fuzzy edge detection for omnidirectional images the use of omnidirectional vision has increased during these past years it provides a very large field of view nevertheless omnidirectional images contain significant radial distortions and conventional image processing is not adapted to these specific images this paper presents an edge detector adapted to the image geometry fuzzy sets will be used to take into account all imprecisions introduced by the sampling process the prewitt filter applied to omnidirectional image will be studied to illustrate this paper

approximation of an arbitrary filter and its recursive implementation abstract filtering is one of the important techniques in computer vision it has been widely used in edge detection image restoration range image segmentation etc however the efficient implementation of an arbitrary filter has been a challenging problem until now in this paper a novel method is proposed to implement an arbitrary filter firstly an efficient recursive structure is proposed to implement any polynomial exponential type pet filter the computational complexity and structure are independent of its filter mask size or its bandwidth secondly a new method is proposed lagurre spectrum decomposition method to obtain the pet approximation of any filters as an example the above method is applied to the approximation and implementation of gaussian filters and experiments have shown that a perfect approximation can be obtained with only third order lagurre bases and therefore only a fourth order recursive filter is needed to implement gaussian filters finally the comparison of the present method with the known ones shows that 1 lagurre polynomial bases are orthogonal with each other so the filter approximation is simple 2 the bases are complete and the completeness guarantees the approximation error can be reduced to zero 3 the method can be used to design both gaussian and any other filters

on the inter conversion between hermite and laguerre local image expansions the nice relationship existing among the hermite gauss and the laguerre gauss image expansions whose basis functions span the same signal space is investigated as a result a novel efficient method for cartesian to polar coordinate inter conversion especially suited for dedicated hardware realization is proposed applications to local image rotation based on the simple steerability of the laguerre gauss expansion and to local image analysis based on gaussian derivatives are considered in detail a possible fixed point realization of the proposed inter conversion scheme is discussed

fast algorithms for low level vision a recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing performing the first and second directional derivatives and carrying out the laplacian of an image these operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered the key to the approach is first the use of an exponentially based filter family and second the use of the recursive filtering applications to edge detection problems and multiresolution techniques are considered and an edge detector allowing the extraction of zero crossings of an image with only 14 operations per output element at any resolution is proposed various experimental results are shown

a representation for shape based on peaks and ridges in the difference of low pass transform this paper defines a multiple resolution representation for the two dimensional gray scale shapes in an image this representation is constructed by detecting peaks and ridges in the difference of lowpass dolp transform descriptions of shapes which are encoded in this representation may be matched efficiently despite changes in size orientation or position motivations for a multiple resolution representation are presented first followed by the definition of the dolp transform techniques are then presented for encoding a symbolic structural description of forms from the dolp transform this process involves detecting local peaks and ridges in each bandpass image and in the entire three dimensional space defined by the dolp transform linking adjacent peaks in different bandpass images gives a multiple resolution tree which describes shape peaks which are local maxima in this tree provide landmarks for aligning manipulating and matching shapes detecting and linking the ridges in each dolp bandpass image provides a graph which links peaks within a shape in a bandpass image and describes the positions of the boundaries of the shape at multiple resolutions detecting and linking the ridges in the dolp three space describes elongated forms and links the largest peaks in the tree the principles for determining the correspondence between symbols in pairs of such descriptions are then described such correspondence matching is shown to be simplified by using the correspondence at lower resolutions to constrain the possible correspondence at higher resolutions

special values of hypergeometric functions and periods of cm elliptic curves let x x 0 6 1 w 6 be the quotient of the shimura curve x 0 6 1 by all the atkin lehner involutions by realizing modular forms on x in two ways one in terms of hypergeometric functions and the other in terms of borcherds forms and using schofer s formula for values of borcherds forms at cm points we obtain special values of certain hypergeometric functions in terms of periods of elliptic curves over overline q with complex multiplication

