comparametric equations with practical applications in quantigraphic image processing it is argued that hidden within the flow of signals from typical cameras through image processing to display media is a homomorphic filter while homomorphic filtering is often desirable there are some occasions where it is not thus cancellation of this implicit homomorphic filter is proposed through the introduction of an antihomomorphic filter this concept gives rise to the principle of quantigraphic image processing wherein it is argued that most cameras can be modeled as an array of idealized light meters each linearly responsive to a semi monotonic function of the quantity of light received integrated over a fixed spectral response profile this quantity depends only on the spectral response of the sensor elements in the camera a particular class of functional equations called comparametric equations is introduced as a basis for quantigraphic image processing these are fundamental to the analysis and processing of multiple images differing only in exposure the gamma correction of an image is presented as a simple example of a comparametric equation for which it is shown that the underlying quantigraphic function does not pass through the origin thus it is argued that exposure adjustment by gamma correction is inherently flawed and alternatives are provided these alternatives when applied to a plurality of images that differ only in exposure give rise to a new kind of processing in the amplitude domain the theoretical framework presented in this paper is applicable to the processing of images from nearly all types of modern cameras this paper is a much revised draft of a 1992 peer reviewed but unpublished report by the author entitled lightspace and the wyckoff principle

weighted repeated median smoothing and filtering we propose weighted repeated median filters and smoothers for robust nonparametric regression in general and for robust online signal extraction from time series in particular the new methods allow us to remove outlying sequences and to preserve discontinuities shifts in the underlying regression function the signal in the presence of local linear trends suitable weighting of the observations according to their distances in the design space reduces the bias arising from nonlinearities and improves the efficiency using larger bandwidths while still distinguishing long term shifts from outlier sequences other localized robust regression techniques like s m and mm estimators as well as weighted l 1 regression are examined for comparison

computation of the para pseudoinverse for oversampled filter banks forward and backward greville formulas frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience in frame expansions the least square signal reconstruction operator is called the dual frame which can be obtained by choosing the synthesis filter bank as the para pseudoinverse of the analysis bank in this paper we study the computation of the dual frame by exploiting the greville formula which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended here we first develop the backward greville formula to handle the case of row deletion based on the forward greville formula we then study the computation of para pseudoinverse for extended filter banks and laplacian pyramids through the backward greville formula we investigate the frame based error resilient transmission over erasure channels the necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived a postfiltering structure is also presented to implement the para pseudoinverse when the transform coefficients in one subband are completely lost

nonlinear wavelet transforms for image coding via lifting we investigate central issues such as invertibility stability synchronization and frequency characteristics for nonlinear wavelet transforms built using the lifting framework the nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework we also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels preliminary compression results for model and real world images demonstrate the promise of our techniques

interactions and outliers in the two way analysis of variance the two way analysis of variance with interactions is a well established and integral part of statistics in spite of its long standing it is shown that the standard definition of interactions is counterintuitive and obfuscates rather than clarifies a different definition of interaction is given which among other advantages allows the detection of interactions even in the case of one observation per cell a characterization of unconditionally identifiable interaction patterns is given and it is proved that such patterns can be identified by the l 1 functional the unconditionally identifiable interaction patterns describe the optimal breakdown behavior of any equivariant location functional from which it follows that the l 1 functional has optimal breakdown behavior possible lack of uniqueness of the l 1 functional can be overcome using an m functional with an external scale derived independently from the observations the resulting procedures are applied to some data sets including one describing the results of an interlaboratory test

robust estimation in structured linear regression a structured linear regression model is one in which there are permanent dependencies among some p row vectors of the n x p design matrix to study structured linear regression we introduce a new class of robust estimators called d estimators which can be regarded as a generalization of the least median of squares and least trimmed squares estimators they minimize a dispersion function of the ordered absolute residuals up to the rank h we investigate their breakdown point and exact fit point as a function of h in structured linear regression it is found that the d and s estimators can achieve the highest possible breakdown point for h appropriately chosen it is shown that both the maximum breakdown point and the corresponding optimal value of h h op are sample dependent they hinge on the design but not on the response the relationship between the breakdown point and the design vanishes when h is strictly larger than h op however when h is smaller than h op the breakdown point depends in a complicated way on the design as well as on the response

