projection distortion analysis for flattened image mosaicing from straight uniform generalized cylinders this paper presents a new approach for reconstructing images mapped or painted on straight uniform generalized cylinders sugc a set of monocular images is taken from di erent viewpoints in order to be mosaiced and to represent the entire scene in detail the expressions of the sugc s projection axis are derived from two cross sections projected onto the image plane based on these axes we derive the sugc localization in the camera coordinate system we explain how we can nd a virtual image representation when the intersection of the two axes is matched to the image center we analyze the perspective distortions when attening a scene which is mapped on a sugc we evaluate the lower and the upper bounds of the necessary number of views in order to represent the entire scene from a sugc by considering the distortions produced by perspective projection a region matching based mosaicing method is proposed to be applied on the attened images in order to obtain the complete scene the mosaiced scene is visualized on a new synthetic surface by a mapping procedure the proposed algorithm is used for the representation of mural paintings located on sugcs with closed cross sections circles for columns or opened cross sections ellipses or parabolas for vaults 2001 pattern recognition society published by elsevier science ltd all rights reserved

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

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

patch based stereo in a general binocular viewing geometry this paper presents a one stage stereo algorithm that yields 3d planar surface patches directly from matching image patch intensity information the method allows an arbitrary rotation and translation between the cameras it is not limited to parallel axis narrow baseline or vergent geometries the key to the approach is to match image patches that have positions shapes sizes orientations and samplings consistent with a hypothesized surface patch and with each other the match error then reflects only the mismatch of patch contents and not the mismatch of patch geometries or samplings the algorithm is quantitatively evaluated against ground truth on real images with difficult viewing geometries and demonstrates an average accuracy of about 1 in estimating surface depths and 10 spl deg in estimating surface normals

shape from regular patterns niis paper describes an aigoritlitr1 to obtaitl local surface orierltatiorr frofti the apparetlt surface pattertl distortion in an image we propose a spherical projection to model perspctiue imaging a trtappitlg is debtled based of1 the measurement of the local distortions of a repeated known rexture pattern due io the image projection 77tis mapping maps an apparent shape on the image sphere lo a locus of possible surface orienrations on the gaussian sphere an ireratiw constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation 7lis algorithm can recover local surface orientation as well as interpolate surjace orientations where no information is auailable xis algorithm is applied to a real image ro demonstrate its perfontlance

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

stereoscopic ranging by matching image modulations we apply an am fm surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system this is used to support the use of modulation based stereo matching where local image phase is used to compute stereo disparities the local image phase is an advantageous feature for image matching since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data local phase shifts however are problematic at high frequencies due to phase wrapping when disparities exceed spl plusmn spl pi we meld powerful multichannel gabor image demodulation techniques for multiscale coarse to fine computation of local image phase with a disparity channel model for depth computation the resulting framework unifies phase based matching approaches with am fm surface image models we demonstrate the concepts in a stereo algorithm that generates a dense accurate disparity map without the problems associated with phase wrapping

model of frequency analysis in the visual cortex and the shape from texture problem this paper addresses the question at the level of cortical cells present in the primary area v1 is the information sufficient to extract the local perspective from the texture starting from a model of complex cells in visual area v1 we propose a biologically plausible algorithm for frequency analysis applied to the shape from texture problem first specific log normal filters are designed in replacement of the classical gabor filters because of their theoretical properties and of their biological plausibility these filters are separable in frequency and orientation and they better sample the image spectrum which makes them appropriate for any pattern analysis technique a method to estimate the local frequency in the image which discards the need to choose the best local scale is designed based on this frequency analysis model a local decomposition of the image into patches leads to the estimation of the local frequency variation which is used to solve the problem of recovering the shape from the texture from the analytical relation between the local frequency and the geometrical parameters under perspective projection it is possible to recover the orientation and the shape of the original image the accuracy of the method is evaluated and discussed on different kind of textures both regular and irregular with planar and curved surfaces and also on natural scenes and psychophysical stimuli it compares favorably to the best existing methods with in addition a low computational cost the biological plausibility of the model is finally discussed

