on critical point detection of digital shapes in this paper we present a nonlinear algorithm for critical point detection cpd of 2d digital shapes the algorithm eliminates the problems arising from curvature approximation and gaussian filtering in the existing algorithms based on the definition of critical level we establish a set of criteria for the design of an effective cpd algorithm for the first time by quantifying the critical level to the modified area confined by three consecutive pseudocritical points a simple but very effective algorithm is developed the comparison of our experimental results with those of many other cpd algorithms shows that the proposed algorithm is superior in that it provides a sequence of figures at every detail level and each has a smaller integral error than the others with the same number of critical points the experimental results on shapes with various complexities also show the algorithm is reliable and robust with regard to noise

fourier transform of a polygonal shape function and its application in electromagnetics the shape function s x y of a planar aperture sigma is defined ashaving value one inside sigma and zero outside the two dimensional fourier transform of s x y when sigma is an n sided polygon is considered and a closed form exact solution is presented applications of these results are described for 1 the calculation of the secondary pattern of a reflector antenna with a noncircular aperture and 2 high frequency transmission through a periodic frequency selective surface

the hermite transform applications it is demonstrated how the hermite transform can be used for image coding and analysis hierarchical coding structures based on increasingly specified basic patterns i e general 2 d patterns general 1 d patterns and specific 1 d patterns such as edges and corners are presented in the image coding application the relation with existing pyramid coders is described a new coding scheme based on local one dimensional image approximations is introduced in the image analysis application the relation between the hermite transform and existing line edge detection schemes is described it is shown that by concentrating on more specific patterns the coding efficiency can be increased since fewer coefficients have to be coded meanwhile sufficient descriptive power can be maintained for approximating the most interesting features in natural images

backlund transformations and loop group actions we construct a local action of the group of rational maps from 2 to gl n on local solutions of flows of the zs akns sl n hierarchy we show that the actions of simple elements linear fractional transformations give local backlund transformations and we derive a permutability formula from different factorizations of a quadratic element we prove that the action of simple elements on the vacuum may give either global smooth solutions or solutions with singularities however the action of the subgroup of the rational maps that satisfy the u n reality condition on the space of global rapidly decaying solutions of the flows in the u n hierarchy is global and the action of a simple element gives a global backlund transformation the actions of certain elements in the rational loop group on the vacuum give rise to explicit time periodic multisolitons multibreathers we show that this theory generalizes the classical backlund theory of the sine gordon equation the group structures of backlund transformations for various hierarchies are determined by their reality conditions we identify the reality conditions the group structures for the sl n u k n k kdv kupershmidt wilson and gel fand dikii hierarchies the actions of linear fractional transformations that satisfy a reality condition modulo the center of the group of rational maps give backlund and darboux transformations for the hierarchy defined by the reality condition since the factorization cannot always be carried out under this reality condition the action is again local and backlund transformations only generate local solutions for these hierarchies unless singular solutions are allowed 2000 john wiley sons inc

image representation by one bit fourier phase theory sampling and coherent image model the problem of recovering an image from its fourier transform phase quantized to one bit or equivalently finding the locations of the zero crossings of the real part of the fourier transform is addressed theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band limited image it is then shown that sampling in the frequency domain presents a major obstacle to obtaining good reconstruction results the one bit fourier phase reconstruction problem is then considered when the original image is coherent i e the image phase is random and highly uncorrelated examples are given which demonstrate that the information loss produced by frequency sampling is not as severe as that in the nonclassical problem motivated by digital phase only holograms a known random diffuser is used as the image phase and a well known iterative reconstruction procedure is extended to incorporate the knowledge of the image phase at each stage of the iteration this reconstruction method produces good image quality by using a few iterations unlike its noncoherent counterpart