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

orthogonal and biorthogonal fir hexagonal filter banks with sixfold symmetry recently hexagonal image processing has attracted attention the hexagonal lattice has several advantages in comparison with the rectangular lattice the conventionally used lattice for image sampling and processing for example a hexagonal lattice needs less sampling points it has better consistent connectivity it has higher symmetry and its structure is plausible to human vision systems the multiresolution analysis method has been used for hexagonal image processing since the hexagonal lattice has high degree of symmetry it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice the orthogonal or prefect reconstruction pr hexagonal filter banks that are available in the literature have only threefold symmetry in this paper we investigate the construction of orthogonal and pr finite impulse response fir hexagonal filter banks with sixfold symmetry we obtain block structures of 7 size refinement seven channel two dimensional orthogonal and pr fir hexagonal filter banks with sixfold rotational symmetry radic7 refinement orthogonal and biorthogonal wavelets based on these block structures are constructed in this paper we also consider fir hexagonal filter banks with axial line symmetry and we present a block structure of fir hexagonal filter banks with pseudo sixfold axial symmetry

color image coding using morphological pyramid decomposition presents a new algorithm that utilizes mathematical morphology for pyramidal coding of color images the authors obtain lossy color image compression by using block truncation coding at the pyramid levels to attain reduced data rates the pyramid approach is attractive due to low computational complexity simple parallel implementation and the ability to produce acceptable color images at moderate data rates in many applications the progressive transmission capability of the algorithm is very useful the authors show experimental results for color images at data rates of 1 89 bits pixel

block median pyramidal transform analysis and denoising applications a nonlinear multiscale pyramidal transform based on nonoverlapping block decompositions using the median operation and a polynomial approximation is considered it is shown that this structure can be useful for denoising of oneand two dimensional 1 d and 2 d signals various denoising techniques are analyzed including methods based on spatially adaptive thresholding and partial cycle spinning algorithms an analytical method for deriving the distribution function of the transform coefficients is also presented this in turn can be used for the selection of thresholds for denoising applications

a new family of nonredundant transforms using hybrid wavelets and directional filter banks we propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks we convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks where we form a nonredundant transform family which exhibits both directional and nondirectional basis functions we demonstrate the potential of the proposed transforms using nonlinear approximation in addition we employ the proposed family in two key image processing applications image coding and denoising and show its efficiency for these applications

a semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data a fundamentally new approach that accurately estimates the camera response function from comparametric data i e pixel data from two differently exposed images over a common field of view is presented it does so by solving for the camera response function from its associated comparametric relation the approach offers several advantageous features including having a complexity that is independent of the number of pixel data considered allowing for the modeling of saturated pixels enabling an inherently constrained optimization problem to be solved in an unconstrained manner and the easy incorporation into an existing framework for joint image registration this is accomplished by approximating the camera response function with a constrained piecewise linear model so that its solution within the comparametric camera relation can be obtained this results in a semiparametric comparametric model optimally determined from pixel data which is directly parameterized in terms of the exposure parameter subsequently it is shown how this semiparametric model is used for exposure estimation from captured images finally we incorporate the semiparametric model within an existing and previously published framework for simultaneous and joint spatial and tonal image registration in order to illustrate the developed model s performance

leverage and breakdown in l 1 regression abstract in this article the notion of leverage of a design point when fitting a linear regression model is interpreted geometrically in the case of least squares fitting the leverage indicators based on the diagonal of the hat matrix are widely applied by interpreting these hat matrix indicators geometrically leverage can be generalized to groups of design points as well as to other methods of fitting the article introduces a leverage indicator that is appropriate for l 1 regression and discusses some aspects of this new diagnostic it is shown that in the case of l 1 regression the leverage indicators have a precise interpretation they tell us about the breakdown and or the exactness of fit as an application the article considers the maximal possible breakdown value of l 1 regression and the choice of designs that achieve this maximum

image registration using log polar mappings for recovery of large scale similarity and projective transformations this paper describes a novel technique to recover large similarity transformations rotation scale translation and moderate perspective deformations among image pairs we introduce a hybrid algorithm that features log polar mappings and nonlinear least squares optimization the use of log polar techniques in the spatial domain is introduced as a preprocessing module to recover large scale changes e g at least four fold and arbitrary rotations although log polar techniques are used in the fourier mellin transform to accommodate rotation and scale in the frequency domain its use in registering images subjected to very large scale changes has not yet been exploited in the spatial domain in this paper we demonstrate the superior performance of the log polar transform in featureless image registration in the spatial domain we achieve subpixel accuracy through the use of nonlinear least squares optimization the registration process yields the eight parameters of the perspective transformation that best aligns the two input images extensive testing was performed on uncalibrated real images and an array of 10 000 image pairs with known transformations derived from the corel stock photo library of royalty free photographic images

