on the asymptotic convergence of b spline wavelets to gabor functions a family of nonorthogonal polynomial spline wavelet transforms is considered these transforms are fully reversible and can be implemented efficiently the corresponding wavelet functions have a compact support it is proven that these b spline wavelets converge to gabor functions modulated gaussian pointwise and in all l sub p norms with 1

fast implementation of the continuous wavelet transform with integer scales we describe a fast noniterative algorithm for the evaluation of continuous spline wavelet transforms at any integer scale m in this approach the input signal and the analyzing wavelet are both represented by polynomial splines the algorithm uses a combination of moving sum and zero padded filters and its complexity per scale is o n where n is the signal length the computation is exact and the implementation is noniterative across scales we also present examples of spline wavelets exhibiting properties that are desirable for either singularity detection first and second derivative operators or gabor like time frequency signal analysis

on scalar extensions and spectral decompositions of complex symmetric operators abstract in this paper we prove that a complex symmetric operator with property is subscalar as a corollary we get that such operators with rich spectra have nontrivial invariant subspaces we also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints

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

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

boundary conditions for young van vliet recursive filtering young and van vliet have designed computationally efficient methods for approximating gaussian based convolutions by running a recursive infinite impulse response iir filter forward over the input signal then running a second iir filter backward over the first filter s output to transition between the two filters they use a suboptimal heuristic that produces significant amplitude and phase distortion for all points within about three standard deviations of the right hand boundary in this correspondence a simple linear transition rule that eliminates this distortion is derived

on stable complete minimal hypersurfaces in r n 1 abstract by using the interior curvature estimate and gromov s compactness theorem we prove that a stable complete minimal hypersurface in rn l with finite total scalar curvature must be a hyperplane this extends the result obtained by p b rard in remarques sur l quation de j simons pitman monographs surveys pure appl math vol 52 1991 pp 47 57

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

acceleration of the shiftable mbi o 1 algorithm for bilateral filtering and nonlocal means a direct implementation of the bilateral filter requires o s2 operations per pixel where s is the effective width of the spatial kernel a fast implementation of the bilateral filter that required o 1 operations per pixel with respect to s was recently proposed this was done by using trigonometric functions for the range kernel of the bilateral filter and by exploiting their so called shiftability property in particular a fast implementation of the gaussian bilateral filter was realized by approximating the gaussian range kernel using raised cosines later it was demonstrated that this idea could be extended to a larger class of filters including the popular non local means filter as already observed a flip side of this approach was that the run time depended on the width r of the range kernel for an image with dynamic range 0 t the run time scaled as o t2 r2 with r this made it difficult to implement narrow range kernels particularly for images with large dynamic range in this paper we discuss this problem and propose some simple steps to accelerate the implementation in general and for small r in particular we provide some experimental results to demonstrate the acceleration that is achieved using these modifications

scale based diffusive image filtering preserving boundary sharpness and fine structures image acquisition techniques often suffer from low signal to noise ratio snr and or contrast to noise ratio cnr although many acquisition techniques are available to minimize these post acquisition filtering is a major off line image processing technique commonly used to improve the snr and cnr a major drawback of filtering is that it often diffuses blurs important structures along with noise here the authors introduce two scale based filtering methods that use local structure size or object scale information to arrest smoothing around fine structures and across even low gradient boundaries the first of these methods uses a weighted average over a scale dependent neighborhood while the other employs scale dependent diffusion conductance to perform filtering both methods adaptively modify the degree of filtering at any image location depending on local object scale object scale allows the authors to accurately use a restricted homogeneity parameter for filtering in regions with fine details and in the vicinity of boundaries while a generous parameter in the interiors of homogeneous regions qualitative experiments based on both phantoms and patient magnetic resonance images show significant improvements using the scale based methods over the extant anisotropic diffusive filtering method in preserving fine details and sharpness of object boundaries quantitative analyses utilizing 25 phantom images generated under a range of conditions of blurring noise and background variation confirm the superiority of the new scale based approaches

on the gradient inverse weighted filter image processing d c c wang et al 1981 presented a gradient inverse weighted giw filter the proposed noise smoothing scheme is based on the observation that variations of gray levels inside a region are smaller than those between regions reducing noise without smearing edges is the advantage of this nonlinear filter as an improvement of the giw filter a new algorithm is introduced examples show that it can preserve edges and smooth noise more efficiently