actions of loop groups on harmonic maps we describe a general framework in which subgroups of the loop group agin act on the space of harmonic maps from s2 to gln this represents a simplification of the action considered by zakharov mikhailov shabat zm zs in that we take the contour for the riemann hilbert problem to be a union of circles however it reduces the basic ingredient to the well known birkhoff decomposition of agin s and this facilitates a rigorous treatment we give various concrete examples of the action and use these to investigate a suggestion of uhlenbeck uh that a limiting version of such an action completion gives rise to her fundamental process of adding a uniton it turns out that this does not occur because completion preserves the energy of harmonic maps however in the special case of harmonic maps from s2 to complex projective space we describe a modification of this completion procedure which does indeed reproduce adding a uniton one aspect of the theory of symmetry groups for diffierential equations is the idea of proliferation of solutions by this is meant that starting with an obvious solution application of symsmetries can lead to further perhaps less obvious solutions in this paper we shall apply the general framework described by zakharov et al zm zs to the harmonic map equation the principal chiral or sigma model of mathematical physics to put this into a wider context we recall that a fundamental discovery in the study of the korteweg de vries and related equations was that the space of solutions admits a certain infinite dimensional symmetry group historically the first manifestation of this via noether s theorem was the appearance of infinitely many conservation laws later this led to an elegant algebraic description of solutions of the equation as the points of an orbit of a representation of an infinite dimensional group see for example wi for a brief description of some of these ideas the existence of previously unnoticed symmetries hidden symmetries for other equations became an interesting possibility and attempts have been made so far with much less success than in the case of the kdv equation to unearth them one such example is the harmonic map equation for maps from a surface d into a compact lie group g or homogeneous space g h the basic observation po uh zm zs which introduces an infinite dimensional group is that harmonic maps from d to g correspond to certain received by the editors february 9 1990 1980 mathematics subject classification 1985 revision primary 58e20 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

smoothing and matching of 3 d space curves we present a new approach to the problem of matching 3 d curves the approach has a low algorithmic complexity in the number of models and can operate in the presence of noise and partial occlusions our method builds upon the seminal work of kishon et al 1990 where curves are first smoothed using b splines with matching based on hashing using curvature and torsion measures however we introduce two enhancements we present experimental results using synthetic data and also using characteristic curves extracted from 3 d medical images an earlier version of this article was presented at the 2nd european conference on computer vision in italy

compact range performance evaluation using aperture near field angular spectrums for a compact range cr the near field angular spectrum can be obtained by making an inverse fourier transform of its aperture spatial near field the characteristics of the aperture design have been carried by the aperture near field angular spectrum the direct wave and edge diffracted waves from the aperture can be separated and distinguished clearly in the angular domain therefore the cr performance can be evaluated and improved accordingly in this paper based on the aperture field convolution method and plane wave spectrum pws theory near field angular spectrums for different apertures have been computed the general criteria for the cr aperture design have been discussed the selections of the whole aperture shape the serration height the serration base length the serration number and the serration shape including isosceles and right angled triangles have been compared at last the near fields of an optimized serrated edge aperture and an original circular aperture in different transverse planes have been computed and compared the width and height of the apertures are all 30 wavelengths in free space in order to suppress the sidelobes a chebyshev window with 50 db sidelobes has been adopted in the spatial angular transform

reconstructions from zero crossings in scale space in computer vision the one parameter family of images obtained from the laplacian of a gaussian filtered version of the image parameterized by the width of the gaussian has proved to be a useful data structure for the extraction of feature data in particular the zero crossings of this so called scale space data are associated with edges and have been proposed by d marr 1982 and others as the basis of a representation of the image data the question arises as to whether the representation is complete and stable the authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations they formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error and they present results showing that the reconstruction is possible but can be unstable they further show that the method applies when gradient data along the zero crossings are included in the representation and they demonstrate empirically that the reconstruction is then stable

