absolute depth estimation from a single defocused image shape from defocus sfd is one of the most popular techniques in monocular 3d vision while most sfd approaches require two or more images of the same scene captured at a fixed view point this paper presents an efficient approach to estimate absolute depth from a single defocused image instead of directly measuring defocus level of each pixel we propose to design a sequence of aperture shape filters to segment a defocused image by defocus level a boundary weighted belief propagation algorithm is employed to obtain a smooth depth map we also give an estimation of depth error extensive experiments show that our approach outperforms the state of the art single image sfd approaches both in precision of the estimated absolute depth and running time

valuations on sobolev spaces all affinely covariant convex body valued valuations on the sobolev space w 1 1 bbb r n are completely classified it is shown that there is a unique such valuation for blaschke addition this valuation turns out to be the operator which associates with each function f in w 1 1 bbb r n the unit ball of its optimal sobolev norm

shape from focus the shape from focus method presented here uses different focus levels to obtain a sequence of object images the sum modified laplacian sml operator is developed to provide local measures of the quality of image focus the operator is applied to the image sequence to determine a set of focus measures at each image point a depth estimation algorithm interpolates a small number of focus measure values to obtain accurate depth estimates a fully automated shape from focus system has been implemented using an optical microscope and tested on a variety of industrial samples experimental results are presented that demonstrate the accuracy and robustness of the proposed method these results suggest shape from focus to be an effective approach for a variety of challenging visual inspection tasks

detection of stellate distortions in mammograms malignant densities in mammograms have an irregular appearance and frequently are surrounded by a radiating pattern of linear spicules in this paper a method is described to detect such stellate patterns this method is based on statistical analysis of a map of pixel orientations if an increase of pixels pointing to a region is found this region is marked as suspicious especially if such an increase is found in many directions orientations of the image intensity map are determined at each pixel using a multiscale approach at a given scale accurate line based orientation estimates are obtained from the output of three directional second order gaussian derivative operators the orientation at the scale at which these operators have maximum response is selected if a line like structure is present at a given site this method provides an estimate of the orientation of this structure whereas in other cases the image noise will generate a random orientation the pixel orientation map is used to construct two operators which are sensitive to radial patterns of straight lines combination of the output of these operators using a classifier allows for detection of stellate patterns different classification methods have been compared and results obtained on a common database are presented around 90 of the malignant cases were detected at rate of one false positive fp per image

hypotheses for image features icons and textons we review ideas about the relationship between qualitative description of local image structure and quantitative description based on responses to a family of linear filters we propose a sequence of three linking hypotheses the first the feature hypothesis is that qualitative descriptions arise from a category system on filter response space the second the icon hypothesis is that the partitioning into categories of filter response space is determined by a system of iconic images one associated with each point of the space the third the texton hypothesis is that the correct images to play the role of icons are those that are the most likely explanations of a vector of filter responses we present results in support of these three hypotheses including new results on 2 d 1st order structure

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

shape from focus using multilayer feedforward neural networks the conventional shape from focus sff methods have inaccuracies because of piecewise constant approximation of the focused image surface fis we propose a scheme for sff based on representation of three dimensional 3 d fis in terms of neural network weights the neural networks are trained to learn the shape of the fis that maximizes the focus measure

lp minkowski valuations on lq spaces abstract all continuous sl n covariant l p minkowski valuations on l q are classified the only non trivial operators appearing in this context are the asymmetric l p moment operators

the structure of locally orderless images we propose a representation of images in which a global but not a local topology is defined the topology is restricted to resolutions up to the extent of the local region of interest roi although the roi s may contain many pixels there is no spatial order on the pixels within the roi the only information preserved is the histogram of pixel values within the roi s this can be considered as an extreme case of a textel texture element image the histogram is the limit of texture where the spatial order has been completely disregarded we argue that locally orderless images are ubiquitous in perception and the visual arts formally the orderless images are most aptly described by three mutually intertwined scale spaces the scale parameters correspond to the pixellation inner scale the extent of the roi s outer scale and the resolution in the histogram tonal scale we describe how to construct locally orderless images how to render them and how to use them in a variety of local and global image processing operations