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

improvements on fast space variant elliptical filtering using box splines it is well known that box filters can be efficiently computed using pre integration and local finite differences by generalizing this idea and by combining it with a nonstandard variant of the central limit theorem we had earlier proposed a constant time or o 1 algorithm that allowed one to perform space variant filtering using gaussian like kernels the algorithm was based on the observation that both isotropic and anisotropic gaussians could be approximated using certain bivariate splines called box splines the attractive feature of the algorithm was that it allowed one to continuously control the shape and size covariance of the filter and that it had a fixed computational cost per pixel irrespective of the size of the filter the algorithm however offered a limited control on the covariance and accuracy of the gaussian approximation in this paper we propose some improvements of our previous algorithm

some bernstein type rigidity theorems abstract we prove some bernstein type rigidity theorems for complete submanifolds in a euclidean space and space like submanifolds of a lorentzian space in particular we obtain a bernstein rigidity theorem for complete minimal submanifolds of arbitrary codimension in euclidean space

growth conditions compact perturbations and operator subdecomposability with applications to generalized cesaro operators abstract we adapt recent results of albrecht and ricker to obtain conditions under which growth constraints on the left resolvent of a banach space operator are preserved under suitable perturbations as an application we establish bishop s property for certain generalized cesaro operators on the classical hardy spaces h p 1 p our methods also apply to unilateral weighted shifts whose weight sequence converges sufficiently rapidly as well as to perturbations of restrictions of a class of generalized scalar operators

spatially variant convolution with scaled b splines we present an efficient algorithm to compute multidimensional spatially variant convolutions or inner products between n dimensional signals and b splines or their derivatives of any order and arbitrary sizes the multidimensional b splines are computed as tensor products of 1 d b splines and the input signal is expressed in a b spline basis the convolution is then computed by using an adequate combination of integration and scaled finite differences as to have for moderate and large scale values a computational complexity that does not depend on the scaling factor to show in practice the benefit of using our spatially variant convolution approach we present an adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector

recursive anisotropic 2 d gaussian filtering based on a triple axis decomposition we describe a recursive algorithm for anisotropic 2 d gaussian filtering based on separating the filter into the cascade of three rather two 1 d filters the filters operate along axes obtained by integer horizontal and or vertical pixel shifts this eliminates interpolation which removes spatial inhomogeneity in the filter and produces more elliptically shaped kernels it also results in a more regular filter structure which facilitates implementation in dsp chips finally it improves matching between filters with the same eccentricity and width but different orientations our analysis and experiments indicate that the computational complexity is similar to an algorithm that operates along two axes 11ms for a 512times512 image using a 3 2 ghz pentium 4 pc on the other hand given a limited set of basis filter axes there is an orientation dependent lower bound on the achievable aspect ratios

gap theorems for minimal submanifolds of a hyperbolic space abstract this paper provides some gap theorems for complete immersed minimal submanifolds of dimension no less than five in a hyperbolic space namely we show that an n 5 dimensional complete immersed minimal submanifold m in a hyperbolic space is totally geodesic if the l 2 norm of a on geodesic balls centered at some point p m has less than quadratic growth and if either sup x m a 2 x is not too large or the l n norm of a on m is small here a is the second fundamental form of m

operators which do not have the single valued extension property abstract in this paper we shall consider the relationships between a local version of the single valued extension property of a bounded operator t l x on a banach space x and some quantities associated with t which play an important role in fredholm theory in particular we shall consider some conditions for which t does not have the single valued extension property at a point o c

cesaro averaging operators on hardy spaces it is shown that the cesaro averaging operator 1 satisfies an inequality which immediately implies that it is bounded on certain hardy spaces including h p 0 p h p 0 p 2 for 0 the operator which is conjugate to on h 2 is also shown to be bounded on h p for 1 p p and 0

points d evaluation pour les operateurs cycliques ayant la propriete de bishop β abstract let t be a linear bounded cyclic operator in a separable complex hilbert space h let b t and ba t denote respectively the set of bounded point evaluation and the set of analytic point evaluation of t we show that if t has the bishop property then ba t b t ap t where ap t is the approximate spectrum of t in the particular case when t is an operator of multiplication by z in a hardy space this was proved by trent pacific j math 80 1979 279 on the other hand using the generalized and the local spectral theory we obtain sufficient conditions on ba t under which the spectrum of t and the local spectrum of t at any y 0 in h coincide at the end results involving the spectral picture of quasi similar cyclic operators are given

least squares image resizing using finite differences we present an optimal spline based algorithm for the enlargement or reduction of digital images with arbitrary noninteger scaling factors this projection based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are b splines of any degree n a noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a for a given choice of basis functions the results of our method are consistently better than those of the standard interpolation procedure the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal to noise ratio the method can be generalized to include other classes of piecewise polynomial functions expressed as linear combinations of b splines and their derivatives