extensions of scale space filtering to machine sensing systems major components of scale space theory are gaussian filtering and the use of zero crossing thresholders and laplacian operators properties of scale space filtering may be useful for data analysis in multiresolution machine sensing systems however these systems typically violate the gaussian filter assumption and often the data analyses used e g trend analysis and classification are not consistent with zero crossing thresholders and laplacian operators the authors extend the results of scale space theory to include these more general conditions in particular it is shown that relaxing the requirement of linear scaling allows filters to have non gaussian spatial characteristics and that relaxing of the scale requirements s to 0 of the impulse response allows the use of scale space filters with limited frequency support i e bandlimited filters bandlimited scale space filters represent an important extension of scale space analysis for machine sensing

smart nonlinear diffusion a probabilistic approach in this paper a stochastic interpretation of nonlinear diffusion equations used for image filtering is proposed this is achieved by relating the problem of evolving smoothing images to that of tracking the transition probability density functions of an underlying random process we show that such an interpretation of e g perona malik equation in turn allows additional insight and sufficient flexibility to further investigate some outstanding problems of nonlinear diffusion techniques in particular upon unraveling the limitations as well as the advantages of such an equation we are able to propose a new approach which is demonstrated to improve performance over existing approaches and more importantly to lift the longstanding problem of a stopping criterion for a nonlinear evolution equation with no data term constraint substantiating examples in image enhancement and segmentation are provided

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

application of scale space to image coding the continuous formulation of scale space is briefly reviewed it is shown that deriving a discrete formulation of scale space requires the solution to a more general problem the optimum approximation of a signal by local patterns the consequences of the theory for the laplacian image pyramid are discussed a pyramid coding scheme based on the discrete scale space formulation is derived preliminary coding results on real images are presented down to 1 b pixel the quality of the coded images is usually very close to that of the originals bit rates below 0 5 b pixel imply a too coarse quantization or even deletion of the prediction error image at the smallest scale and consequently always result in images that are noticeably unsharp in the intermediate region different degrees of quantization noise and unsharpness are present at comparable data rates the linear variation coder generates less quantization noise in uniform regions while the scale space coder gives a slightly better edge reproduction

an efficient hybrid go pws algorithm to analyze conformal serrated edge reflectors for millimeter wave compact range a method to analyze parabolic reflectors with arbitrary piecewise rim is presented in this communication this kind of reflectors when operating as collimators in compact range facilities needs to be large in terms of wavelength their analysis is very inefficient when it is carried out with fullwave mom techniques and it is not very appropriate for designing with po techniques also fast go formulations do not offer enough accuracy to reach performance results the proposed algorithm is based on a go pws hybrid scheme using analytical as well as non analytical formulations on one side an analytical treatment of the polygonal rim reflectors is carried out on the other side non analytical calculi are based on efficient operations such as m2 order 2 dimensional fft a combination of these two techniques in the algorithm ensures real ad hoc design capabilities reached through analysis speedup the purpose of the algorithm is to obtain an optimal conformal serrated edge reflector design through the analysis of the field quality within the quiet zone that it is able to generate in its forward half space

serrated edge design and field analysis in spatial time and angular domains for improving the field uniformity of beam combiner edge diffraction of a beam combiner will adversely affect the field uniformity in the observation plane in order to suppress the edge diffraction the serrated edge design method is proposed according to the equivalence principle a field uniformity analysis method was proposed to compute the spatial field distribution radiated from the aperture of a beam combiner in order to separate the direct wave from diffracted wave the spatial field is transformed into the time and angular domain spectrum by inverse fourier transform first the height of serrations is designed by analog of the equivalent trapezoidal amplitude taper then the number of serrations was designed by the assumption of isosceles and right triangles finally the shape of serrations was designed by changing the interior angle of serrations a serrated edge design example is also proposed and analyzed by comparing the field uniformity in spatial time and angular domains before and after serrating the edges the amplitude and phase ripples decrease from 1 85 db and 12 16 to 0 53 db and 3 98 respectively the results show that the field uniformity is significantly improved