analysis of low bit rate image transform coding calculations based on high resolution quantizations prove that the distortion rate d r of an image transform coding is proportional to 2 sup 2r when r is large enough in wavelet and block cosine bases we show that if r 1 bit pixel then d r varies like r sup 1 2 spl gamma where spl gamma remains of the order of 1 for most natural images the improved performance of embedded codings in wavelet bases is analyzed at low bit rates we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors

planar surface orientation from texture spatial frequencies abstract this paper presents a computational model and a practical algorithm for determining the three dimensional orientation of a planar surface from visual texture information the model consists of three parts 1 a local spatial frequency based texture representation 2 a model describing the projection of surface texture to image texture and 3 a solution of the texture projection model for the surface orientation under an assumption of surface texture homogeneity the algorithm first measures the dominant frequency at each image point using three wavelet like transforms and then finds the surface orientation that minimizes the variance of the image frequencies backprojections the algorithm is tested on photographs of real world surfaces exhibiting an average accuracy of better than 3 in slant and 4 in tilt the current model and algorithm are more accurate yet substantially simpler than earlier versions of this approach

rotated orthogonal transform rot for motion compensation residual coding discrete cosine transform dct is the orthogonal transform that is most commonly used in image and video compression the motion compensation residual mc residual is also compressed with the dct in most video codecs however the mc residual has different characteristics from a nature image in this paper we develop a new orthogonal transform rotated orthogonal transform rot that can perform better on the mc residual than the dct for coding purposes we derive the proposed rot based on orthogonal constrained l1 norm minimization problem for its sparse property using the dct matrix as the starting point a better orthogonal transform matrix is derived in addition by exploring inter frame dependency and local motion activity transmission of substantial side information is avoided the experiment results confirm that with small computation overhead the rot is adaptive to change of local spatial characteristic of mc residual frame and provides higher compression efficiency for the mc residual than dct especially for high and complex motion videos

shape from texture without boundaries we describe a shape from texture method that constructs an estimate of surface geometry using only the deformation of individual texture elements our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of elements the method assumes that surface texture elements are drawn from a number of different types each of fixed shape neither the shape of the elements nor the number of types need be known in advance we show that with this assumption and assuming a generic scaled orthographic view and texture each type of texture element can be reconstructed in a frontal coordinate system from image instances interest point methods supply a method of simultaneously obtaining instances of each texture element automatically and defining each type of element furthermore image instances that have been marked in error can be identified and ignored using the expectation maximization algorithm a further em procedure yields a surface reconstruction and a relative irradiance map from the data we provide numerous examples of reconstructions for images of real scenes show a comparison between our reconstruction and range maps and demonstrate that the reconstructions display geometric and irradiance phenomena that can be observed in the original image

directionlets using in phase lifting for image representation directionlets allow a construction of perfect reconstruction and critically sampled multidirectional anisotropic basis yet retaining the separable filtering of standard wavelet transform however due to the spatially varying filtering and downsampling direction it is forced to apply spatial segmentation and process each segment independently because of this independent processing of the image segments directionlets suffer from the following two major limitations when applied to say image coding first failure to exploit the correlation across block boundaries degrades the coding performance and also induces blocking artifacts thus making it mandatory to use de blocking filter at low bit rates second spatial scalability i e minimum segment size or the number of levels of the transform is limited due to independent processing of segments we show that with simple modifications in the block boundaries we can overcome these limitations by what we call in phase lifting implementation of directionlets in the context of directionlets using in phase lifting we identify different possible groups of downsampling matrices that would allow the construction of a multilevel transform without forcing independent processing of segments both with and without any modifications in the segment boundary experimental results in image coding show objective and subjective improvements when compared with the directionlets applied independently on each image segment as an application using both the in phase lifting implementation of directionlets and the adaptive directional lifting we have constructed an adaptive directional wavelet transform which has shown improved image coding performance over these adaptive directional wavelet transforms