a class of invariant valuations on lip sn 1 abstract we provide an integral representation for continuous valuations defined on the space lip s n 1 of lipschitz continuous functions on the unit n 1 sphere which are invariant under rotations and under the addition of linear functions restricted to the unit sphere invariant

continuity and representation of valuations on star bodies abstract it is shown that every continuous valuation defined on n dimensional star bodies has an integral representation in terms of the radial function our argument is based on the non trivial fact that continuous valuations are uniformly continuous on bounded sets we also characterize continuous valuations on the n dimensional star bodies that arise as restriction of a measure on r n

approximate solution of hamilton jacobi inequality by neural networks this paper discusses a problem of solving hamilton jacobi inequality which is a main difficulty in nonlinear h control application a neural networks approach is presented to obtain an approximate solution of hamilton jacobi inequality it will be shown that the problem can be formulated as a maximum value function optimization problem and then be solved by the proposed learning algorithm the algorithm is developed based on nondifferentiable optimization theory the effectiveness of the proposed method is demonstrated by numerical examples

a novel algorithm for estimation of depth map using image focus for 3d shape recovery in the presence of noise three dimensional shape recovery from one or multiple observations is a challenging problem of computer vision in this paper we present a new focus measure for the estimation of a depth map using image focus this depth map can subsequently be used in techniques and algorithms leading to the recovery of a three dimensional structure of the object a requirement of a number of high level vision applications the proposed focus measure has shown robustness in the presence of noise as compared to the earlier focus measures this new focus measure is based on an optical transfer function implemented in the fourier domain the results of the proposed focus measure have shown drastic improvements in estimation of a depth map with respect to the earlier focus measures in the presence of various types of noise including gaussian shot and speckle noises the results of a range of focus measures are compared using root mean square error and correlation metric measures

radial continuous rotation invariant valuations on star bodies we characterize the positive radial continuous and rotation invariant valuations v defined on the star bodies of rn as the applications on star bodies which admit an integral representation with respect to the lebesgue measure that is v k sn 1 k dm where is a positive continuous function k is the radial function associated to k and m is the lebesgue measure on sn 1 as a corollary we obtain that every such valuation can be uniformly approximated on bounded sets by a linear combination of dual quermassintegrals

shape retrieval based on dynamic programming we propose a shape matching algorithm for deformed shapes based on dynamic programming our algorithm is capable of grouping together segments at finer scales in order to come up with appropriate correspondences with segments at coarser scales we illustrate the effectiveness of our algorithm in retrieval of shapes by content on two different two dimensional 2 d datasets one of static hand gesture shapes and another of marine life shapes we also demonstrate the superiority of our approach over traditional approaches to shape matching and retrieval such as fourier descriptors and geometric and sequential moments our evaluation is based on human relevance judgments following a well established methodology from the information retrieval field

maximum likelihood orientation estimation of 1 d patterns in laguerre gauss subspaces a method for measuring the orientation of linear 1 d patterns based on a local expansion with laguerre gauss circular harmonic lg ch functions is presented it lies on the property that the polar separable lg ch functions span the same space as the 2 d cartesian separable hermite gauss 2 d hg functions exploiting the simple steerability of the lg ch functions and the peculiar block linear relationship among the two expansion coefficients sets maximum likelihood ml estimates of orientation and cross section parameters of 1 d patterns are obtained projecting them in a proper subspace of the 2 d hg family it is shown in this paper that the conditional ml solution derived by elimination of the cross section parameters surprisingly yields the same asymptotic accuracy as the ml solution for known cross section parameters the accuracy of the conditional ml estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials a thorough proof of the key relationship between the lg ch and the 2 d hg expansions is also provided

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

efficient diffusion coefficient for image denoising diffusion coefficient has an important role in the performance of partial differential equation pde based image denoising techniques commonly the classical perona malik pm diffusion coefficient is widely used in pde based noise removal algorithms in this paper pm diffusion coefficient is analyzed regarding to its flux based on the analysis pm flux for regions where the gradient magnitude is higher than smoothing threshold may lead to undesirable blurring effect and edge displacement to address these issues the image is divided into three segments based on the gradient magnitude regions where the gradient is lower than the smoothing threshold regions where the gradient is between the smoothing threshold and inflection point of flux and regions where the gradient magnitude is higher than inflection point we define the conditions that should be considered in these three segments then a diffusion coefficient satisfying all these conditions is computed experimental results confirm the performance of the proposed method with regard to peak signal to noise ratio psnr mean structural similarity mssim universal quality index uqi visual information fidelity vif feature similarity fsim information content weighted ssim iw ssim and visual quality

