wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

shape estimation from shading defocus and correspondence using light field angular coherence light field cameras are quickly becoming commodity items with consumer and industrial applications they capture many nearby views simultaneously using a single image with a micro lens array thereby providing a wealth of cues for depth recovery defocus correspondence and shading in particular apart from conventional image shading one can refocus images after acquisition and shift one s viewpoint within the sub apertures of the main lens effectively obtaining multiple views we present a principled algorithm for dense depth estimation that combines defocus and correspondence metrics we then extend our analysis to the additional cue of shading using it to refine fine details in the shape by exploiting an all in focus image in which pixels are expected to exhibit angular coherence we define an optimization framework that integrates photo consistency depth consistency and shading consistency we show that combining all three sources of information defocus correspondence and shading outperforms state of the art light field depth estimation algorithms in multiple scenarios

a generalized depth estimation algorithm with a single image a depth estimation algorithm proposed by a p pentland 1987 is generalized in the proposed algorithm the raw image data in the vicinity of the edge is used to estimate the depth from defocus since no differentiation operation on the image data is required before the optimization process the method is less sensitive to the noise disturbance of measurements furthermore the edge orientation that was critical in pentland s approach will not be required in the case this algorithm is then applied to synthetic images containing various amounts of noise to test its performance experimental results indicate that the depth estimation errors are kept within 5 of true values on the average when it is applied to real images

an mrf model based approach to simultaneous recovery of depth and restoration from defocused images in this paper we propose a map markov random field mrf based scheme for recovering the depth and the focused image of a scene from two defocused images the space variant blur parameter and the focused image of the scene are both modeled as mrfs and their map estimates are obtained using simulated annealing the scheme is amenable to the incorporation of smoothness constraints on the spatial variations of the blur parameter as well as the scene intensity it also allows for inclusion of line fields to preserve discontinuities the performance of the proposed scheme is tested on synthetic as well as real data and the estimates of the depth are found to be better than that of the existing window based depth from defocus technique the quality of the space variant restored image of the scene is quite good even under severe space varying blurring conditions

fusing images with different focuses using support vector machines many vision related processing tasks such as edge detection image segmentation and stereo matching can be performed more easily when all objects in the scene are in good focus however in practice this may not be always feasible as optical lenses especially those with long focal lengths only have a limited depth of field one common approach to recover an everywhere in focus image is to use wavelet based image fusion first several source images with different focuses of the same scene are taken and processed with the discrete wavelet transform dwt among these wavelet decompositions the wavelet coefficient with the largest magnitude is selected at each pixel location finally the fused image can be recovered by performing the inverse dwt in this paper we improve this fusion procedure by applying the discrete wavelet frame transform dwft and the support vector machines svm unlike dwt dwft yields a translation invariant signal representation using features extracted from the dwft coefficients a svm is trained to select the source image that has the best focus at each pixel location and the corresponding dwft coefficients are then incorporated into the composite wavelet representation experimental results show that the proposed method outperforms the traditional approach both visually and quantitatively

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

on the realizability of biorthogonal m dimensional two band filter banks we show an algebraic approach for the design of ladder structures for causal biorthogonal filter banks the key ingredient of the approach is known in literature as euclid s algorithm using this algorithm we derive some strong result on the design freedom for ladder structures in particular we show that the dimensionality of the problem plays an important role we end by with some conjectures concerning the extensions to multichannel and noncausal filter banks

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

pade table continued fraction expansion and perfect reconstruction filter banks we investigate the relationships among the pade table continued fraction expansions and perfect reconstruction pr filter banks we show how the pade table can be utilized to develop a new lattice structure for general two channel bi orthogonal perfect reconstruction pr filter banks this is achieved through characterization of all two channel biorthogonal pr filter banks the parameterization found using this method is unique for each filter bank similar to any other lattice structure the pr property is achieved structurally and the quantization of the parameters of the lattice does not effect this property furthermore we demonstrate that for a given filter the set of all complementary filters can be uniquely specified by two parameters namely the end to end delay of the system and a scalar quantity finally we investigate the convergence of the successive filters found through the proposed lattice structure and develop a sufficient condition for this convergence