shape from texture general principle abstract the 3d shape of a textured surface is recovered from its projected image on the assumption that the texture is homogeneously distributed our method does not require recognition of the structure regularity periodicity parallelism orthogonality etc of the texture distribution first the homogeneity of a discrete texture is precisely defined in terms of the theory of distributions next distortion of the observed texture due to perspective projection is described in terms of the first fundamental form expressed as a function of the image coordinates based on this result the 3d recovery equations for determining the surface shape are derived for both planar and curved surfaces some numerical schemes for solving these equations are proposed ambiguity in the interpretation of curved surfaces is also analyzed finally some numerical examples for synthetic data are presented and our method is compared with other existing methods

depth estimation from image structure in the absence of cues for absolute depth measurements as binocular disparity motion or defocus the absolute distance between the observer and a scene cannot be measured the interpretation of shading edges and junctions may provide a 3d model of the scene but it will not provide information about the actual scale of the space one possible source of information for absolute depth estimation is the image size of known objects however object recognition under unconstrained conditions remains difficult and unreliable for current computational approaches we propose a source of information for absolute depth estimation based on the whole scene structure that does not rely on specific objects we demonstrate that by recognizing the properties of the structures present in the image we can infer the scale of the scene and therefore its absolute mean depth we illustrate the interest in computing the mean depth of the scene with application to scene recognition and object detection

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

shape from periodic texture using the eigenvectors of local affine distortion shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly without the need for iterative numerical optimization we work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks the key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces in particular the leading eigenvector points in the tilt direction although not as geometrically transparent the direction of the second eigenvector can be used to estimate the slant direction the required affine distortion matrices are computed using the correspondences between spectral peaks established on the basis of their energy ordering we apply the method to a variety of real world and synthetic imagery

new approach to the design of low complexity 9 7 tap wavelet filters with maximum vanishing moments in this paper we present a novel approach for the design of 9 7 near perfect reconstruction wavelets that are efficient for image compression these wavelets have maximum vanishing moments for both decomposition and reconstruction filters among the existing 9 7 tap wavelet filters the cohen daubechies feauveau cdf 9 7 are known to have the largest regularity however these wavelets have irrational coefficients thus requiring infinite precision implementation unlike state of art designs that compromise vanishing moments for attaining low complexity coefficients our algorithm ensures both we start with a spline function of length 5 and select the remaining factors to obtain wavelets with rationalized coefficients by proper choice of design parameters it is possible to find very low complexity dyadic wavelets with compact support we suggest a near half band criterion to attain a suitable combination of low pass analysis and decomposition filters the designed filter bank is found to give significant hardware advantage as compared with existing filter pairs moreover these low complexity wavelets have characteristics similar to standard cdf 9 7 wavelets the designed wavelets are tested for their suitability in applications such as image compression simulations results depict that the designed wavelets give comparable performances on most of the benchmark images subsequently they can be used in applications that require fewer computations and lesser hardware

analyzing image structure by multidimensional frequency modulation we develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images we begin with the widely accepted definition of the instantaneous frequency vector if as the gradient of the phase and define the instantaneous frequency gradient tensor ifgt as the tensor of component derivatives of the if vector frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the ifgt using the ifgt we derive the ordinary differential equations odes that describe image flowlines we study the diagonalization of the odes of multidimensional frequency modulation on the ifgt eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates we illustrate these new methods of image pattern analysis on textured and fingerprint images we envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity examples of such textures abound in nature

orientation sensitive interpolative pyramids for lossless and progressive image coding this paper presents a modified jpeg coder that is applied to the compression of mixed documents containing text natural images and graphics for printing purposes the modified jpeg coder proposed in this paper takes advantage of the distinct perceptually significant regions in these documents to achieve higher perceptual quality than the standard jpeg coder the region adaptivity is performed via classified thresholding being totally compliant with the baseline standard a computationally efficient classification algorithm is presented and the improved performance of the classified jpeg coder is verified