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

image representation by sign information image representation by sign data in its most general context is considered for the case when f is a two dimensional signal the authors study conditions under which f is determined by its sign or in other words by its quantization to 1 bit of information this study is carried out in two different directions first theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band limited image an interesting paradigm arising in theoretical computer vision is then posed are the zero crossing of f convolved with a laplacian of a gaussian at a single channel enough for unambiguously representing f second the problem of the completeness of the representation when the position of the zero crossings is known only approximately is addressed it is shown that when sign f is sampled significant ambiguities are introduced in the representation experimental results are presented which were obtained from an iterative algorithm devised to reconstruct real images from multiscale sign information

constrained regularized differentiation numerical differentiation is an ill posed problem this article demonstrates that the application of the regularization theory together with the methods of projections on convex sets of constraints improve the accuracy of the derivatives calculation simulation results are presented and the applications of the proposed method to edge detection are discussed

a class of 1 d gas flows soluble by the inverse scattering transform abstract we first show that the euler equations of 1 dimensional adiabatic gas dynamics with arbitrary equation of state present a symmetry s of order three i e such that s3 1 for a particular class of equations of state which may be viewed as representing the geometrical center of the symmetry a higher symmetry exists the sl 3 symmetry in agreement with the results of ref 2 for these equations of state we derive riemann invariants and are thus able to reduce the system of the euler s equations to a mere second order equation versus characteristic coordinates that equation turns out to be soluble by an inverse scattering method with a third order scattering operator as shown in ref 6 we thus provide a first instance of soliton propagation on a nondissipative gaseous background it must be noted however that these are solitons in a mathematical sense only as the space time in which they propagate uniformly does not coincide with ordinary space time

iterative smoothed residuals a low pass filter for smoothing with controlled shrinkage we present a linear smoothing operator which has low pass characteristics similar to a butterworth filter and limited spatial extent similar to a gaussian the smoothing operator also has closed forms in the spatial and frequency domains which facilitate analysis and implementation a formula is derived that allows us to explicitly control shrinkage

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

scale based detection of corners of planar curves a technique for detecting and localizing corners of planar curves is proposed the technique is based on gaussian scale space which consists of the maxima of absolute curvature of the boundary function presented at all scales the scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners the analysis shows that the resulting scale space contains line patterns that either persist terminate or merge with a neighboring line next the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales finally a multiple scale corner detection scheme is developed using a coarse to fine tree parsing technique the parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales experiments were performed to show that the scale space corner detector is reliable for objects with multiple size features and noisy boundaries and compares favorably with other corner detectors tested

on detecting dominant points abstract detecting dominant points is a crucial preprocessing step for shape recognition and point based motion estimation polygonal approximation has been a commonly used approach in detecting dominant points this paper presents two alternatives which detect stable dominant points in the first method we find a set of positive maximum and negative minimum curvature points along the gaussian smoothed boundary followed by a split and merge polygonal approximation algorithm the resulting break points vertices of the approximated polygon are the dominant points experimental results show that dominant points obtained by this method are less sensitive to the orientation of the boundary than other polygonal approximation algorithms in the sense that the number and the location of the dominant points along the contour remain relatively unchanged in the second method we smooth a boundary by a gaussian filter using various widths until the extreme curvature points remain relatively unchanged for a range of filter widths the resulting extreme curvature points which are stable to orientation and a reasonable range of scaling are the dominant points

a multiscanning approach based on morphological filtering it is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of gaussian shaped filters of different sizes to show the validity of this method the authors concentrated on an application that involves forming scale space image of a 2 d shape using morphological opening filtering a proof is given to show that morphological opening filtering has a property of not introducing additional zero crossings as one moves to a coarser scale this is a different result from the conclusion by a l yuille and t a poggio ibid vol pami 8 jan 1986 that the gaussian filter is the only filter with this property in addition opening filtering is computationaly simpler than the gaussian filter

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

image enhancement by nonlinear extrapolation in frequency space a technique for enhancing the perceptual sharpness of an image is described the enhancement algorithm augments the frequency content of the image using shape invariant properties of edges across scale by using a nonlinearity that generates phase coherent higher harmonics the procedure utilizes the laplacian transform and the laplacian pyramid image representation results are presented depicting the power spectra augmentation and the visual enhancement of several images simplicity of computations and ease of implementation allow for real time applications such as high definition television hdtv