measure of image sharpness using eigenvalues this paper deals with the design and implementation of a novel image sharpness metric based on the statistical approach this sharpness metric is derived by modelling the image sharpness problem as a generalized eigenvalues problem this problem is solved using rayleigh quotient optimization where relevant statistical information of an image is extracted and then represented through a series of eigenvalues the novelty of this paper comes from the application of eigenvalues in image sharpness metric formulation to provide robust assessment with the presence of various blur and noisy conditions firstly the input image is normalized by its energy to minimize the effects caused by image contrast secondly the covariance matrix is computed from this normalized image before it is diagonalized using singular values decomposition svd to obtain a series of eigenvalues finally the image sharpness of the normalized image is determined by the trace of the first several eigenvalues the performance of the proposed metric is gauged by comparing with several objective image sharpness metrics experimental results using synthetic and real images with known and unknown distortion conditions show the robustness and feasibility of the proposed metric in providing relative image sharpness in particular the proposed metric provides wider working range and more precise prediction consistency under all tested deformation conditions although it is slightly expensive in terms of computation than other metrics

perfect reconstruction fir filter banks some properties and factorizations perfect reconstruction finite impulse response fir filter banks are analyzed both in the z transform and time domains showing the alternatives between designs in the two domains various classes of perfect reconstruction schemes are indicated and relations between previously known systems are given windowed modulated filter banks with low computational complexity and perfect reconstruction are shown new factorizations of polyphase filter matrices leading in particular to linear phase filters are given the computational complexity and the architecture of the new structures are indicated

double products and hypersymplectic structures on ℝ4n in this paper we give a procedure to construct hypersymplectic structures on 4n beginning with affine symplectic data on 2n these structures are shown to be invariant by a 3 step nilpotent double lie group and the resulting metrics are complete and not necessarily flat explicit examples of this construction are exhibited

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

multifocus image fusion by combining with mixed order structure tensors and multiscale neighborhood a new fusion scheme based on multiscale neighborhood technique is proposed for multifocus image fusion a new focus measure by combining the structure tensors of mixed order differential is developed an effective focused region detection method is presented based on multiscale neighborhood technique an averaging fusion scheme is presented based on the fusion decision maps of different scale for uncertain regions our method outperforms the traditional methods in various experiments in this study we propose a new method for multifocus image fusion by combining with the structure tensors of mixed order differentials and the multiscale neighborhood in this method the structure tensor of an integral differential is utilized to detect the high frequency regions and the structure tensor of the fractional differential is used to detect the low frequency regions to improve the performance of the fusion method we propose a new focus measure based on the multiscale neighborhood technique to generate the initial fusion decision maps by exploiting the advantages of different scales next based on the multiscale neighborhood technique a post processing method is used to update the initial fusion decision maps during the fusion process the pixels located in the focused inner regions are selected to produce the fused image in order to avoid discontinuities in the transition zone between the focused and defocused regions we propose a new averaging scheme based on the fusion decision maps at different scales our experimental results demonstrate that the proposed method outperformed the conventional multifocus image fusion methods in terms of both their subjective and objective quality

a moment preserving approach for depth from defocus abstract for range sensing using depth from defocus methods the distance d of a point object from the lens can be evaluated by the concise depth formula d p q d b where p and q are constants for a given camera setting and db is the diameter of the blur circle for the point object on the image detector plane the amount of defocus db is traditionally estimated from the spatial parameter of a gaussian point spread function using a complex iterative solution in this paper we use a straightforward and computationally fast method to estimate the amount of defocus from a single camera the observed gray level image is initially converted into a gradient image using the sobel edge operator for the edge point of interest the proportion of the blurred edge region pe in a small neighborhood window is then calculated using the moment preserving technique the value of pe increases as the amount of defocus increases and therefore is used as the description of degradation of the point spread function in addition to the use of the geometric depth formula for depth estimation artificial neural networks are also proposed in this study to compensate for the estimation errors from the depth formula experiments have shown promising results that the rms depth errors are within 5 for the depth formula and within 2 for the neural networks