on local region models and a statistical interpretation of the piecewise smooth mumford shah functional the mumford shah functional is a general and quite popular variational model for image segmentation in particular it provides the possibility to represent regions by smooth approximations in this paper we derive a statistical interpretation of the full piecewise smooth mumford shah functional by relating it to recent works on local region statistics moreover we show that this statistical interpretation comes along with several implications firstly one can derive extended versions of the mumford shah functional including more general distribution models secondly it leads to faster implementations finally thanks to the analytical expression of the smooth approximation via gaussian convolution the coordinate descent can be replaced by a true gradient descent

bi exponential edge preserving smoother edge preserving smoothers need not be taxed by a severe computational cost we present in this paper a lean algorithm that is inspired by the bi exponential filter and preserves its structure a pair of one tap recursions by a careful but simple local adaptation of the filter weights to the data we are able to design an edge preserving smoother that has a very low memory and computational footprint while requiring a trivial coding effort we demonstrate that our filter a bi exponential edge preserving smoother or beeps has formal links with the traditional bilateral filter on a practical side we observe that the beeps also produces images that are similar to those that would result from the bilateral filter but at a much reduced computational cost the cost per pixel is constant and depends neither on the data nor on the filter parameters not even on the degree of smoothing

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

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

a new variational approach for restoring images with multiplicative noise this paper proposes a novel variational model for restoration of images corrupted with multiplicative noise it combines a fractional order total variational filter with a high order pde laplacian norm the combined approach is able to preserve edges while avoiding the blocky effect in smooth regions this strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori map semi implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional to improve the numerical results we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial and error method the existence and uniqueness of a solution to the proposed variational model is established in this study parameter dependence is also discussed experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding pde methods

parametric oriented fitting for local contrast enhancement local image contrast enhancement methods extract more informative details comparing with the global methods yet the traditional schemes require to access all of the pixels in a local region to obtain the cumulative distribution function cdf for further enhancement i e adaptive histogram equalization ahe and thus the time complexity drastically increases accordingly when the block size increases consequently some speed up ingenuities such as block wise strategy and simple proportionally averaging manner are employed to cope with this issue yet serious blocking artifact or low contrast issues are accompanied in this study a local enhancement method namely corrected parametric oriented histogram equalization cpohe is proposed to effectively yield enhanced results with high contrast and artifact free texture using the concept of integral image and further correct the accompanied distortion as documented in the experimental results the proposed method provides a high practical value for applied in visual perception biometric and tracking detection applications

a class of constrained clustering algorithms for object boundary extraction boundary extraction is a key task in many image analysis operations this paper describes a class of constrained clustering algorithms for object boundary extraction that includes several well known algorithms proposed in different fields deformable models constrained clustering data ordering and traveling salesman problems the algorithms belonging to this class are obtained by the minimization of a cost function with two terms a quadratic regularization term and an image dependent term defined by a set of weighting functions the minimization of the cost function is achieved by lowpass filtering the previous model shape and by attracting the model units toward the centroids of their attraction regions to define a new algorithm belonging to this class the user has to specify a regularization matrix and a set of weighting functions that control the attraction of the model units toward the data the usefulness of this approach is twofold it provides a unified framework for many existing algorithms in pattern recognition and deformable models and allows the design of new recursive schemes

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

fast anisotropic gauss filtering we derive the decomposition of the anisotropic gaussian in a one dimensional 1 d gauss filter in the x direction followed by a 1 d filter in a nonorthogonal direction spl phi so also the anisotropic gaussian can be decomposed by dimension this appears to be extremely efficient from a computing perspective an implementation scheme for normal convolution and for recursive filtering is proposed also directed derivative filters are demonstrated for the recursive implementation filtering an 512 spl times 512 image is performed within 40 msec on a current state of the art pc gaining over 3 times in performance for a typical filter independent of the standard deviations and orientation of the filter accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error the anisotropic gaussian filtering method allows fast calculation of edge and ridge maps with high spatial and angular accuracy for tracking applications the normal anisotropic convolution scheme is more advantageous with applications in the detection of dashed lines in engineering drawings the recursive implementation is more attractive in feature detection applications for instance in affine invariant edge and ridge detection in computer vision the proposed computational filtering method enables the practical applicability of orientation scale space analysis