image coding using dual tree discrete wavelet transform in this paper we explore the application of 2 d dual tree discrete wavelet transform ddwt which is a directional and redundant transform for image coding three methods for sparsifying ddwt coefficients i e matching pursuit basis pursuit and noise shaping are compared we found that noise shaping achieves the best nonlinear approximation efficiency with the lowest computational complexity the interscale intersubband and intrasubband dependency among the ddwt coefficients are analyzed three subband coding methods i e spiht ebcot and tce are evaluated for coding ddwt coefficients experimental results show that tce has the best performance in spite of the redundancy of the transform our ddwt tce scheme outperforms jpeg2000 up to 0 70 db at low bit rates and is comparable to jpeg2000 at high bit rates the ddwt tce scheme also outperforms two other image coders that are based on directional filter banks to further improve coding efficiency we extend the ddwt to an anisotropic dual tree discrete wavelet packets addwp which incorporates adaptive and anisotropic decomposition into ddwt the addwp subbands are coded with tce coder experimental results show that addwp tce provides up to 1 47 db improvement over the ddwt tce scheme outperforming jpeg2000 up to 2 00 db reconstructed images of our coding schemes are visually more appealing compared with dwt based coding schemes thanks to the directionality of wavelets

adaptive directional lifting based wavelet transform for image coding we present a novel 2 d wavelet transform scheme of adaptive directional lifting adl in image coding instead of alternately applying horizontal and vertical lifting as in present practice adl performs lifting based prediction in local windows in the direction of high pixel correlation hence it adapts far better to the image orientation features in local windows the adl transform is achieved by existing 1 d wavelets and is seamlessly integrated into the global wavelet transform the predicting and updating signals of adl can be derived even at the fractional pixel precision level to achieve high directional resolution while still maintaining perfect reconstruction to enhance the adl performance a rate distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features experimental results show that the proposed adl based image coding technique outperforms jpeg 2000 in both psnr and visual quality with the improvement up to 2 0 db on images with rich orientation features

multiscale am fm demodulation and image reconstruction methods with improved accuracy we develop new multiscale amplitude modulation frequency modulation am fm demodulation methods for image processing the approach is based on three basic ideas i am fm demodulation using a new multiscale filterbank ii new accurate methods for instantaneous frequency if estimation and iii multiscale least squares am fm reconstructions in particular we introduce a variable spacing local linear phase vs llp method for improved instantaneous frequency if estimation and compare it to an extended quasilocal method and the quasi eigen function approximation qea it turns out that the new vs llp method is a generalization of the qea method where we choose the best integer spacing between the samples to adapt as a function of frequency we also introduce a new quasi local method qlm for if and ia estimation and discuss some of its advantages and limitations the new if estimation methods lead to significantly improved estimates we present different multiscale decompositions to show that the proposed methods can be used to reconstruct and analyze general images

estimating planar surface orientation using bispectral analysis in this correspondence we propose a direct method for estimating the orientation of a plane from a single view under perspective projection assuming that the underlying planar texture has random phase we show that the nonlinearities introduced by perspective projection lead to higher order correlations in the frequency domain we also empirically show that these correlations are proportional to the orientation of the plane minimization of these correlations using tools from polyspectral analysis yields the orientation of the plane we show the efficacy of this technique on synthetic and natural images

shape from texture using local spectral moments presents a non feature based solution to the problem of computing the shape of curved surfaces from texture information first the use of local spatial frequency spectra and their moments to describe texture is discussed and motivated a new more accurate method for measuring the local spatial frequency moments of an image texture using gabor elementary functions and their derivatives is presented also described is a technique for separating shading from texture information which makes the shape from texture algorithm robust to the shading effects found in real imagery second a detailed model for the projection of local spectra and spectral moments of any surface reflectance patterns not just textures is developed third the conditions under which the projection model can be solved for the orientation of the surface at each point are explored unlike earlier non feature based curved surface shape from texture approaches the assumption that the surface texture is isotropic is not required surface texture homogeneity can be assumed instead the algorithm s ability to operate on anisotropic and nondeterministic textures and on both smooth and rough textured surfaces is demonstrated