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

solid extensions of the cesaro operator on the hardy space h2 d abstract we introduce and study the largest banach space of analytic functions on the unit disc which is solid for the coefficient wise order and to which the classical cesaro operator c h 2 h 2 can be continuously extended while still maintaining its values in h 2 properties of this banach space h c e s 2 as well as a characterization of individual analytic functions which belong to h c e s 2 are presented in addition both the multiplier space of h c e s 2 and the spectrum of c h c e s 2 h c e s 2 are determined

on local spectral properties of complex symmetric operators abstract in this paper we study properties of complex symmetric operators in particular we prove that every complex symmetric operator having property or is decomposable moreover we show that complex symmetric operator t has dunford s property c and it satisfies weyl s theorem if and only if its adjoint does

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

on complex symmetric operator matrices abstract an operator t l h is said to be complex symmetric if there exists a conjugation j on h such that t j t j in this paper we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications in particular we consider the operator matrix of the form t a b 0 j a j where j is a conjugation on h we show that if a is complex symmetric then t is decomposable if and only if a is furthermore we provide some conditions so that a weyl s theorem holds for the operator matrix t

on the generalized resolvent in banach spaces abstract we construct for a closed densely defined operator a on a banach space x a generalized resolvent on the domain of fredholm regularity of a meromorphic in the fredholm domain a of a

characterizations of perturbations of spectra of 2 2 upper triangular operator matrices abstract when a b h and b b k are given we denote by m c the operator acting on the infinite dimensional separable hilbert space h k of the form m c a c 0 b in this paper we first give some necessary and sufficient conditions for m c to be a left invertible operator an upper semi weyl upper semi fredholm operator for some c b k h which extend the corresponding results in cao et al 2006 4 cao and meng 2005 5 hwang and lee 2001 12 and li and du 2006 15 then we present some counter examples

theoretical analysis of the max median filter median filtering has been used successfully for extracting features from noisy one dimensional signals however the extension of the one dimensional case to higher dimensions has not always yielded satisfactory results although noise suppression is obtained too much signal distortion is introduced and many features of interest are lost in this paper we introduce a multidimensional filter based on a combination of one dimensional median estimates it is shown that threshold decomposition holds for this class of filters making the deterministic analysis simpler invariant signals to the filter called root signals consist of very low resolution features making this filter much more attractive than conventional median filters

optimal edge preserving hybrid filters based on the least mean square error criterion at the edge position a new algorithm is presented to obtain a class of optimal edge preserving hybrid filters that include the lee 1980 additive filter and the gradient inverse weighted filter as a result we show that the gain of the lee additive filter is not optimal and derive the optimal form of this filter in addition some examples are given

singularity theory and phantom edges in scale space the process of detecting edges in a one dimensional signal by finding the zeros of the second derivative of the signal can be interpreted as the process of detecting the critical points of a general class of contrast functions that are applied to the signal it is shown that the second derivative of the contrast function at the critical point is related to the classification of the associated edge as being phantom or authentic the contrast of authentic edges decreases with filter scale while the contrast of phantom edges are shown to increase with scale as the filter scale increases an authentic edge must either turn into a phantom edge or join with a phantom edge and vanish the points in the scale space at which these events occur are seen to be singular points of the contrast function using ideas from singularity or catastrophy theory the scale map contours near these singular points are found to be either vertical or parabolic

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

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

means of unitaries conjugations and the friedrichs operator abstract if c is a conjugation an isometric conjugate linear involution on a separable complex hilbert space h then t b h is called c symmetric if t c t c in this note we prove that each c symmetric contraction t is the mean of two c symmetric unitary operators we discuss several corollaries and an application to the friedrichs operator of a planar domain

variational problems and partial differential equations on implicit surfaces a novel framework for solving variational problems and partial differential equations for scalar and vector valued data defined on surfaces is introduced in this paper the key idea is to implicitly represent the surface as the level set of a higher dimensional function and to solve the surface equations in a fixed cartesian coordinate system using this new embedding function the equations are then both intrinsic to the surface and defined in the embedding space this approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces as is commonly done in the literature we describe the framework and present examples in computer graphics and image processing applications including texture synthesis flow field visualization and image and vector field intrinsic regularization for data defined on 3d surfaces