groupwise geometric and photometric direct image registration image registration consists in estimating geometric and photometric transformations that align two images as best as possible the direct approach consists in minimizing the discrepancy in the intensity or color of the pixels the inverse compositional algorithm has been recently proposed by baker et al for the direct estimation of groupwise geometric transformations it is efficient in that it performs several computationally expensive calculations at a pre computation phase photometric transformations act on the value of the pixels they account for effects such as lighting change jointly estimating geometric and photometric transformations is thus important for many tasks such as image mosaicing we propose an algorithm to jointly estimate groupwise geometric and photometric transformations while preserving the efficient pre computation based design of the original inverse compositional algorithm it is called the dual inverse compositional algorithm it uses different approximations than the simultaneous inverse compositional algorithm and handles groupwise geometric and global photometric transformations its name stems from the fact that it uses an inverse compositional update rule for both the geometric and the photometric transformations we demonstrate the proposed algorithm and compare it to previous ones on simulated and real data this shows clear improvements in computational efficiency and in terms of convergence

ranging through gabor logons a consistent hierarchical approach in this work the correspondence problem in stereo vision is handled by matching two sets of dense feature vectors inspired by biological evidence these feature vectors are generated by a correlation between a bank of gabor sensors and the intensity image the sensors consist of two dimensional gabor filters at various scales spatial frequencies and orientations which bear close resemblance to the receptive field profiles of simple v1 cells in visual cortex a hierarchical stochastic relaxation method is then used to obtain the dense stereo disparities unlike traditional hierarchical methods for stereo feature based hierarchical processing yields consistent disparities to avoid false matchings due to static occlusion a dual matching based on the imaging geometry is used

image enhancement based on a nonlinear multiscale method an image enhancement method that reduces speckle noise and preserves edges is introduced the method is based on a new nonlinear multiscale reconstruction scheme that is obtained by successively combining each coarser scale image with the corresponding modified interscale image simulation results are included to demonstrate the performance of the proposed method

breakdown and groups the concept of breakdown point was introduced by hampel ph d dissertation 1968 univ california berkeley ann math statist 42 1971 1887 1896 and developed further by among others huber robust statistics 1981 wiley new york and donoho and huber in a festschrift for erich l lehmann 1983 157 184 wadsworth belmont ca it has proved most successful in the context of location scale and regression problems attempts to extend the concept to other situations have not met with general acceptance in this paper we argue that this is connected to the fact that in the location scale and regression problems the translation and affine groups give rise to a definition of equivariance for statistical functionals comparisons in terms of breakdown points seem only useful when restricted to equivariant functionals and even here the connection between breakdown and equivariance is a tenuous one institute of mathematical statistics 2005

exact solutions of one pattern formation model abstract the nonlinear evolution equation for describing the pattern formation processes on the semiconductor surfaces under ion beam bombardment is studied the painleve analysis of equation is considered the new elliptic solution of this equation is obtained

detail enhanced exposure fusion in a typical processing chain of image enhancement an exposure fusion scheme can be used to synthesize a more detailed low dynamic range ldr image directly from a set of differently exposed ldr images without generation of an intermediate high dynamic range image in this brief we introduce a new quadratic optimization based method to extract fine details from a vector field the new method extracts fine details from a set of differently exposed ldr images simultaneously the extracted fine details are then added to an intermediate ldr image which is fused by simply using an existing exposure fusion scheme with this the proposed scheme can enhance fine details to produce sharper images

simultaneous homographic and comparametric alignment of multiple exposure adjusted pictures of the same scene an approach is presented that can simultaneously align multiple exposure adjusted pictures of the same scene both in their spatial coordinates as well as in their pixel values the approach is featureless and produces an image mosaic at a common spatial and exposure reference and also addresses the misalignment problem common to methods that compose mosaics from only pair wise registered image pairs the objective function considered minimizes the sum of the collective variance over pixels of a global coordinate grid on which to create the final image the models employed relate images spatially by homographic transformations and tonally by comparametric functions the importance of performing joint spatial and tonal registration on exposure adjusted images is emphasized by providing two examples in which spatial only registration fails the performance between pair wise and simultaneous registration under both spatial only and joint registration procedures is discussed

exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid exact travelling wave solutions in terms of the weierstrass p function of the equation eta t a0 eta x a1 eta eta x a2 eta xxx b0 eta xx b 1 eta eta x x b2 eta xxxx 0 are obtained these solutions may describe particularly both the evolution of a bounded conoidal wave and kink shaped waves

video orbits of the projective group a simple approach to featureless estimation of parameters we present direct featureless methods for estimating the eight parameters of an exact projective homographic coordinate transformation to register pairs of images together with the application of seamlessly combining a plurality of images of the same scene resulting in a single image or new image sequence of greater resolution or spatial extent the approach is exact for two cases of static scenes 1 images taken from the same location of an arbitrary three dimensional 3 d scene with a camera that is free to pan tilt rotate about its optical axis and zoom or 2 images of a flat scene taken from arbitrary locations the featureless projective approach generalizes interframe camera motion estimation methods that have previously used a camera model which lacks the degrees of freedom to exactly characterize such phenomena as camera pan and tilt and or which have relied upon finding points of correspondence between the image frames the featureless projective approach which operates directly on the image pixels is shown to be superior in accuracy and the ability to enhance the resolution the proposed methods work well on image data collected from both good quality and poor quality video under a wide variety of conditions sunny cloudy day night these new fully automatic methods are also shown to be robust to deviations from the assumptions of static scene and no parallax