improved estimation of defocus blur and spatial shifts in spatial domain a homotopy based approach this paper presents a homotopy based algorithm for the recovery of depth cues in the spatial domain the algorithm specifically deals with defocus blur and spatial shifts that is 2d motion stereo disparities and or zooming disparities these cues are estimated from two images of the same scene acquired by a camera evolving in time and or space we show that they can be simultaneously computed by resolving a system of equations using a homotopy method the proposed algorithm is tested using synthetic and real images the results confirm that the use of a homotopy method leads to a dense and accurate estimation of depth cues this approach has been integrated into an application for relief estimation from remotely sensed images

a modified fuzzy c means image segmentation algorithm for use with uneven illumination patterns a novel fuzzy c mean fcm algorithm is proposed for use when active or structured light patterns are projected onto a scene the underlying inhomogeneous illumination intensity due to the point source nature of the projection surface orientation and curvature has been estimated and its effect on the object segmentation minimized firstly we modified the recursive fcm algorithm to include biased illumination field estimation new clustering center and fuzzy clustering functions resulted based on the intensity and average intensity of a pixel neighborhood based object function finally a dilation operator was used on the initial segmented image for further refinement experimental results showed the proposed method was effective for segmenting images illuminated by patterns containing underlying biased intensity fields a higher accuracy was obtained than for traditional fcm and thresholding techniques

toric hypersymplectic quotients we study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space r 4d by the action of a compact abelian group these 4n dimensional quotients carry a multi hamilitonian action of an n torus the image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in r 3n we give precise conditions for smoothness and non degeneracy of such quotients and show how some properties of the quotient geometry and topology are constrained by the combinatorics of the cone configurations examples are studied including non trivial structures on r 4n and metrics on complements of hypersurfaces in compact manifolds

subband coding of images using asymmetrical filter banks we address the problem of the choice of subband filters in the context of image coding the ringing effects that occur in subband based compression schemes are the major unpleasant distortions a new set of two band filter banks suitable for image coding applications is presented the basic properties of these filters are linear phase perfect reconstruction asymmetric length and maximum regularity the better overall performances compared to the classical qmf subband filters are explained the asymmetry of the filter lengths results in a better compaction of the energy especially in the highpass subbands moreover the quantization error is reduced due to the short lowpass synthesis filter the undesirable ringing effect is considerably reduced due to the good step response of the synthesis lowpass filter the proposed design takes into account the statistics of natural images and the effect of quantization errors in the reconstructed images which explains the better coding performance

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

multi scale blur estimation and edge type classification for scene analysis signatures in this work are multi scale representations of local gray level information tied to places in gray scale images where regional differences are locally maximal the information may involve the regional differences themselves called gaussian differences or signed normalized gradient magnitudes korn 1988 or distance relations between edges apparent width measurements or absence of edges in pulse edge pairs at coarser scales using signatures involves the classical problem mentioned by marr and others of relating information across scales a novel result is that a fruitful way of doing this is to build scale paths from coarse to fine exploiting edge focusing and associate with pixel positions along these paths the three quantities gaussian differences apparent width and the binary information absence presence of edges in edge pairs such a structure if used together with proper conditional tests serves the purpose of classifying edges with respect to profile type and can also be used for measuring global contrast degree of diffuseness deblurred line width and qualitative labels such as diffuse versus sharp the structure is used simultaneously for labelling tasks and quantitative measurements theory on apparent widths absence presence of edges in pulse edge pairs is developed for measuring diffuseness and global contrast from gaussian difference signatures a linear least squares approach is suggested extensive experimental results are presented possible applications are in image segementation junction analysis and depth from defocus for the purpose of distinguishing between objects and illumination phenomena such as diffuse shadow edges classification of contours with respect to diffuseness seems useful

stereo matching with color weighted correlation hierarchical belief propagation and occlusion handling in this paper we formulate a stereo matching algorithm with careful handling of disparity discontinuity and occlusion the algorithm works with a global matching stereo model based on an energy minimization framework the global energy contains two terms the data term and the smoothness term the data term is first approximated by a color weighted correlation then refined in occluded and low texture areas in a repeated application of a hierarchical loopy belief propagation algorithm the experimental results are evaluated on the middlebury data sets showing that our algorithm is the top performer among all the algorithms listed there