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

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

fast o 1 bilateral filtering using trigonometric range kernels it is well known that spatial averaging can be realized in space or frequency domain using algorithms whose complexity does not scale with the size or shape of the filter these fast algorithms are generally referred to as constant time or o 1 algorithms in the image processing literature along with the spatial filter the edge preserving bilateral filter involves an additional range kernel this is used to restrict the averaging to those neighborhood pixels whose intensity are similar or close to that of the pixel of interest the range kernel operates by acting on the pixel intensities this makes the averaging process nonlinear and computationally intensive particularly when the spatial filter is large in this paper we show how the o 1 averaging algorithms can be leveraged for realizing the bilateral filter in constant time by using trigonometric range kernels this is done by generalizing the idea presented by porikli i e using polynomial kernels the class of trigonometric kernels turns out to be sufficiently rich allowing for the approximation of the standard gaussian bilateral filter the attractive feature of our approach is that for a fixed number of terms the quality of approximation achieved using trigonometric kernels is much superior to that obtained by porikli using polynomials

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

resolvant generalise et separation des points singuliers quasi fredholm c apostol et k clancey trans amer math soc 215 1976 293 300 ont introduit la notion de projection spectrale generalisee cette notion permet en particulier de separer les ensembles finis de points singuliers dans le domaine semi fredholm s a d un operateur a borne dans un hilbert h dans ce travail on se propose de generaliser ce resultat au domaine quasi fredholm de a q a et pour cela nous donnons une nouvelle representation triangulaire du type d apostol

essential point spectra of operator matrices trough local spectral theory abstract for a b x b b y and c b y x let m c be the operator defined on x y by a c 0 b in this paper we study defect set a b m c where is the browder spectrum the essential approximate point spectrum and browder essential approximate point spectrum we then give application for weyl s and browder s theorems

complex symmetric partial isometries an operator t b h is complex symmetric if there exists a conjugate linear isometric involution c h h so that t ct c we provide a concrete description of all complex symmetric partial isometries in particular we prove that any partial isometry on a hilbert space of dimension 4 is complex symmetric

fir median hybrid filters this paper introduces a new generalized class of median type filters which we call fir median hybrid fmh filters the input signal x n is filtered with m linear phase fir filters and the output of the fmh filter is the median of the outputs of the fir filters the statistical properties of the fmh filters are analyzed for input signals with gaussian double exponential and uniform density functions it is shown that fmh filters have essentially the same statistical properties and same type of root signals as the standard median sm filters fmh filters preserve corner points and ramps and attenuate impulsive type noise components effectively an interesting subclass of the fmh filters requiring only one scaling multiplier two additions and three compare swap operations irrespective of the filter length is introduced in the examples speed improvement by a factor of 450 is obtained over an otherwise approximately equivalent sm filter

the koebe semigroup and a class of averaging operators on hp d we study on the hardy space h p the operators t f given by formule where f z is analytic on the unit disc d and has re f z 0 each such operator is closely related to a strongly continuous semigroup of weighted composition operators by studying first an extremal such semigroup the koebe semigroup we are able to obtain the upper bound t f p 2p re 1 f 0 im 1 f 0 for the norm we also show that t f is compact on h p if and only if the measure in the herglotz representation of 1 f is continuous

an optimal nonorthogonal separation of the anisotropic gaussian convolution filter we give an analytical and geometrical treatment of what it means to separate a gaussian kernel along arbitrary axes in ropfn and we present a separation scheme that allows us to efficiently implement anisotropic gaussian convolution filters for data of arbitrary dimensionality based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed the proposed method relies on nonorthogonal convolution axes and works completely in image space thus it avoids the need for a fast fourier transform fft subroutine depending on the accuracy and speed requirements different interpolation schemes and methods to implement the one dimensional gaussian finite impulse response and infinite impulse response can be integrated special emphasis is put on analyzing the performance and accuracy of the new method in particular we show that without any special optimization of the source code it can perform anisotropic gaussian filtering faster than methods relying on the fft

consistent invertibility of upper triangular operator matrices abstract let h and k be separable infinite dimensional hilbert spaces and let a b h and b b k be given operators a necessary and sufficient condition is obtained for a c 0 b to be a ci operator for some respectively every c b k h furthermore some related results are obtained

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

resolvent estimates and decomposable extensions of generalized cesaro operators we determine the spectrum of generalized cesaro operators with essentially rational symbols acting on various spaces of analytic functions including hardy spaces weighted bergman and dirichlet spaces then we show that in all cases these operators are subdecomposable c 2009 elsevier inc all rights reserved