block coordinate gauss newton optimization and constrained monotone regression for image registration in the presence of outlier objects in this paper we propose the block coordinate gauss newton regression method in order to conduct a correlation based registration considering the intensity difference between images in the presence of outlier objects in the proposed method the parameters are decomposed into two blocks one of which is for the spatial registration and the other for the intensity compensation the two blocks are sequentially updated by the gauss newton update and the polynomial regression respectively because of the separated blocks we can perform a joint optimization with low computational complexity and high implementation flexibility for example we apply separately appropriate scaling techniques to the parameter blocks for a stable and fast convergence of the algorithm furthermore we apply the constrained monotone regression with a robust outlier detection scheme for the intensity compensation block from numerical results it is shown that the proposed algorithm more effectively performs a correlation based registration considering the intensity difference alleviating the influence of the outlier objects compared to the traditional registration algorithms that perform the joint optimization

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

wavelet transforms associated with finite cyclic groups multiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers an important class of multiresolution decompositions are the laplacian pyramid schemes in which the resolution is successively halved by recursively low pass filtering the signal under analysis and decimating it by a factor of two in general the principal framework within which multiresolution techniques have been studied and applied is the same as that used in the discrete time fourier analysis of sequences of complex numbers an analogous framework is developed for the multiresolution analysis of finite length sequences of elements from arbitrary fields attention is restricted to sequences of length 2 sup n for n a positive integer so that the resolution may be recursively halved to completion as in finite length fourier analysis a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields

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

the dual bootstrap iterative closest point algorithm with application to retinal image registration motivated by the problem of retinal image registration this paper introduces and analyzes a new registration algorithm called dual bootstrap iterative closest point dual bootstrap icp the approach is to start from one or more initial low order estimates that are only accurate in small image regions called bootstrap regions in each bootstrap region the algorithm iteratively 1 refines the transformation estimate using constraints only from within the bootstrap region 2 expands the bootstrap region and 3 tests to see if a higher order transformation model can be used stopping when the region expands to cover the overlap between images steps 1 and 3 the bootstrap steps are governed by the covariance matrix of the estimated transformation estimation refinement step 2 uses a novel robust version of the icp algorithm in registering retinal image pairs dual bootstrap icp is initialized by automatically matching individual vascular landmarks and it aligns images based on detected blood vessel centerlines the resulting quadratic transformations are accurate to less than a pixel on tests involving approximately 6000 image pairs it successfully registered 99 5 of the pairs containing at least one common landmark and 100 of the pairs containing at least one common landmark and at least 35 image overlap

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

progressive image transmission using vector quantization on images in pyramid form a progressive image transmission scheme in which vector quantization is applied to images represented by pyramids is proposed a mean pyramid representation of an image is first built up by forming a sequence of reduced size images by averaging over blocks of 2 2 pixels a difference pyramid is then built up by taking the differences between successive levels in the mean pyramid progressive transmission is achieved by sending all the nodes in the difference pyramid starting from the top level and ending at the bottom level the kth approximate image can be formed by adding the information of level k to the previously reproduced k 1 st approximation to gain efficiency vector quantization is applied to the difference pyramid of the image on a level by level basis if the errors due to quantization at level k are properly delivered and included in the next level k 1 then it is demonstrated that the original image can be reconstructed an entropy coder is used to encode the final residual error image losslessly thus ensuring perfect reproduction of the original image the experiments demonstrate that it is possible to achieve simultaneously lossless and progressive transmission with compression at the intermediate level the use of vector quantization results in a coding gain over that obtained using only a huffman coder excellent reproduction is achieved at a bit rate of only 0 06 bits pixel

on two channel filter banks with directional vanishing moments the contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform one way to guarantee good approximation behavior is to let the directional filters in the contourlet filter bank have sharp frequency response this requires filters with large support size we seek to isolate the key filter property that ensures good approximation in this direction we propose filters with directional vanishing moments dvm these filters we show annihilate information along a given direction we study two channel filter banks with dvm filters we provide conditions under which the design of dvm filter banks is possible a complete characterization of the product filter is thus obtained we propose a design framework that avoids 2 d factorization using the mapping technique the filters designed when used in the contourlet transform exhibit nonlinear approximation comparable to the conventional filters while being shorter and therefore providing better visual quality with less ringing artifacts furthermore experiments show that the proposed filters outperform the conventional ones in image approximation and denoising