a distance measure and a feature likelihood map concept for scale invariant model matching this paper presents two approaches for evaluating multi scale feature based object models within the first approach a scale invariant distance measure is proposed for comparing two image representations in terms of multi scale features based on this measure the maximisation of the likelihood of parameterised feature models allows for simultaneous model selection and parameter estimation the idea of the second approach is to avoid an explicit feature extraction step and to evaluate models using a function defined directly from the image data for this purpose we propose the concept of a feature likelihood map which is a function normalised to the interval 0 1 and that approximates the likelihood of image features at all points in scale space to illustrate the applicability of both methods we consider the area of hand gesture analysis and show how the proposed evaluation schemes can be integrated within a particle filtering approach for performing simultaneous tracking and recognition of hand models under variations in the position orientation size and posture of the hand the experiments demonstrate the feasibility of the approach and that real time performance can be obtained by pyramid implementations of the proposed concepts

invariant valuations on star shaped sets the brunn minkowski theory of convex bodies and mixed volumes has provided many tools for solving problems involving projections and valuations of compact convex sets in euclidean space among the most beautiful results of twentieth century convexity is hadwiger s characterization theorem for the elementary mixed volumes quermassintegrals see 3 5 9 hadwiger s characterization leads to effortless proofs of numerous results in geometric convexity including mean projection formulas for convex bodies 13 p 294 and various kinematic formulas 7 12 14 15 hadwiger s theorem also provides a connection between rigid motion invariant set functions and symmetric polynomials 1 7 recently advancements have been made in a theory introduced by lutwak 8 that is dual to the brunn minkowski theory a theory tailored for dealing with analogous questions involving star shaped sets and intersections with subspaces see also 2 4 6 in the dual theory convex bodies are replaced by star shaped sets and support functions are replaced by radial functions hadwiger s characterizaton theorem is of such fundamental importance that any candidate for a dual theory must possess a dual analogue however the dual theory in its original form was not sufficiently rich to be able to accommodate a dual of hadwiger s theorem in 6 it was shown that the natural setting for the dual theory is larger than that envisioned by previous investigators by defining the dual topology on star shaped sets in terms of the l topology on the space of n integrable functions on the unit sphere the author was able to extend the dual theory to a broad class of star shaped sets called l stars many new theorems can be proved within this larger framework including a hadwiger style classification theorem for continuous valuations on star shaped sets that are homogeneous with respect to dilation in the present paper we discard the stringent requirement of homogeneity and continue with classification theorems for continuous valuations on article no ai971601

local orientation analysis in images by means of the hermite transform we introduce new theoretical results on how the local differential structure in images can be described processed and coded efficiently by means of the hermite transform it is shown that the hermite transform can take many alternative forms all of which have their specific advantages the various forms of the hermite transform correspond to different ways of coding the local orientation in the image and we describe a systematic theory based on well known principles from vector spaces for deriving such alternative forms one specific case called the sampled hermite transform is shown to be especially interesting for adaptive image processing and coding an application in the field of adaptive noise reduction is included by way of illustration

shape from focus using fast discrete curvelet transform a new method for focus measure computation is proposed to reconstruct 3d shape using image sequence acquired under varying focus plane adaptive histogram equalization is applied to enhance varying contrast across different image regions for better detection of sharp intensity variations fast discrete curvelet transform fdct is employed for enhanced representation of singularities along curves in an input image followed by noise removal using bivariate shrinkage scheme based on locally estimated variance the fdct coefficients with high activity are exploited to detect high frequency variations of pixel intensities in a sequence of images finally focus measure is computed utilizing neighborhood support of these coefficients to reconstruct the shape and a well focused image of the scene being probed

a homogeneous decomposition theorem for valuations on convex functions abstract the existence of a homogeneous decomposition for continuous and epi translation invariant valuations on super coercive functions is established continuous and epi translation invariant valuations that are epi homogeneous of degree n are classified by duality corresponding results are obtained for valuations on finite valued convex functions