multidimensional quasi eigenfunction approximations and multicomponent am fm models we develop multicomponent am fm models for multidimensional signals the analysis is cast in a general n dimensional framework where the component modulating functions are assumed to lie in certain sobolev spaces for both continuous and discrete linear shift invariant lsi systems with am fm inputs powerful new approximations are introduced that provide closed form expressions for the responses in terms of the input modulations the approximation errors are bounded by generalized energy variances quantifying the localization of the filter impulse response and by sobolev norms quantifying the smoothness of the modulations the approximations are then used to develop novel spatially localized demodulation algorithms that estimate the am and fm functions for multiple signal components simultaneously from the channel responses of a multiband linear filterbank used to isolate components two discrete computational paradigms are presented dominant component analysis estimates the locally dominant modulations in a signal which are useful in a variety of machine vision applications while channelized components analysis delivers a true multidimensional multicomponent signal representation we demonstrate the techniques on several images of general interest in practical applications and obtain reconstructions that establish the validity of characterizing images of this type as sums of locally narrowband modulated components

computing local surface orientation and shape from texture forcurved surfaces shape from texture is best analyzed in two stages analogous to stereopsis and structure from motion a computing the texture distortion from the image and b interpreting the texture distortion to infer the orientation and shape of the surface in the scene we model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters we have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis one need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy we use non linear minimization of a least squares error criterion to recover the surface orientation slant and tilt and shape principal curvatures and directions based on the estimated affine transforms in a number of different directions a simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape a sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture

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

estimation of orientation of a textured planar surface using projective equations and separable analysis with m channel wavelet decomposition estimation of the orientation of a textured planar surface is one of the basic tasks in the area of shape from texture for the solution of this task many successful approaches were proposed in this paper we have examined a few unaddressed questions first is there a mathematical formulation that relates the spectral characteristics of the texture pattern and the orientation of an inclined planar surface in a polar coordinate system second is there a good wavelet based approach that produces an accurate estimate of the orientation angle of the textured planar surface by analyzing the spectral behavior of one single uncalibrated image to answer these questions at first we present the formulation of a texture projective equation which relates the depth and orientation of an inclined planar surface in a polar coordinate system with the spectral properties of its image texture a suitable imaging geometry has been considered to enable separable analysis of the effect of inclination of the texture surface next a method for shape from texture is presented based on discrete wavelet analysis to estimate the orientation of the planar surface this approach although designed mainly for m channel wavelets is also applicable for dyadic wavelet analysis texture characteristics in the subbands of wavelet decomposition are analyzed using scalograms and quantitatively evaluated based on texture projective equations the proposed method of estimation of the orientation of a planar texture surface is evaluated using a set of simulated and real world textured images

on the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators in this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth of these iterations we use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates than in the general case and thus can be of use for pseudorandom number generation

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

directional filtering transform for image intra frame compression while directional adaption is introduced into traditional transforms different orders of two 1 d transforms will result in different results of one 2 d transform based upon an anisotropic image model this paper analyzes the effect of transform orders in terms of theoretical coding gain our results reveal that the transform orders have little effect on the coding gain with full decomposition good directional modes and good interpolation however in practical compression schemes since high pass bands are not decomposed fully because of the consideration on complexity different transform orders have different coding performances which can be solved by an adaptive transform order motivated by our analyzed results a directional filtering transform dft in order to distinguish from the common usage on dft is proposed in this paper to better exploit correlations among samples in h 264 intraframe coding it provides an evenly distributed set of prediction modes with an adaptive transform order both interblock and intrablock correlations are exploited in this scheme experimental results in h 264 intraframe coding demonstrate its superiority both objectively and subjectively

efficient least absolute deviation adaptive wavelet filter bank compact representation of signals and images is a key for many applications compactness is often achieved through linear transforms with good energy concentration property we present an adaptive wavelet filter bank with fixed number of vanishing moments plus additional local adaptation proposed adaptation method is conducted at each sample according to the least absolute deviation lad criterion fixed vanishing moments provide for polynomial annihilation adaptation is aimed to achieve maximum sparseness for a wider class of signals such as sine waves lad criterion results in more accurate adaptation on sudden changes of signal statistics in this paper an efficient lad realization is proposed in spite of nonexistence of the closed form solution combining least squares and lad criterion we have achieved unbiased adaptation robust to noise due to its simplicity and acceptable computational speed the proposed scheme is a good candidate for the real world applications in this paper advantages of the proposed scheme are shown in signal denoising and reconstruction