jointly registering images in domain and range by piecewise linear comparametric analysis this paper describes an approach whereby comparametric analysis is used in jointly registering image pairs in their domain and range i e in their spatial coordinates and pixel values respectively this is accomplished by approximating a camera s nonlinear comparametric function with a constrained piecewise linear one the optimal fitting of this approximation to comparagram data is then used in a re parameterized version of the camera s comparametric function to estimate the exposure difference between images doing this allows the inherently nonlinear problem of joint domain and range registration to be performed using a computationally attractive least squares formalism the paper first presents the range registration process and then describes the strategy for performing the joint registration the models used allow for the pair wise registration of images taken from a camera that can automatically adjust its exposure as well as tilt pan rotate and zoom about its optical center results concerning the joint registration as well as range only registration are provided to demonstrate the method s effectiveness

application of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations abstract the application of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth sixth and seventh order are obtained the efficiency of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations is demonstrated

multiscale hybrid linear models for lossy image representation in this paper we introduce a simple and efficient representation for natural images we view an image in either the spatial domain or the wavelet domain as a collection of vectors in a high dimensional space we then fit a piece wise linear model i e a union of affine subspaces to the vectors at each downsampling scale we call this a multiscale hybrid linear model for the image the model can be effectively estimated via a new algebraic method known as generalized principal component analysis gpca the hybrid and hierarchical structure of this model allows us to effectively extract and exploit multimodal correlations among the imagery data at different scales it conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation e g dct wavelets or an adaptive uni modal linear transformation e g pca or a multimodal model that uses only cluster means e g vq we will justify both quantitatively and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost despite a small overhead of the model our careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal to noise ratios than many existing methods including wavelets we also briefly address how the same hybrid linear modeling paradigm can be extended to be potentially useful for other applications such as image segmentation

efficient synthesis of gaussian filters by cascaded uniform filters gaussian filtering is an important tool in image processing and computer vision in this paper we discuss the background of gaussian filtering and look at some methods for implementing it consideration of the central limit theorem suggests using a cascade of simple filters as a means of computing gaussian filters among simple filters uniform coefficient finite impulse response digital filters are especially economical to implement the idea of cascaded uniform filters has been around for a while 13 16 we show that this method is economical to implement has good filtering characteristics and is appropriate for hardware implementation we point out an equivalence to one of burt s methods 1 3 under certain circumstances as an extension we describe an approach to implementing a gaussian pyramid which requires approximately two addition operations per pixel per level per dimension we examine tradeoffs in choosing an algorithm for gaussian filtering and finally discuss an implementation

optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images optimal hierarchical coding is sought for progressive or scalable image transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal and subband image coders are determined for images subject to corruption by quantization or transmission noise given arbitrary analysis filters and assuming adequate knowledge of the noise statistics optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal and subband image decompositions experimental results illustrate the implementation and performance of the optimal coders

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

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

optimal generating kernels for image pyramids by piecewise fitting a novel class of generating kernels for image pyramids is introduced when these kernels are convolved with intensity functions of images continuous piecewise surfaces composed of polynomial tensor products are fitted to the intensity functions the fittings are optimal in the sense that the mean square error between them and the original intensity functions is minimized two members of the class are introduced and symmetry normalization unimodality and equal contribution properties are proved these kernels possess attractive properties such as small window size fast inverse transformation and minimum error experiments show that they compare favorably with existing ones in terms of mean square error

estimation of variance components with high breakdown point and high efficiency summary for the one way random effects model three noniterative robust variance component estimators are investigated for these estimators block breakdown points measurement breakdown points and efficiency are derived it is shown that the block breakdown points are approximating 50 and that the measurement breakdown points are not smaller than 25 by deriving the asymptotic normal distribution of these estimators we show that two of the new estimators have an asymptotic efficiency greater than 82 and under certain circumstances up to 96 competing estimators have lower breakdown points and lower efficiencies a simulation study shows that the high efficiency also appears for finite samples the use of the estimators for interlaboratory tests is demonstrated in a practical example

stereo correspondence by surface reconstruction an algorithm that solves the computational stereo correspondence and the surface reconstruction is presented the algorithm integrates the reconstruction process in the correspondence analysis by means of multipass attribute matching and disparity refinement in the matching process the requirement of attribute similarity is relaxed with the pass number while the requirement for agreement between the predicted and the measured disparity is tightened disparity discontinuities and occluded areas are detected by analyzing the partial derivatives of the reconstructed disparity surface results on synthetic and on real stereo image pairs are reported