well posedness of two nonrigid multimodal image registration methods image registration methods may be designed as solutions of minimization problems on a set of geometric deformations in the nonrigid case solving these problems often means computing the steady state of a system of evolution equations involving the gradient of the error criterion defined from the euler lagrange equations of the corresponding minimization problem the well posedness of the registration methodrequires showing the existence of a solution to the minimization problem as well as that of a stable solution of the evolution equations derived from it we provide such proofs in the case where the error criterion is derived from two different statistical similarity measures global mutual information and local cross covariance we also describe our numerical implementation for solving the corresponding evolution equations and show examples of registrations of real 2d and 3d images achieved with these algorithms the proofs are quite general and can be applied to most of the known nonrigid image

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

fast space variant elliptical filtering using box splines the efficient realization of linear space variant non convolution filters is a challenging computational problem in image processing in this paper we demonstrate that it is possible to filter an image with a gaussian like elliptic window of varying size elongation and orientation using a fixed number of computations per pixel the associated algorithm which is based upon a family of smooth compactly supported piecewise polynomials the radially uniform box splines is realized using preintegration and local finite differences the radially uniform box splines are constructed through the repeated convolution of a fixed number of box distributions which have been suitably scaled and distributed radially in an uniform fashion the attractive features of these box splines are their asymptotic behavior their simple covariance structure and their quasi separability they converge to gaussians with the increase of their order and are used to approximate anisotropic gaussians of varying covariance simply by controlling the scales of the constituent box distributions based upon the second feature we develop a technique for continuously controlling the size elongation and orientation of these gaussian like functions finally the quasi separable structure along with a certain scaling property of box distributions is used to efficiently realize the associated space variant elliptical filtering which requires o 1 computations per pixel irrespective of the shape and size of the filter

on optimal linear filtering for edge detection in this paper we revisit the analytical expressions of the three canny s 1983 criteria for edge detection quality good detection good localization and low multiplicity of false detections our work differs from canny s work on two essential points here the criteria are given for discrete sampled signals i e for the real implemented filters instead of a single step edge as input signal we use pulses of various width the proximity of other edges affects the quality of the detection process this is taken into account in the new expressions of these criteria we derive optimal filters for each of the criteria and for any combination of them in particular we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria the upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter exponential deriche 1987 and first derivative of gaussian filters are evaluated our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed

a new generalised α scale spaces quadrature filters abstract the scale spaces is a recent theory that open new possibilities of phase based image processing it is a parameterised class 0 1 of linear scale space representations which allows a continuous connection beyond the well known gaussian scale space 1 in this paper we make use of this unified representation to derive new families of band pass quadrature filters built from derivatives and difference of the scale space generating kernels this construction leads to generalised kernel filters including the commonly known families derived from the gaussian and the poisson kernels the properties of each family are first studied and then experiments on one and two dimensional signals are shown to exemplify how the suggested filters can be used for edge detection this work is complemented by an experimental evaluation which demonstrates that the new proposed filters are a good alternative to the commonly used log gabor filter

a new adaptive framework for unbiased orientation estimation in textured images this paper focuses on directional texture analysis we propose a new approach for orientation estimation this approach hinges on two classes of convolution masks i e the gradient and the valleyness operators we provide a framework for their optimization regarding bias reduction and noise robustness as the gradient and the valleyness operators are complementary we propose a combination named gv joe this combination consists in using the gradient on inflexion pixels the valleyness on crests and valleys and a linear mixture of both elsewhere we implement an adaptive selection of the size of our operators in order to take into account the variations of the texture scale in the image we apply our approach both on synthetic and natural textures these experiments show that when used separately both classes of operators are more accurate than classical derivative approaches in noisy cases the gv joe implementation improves the robustness of our operators without affecting their accuracy moreover compared to well known orientation estimators it gives the best estimates in the most difficult cases i e for high frequency textures and low snr

