance for the recognition of handwritten characters or of faces showing different facial expressions

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

quantum super spheres and their transformation groups representations and little t jacobi polynomials abstract quantum super 2 spheres and the corresponding quantum super transformation group are introduced in analogy to the well known quantum 2 spheres and quantum sl 2 connection between little t jacobi polynomials and the finite dimensional representations of the quantum super group is formulated and the peter weyl theorem is obtained

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

mosaic models for images ii geometric properties of components in coverage mosaics abstract this paper deals with digital patterns generated by a class of random geometric processes proposed as models for images it derives expressions for the expected area and width of a connected component the expected number of components and the expected total perimeter in such patterns experiments conducted to verify some of the results are reported these results can be used for fitting the models to a given ensemble of images

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

basic hypergeometric functions and covariant spaces for even dimensional representations of uq osp 1 2 representations of the quantum superalgebra uq osp 1 2 and their relations to the basic hypergeometric functions are investigated we first establish clebsch gordan decomposition for the superalgebra uq osp 1 2 in which the representations having no classical counterparts are incorporated formulae for these clebsch gordan coefficients are derived and is observed that they may be expressed in terms of the q hahn polynomials we next investigate representations of the quantum supergroup ospq 1 2 which are not well defined in the classical limit employing the universal matrix the representation matrices are obtained explicitly and found to be related to the little q jacobi polynomials characteristically the relation q q is satisfied in all cases using the clebsch gordan coefficients derived here we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup ospq 1 2

mosaic models for images iii spatial correlation in mosaics abstract this paper deals with digital patterns generated by a class of random geometric processes proposed as models for images the joint gray level probability density for pairs of points at given separations is used to derive various second order image statistics including the autocorrelation edge density and variogram in modeling images using these processes these results can be used for fitting models to a given ensemble of images

techniques for segmenting image curves into meaningful descriptions abstract this paper describes an approach to the detection of straight lines and circular arcs in images the algorithm uses a measure based on significance proposed by d g lowe three dimensional object recognition from single two dimensional images artificial intelligence 31 355 395 1987 edge points are processed to produce a description combining lines and arcs no thresholds are required for either 1 fitting the best lines and arcs to the data or 2 choosing between the best line and arc fits as the most appropriate description results are presented demonstrating the performance on complex images

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

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

a class of direct methods for linear systems a class of methods of direct type for solving determined or underdetermined full rank or deficient rank linear systems is presented and theoretically analyzed the class can be considered as a generalization of the methods of brent and brown as restricted to linear systems and implicitly contains orthogonal lu andll t factorization methods

supplementary projections for the acceleration of kaczmarz algorithm abstract when solving a linear least squares problem using the classical kaczmarz solver usually different accelerating techniques are employed we study a method of adding to the original problem supplementary directions for projection as linear combinations of rows or columns in order to conserve the sparsity pattern of the system matrix we propose an algorithm which computes an initial transformation via clustering based on the sparsity similarity numerical experiments show that as the number of clusters is increased the acceleration is decreased

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 differential model of the complex cell the receptive fields of simple cells in the visual cortex can be understood as linear filters these filters can be modeled by gabor functions or gaussian derivatives gabor functions can also be combined in an energy model of the complex cell response this letter proposes an alternative model of the complex cell based on gaussian derivatives it is most important to account for the insensitivity of the complex response to small shifts of the image the new model uses a linear combination of the first few derivative filters at a single position to approximate the first derivative filter at a series of adjacent positions the maximum response over all positions gives a signal that is insensitive to small shifts of the image this model unlike previous approaches is based on the scale space theory of visual processing in particular the complex cell is built from filters that respond to the 2d differential structure of the image the computational aspects of the new model are studied in one and two dimensions using the steerability of the gaussian derivatives the response of the model to basic images such as edges and gratings is derived formally the response to natural images is also evaluated using statistical measures of shift insensitivity the neural implementation and predictions of the model are discussed

mosaic models for textures this paper deals with a class of image models based on random geometric processes theoretical and empirical results on properties of patterns generated using these models are summarized these properties can be used as aids in fitting the models to images

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

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

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