analysis and enhancements to piecewise linear comparametric image registration this correspondence details enhancements to previous work on piecewise linear comparametric image registration the enhancements come in the form of slope constraints and knots location selection in the comparametric modeling an analysis of the properties of comparametric functions leads to two general slope constraints that along with a knot location selection based on the reference image s pixel value distribution serves to reduce error and sensitivity to the number of segments considered as well as allow for the solution to cases in which there are gaps in the comparagram results on real images are presented

spherical mosaics with quaternions and dense correlation we describe an algorithm for generating spherical mosaics from a collection of images acquired from a common optical center the algorithm takes as input an arbitrary number of partially overlapping images an adjacency map relating the images initial estimates of the rotations relating each image to a specified base image and approximate internal calibration information for the camera the algorithm s output is a rotation relating each image to the base image and revised estimates of the camera s internal parameters our algorithm is novel in the following respects first it requires no user input our image capture instrumentation provides both an adjacency map for the mosaic and an initial rotation estimate for each image second it optimizes an objective function based on a global correlation of overlapping image regions third our representation of rotations significantly increases the accuracy of the optimization finally our representation and use of adjacency information guarantees globally consistent rotation estimates the algorithm has proved effective on a collection of nearly four thousand images acquired from more than eighty distinct optical centers the experimental results demonstrate that the described global optimization strategy is superior to non global aggregation of pair wise correlation terms and that it successfully generates high quality mosaics despite significant error in initial rotation estimates

existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity the inverse balancing method for the determination of the necessary conditions of existence of solitary solutions to mth order differential equations with nth order polynomial nonlinearity is presented in this paper it is shown that the order of possible solitary solutions does not increase if orders of the differential equation and the polynomial nonlinearity increase furthermore the relationships between the order of the solitary solution and the order of the equation and the nonlinearity are given in the explicit form

automatic panoramic image stitching using invariant features this paper concerns the problem of fully automated panoramic image stitching though the 1d problem single axis of rotation is well studied 2d or multi row stitching is more difficult previous approaches have used human input or restrictions on the image sequence in order to establish matching images in this work we formulate stitching as a multi image matching problem and use invariant local features to find matches between all of the images because of this our method is insensitive to the ordering orientation scale and illumination of the input images it is also insensitive to noise images that are not part of a panorama and can recognise multiple panoramas in an unordered image dataset in addition to providing more detail this paper extends our previous work in the area brown and lowe 2003 by introducing gain compensation and automatic straightening steps

significance linked connected component analysis for wavelet image coding the success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation there have been several very competitive wavelet coders developed namely shapiro s 1993 embedded zerotree wavelets ezw servetto et al s 1995 morphological representation of wavelet data mrwd and said and pearlman s see ieee trans circuits syst video technol vol 6 p 245 50 1996 set partitioning in hierarchical trees spiht we develop a novel wavelet image coder called significance linked connected component analysis slcca of wavelet coefficients that extends mrwd by exploiting both within subband clustering of significant coefficients and cross subband dependency in significant fields extensive computer experiments on both natural and texture images show convincingly that the proposed slcca outperforms ezw mrwd and spiht for example for the barbara image at 0 25 b pixel slcca outperforms ezw mrwd and spiht by 1 41 db 0 32 db and 0 60 db in psnr respectively it is also observed that slcca works extremely well for images with a large portion of texture for eight typical 256 spl times 256 grayscale texture images compressed at 0 40 b pixel slcca outperforms spiht by 0 16 db 0 63 db in psnr this performance is achieved without using any optimal bit allocation procedure thus both the encoding and decoding procedures are fast

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

nonmetric calibration of wide angle lenses and polycameras images taken with wide angle cameras tend to have severe distortions which pull points towards the optical center this paper proposes a simple method for recovering the distortion parameters without the use of any calibration objects since distortions cause straight lines in the scene to appear as curves in the image our algorithm seeks to find the distortion parameters that map the image curves to straight lines the user selects a small set of points along the image curves recovery of the distortion parameters is formulated as the minimization of an objective function which is designed to explicitly account for noise in the selected image points experimental results are presented for synthetic data as well as real images we also present the idea of a polycamera which is defined as a tightly packed camera cluster possible configurations are proposed to capture very large fields of view such camera clusters tend to have a nonsingle viewpoint we therefore provide analysis of what we call the minimum working distance for such clusters finally we present results for a polycamera consisting of four wide angle sensors having a minimum working distance of about 4 m on undistorting the acquired images using our proposed technique we create real time high resolution panoramas