optimal depth estimation by combining focus measures using genetic programming three dimensional 3d shape reconstruction is a fundamental problem in machine vision applications shape from focus sff is one of the passive optical methods for 3d shape recovery that uses degree of focus as a cue to estimate 3d shape in this approach usually a single focus measure operator is applied to measure the focus quality of each pixel in the image sequence however the applicability of a single focus measure is limited to estimate accurately the depth map for diverse type of real objects to address this problem we develop optimal composite depth ocd function through genetic programming gp for accurate depth estimation the ocd function is constructed by optimally combining the primary information extracted using one or more focus measures the genetically developed composite function is then used to compute the optimal depth map of objects the performance of the developed nonlinear function is investigated using both the synthetic and the real world image sequences experimental results demonstrate that the proposed estimator is more useful in computing accurate depth maps as compared to the existing sff methods moreover it is found that the heterogeneous function is more effective than homogeneous function

a novel iterative shape from focus algorithm based on combinatorial optimization shape from focus sff is a technique to estimate the depth and 3d shape of an object from a sequence of images obtained at different focus settings in this paper the sff is presented as a combinatorial optimization problem the proposed algorithm tries to find the combination of pixel frames which produces maximum focus measure computed over pixels lying on those frames to reduce the high computational complexity a local search method is proposed after the estimate of the initial depth map solution of an object the neighborhood is defined and an intermediate image volume is generated from the neighborhood the updated depth map solution is found from the intermediate image volume this update process of the depth map solution continues until the amount of improvement is negligible the results of the proposed sff algorithm have shown significant improvements in both the accuracy of the depth map estimation and the computational complexity with respect to the existing sff methods

analysis of focus measure operators for shape from focus shape from focus sff has widely been studied in computer vision as a passive depth recovery and 3d reconstruction method one of the main stages in sff is the computation of the focus level for every pixel of an image by means of a focus measure operator in this work a methodology to compare the performance of different focus measure operators for shape from focus is presented and applied the selected operators have been chosen from an extensive review of the state of the art the performance of the different operators has been assessed through experiments carried out under different conditions such as image noise level contrast saturation and window size such performance is discussed in terms of the working principles of the analyzed operators

the improbability of harris interest points an elementary characterization of the map underlying harris corners also known as harris interest points or key points is provided two principal and basic assumptions made are 1 local image structure is captured in an uncommitted way simply using weighted raw image values around every image location to describe the local image information and 2 the lower the probability of observing the image structure present in a particular point the more salient or interesting this position is i e saliency is related to how uncommon it is to see a certain image structure how surprising it is through the latter assumption the axiomatization proposed makes a sound link between image saliency in computer vision on the one hand and on the other computational models of preattentive human visual perception where exactly the same definition of saliency has been proposed because of this link the characterization provides a compelling case in favor of harris interest points over other approaches

star valuations and dual mixed volumes since its creation by brunn and minkowski what has become known as the brunn minkowski theory has provided powerful machinery to solve a broad variety of inverse problems with stereological data the machinery of the brunn minkowski theory includes mixed volumes of minkowski symmetrization techniques such as those of steiner and blaschke isoperimetric inequalities such as the brunn minkowski minkowski and aleksandrov fenchel inequalities integral transforms such as the cosine transform and important auxiliary bodies associated with these transforms such as minkowski s projection bodies schneider s recent book 22 on the brunn minkowski theory is the best available introduction to the subject while the brunn minkowski theory has proven to be of enormous value in answering inverse questions regarding projections of convex bodies onto subspaces the theory has been of little value in answering inverse questions with data regarding intersections with subspaces however recent advancements have been made in the development of a dual brunn minkowski theory 3 4 5 6 8 9 11 13 16 23 26 27 28 29 which has been tailored specifically for dealing with such questions in contrast to the brunn minkowski theory in the dual theory convex bodies are replaced by star shaped sets and projections onto subspaces are replaced by intersections with subspaces the machinery of the dual theory includes dual mixed volumes introduced by lutwak 15 16 dual isoperimetric inequalities 16 and important auxiliary bodies known as intersection bodies first introduced by busemann for special centered convex bodies in 1 later defined for star shaped sets by lutwak 16 see also 9 a comprehensive introduction to geometric tomography including the dual brunn minkowski theory may be found in gardner s book 17 unfortunately there still remain fundamental and foundational problems with the dual brunn minkowski theory one of the most beautiful and article no 0048