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

weyl type theorems of 2 2 upper triangular operator matrices abstract let m c a c 0 b be an upper triangular operator matrix on the hilbert space h h where h is a hilbert space in this paper necessary and sufficient conditions for m c a b are obtained where is the essential spectrum the weyl spectrum the browder spectrum the essential approximate point spectrum and the browder essential approximate point spectrum for m c we further investigate the relationship among weyl type theorems such as weyl s a weyl s browder s and a browder s theorems

self adjoint perturbations of spectra for upper triangular operator matrices abstract this paper is concerned with the self adjoint perturbations of the spectra for the upper triangular partial operator matrix with given diagonal entries a necessary and sufficient condition is given under which such operator matrix admits a weyl fredholm operator completion by choosing some bounded self adjoint operator it is shown that the self adjoint perturbation of the weyl essential spectrum can be the proper set of the general perturbation combining the spectral properties we further characterize the perturbation of the weyl essential spectrum for hamiltonian operators

invertible composition operators on hp abstract the weakly closed algebras generated by certain sets of composition operators are shown to be reflexive a structure theorem for invertible composition operators on h2 is obtained and used to show that such operators are reflexive the structure theorem shows that invertible hyperbolic composition operators are similar to cosubnormal operators built up from bilateral weighted shifts another consequence of the structure theorem is that the composition operators induced by hyperbolic disc automorphisms are universal thus the general invariant subspace problem for hilbert space operators is contained in the problem of determining the invariant subspace lattices of these operators

the semi fredholmness of 2 2 operator matrices abstract let h 1 and h 2 be separable infinite dimensional hilbert spaces and let a b h 1 b b h 2 and c b h 2 h 1 be given operators a necessary and sufficient condition is obtained for a c x b to be a right left fredholm operator for some x b h 1 h 2

on the spectrum of the cesaro operator on spaces of analytic functions this paper concerns the cesaro operator acting on various spaces of analytic functions on the unit disc the remarkable fact that this operator is subnormal when acting on the hardy space h2 has lead to extensive studies of its spectral picture on other spaces of this type we present some of the methods that have been used to obtain information about the spectrum of the cesaro operator acting on hardy and bergman spaces and give a unified approach to these problems which also yields new results in this direction in particular we prove that the cesaro operator is subdecomposable on h1 and on the standard weighted bergman spaces 0

a class of integral operators on spaces of analytic functions abstract we determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators t f z z 1 1 z 0 z f 1 1 d acting on either the analytic besov spaces or other banach spaces of analytic functions on the unit disc including the classical hardy and weighted bergman spaces as well as certain dirichlet spaces and generalized bloch spaces our results unify and extend recent work by aleman and persson 2 the current authors 4 and albrecht and miller 1

the classes of local spectral theory in this paper we consider several classes of operators on a complex hilbert space which appear in local spectral theory a complete description in terms of properties of various parts of the spectrum is obtained for the operators in the closure and for the operators in the interior of each of these classes

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

continuity of spectrum and approximate point spectrum on operator matrices abstract let x and y be given banach spaces for a b x b b y and c b y x let m c be the operator defined on x y by m c a c 0 b in this paper we give conditions for continuity of at m c through continuity of at a and b where can be equal to the spectrum or approximate point spectrum

on the closure of the complex symmetric operators compact operators and weighted shifts abstract we study the closure cso of the set cso of all complex symmetric operators on a separable infinite dimensional complex hilbert space among other things we prove that every compact operator in cso is complex symmetric using a construction of kakutani as motivation we also describe many properties of weighted shifts in cso cso in particular we show that weighted shifts which demonstrate a type of approximate self similarity belong to cso cso as a byproduct of our treatment of weighted shifts we explain several ways in which our result on compact operators is optimal

spectral properties of cesaro like operators on weighted bergman spaces abstract we determine spectral pictures and resolvent estimates for a class of integral operators on the weighted bergman spaces l a p d m for p 1 1 and show in particular these operators are subdecomposable moreover in the case that p 2 we show that some of these operators are subnormal some are normaloid and some are subscalar

carleson measures multipliers and integration operators for spaces of dirichlet type for 0 1 we let d p denote the space of those functions f which are analytic in the unit disc d z c z 1 and satisfy d 1 z 2 f z p dx dy in this paper we characterize the positive borel measures in d such that d p l q d 0 p q we also characterize the pointwise multipliers from d p to d q 0 p q i fp 2 p in particular we prove that if

perturbation of spectra of operator matrices and local spectral theory abstract for a l x b l y and c l y x we denote by m c the operator defined on x y by a c 0 b in this article we study defect set d a b m c for different spectra including the spectrum the essential spectrum weyl spectrum and the approximate point spectrum we then apply the obtained results to the stability of such spectra d and the classes of operators c for which stability holds of m c using local spectral theory