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

image filtering using multiresolution representations it is shown how multiresolution representations can be used for filter design and implementation these representations provide a coarse frequency decomposition of the image which forms the basis for two filtering techniques the first method based on image pyramids is used for approximating the convolution of an image with a given mask in this technique a filter is designed using a least squares procedure based on filters synthesized from the basic pyramid equivalent filters the second method is an adaptive noise reduction algorithm an optimally filtered image is synthesized from the multiresolution levels which in this case are maintained at the original sampling density individual pixels of the image representation are linearly combined under a minimum mean square error criterion this uses a local signal to noise ratio estimate to provide the best compromise between noise removal and resolution loss

image registration by super curves we solve the 2 d affine image registration problem by curve matching and alignment our approach starts with a super curve which is formed by superimposing two affine related curves in one coordinate system we use b spline fusion technique to find a single b spline approximation of the super curve and a registration between the two curves simultaneously this approach achieves superior accuracy and efficiency in curve matching and alignment we then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps which are affine invariant the combination of edge detection and curve alignment lead to accurate image registration

nonmetric calibration of camera lens distortion differential methods and robust estimation this paper addresses the problem of calibrating camera lens distortion which can be significant in medium to wide angle lenses our approach is based on the analysis of distorted images of straight lines we derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines unlike the other existing approaches we also provide fast closed form solutions to the distortion coefficients we prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm our approach provides a way to get around this and at the same time it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise robust results in addition while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another we present a robust approach to distortion calibration based on the least median of squares estimator our approach is thus able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three dimensional linear segments experiments to evaluate the performance of this approach on synthetic and real data are reported

inconsistency of resampling algorithms for high breakdown regression estimators and a new algorithm because high breakdown estimators hbes are impractical to compute exactly in large samples approximate algorithms are used the algorithm generally produces an estimator with a lower consistency rate and breakdown value than the exact theoretical estimator this discrepancy grows with the sample size with the implication that huge computations are needed for good approximations in large high dimension samples the workhorse for hbes has been the elemental set or basic resampling algorithm this turns out to be completely ineffective in high dimensions with high levels of contamination however enriching it with a concentration step turns it into a method that can handle even high levels of contamination provided that the regression outliers are located on random cases it remains ineffective if the regression outliers are concentrated on high leverage cases we focus on the multiple regression problem but several of the broad conclusions notably those of the inadequacy of fixed numbers of

decoupled linear estimation of affine geometric deformations and nonlinear intensity transformations of images we consider the problem of registering two observations on an arbitrary object where the two are related by a geometric affine transformation of their coordinate systems and by a nonlinear mapping of their intensities more generally the framework is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object we show that the original high dimensional nonlinear and nonconvex search problem of simultaneously recovering the geometric and radiometric deformations can be represented by an equivalent sequence of two linear systems a solution of this sequence yields an exact explicit and efficient solution to the joint estimation problem

wrap around effect removal finite ridgelet transform for multiscale image denoising denoising in wavelet domain is an attractive research field recently the research focused on finding some algorithms that can detect line singularities of image while smoothing noise based on the finite radon transform a finite ridgelet transform was derived for this purpose but the wrap around effect of the finite radon transform limits its power greatly in this paper a way is pointed out to remove the wrap around effect of the finite radon transform by embedding it into a moving window pyramid a multiscale image denoising algorithm is developed

an fft based technique for translation rotation and scale invariant image registration this correspondence discusses an extension of the well known phase correlation technique to cover translation rotation and scaling fourier scaling properties and fourier rotational properties are used to find scale and rotational movement the phase correlation technique determines the translational movement this method shows excellent robustness against random noise

efficient image segmentation using partial differential equations and morphology the goal of this paper is to investigate segmentation methods that combine fast preprocessing algorithms using partial differential equations pdes with a watershed transformation with region merging we consider two well founded pde methods a nonlinear isotropic diffusion filter that permits edge enhancement and a convex nonquadratic variational image restoration method which gives good denoising for the diffusion filter an efficient algorithm is applied using an additive operator splitting aos that leads to recursive and separable filters for the variational restoration method a novel algorithm is developed that uses aos schemes within a gaussian pyramid decomposition examples demonstrate that preprocessing by these pde techniques significantly improves the watershed segmentation and that the resulting segmentation method gives better results than some traditional techniques the algorithm has linear complexity and it can be used for arbitrary dimensional data sets the typical cpu time for segmenting a 256 image on a modern pc is far below one second

texture features for classification of ultrasonic liver images the classification of ultrasonic liver images is studied making use of the spatial gray level dependence matrices the fourier power spectrum the gray level difference statistics and the laws texture energy measures features of these types are used to classify three sets of ultrasonic liver images normal liver hepatoma and cirrhosis 30 samples each the bayes classifier and the hotelling trace criterion are employed to evaluate the performance of these features from the viewpoint of speed and accuracy of classification it is found that these features do not perform well enough hence a new texture feature set multiresolution fractal features based on multiple resolution imagery and the fractional brownian motion model is proposed to detect diffuse liver diseases quickly and accurately fractal dimensions estimated at various resolutions of the image are gathered to form the feature vector texture information contained in the proposed feature vector is discussed a real time implementation of the algorithm produces about 90 correct classification for the three sets of ultrasonic liver images