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

edge based compression of cartoon like images with homogeneous diffusion edges provide semantically important image features in this paper a lossy compression method for cartoon like images is presented which is based on edge information edges together with some adjacent grey colour values are extracted and encoded using a classical edge detector binary compression standards such as jbig and state of the art encoders such as paq when decoding information outside these encoded data is recovered by solving the laplace equation i e we inpaint with the steady state of a homogeneous diffusion process for the discrete reconstruction problem we prove existence and uniqueness and establish a maximum minimum principle furthermore we describe an efficient multigrid algorithm the result is a simple codec that is able to encode and decode in real time we show that for cartoon like images this codec can outperform the jpeg standard and even its more advanced successor jpeg2000

on the convergence of planar curves under smoothing curve smoothing has two important applications in computer vision and image processing 1 the curvature scale space css technique for shape analysis and 2 the gaussian filter for noise suppression in this paper we study how planar curves converge as they are smoothed with increasing scales first two types of convergence behavior are clarified the coined term shrinkage refers to the reduction of arc length of a smoothed planar curve which describes the convergence of the curve latitudinally and another coined term collapse refers to the movement of each point to its limiting position which describes the convergence of the curve longitudinally a systematic study on the shrinkage and collapse of three categories of curve models is then presented the corner models helps to reveal how the local structures of planar curves collapse and what the smoothed curves may converge to the sawtooth models allows us to gain insights regarding how noise is suppressed from noisy planar curves by the gaussian filter our investigation on the closed curves shows that each curve collapses to a point at its center of mass however different curves may yield different limiting shapes at the infinity scale finally based upon the derived results the performance of the css technique in corner detection and shape representation is analyzed and a fast implementation method of the gaussian filter for noise suppression is proposed

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

edges transitions and criticality in this article various notions of edges encountered in digital image processing are reviewed in terms of compact representation or completion we show that critical exponents defined in statistical physics lead to a much more coherent definition of edges consistent across the scales in acquisitions of natural phenomena such as high resolution natural images or turbulent acquisitions edges belong to the multiscale hierarchy of an underlying dynamics they are understood from a statistical perspective well adapted to fit the case of natural images numerical computation methods for the evaluation of critical exponents in the non ergodic case are recalled which apply for the vast majority of natural images we study the framework of reconstructible systems in a microcanonical formulation show how it redefines edge completion and how it can be used to evaluate and assess quantitatively the adequation of edges as candidates for compact representations we study with particular attention the case of turbulent data in which edges in the classical sense are particularly challenged tests are conducted and evaluated on a standard database for natural images we test the newly introduced compact representation as an ideal candidate for evaluating turbulent cascading properties of complex images and we show better reconstruction performance than the classical tested methods highlightsclassical edge detection algorithms are reviewed in terms of completion a new edge detection scheme based on multiscale hierarchical classification assessing the consistency of edges across scales evaluating edge performance through the framework of reconstructible systems comparing the performance with classical edge operators

tzitzeica transformation is a dressing action we classify the simplest rational elements in a twisted loop group and prove that dressing actions of them on proper indefinite affine spheres give the classical tzitzeica transformation and its dual we also give the group point of view of the permutability theorem construct complex tzitzeica transformations and discuss the group structure for these transformations

a gradient based parameter free approach to shape optimization in shape optimization the independent node movement approach wherein finite element node coordinates are used directly as design variables allows the most freedom for shape change and avoids the time consuming parameterization preprocess however this approach lacks a length scale control that is necessary to ensure a well posed shape optimization problem and avoid numerical instability motivated by the success of filtering techniques that impose minimum length scales in topology optimization we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

local reproducible smoothing without shrinkage a simple local smoothing filter is defined for curves or surfaces combining the advantages of gaussian smoothing and fourier curve description unlike gaussian filters the filter described has no shrinkage problem repeated application of the filter does not yield a curve or surface smaller than the original but simply reproduces the approximate result that would have been obtained by a single application at the largest scale unlike fourier description the filter is local in space the wavelet transform of y meyer 1989 is also shown to have these properties