the texture gradient equation for recovering shape from texture studies the recovery of shape from texture under perspective projection we regard shape from texture as a statistical estimation problem the texture being the realization of a stochastic process we introduce warplets which generalize wavelets over the 2d affine group at fine scales the warpogram of the image obeys a transport equation called texture gradient equation in order to recover the 3d shape of the surface one must estimate the deformation gradient which measures metric changes in the image this is made possible by imposing a notion of homogeneity for the original texture according to which the deformation gradient is equal to the velocity of the texture gradient equation by measuring the warplet transform of the image at different scales we obtain a deformation gradient estimator

estimating the perspective pose of texture planes using spectral analysis on the unit sphere multiple vanishing point detection provides the key to recovering the perspective pose of textured planes if vanishing points are to be detected from spectral information then there are two computational problems that need to be solved firstly the search of the extended image plane is unbounded and hence the location of vanishing points at or near infinity is difficult secondly correspondences between local spectra need to be established so that vanishing points can be triangulated in this paper we offer a way of overcoming these two difficulties we overcome the problem of unbounded search by mapping the information provided by local spectral moments onto the unit sphere according to our representation the position and direction of each local spectrum maps onto a great circle on the unit sphere the need for correspondences is overcome by accumulating the great circle intercepts vanishing points occur at local accumulator maxima on the unit sphere to improve the accuracy of the recovered perspective pose parameters for highly slanted planes we use an adaptive spectral window this selects the window so as to reduce spectral defocusing by minimising the determinant of the spectral covariance matrix we experiment with the new shape from texture technique on both synthetic and real world data here it proves to be an accurate and robust means of estimating perspective pose

a 2 d orientation adaptive prediction filter in lifting structures for image coding lifting style implementations of wavelets are widely used in image coders a two dimensional 2 d edge adaptive lifting structure which is similar to daubechies 5 3 wavelet is presented the 2 d prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image consequently the prediction domain is allowed to rotate spl plusmn 45 spl deg in regions with diagonal gradient the gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction and no multiplications are required

a two component model of texture for analysis and synthesis a model of natural texture based on a structural component that uses affine coordinate transformations and a stochastic residual component is presented it is argued that the selection of an appropriate analysis scale can be formulated in terms of a tradeoff between the rate at which parameters are generated and the distortion resulting from the approximation by the structural component an efficient algorithm for identifying the parameters of the structural model is described and its utility demonstrated on a number of synthetic and natural textures

optimal parameter selection in the phase differencing algorithm for 2 d phase estimation a parametric model and a corresponding algorithm for estimating two dimensional 2 d phase functions were presented in a previous paper the performance of the phase estimation algorithm and hence the performance of any algorithm that employs it strongly depends on the choice of the two free parameters of the algorithm in this correspondence we systematically analyze the performance of the phase estimation algorithm and derive rules for selecting the algorithm parameters such that the mean squared error in estimating the signal phase is minimized it is shown analytically and verified using monte carlo simulations that this choice of parameters results in unbiased estimates of the phase and spatial frequency functions the variances of both the estimated phase and frequency functions are very close to the corresponding cramer rao lower bounds

directional lapped transforms for image coding in this paper we present the design of directional lapped transforms for image coding a lapped transform which can be implemented by a prefilter followed by a discrete cosine transform dct can be factorized into elementary operators the corresponding directional lapped transform is generated by applying each elementary operator along a given direction the proposed directional lapped transforms are not only nonredundant and perfectly reconstructed but they can also provide a basis along an arbitrary direction these properties along with the advantages of lapped transforms make the proposed transforms appealing for image coding a block based directional transform scheme is also presented and integrated into hd phtoto one of the state of the art image coding systems to verify the effectiveness of the proposed transforms