non parametric blur map regression for depth of field extension real camera systems have a limited depth of field dof which may cause an image to be degraded due to visible misfocus or too shallow dof in this paper we present a blind deblurring pipeline able to restore such images by slightly extending their dof and recovering sharpness in regions slightly out of focus to address this severely ill posed problem our algorithm relies first on the estimation of the spatially varying defocus blur drawing on local frequency image features a machine learning approach based on the recently introduced regression tree fields is used to train a model able to regress a coherent defocus blur map of the image labeling each pixel by the scale of a defocus point spread function a non blind spatially varying deblurring algorithm is then used to properly extend the dof of the image the good performance of our algorithm is assessed both quantitatively using realistic ground truth data obtained with a novel approach based on a plenoptic camera and qualitatively with real images

multiresolution 3 d range segmentation using focus cues this paper describes a novel system for computing a three dimensional 3 d range segmentation of an arbitrary visible scene using focus information the process of range segmentation is divided into three steps an initial range classification a surface merging process and a 3 d multiresolution range segmentation first range classification is performed to obtain quantized range estimates the range classification is performed by analyzing focus cues within a bayesian estimation framework a combined energy functional measures the degree of focus and the gibbs distribution of the class field the range classification provides an initial range segmentation second a statistical merging process is performed to merge the initial surface segments this gives a range segmentation at a coarse resolution third 3 d multiresolution range segmentation 3 d mrs is performed to refine the range segmentation into finer resolutions the proposed range segmentation method does not require initial depth estimates it allows the analysis of scenes containing multiple objects and it provides a rich description of the 3 d structure of a scene

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

detection of intensity changes with subpixel accuracy using laplacian gaussian masks we present a system that takes a gray level image as input locates edges with subpixel accuracy and links them into lines edges are detected by finding zero crossings in the convolution of the image with laplacian of gaussian log masks the implementation differs markedly from m i t s as we decompose our masks exactly into a sum of two separable filters instead of the usual approximation by a difference of two gaussians dog subpixel accuracy is obtained through the use of the facet model 1 we also note that the zero crossings obtained from the full resolution image using a space constant for the gaussian and those obtained from the 1 n resolution image with 1 n pixel accuracy and a space constant of n for the gaussian are very similar but the processing times are very different finally these edges are grouped into lines using the technique described in 2

image multidistortion estimation we present a method for estimating the amount of noise and blur in a distorted image our method is based on the multiscale structural similarity ms ssim framework that although designed to measure image quality is used to estimate the amount of blur and noise in a degraded image given a reference image we show that there exists a bijective mapping between the 2 d noise blur space and the 3 d ms ssim space which allows to recover distortion parameters that mapping allows to formulate the multidistortion estimation problem as a classical optimization problem various search strategies such as newton simplex newuoa and brute force search are presented and compared we also show that a bicubic patch can be used to approximate the bijective mapping between the noise blur space and the 3 d ms ssim space interestingly the use of such a patch reduces the processing time by a factor of 40 without significantly reducing precision based on quantitative results we show that the amount of different types of blur and noise in a distorted image can be recovered with accuracy of roughly 2 and 8 respectively our methods are compared with four state of the art noise and blur estimation techniques

optimal edge detector design i parameter selection and noise effects this paper comments on the optimality of the laplacian of a gaussian edge detection filter which localizes edges through zero crossings in the filtered image the arguments of both marr and hildreth and dickey and shanmugam are reviewed to establish that the filter is optimal in the sense of maximizing output image energy near edge features this filter s principal advantage over other edge detectors is that its response is user adjustable through selection of a single parameter the gaussian standard deviation however no clear method for the selection of this parameter has been provided the problem is addressed here by applying the filter to two ideal periodic edge models blurred by a gaussian distribution point spread function the observed response to the edge spacing and blur standard deviation is then translated into a filter parameter design procedure the problems of optimum filter performance in the presence of additive gaussian noise are then addressed the problem of selecting the sampled filter s coefficient word size is dealt with in a companion paper