area and length preserving geometric invariant scale spaces in this paper area preserving multi scale representations of planar curves are described this allows smoothing without shrinkage at the same time preserving all the scale space properties the representations are obtained deforming the curve via geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant when the euclidean geometric heat flow is used the resulting representation is euclidean invariant and similarly it is affine invariant when the affine one is used the flows are geometrically intrinsic to the curve and exactly satisfy all the basic requirements of scale space representations in the case of the euclidean heat flow it is completely local as well the same approach is used to define length preserving geometric flows a similarity scale invariant geometric heat flow is studied as well in this work

local variance controlled forward and backward diffusion for image enhancement and noise reduction in order to improve signal to noise ratio snr and contrast to noise ratio this paper introduces a local variance controlled forward and backward lvcfab diffusion algorithm for edge enhancement and noise reduction in our algorithm an alternative fab diffusion algorithm is proposed the results for the alternative fab algorithm show better algorithm behavior than other existing diffusion fab approaches furthermore two distinct discontinuity measures and the alternative fab diffusion are incorporated into a lvcfab diffusion algorithm where the joint use of the two measures leads to a complementary effect for preserving edge features in digital images this lvc mechanism adaptively modifies the degree of diffusion at any image location and is dependent on both local gradient and inhomogeneity qualitative experiments based on general digital images and magnetic resonance images show significant improvements when the lvcfab diffusion algorithm is used versus the existing anisotropic diffusion and the previous fab diffusion algorithms for enhancing edge features and improving image contrast quantitative analyses based on peak snr confirm the superiority of the proposed lvcfab diffusion algorithm

compact range reflector analysis using the plane wave spectrum approach with an adjustable sampling rate an improved method for determining the test zone field of compact range reflectors is presented the plane wave spectrum pws approach is used to obtain the test zone field from knowledge of the reflector aperture field distribution the method is particularly well suited to the analysis of reflectors with a linearly serrated rim for reduced edge diffraction computation of the pws of the reflector aperture field is facilitated by a closed form expression for the fourier transform of a polygonal window function inverse transformation in the test zone region is accomplished using a fast fourier transform fft algorithm with a properly adjusted sampling rate which is a function of both the reflector size and the distance from the reflector the method is validated by comparison with results obtained using surface current and aperture field integration techniques the performance of several serrated reflectors is evaluated in order to observe the effects of edge diffraction on the test zone fields

hyper complex four manifolds from the tzitzeica equation it is shown how solutions to the tzitzeica equation can be used to construct a family of pseudo hyper complex metrics in four dimensions

optimal estimation of contour properties by cross validated regularization the problem of estimating the properties of smooth continuous contours from discrete noisy samples is used as vehicle to demonstrate the robustness of cross validated regularization applied to a vision problem a method for estimation of contour properties based on smoothing spline approximations is presented generalized cross validation is to devise an automatic algorithm for finding the optimal value of the smoothing regularization parameter from the data the cross validated smoothing splines are then used to obtain optimal estimates of the derivatives of quantized contours experimental results are presented which demonstrate the robustness of the method applied to the estimation of curvature of quantized contours under variable scale rotation and partial occlusion these results suggest the application of generalized cross validation to other computer vision algorithms involving regularization

maximum likelihood localization of 2 d patterns in the gauss laguerre transform domain theoretic framework and preliminary results usual approaches to localization i e joint estimation of position orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures which allow for position estimation independent of scale and orientation in this paper a maximum likelihood method for pattern localization working in the gauss laguerre transform glt domain is presented the glt is based on an orthogonal family of circular harmonic functions with specific radial profiles which permits optimum joint estimation of position and scale rotation parameters looking at the maxima of a gauss laguerre likelihood map the fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the cramer rao lower bound application of the ml estimation method is discussed and an example is provided