mode kn factor analysis for image ensembles in this corespondence we study the extra factor estimation problem with the assumption that the training image ensemble is expressed as an nth order tensor with the nth dimension characterizing all features for an image and other dimensions for different extra factors such as illuminations poses and identities to overcome the local minimum issue of conventional algorithms designed for this problem we present a novel statistical learning framework called mode kn factor analysis for obtaining a closed form solution to estimating the extra factors of any test image in the learning stage for the kth k ne n dimension of the data tensor the mode kn patterns are constructed by concatenating the feature dimension and the kth extra factor dimension and then a mode kn factor analysis model is learnt based on the mode kn patterns unfolded from the original data tensor in the inference stage for a test image the mode classification of the kth dimension is performed within a probabilistic framework the advantages of mode kn factor analysis over conventional tensor analysis algorithms are twofold 1 a closed form solution instead of iterative sub optimal solution as conventionally is derived for estimating the extra factor mode of any test image and 2 the classification capability is enhanced by interacting with the process of synthesizing data of all other modes in the k th dimension experiments on the pointing 04 and cmu pie databases for pose and illumination estimation both validate the superiority of the proposed algorithm over conventional algorithms for extra factor estimation

on bounds of shift variance in two channel multirate filter banks critically sampled multirate fir filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage we assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged we express these changes by a so called commutator we then derive a sharp upper bound for shift variance via the operator norm of the commutator which is independent of the input signal its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator leading to a matrix norm which depends on frequency this bound can be regarded as a worst case instance holding for all input signals for two channel fir filter banks with perfect reconstruction pr we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used moreover the framework allows to identify the signals for which the upper bound is almost reached as so called near maximizers of the frequency dependent matrix norm for unitary pr filter banks these near maximizers are shown to be narrow band signals to complement this worst case bound we derive an additional bound on shift variance for input signals with given amplitude spectra where we use wide band model spectra instead of narrow band signals like the operator norm this additional bound is based on the above frequency dependent matrix norm we provide results for various critically sampled two channel filter banks such as quadrature mirror filters pr conjugated quadrature filters wavelets and biorthogonal filters banks

polynomials in logistic function and solitary waves of nonlinear differential equations properties of polynomials in logistic function are studied it is demonstrated that these polynomials can be used for construction of exact solutions to nonlinear differential equations nonlinear differential equations with exact solutions in the form of polynomials in logistic function are found it is shown there are solitary waves of nonlinear differential equations described by polynomial in logistic function with many maximum and minimum

group selection via adjusted weighted least absolute deviation regression abstract in applications predictors are naturally grouped with some variables in nonzero groups being irrelevant simultaneously variable selection at both the group and within group levels is more desirable in addition to achieve a robust estimation against outliers in both covariates and responses combining the excellent properties of weighted least absolute deviation wlad and least squares we propose an adjusted wlad awlad regression estimator with the adaptive group bridge penalty importantly we demonstrate that the awlad estimator enjoys the oracle property when the number of parameters grows with the sample size simulation studies and a real data analysis indicate that the awlad has superior performance in the finite sample cases

moment forms invariant to rotation and blur in arbitrary number of dimensions we present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions moment invariants to convolution with an arbitrary centrosymmetric filter are derived first and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance several examples of the invariants are calculated explicitly to illustrate the proposed procedure their invariance robustness and capability of using in template matching and in image registration are demonstrated on 3d mri data and 2d indoor images

true multi image alignment and its application to mosaicing and lens distortion correction multiple images of a scene are related through 2d 3d view transformations and linear and nonlinear camera transformations we present an algorithm for true multi image alignment that does not rely on the measurements of a reference image being distortion free the algorithm is developed to specifically align and mosaic images using parametric transformations in the presence of lens distortion when lens distortion is present none of the images can be assumed to be ideal in our formulation all the images are modeled as intensity measurements represented in their respective coordinate systems each of which is related to an ideal coordinate system through an interior camera transformation and an exterior view transformation the goal of the accompanying algorithm is to compute an image in the ideal coordinate system while solving for the transformations that relate the ideal system with each of the data images key advantages of the technique presented in this paper are i no reliance on one distortion free image ii ability to register images and compute coordinate transformations even when the multiple images are of an extended scene with no overlap between the first and last frame of the sequence and iii ability to handle linear and nonlinear transformations within the same framework results of applying the algorithm are presented for the correction of lens distortion and creation of video mosaics