joint histogram based cost aggregation for stereo matching this paper presents a novel method for performing efficient cost aggregation in stereo matching the cost aggregation problem is reformulated from the perspective of a histogram giving us the potential to reduce the complexity of the cost aggregation in stereo matching significantly differently from previous methods which have tried to reduce the complexity in terms of the size of an image and a matching window our approach focuses on reducing the computational redundancy that exists among the search range caused by a repeated filtering for all the hypotheses moreover we also reduce the complexity of the window based filtering through an efficient sampling scheme inside the matching window the tradeoff between accuracy and complexity is extensively investigated by varying the parameters used in the proposed method experimental results show that the proposed method provides high quality disparity maps with low complexity and outperforms existing local methods this paper also provides new insights into complexity constrained stereo matching algorithm design

edge and depth from focus this paper proposes a novel method to obtain the reliable edge and depth information by integrating a set of multi focus images i e a sequence of images taken by systematically varying a camera parameter focus in previous work on depth measurement using focusing or defocusing the accuracy depends upon the size and location of local windows where the amount of blur is measured in contrast no windowing is needed in our method the blur is evaluated from the intensity change along corresponding pixels in the multi focus images such a blur analysis enables us not only to detect the edge points without using spatial differentiation but also to estimate the depth with high accuracy in addition the analysis result is stable because the proposed method involves integral computations such as summation and least square model fitting this paper first discusses the fundamental properties of multi focus images based on a step edge model then two algorithms are presented edge detection using an accumulated defocus image which represents the spatial distribution of blur and depth estimation using a spatio focal image which represents the intensity distribution along focus axis the experimental results demonstrate that the highly precise measurement has been achieved 0 5 pixel position fluctuation in edge detection and 0 2 error at 2 4 m in depth estimation

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

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

rational filters for passive depth from defocus a fundamental problem in depth from defocus is the measurement of relative defocus between images the performance of previously proposed focus operators are inevitably sensitive to the frequency spectra of local scene textures as a result focus operators such as the laplacian of gaussian result in poor depth estimates an alternative is to use large filter banks that densely sample the frequency space though this approach can result in better depth accuracy it sacrifices the computational efficiency that depth from defocus offers over stereo and structure from motion we propose a class of broadband operators that when used together provide invariance to scene texture and produce accurate and dense depth maps since the operators are broadband a small number of them are sufficient for depth estimation of scenes with complex textural properties in addition a depth confidence measure is derived that can be computed from the outputs of the operators this confidence measure permits further refinement of computed depth maps experiments are conducted on both synthetic and real scenes to evaluate the performance of the proposed operators the depth detection gain error is less than 1 irrespective of texture frequency depth accuracy is found to be 0 5 1 2 of the distance of the object from the imaging optics

lagrange multiplier approaches to the design of two channel perfect reconstruction linear phase fir filter banks the authors present two approaches to the design of two channel perfect reconstruction linear phase finite impulse response fir filter banks both approaches analyze and design the impulse responses of the analysis filter bank directly the synthesis filter bank is then obtained by simply changing the signs of odd order coefficients in the analysis filter bank the approach deals with unequal length filter banks by designing the lower length filters first one can take advantage of the fact that the number of variables for designing the higher length filters is more than the number of perfect reconstruction constraint equations the second approach generalizes the first and covers the design for all parts of linear phase perfect reconstruction constraint equations

analysis of photometric properties of occluding edges by the reversed projection blurring model this paper analyzes photometric properties of occluding edges and proves that an object surface behind a nearer object is partially observable beyond the occluding edges we first discuss a limitation of the image blurring model using the convolution and then present an optical flux based blurring model named the reversed projection blurring rpb model unlike the multicomponent blurring model proposed by nguyen et al the rpb model enables us to explore the optical phenomena caused by a shift variant point spread function that appears at a depth discontinuity using the rpb model theoretical analysis of occluding edge properties are given and two characteristic phenomena are shown 1 a blurred occluding edge produces the same brightness profiles as would be predicted for a surface edge on the occluding object when the occluded surface radiance is uniform and 2 a nonmonotonic brightness transition would be observed in blurred occluding edge profiles when the occluded object has a surface edge experimental results using real images have demonstrated the validity of the rpb model as well as the observability of the characteristic phenomena of blurred occluding edges