the finite ridgelet transform for image representation the ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines we propose an orthonormal version of the ridgelet transform for discrete and finite size images our construction uses the finite radon transform frat as a building block to overcome the periodization effect of a finite transform we introduce a novel ordering of the frat coefficients we also analyze the frat as a frame operator and derive the exact frame bounds the resulting finite ridgelet transform frit is invertible nonredundant and computed via fast algorithms furthermore this construction leads to a family of directional and orthonormal bases for images numerical results show that the frit is more effective than the wavelet transform in approximating and denoising images with straight edges

noise adaptive soft switching median filter existing state of the art switching based median filters are commonly found to be nonadaptive to noise density variations and prone to misclassifying pixel characteristics at high noise density interference this reveals the critical need of having a sophisticated switching scheme and an adaptive weighted median filter we propose a novel switching based median filter with incorporation of fuzzy set concept called the noise adaptive soft switching median nasm filter to achieve much improved filtering performance in terms of effectiveness in removing impulse noise while preserving signal details and robustness in combating noise density variations the proposed nasm filter consists of two stages a soft switching noise detection scheme is developed to classify each pixel to be uncorrupted pixel isolated impulse noise nonisolated impulse noise or image object s edge pixel no filtering or identity filter standard median sm filter or our developed fuzzy weighted median fwm filter will then be employed according to the respective characteristic type identified experimental results show that our nasm filter impressively outperforms other techniques by achieving fairly close performance to that of ideal switching median filter across a wide range of noise densities ranging from 10 to 70

rational filter design for depth from defocus the paper describes a new simple procedure to determine the rational filters that are used in the depth from defocus dfd procedure previously researched by watanabe and nayar 1998 4 their dfd uses two differently defocused images and the filters accurately model the relative defocus in the images and provide a fast calculation of distance this paper presents a simple method to determine the filter coefficients by separating the m p ratio into a linear and a cubic error correction model the method avoids the previous iterative minimisation technique and computes efficiently the model has been verified by comparison with the theoretical m p ratio the proposed filters have been compared with the previous for frequency response closeness of fit to m p rotational symmetry and measurement accuracy experiments were performed for several defocus conditions it was observed that the new filters were largely insensitive to object texture and modelled the blur more precisely than the previous experiments with real planar images demonstrated a maximum rms depth error of 1 18 for the proposed compared to 1 54 for the previous filters complicated objects were also accurately measured

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

nonlinear approach for enhancement of image focus volume in shape from focus mostly shape from focus algorithms use local averaging using a fixed rectangle window to enhance the initial focus volume in this linear filtering the window size affects the accuracy of the depth map a small window is unable to suppress the noise properly whereas a large window oversmoothes the object shape moreover the use of any window size smoothes focus values uniformly consequently an erroneous depth map is obtained in this paper we suggest the use of iterative 3 d anisotropic nonlinear diffusion filtering andf to enhance the image focus volume in contrast to linear filtering andf utilizes the local structure of the focus values to suppress the noise while preserving edges the proposed scheme is tested using image sequences of synthetic and real objects and results have demonstrated its effectiveness

generic neighborhood operators a method that treats linear neighborhood operators within a unified framework that enables linear combinations concatenations resolution changes or rotations of operators to be treated in a canonical manner is presented various families of operators with special kinds of symmetries such as translation rotation magnification are explicitly constructed in 1 d 2 d and 3 d a concept of order is defined and finite orthonormal bases of functions closely connected with the operators of various orders are constructed linear transformations between the various representations are considered the method is based on two fundamental assumptions a decrease of resolution should not introduce spurious detail and the local operators should be self similar under changes of resolution these assumptions merely sum up the even more general need for homogeneity isotropy scale invariance and separability of independent dimensions of front end processing in the absence of a priori information

a hitherto unnoticed singularity of scale space a hitherto unnoticed singularity of scale space occurs only at isolated points in scale space thus it does not generically occur for single images but it can occur occasionally in members of time sequences say it occurs at those critical points of the image at which the laplacean of the illuminance vanishes a nongeneric condition the structure of scale space in an infinitesimal neighborhood of such a singularity is explored the effect of the singularity of mappings between copies of an image at different levels of resolution is evaluated and checked with a numerical calculation