parameter estimation of 2 d random amplitude polynomial phase signals phase information has fundamental importance in many two dimensional 2 d signal processing problems in this paper we consider 2 d signals with random amplitude and a continuous deterministic phase the signal is represented by a random amplitude polynomial phase model a computationally efficient estimation algorithm for the signal parameters is presented the algorithm is based on the properties of the mean phase differencing operator which is introduced and analyzed assuming that the signal is observed in additive white gaussian noise and that the amplitude field is gaussian as well we derive the cramer rao lower bound crb on the error variance in jointly estimating the model parameters the performance of the algorithm in the presence of additive white gaussian noise is illustrated by numerical examples and compared with the crb

orientation adaptive subband coding of images in the subband coding of images directionality of image features has thus far been exploited very little the proposed subband coding scheme utilizes orientation of local image features to avoid the highly objectionable gibbs like phenomena observed at reconstructed image edges with conventional subband schemes at low bit rates at comparable bit rates the subjective image quality obtained by our orientation adaptive scheme is considerably enhanced over a conventional separable subband coding scheme as well as other separable approaches such as the jpeg compression standard

rate distortion analysis of directional wavelets the inefficiency of separable wavelets in representing smooth edges has led to a great interest in the study of new 2 d transformations the most popular criterion for analyzing these transformations is the approximation power transformations with near optimal approximation power are useful in many applications such as denoising and enhancement however they are not necessarily good for compression therefore most of the nearly optimal transformations such as curvelets and contourlets have not found any application in image compression yet one of the most promising schemes for image compression is the elegant idea of directional wavelets diws while these algorithms outperform the state of the art image coders in practice our theoretical understanding of them is very limited in this paper we adopt the notion of rate distortion and calculate the performance of the diw on a class of edge like images our theoretical analysis shows that if the edges are not sharp the diw will compress them more efficiently than the separable wavelets it also demonstrates the inefficiency of the quadtree partitioning that is often used with the diw to solve this issue we propose a new partitioning scheme called megaquad partitioning our simulation results on real world images confirm the benefits of the proposed partitioning algorithm promised by our theoretical analysis

a new framework for complex wavelet transforms although the discrete wavelet transform dwt is a powerful tool for signal and image processing it has three serious disadvantages shift sensitivity poor directionality and lack of phase information to overcome these disadvantages we introduce two stage mapping based complex wavelet transforms that consist of a mapping onto a complex function space followed by a dwt of the complex mapping unlike other popular transforms that also mitigate dwt shortcomings the decoupled implementation of our transforms has two important advantages first the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy this allows us to create a directional non redundant complex wavelet transform with potential benefits for image coding systems to the best of our knowledge no other complex wavelet transform is simultaneously directional and non redundant the second advantage of our approach is the flexibility to use any dwt in the transform implementation as an example we can exploit this flexibility to create the complex double density dwt cddwt a shift insensitive directional complex wavelet transform with a low redundancy of 3 sup m 1 2 sup m 1 in m dimensions to the best of our knowledge no other transform achieves all these properties at a lower redundancy

multiresolution image representation using combined 2 d and 1 d directional filter banks in this paper effective multiresolution image representations using a combination of 2 d filter bank fb and directional wavelet transform wt are presented the proposed methods yield simple implementation and low computation costs compared to previous 1 d and 2 d fb combinations or adaptive directional wt methods furthermore they are nonredundant transforms and realize quad tree like multiresolution representations in applications on nonlinear approximation image coding and denoising the proposed filter banks show visual quality improvements and have higher psnr than the conventional separable wt or the contourlet

lossless image compression based on optimal prediction adaptive lifting and conditional arithmetic coding the optimal predictors of a lifting scheme in the general n dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row column sampling in each case the efficiency of the linear predictors is enhanced nonlinearly directional postprocessing is used in the quincunx case and adaptive length postprocessing in the row column case both methods are seen to perform well the resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation we further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution based lossless image coding