a closed form solution to retinex with nonlocal texture constraints we propose a method for intrinsic image decomposition based on retinex theory and texture analysis while most previous methods approach this problem by analyzing local gradient properties our technique additionally identifies distant pixels with the same reflectance through texture analysis and uses these nonlocal reflectance constraints to significantly reduce ambiguity in decomposition we formulate the decomposition problem as the minimization of a quadratic function which incorporates both the retinex constraint and our nonlocal texture constraint this optimization can be solved in closed form with the standard conjugate gradient algorithm extensive experimentation with comparisons to previous techniques validate our method in terms of both decomposition accuracy and runtime efficiency

multiple depth layers and all in focus image generations by blurring and deblurring operations the depth map and all in focus generations from a single image are proposed the depth map bases on the characteristic curve of coc vs the depth characteristic curve of a camera all in focus image generation is from the estimated depth map a joint deblurring process is proposed to generate an all in focus image in this work we propose novel methods for the generation of multiple depth layers and all in focus images multiple depth layers are produced by applying a sequence of blurring and deblurring operations to determine the depth the proposed method makes no assumptions with regard to the properties of the scene in resolving depth ambiguity in complex images we also developed a method by which to generate all in focus images in which the sharpness is preserved and instabilities imposed by conventional deblurring operations largely eliminated this method involves updating outliers for which depth was over estimated while compensating for errors in the estimation of depth imposed by deblurring

the vortex filament in the minkowski 3 space and generalized bi schrodinger maps by extending the concept of generalized bi schrodinger maps to the case that the target manifold is a para kahler manifold we show that the third order timelike and spacelike correction models of the vortex filament in the minkowski 3 space are equivalent to the generalized bi schrodinger maps from to the hyperbolic 2 space and the de sitter 2 space respectively as a consequence all three typical second to fourth order integrable systems of the akns hierarchy are interpreted in a unified way in terms of generalized bi schrodinger maps based on this exploitation and a general discussion of the generalized bi schodinger maps from into an arbitrary riemannian surface we reveal a property of generalized bi schrodinger maps that is not admitted for schrodinger maps

integration of multiresolution image segmentation and neural networks for object depth recovery a novel technique for three dimensional depth recovery based on two coaxial defocused images of an object with added pattern illumination is presented the approach integrates object segmentation with depth estimation firstly segmentation is performed by a multiresolution based approach to isolate object regions from the background given the presence of blur and pattern illumination the segmentation has three sub procedures image pyramid formation linkage adaptation and unsupervised clustering these maximise the object recognition capability while ensuring accurate position information for depth estimation lower resolution information with a strong correlation to depth is fed into a three layered neural network as input feature vectors and processed using a back propagation algorithm the resulting depth model of object recovery is then used with higher resolution data to obtain high accuracy depth measurements experimental results are presented that show low error rates and the robustness of the model with respect to pattern variation and inaccuracy in optical settings

optimal edge detector design ii coefficient quantization a companion paper describes the design and implementation of the laplacian of a gaussian edge detection filter which localizes edges through zero crossings in the filtered image accuracy in the presence of noise has been found to be proportional to the square root of the filter s standard deviation digital implementation of any continuous filter requires sampling and coefficient quantization the sampled filter was examined but a method is proposed here for selection of a minimum coefficient word size for direct form implementation to satisfy in band rejection bounds