real time focus range sensor structures of dynamic scenes can only be recovered using a real time range sensor depth from defocus offers an effective solution to fast and dense range estimation however accurate depth estimation requires theoretical and practical solutions to a variety of problems including recovery of textureless surfaces precise blur estimation and magnification variations caused by defocusing both textured and textureless surfaces are recovered using an illumination pattern that is projected via the same optical path used to acquire images the illumination pattern is optimized to maximize accuracy and spatial resolution in computed depth the relative blurring in two images is computed using a narrow band linear operator that is designed by considering all the optical sensing and computational elements of the depth from defocus system defocus invariant magnification is achieved by the use of an additional aperture in the imaging optics a prototype focus range sensor has been developed that has a workspace of 1 cubic foot and produces up to 512 spl times 480 depth estimates at 30 hz with an average rms error of 0 2 several experimental results are included to demonstrate the performance of the sensor

radial continuous valuations on star bodies we show that a radial continuous valuation defined on the n dimensional star bodies extends uniquely to a continuous valuation on the n dimensional bounded star sets moreover we provide an integral representation of every such valuation in terms of the radial function which is valid on the dense subset of the simple borel star sets along the way we also show that every radial continuous valuation defined on the n dimensional star bodies can be decomposed as a sum v v v where both v and v are positive radial continuous valuations

shape from focus by tensor voting in this correspondence we address the task of recovering shape from focus sff as a perceptual organization problem in 3 d using tensor voting depth hypotheses from different focus operators are validated based on their likelihood to be part of a coherent 3 d surface thereby exploiting scene geometry and focus information to generate reliable depth estimates the proposed method is fast and yields significantly better results compared with existing sff methods

improving shape from focus using defocus cue the shape from focus sff method uses a sequence of frames to estimate the structure of a 3 d object its accuracy depends on the step size by which the translational table is moved while capturing the images existing sff algorithms use an ad hoc interpolation strategy to account for the error due to the finite step size we propose an improved sff method that uses relative defocus blur derived from actual image data to arrive at the final estimates of the structure of the object a space variant image restoration scheme is also proposed to obtain a focused image of the 3 d object the reconstructed 3 d structure as well as the quality of the restored image are superior for the proposed method in comparison to traditional sff

sampling for shape from focus in optical microscopy shape from focus sff which relies on image focus as a cue within sequenced images represents a passive technique in recovering object shapes in scenes although numerous methods have been recently proposed less attention has been paid to particular factors affecting them in regard to sff one such critical factor impacting system application is the total number of images a large data set requires a huge amount of computation power whereas decreasing the number of images causes shape reconstruction to be crude and erroneous the total number of images is inversely proportional to interframe distance or sampling step size in this paper interframe distance or sampling step size criteria for sff systems have been formulated in particular light ray focusing is approximated by the use of a gaussian beam followed by the formulation of a sampling expression using nyquist sampling consequently a fitting function for focus curves is also obtained experiments are performed on simulated and real objects to validate the proposed schemes

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

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

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

the generic bilinear calibration estimation problem we identify a very general recurring pattern in a number of well known problems in biological and machine vision many problems are of a peculiar double sided nature one attempts to estimate certain properties of the environment using a certain type of equipment and simultaneously one attempts to calibrate the same equipment on the structure of the environment at first sight this appears the kind of the chicken and the egg problem that might well prove to be insoluble however due to basic constraints that universally apply e g the world is only three dimensional a solution up to a certain class of ambiguity transformations often exists the more complicated the problem is the less important the remaining ambiguity will be at least in a relative sense many well known problems are special in that they can be cast in bilinear form sometimes after transformation or the introduction of dummy variables instances include photometric stereo photometric estimations e g of lightness local differential image operators a variety of photogrammetric problems etc it turns out that many of these problems and together these make up a large fraction of the generic problems in machine vision today can be cast in a simple universal framework this framework enables one to handle arbitrarily large that is not minimal consistent configurations noisy thus inconsistent date sets automatically the level at which prior information either of a deterministic or a statistical nature is used assumptions such as constant albedo rigidity uniform distributions etc is clearly separated as an additional typically nonlinear stage