compressed sensing with wavelet domain dependencies for coronary mri a retrospective study coronary magnetic resonance imaging mri is a noninvasive imaging modality for diagnosis of coronary artery disease one of the limitations of coronary mri is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions compressed sensing cs has been recently utilized to accelerate image acquisition in mri in this paper we develop an improved cs reconstruction method bayesian least squares gaussian scale mixture bls gsm that uses dependencies of wavelet domain coefficients to reduce the observed blurring and reconstruction artifacts in coronary mri using traditional l1 regularization images of left and right coronary mri was acquired in 7 healthy subjects with fully sampled k space data the data was retrospectively undersampled using acceleration rates of 2 4 6 and 8 and reconstructed using l1 thresholding l1 minimization and bls gsm thresholding reconstructed right and left coronary images were compared with fully sampled reconstructions in vessel sharpness and subjective image quality 1 4 for poor excellent mean square error mse was also calculated for each reconstruction there were no significant differences between the fully sampled image score versus rate 2 4 or 6 for bls gsm for both right and left coronaries n s however for l1 thresholding significant differences p 0 05 were observed for rates higher than 2 and 4 for right and left coronaries respectively l1 minimization also yields images with lower scores compared to the reference for rates higher than 4 for both coronaries these results were consistent with the quantitative vessel sharpness readings bls gsm allows acceleration of coronary mri with acceleration rates beyond what can be achieved with l1 regularization

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

compressive bilateral filtering this paper presents an efficient constant time bilateral filter that produces a near optimal performance tradeoff between approximate accuracy and computational complexity without any complicated parameter adjustment called a compressive bilateral filter cblf the constant time means that the computational complexity is independent of its filter window size although many existing constant time bilateral filters have been proposed step by step to pursue a more efficient performance tradeoff they have less focused on the optimal tradeoff for their own frameworks it is important to discuss this question because it can reveal whether or not a constant time algorithm still has plenty room for improvements of performance tradeoff this paper tackles the question from a viewpoint of compressibility and highlights the fact that state of the art algorithms have not yet touched the optimal tradeoff the cblf achieves a near optimal performance tradeoff by two key ideas 1 an approximate gaussian range kernel through fourier analysis and 2 a period length optimization experiments demonstrate that the cblf significantly outperforms state of the art algorithms in terms of approximate accuracy computational complexity and usability

the first chern form on moduli of parabolic bundles for moduli space of stable parabolic bundles on a compact riemann surface we derive an explicit formula for the curvature of its canonical line bundle with respect to quillen s metric and interprete it as a local index theorem for the family of overline partial operators in the associated parabolic endomorphism bundles the formula consists of two terms one standard proportional to the canonical kahler form on the moduli space and one nonstandard called a cuspidal defect that is defined by means of special values of the eisenstein maass series the cuspidal defect is explicitly expressed through the curvature forms of certain natural line bundles on the moduli space related to the parabolic structure we also compare our result with witten s volume computation

fast computation of unbiased intensity derivatives in images using separable filters in this paper we prove that all high order non biased spatial intensity derivative operators in images can be computed using linear combinations of separable filters the separable filters are the same as those used by haralick 1984 but different linear combinations are taken a comparison of the number of operations necessary to compute the derivatives using separable and non separable filters is made the conclusion of our analysis is that the optimal way to compute the needed derivatives depends on which derivatives we have to compute on the size of the window and on the order of expansion finally we discuss the performance of an edge detector using these derivatives for unsmoothed and smoothed step edges

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

a multi scale edge detector abstract a multi scale edge detector with subpixel accuracy is described a subpixel laplacian edge detector recursively implemented is run at different scales and the recovered edge information is combined the multi scale edge detection is based on the behavior of edges in scale space and takes into account their physical phenomena with this purpose in mind four step edge models are considered the ideal the blurred the pulse and the staircase it is emphasized that the use of two scales the larger and the smaller is sufficient for good edge detection furthermore a set of rules is derived for combining edge information obtained from a laplacian detector which has some special properties however this type of edge detector gives at least two classes of false edges one of which cannot be eliminated by the usual thresholding methods an appropriate thresholding algorithm is given taking into account the origin of the false edges and their behavior in scale space

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

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data