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

development of autofocusing algorithm based on fuzzy transforms in this paper we propose a new passive auto focusing algorithm to acquire images with enhanced quality through a digital camera the focus measure operations play a key role in a passive auto focusing method the proposed focus measure operation is based on a localized version of image variance method the localization of the image variance focus measure operation can be implemented with the use of fuzzy partition and fuzzy transform in order to validate our approach experimental comparative studies are conducted on test images with the use of different focus measure operators the selected operators have been chosen from an extensive review of the state of the art approaches a comparative analysis demonstrates that the proposed algorithm is superior to the conventional methods

a multiple baseline stereo a stereo matching method that uses multiple stereo pairs with various baselines generated by a lateral displacement of a camera to obtain precise distance estimates without suffering from ambiguity is presented matching is performed simply by computing the sum of squared difference ssd values the ssd functions for individual stereo pairs are represented with respect to the inverse distance and are then added to produce the sum of ssds this resulting function is called the sssd in inverse distance it is shown that the sssd in inverse distance function exhibits a unique and clear minimum at the correct matching position even when the underlying intensity patterns of the scene include ambiguities or repetitive patterns the authors first define a stereo algorithm based on the sssd in inverse distance and present a mathematical analysis to show how the algorithm can remove ambiguity and increase precision experimental results with real stereo images are presented to demonstrate the effectiveness of the algorithm

bayesian depth from defocus with shading constraints we present a method that enhances the performance of depth from defocus dfd through the use of shading information dfd suffers from important limitations namely coarse shape reconstruction and poor accuracy on textureless surfaces that can be overcome with the help of shading we integrate both forms of data within a bayesian framework that capitalizes on their relative strengths shading data however is challenging to accurately recover from surfaces that contain texture to address this issue we propose an iterative technique that utilizes depth information to improve shading estimation which in turn is used to elevate depth estimation in the presence of textures the shading estimation can be performed in general scenes with unknown illumination using an approximate estimate of scene lighting with this approach we demonstrate improvements over existing dfd techniques as well as effective shape reconstruction of textureless surfaces

shape from defocus via diffusion defocus can be modeled as a diffusion process and represented mathematically using the heat equation where image blur corresponds to the diffusion of heat this analogy can be extended to nonplanar scenes by allowing a space varying diffusion coefficient the inverse problem of reconstructing 3d structure from blurred images corresponds to an inverse diffusion that is notoriously ill posed we show how to bypass this problem by using the notion of relative blur given two images within each neighborhood the amount of diffusion necessary to transform the sharper image into the blurrier one depends on the depth of the scene this can be used to devise a global algorithm to estimate the depth profile of the scene without recovering the deblurred image using only forward diffusion

neutral calabi yau structures on kodaira manifolds we construct neutral calabi yau metrics and hypersymplectic structures on some kodaira manifolds our structures are symmetric with respect to the central tori

analysis design and implementation of two channel linear phase filter banks a new approach the problem of designing two channel perfect reconstruction fir filter banks with linear phase analysis and synthesis filters is revisited based on a new algebraic formulation all the possible factorized forms for this two band filter bank are derived we thus obtain complete and canonical solutions for the filter banks composed of odd order symmetric and antisymmetric filters type a systems and for those built with symmetric even order filters type b systems a strong characteristic of these new cascade structures which until now had not been identified is related to a defectivity property taking this into account is the key issue to cover all the fir solutions and to design cascade structures being robust to the quantization of their parameters design examples are provided that illustrate our method

the geometry of recursion operators we study the fields of endomorphisms intertwining pairs of symplectic structures using these endomorphisms we prove an analogue of moser s theorem for simultaneous isotopies of two families of symplectic forms we also consider the geometric structures defined by pairs and triples of symplectic forms for which the squares of the intertwining endomorphisms are plus or minus the identity for pairs of forms we recover the notions of symplectic pairs and of holomorphic symplectic structures for triples we recover the notion of a hypersymplectic structure and we also find three new structures that have not been considered before one of these is the symplectic formulation of hyper kahler geometry which turns out to be a strict generalization of the usual definition in terms of differential or kahler geometry

a homotopy based approach for computing defocus blur and affine transform simultaneously this paper presents a homotopy based algorithm for a simultaneous recovery of defocus blur and the affine parameters of apparent shifts between planar patches of two pictures these parameters are recovered from two images of the same scene acquired by a camera evolving in time and or space and for which the intrinsic parameters are known using limited taylor s expansion one of the images and its partial derivatives is expressed as a function of the partial derivatives of the two images the blur difference the affine parameters and a continuous parameter derived from homotopy methods all of these unknowns can thus be directly computed by resolving a system of equations at a single scale the proposed algorithm is tested using synthetic and real images the results confirm that dense and accurate estimation of the previously mentioned parameters can be obtained

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

anti self dual conformal structures with null killing vectors from projective structures using twistor methods we explicitly construct all local forms of four dimensional real analytic neutral signature anti self dual conformal structures m g with a null conformal killing vector we show that m is foliated by anti self dual null surfaces and the two dimensional leaf space inherits a natural projective structure the twistor space of this projective structure is the quotient of the twistor space of m g by the group action induced by the conformal killing vector

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

shape from shading with a linear triangular element surface model the authors propose to combine a triangular element surface model with a linearized reflectance map to formulate the shape from shading problem the main idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements and express the approximating surface as a linear combination of a set of nodal basis functions since the surface normal of a triangular element is uniquely determined by the heights of its three vertices or nodes image brightness can be directly related to nodal heights using the linearized reflectance map the surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique the proposed method does not require any integrability constraint or artificial assumptions on boundary conditions simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method

discrete wavelet transform based on cyclic convolutions a filterbank in which cyclic convolutions are used in place of linear convolutions will be referred to as a cyclic convolution filterbank ccfb a dyadic tree structured ccfb can be used to perform a discrete wavelet transform suitable for coding based on symmetric extension methods this paper derives two types of efficient implementation techniques for the tree structured ccfb one using complex arithmetic and one using only real arithmetic in addition the present paper analyzes in detail the perfect reconstruction pr condition for the two channel ccfb and shows that this condition is much less restrictive than that of usual two channel filterbanks when each of the two channel ccfbs constituting a tree structured ccfb is designed to be pr the whole system is pr a quadrature mirror filter qmf ccfb having the pr property is demonstrated to be easily designed using a standard filter design subroutine in contrast designing a linear phase pr fir qmf bank that has good frequency response is not possible when filters are realized by linear convolutions

a geometric approach to shape from defocus we introduce a novel approach to shape from defocus i e the problem of inferring the three dimensional 3d geometry of a scene from a collection of defocused images typically in shape from defocus the task of extracting geometry also requires deblurring the given images a common approach to bypass this task relies on approximating the scene locally by a plane parallel to the image the so called equifocal assumption we show that this approximation is indeed not necessary as one can estimate 3d geometry while avoiding deblurring without strong assumptions on the scene solving the problem of shape from defocus requires modeling how light interacts with the optics before reaching the imaging surface this interaction is described by the so called point spread function psf when the form of the psf is known we propose an optimal method to infer 3d geometry from defocused images that involves computing orthogonal operators which are regularized via functional singular value decomposition when the form of the psf is unknown we propose a simple and efficient method that first learns a set of projection operators from blurred images and then uses these operators to estimate the 3d geometry of the scene from novel blurred images our experiments on both real and synthetic images show that the performance of the algorithm is relatively insensitive to the form of the psf our general approach is to minimize the euclidean norm of the difference between the estimated images and the observed images the method is geometric in that we reduce the minimization to performing projections onto linear subspaces by using inner product structures on both infinite and finite dimensional hilbert spaces both proposed algorithms involve only simple matrix vector multiplications which can be implemented in real time

depth from defocus a spatial domain approach a new method named stm is described for determining distance of objects and rapid autofocusing of camera systems stm uses image defocus information and is based on a new spatial domain convolution deconvolution transform the method requires only two images taken with different camera parameters such as lens position focal length and aperture diameter both images can be arbitrarily blurred and neither of them needs to be a focused image therefore stm is very fast in comparison with depth from focus methods which search for the lens position or focal length of best focus the method involves simple local operations and can be easily implemented in parallel to obtain the depth map of a scene stm has been implemented on an actual camera system named sparcs experiments on the performance of stm and their results on real world planar objects are presented the results indicate that the accuracy of stm compares well with depth from focus methods and is useful in practical applications the utility of the method is demonstrated for rapid autofocusing of electronic cameras