multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

multifocusing and depth estimation using a color shift model based computational camera this paper presents a novel approach to depth estimation using a multiple color filter aperture mca camera and its application to multifocusing an image acquired by the mca camera contains spatially varying misalignment among rgb color channels where the direction and length of the misalignment is a function of the distance of an object from the plane of focus therefore if the misalignment is estimated from the mca output image multifocusing and depth estimation become possible using a set of image processing algorithms we first segment the image into multiple clusters having approximately uniform misalignment using a color based region classification method and then find a rectangular region that encloses each cluster for each of the rectangular regions in the rgb color channels color shifting vectors are estimated using a phase correlation method after the set of three clusters are aligned in the opposite direction of the estimated color shifting vectors the aligned clusters are fused to produce an approximately in focus image because of the finite size of the color filter apertures the fused image still contains a certain amount of spatially varying out of focus blur which is removed by using a truncated constrained least squares filter followed by a spatially adaptive artifacts removing filter experimental results show that the mca based multifocusing method significantly enhances the visual quality of an image containing multiple objects of different distances and can be fully or partially incorporated into multifocusing or extended depth of field systems the mca camera also realizes single camera based depth estimation where the displacement between multiple apertures plays a role of the baseline of a stereo vision system experimental results show that the estimated depth is accurate enough to perform a variety of vision based tasks such as image understanding description and robot vision

a new twist two step iterative shrinkage thresholding algorithms for image restoration iterative shrinkage thresholding 1st algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems this class of problems results from combining a linear observation model with a nonquadratic regularizer e g total variation or wavelet based regularization it happens that the convergence rate of these 1st algorithms depends heavily on the linear observation operator becoming very slow when this operator is ill conditioned or ill posed in this paper we introduce two step 1st twist algorithms exhibiting much faster convergence rate than 1st for ill conditioned problems for a vast class of nonquadratic convex regularizers lscrp norms some besov norms and total variation we show that twist converges to a minimizer of the objective function for a given range of values of its parameters for noninvertible observation operators we introduce a monotonic version of twist mtwist although the convergence proof does not apply to this scenario we give experimental evidence that mtwist exhibits similar speed gains over ist the effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples

reciprocal focus profile a focus profile having a steeper peak is more resistant to image noise in the autofocus af process of a digital camera however a focus profile of such shape normally has a flatter out of focus region on either side of the profile resulting in a slow af process due to the lack of clue about where the lens should move when the lens is in such regions to address the problem we provide a statistical analysis of the focus profile and show that a strictly monotonic transformation of the focus profile preserves the accuracy of the af on the basis of this analysis we propose a new focus profile representation that transforms the focus profile to the reciprocal domain in which the reciprocal focus profile is modeled by a polynomial function this transformation makes the af mathematically tractable and boosts the search speed experimental results are shown to demonstrate the advantage of the proposed representation

threshold for monotone symmetric properties through a logarithmic sobolev inequality threshold phenomena are investigated using a general approach following talagrand ann probab 22 1994 1576 1587 and friedgut and kalai proc amer math soc 12 1999 1017 10541 the general upper bound for the threshold width of symmetric monotone properties is improved this follows from a new lower bound on the maximal influence of a variable on a boolean function the method of proof is based on a well known logarithmic sobolev inequality on 0 1 n this new bound is shown to be asymptotically optimal

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

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

on triangular norm based propositional fuzzy logics abstract fuzzy logics based on triangular norms and their corresponding conorms are investigated an affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given tautologies contradictions and contigencies with respect to such fuzzy logics are studied in particular for the important cases of min max and ukasiewicz logics finally fundamental t norm based fuzzy logics are shown to provide a gradual transition between min max and ukasiewicz logics

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

geometrical methods in wajsberg hoops abstract the aim of this paper is to show that certain geometric methods originally developed for investigating ukasiewicz many valued logics may be profitably applied to the study of classes of partially ordered residuated monoids we substantiate this claim by characterizing all free wajsberg hoops in terms of mcnaughton functions over the n cube and by giving complete axiomatizations for all varieties of wajsberg hoops

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

pointwise shape adaptive dct for high quality denoising and deblocking of grayscale and color images the shape adaptive discrete cosine transform sa dct transform can be computed on a support of arbitrary shape but retains a computational complexity comparable to that of the usual separable block dct b dct despite the near optimal decorrelation and energy compaction properties application of the sa dct has been rather limited targeted nearly exclusively to video compression in this paper we present a novel approach to image filtering based on the sa dct we use the sa dct in conjunction with the anisotropic local polynomial approximation intersection of confidence intervals technique which defines the shape of the transform s support in a pointwise adaptive manner the thresholded or attenuated sa dct coefficients are used to reconstruct a local estimate of the signal within the adaptive shape support since supports corresponding to different points are in general overlapping the local estimates are averaged together using adaptive weights that depend on the region s statistics this approach can be used for various image processing tasks in this paper we consider in particular image denoising and image deblocking and deringing from block dct compression a special structural constraint in luminance chrominance space is also proposed to enable an accurate filtering of color images simulation experiments show a state of the art quality of the final estimate both in terms of objective criteria and visual appearance thanks to the adaptive support reconstructed edges are clean and no unpleasant ringing artifacts are introduced by the fitted transform

equational characterization of all varieties of mv algebras abstract it is known that all subvarieties of mv algebras are finitely axiomatizable in the literature one can find equational characterizations of certain subvarieties such as mv n algebras in this paper we write down equational bases for all mv varieties and prove a representation theorem for each subvariety

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

weight distribution and list decoding size of reed muller codes the weight distribution and list decoding size of reed muller codes are studied in this work given a weight parameter we are interested in bounding the number of reed muller codewords with weight up to the given parameter and given a received word and a distance parameter we are interested in bounding the size of the list of reed muller codewords that are within that distance from the received word obtaining tight bounds for the weight distribution of reed muller codes has been a long standing open problem in coding theory dating back to 1976 in this work we make a new connection between computer science techniques used to study low degree polynomials and these coding theory questions this allows us to resolve the weight distribution and list decoding size of reed muller codes for all distances previous results could only handle bounded distances azumi kasami and tokura gave bounds on the weight distribution which hold up to 2 5 times the minimal distance of the code and gopalan klivans and zuckerman gave bounds on the list decoding size which hold up to the johnson bound

improvements in shape from focus for holographic reconstructions with regard to focus operators neighborhood size and height value interpolation this paper presents a shape from focus method which is improved with regard to the mathematical operator used for contrast measurement the selection of the neighborhood size surface refinement through interpolation and surface postprocessing three dimensional models of living human faces are presented with such a high resolution that single hairs are visible

evolving estimators of the pointwise holder exponent with genetic programming the regularity of a signal can be numerically expressed using holder exponents which characterize the singular structures a signal contains in particular within the domains of image processing and image understanding regularity based analysis can be used to describe local image shape and appearance however estimating the holder exponent is not a trivial task and current methods tend to be computationally slow and complex this work presents an approach to automatically synthesize estimators of the pointwise holder exponent for digital images this task is formulated as an optimization problem and genetic programming gp is used to search for operators that can approximate a traditional estimator the oscillations method experimental results show that gp can generate estimators that achieve a low error and a high correlation with the ground truth estimation furthermore most of the gp estimators are faster than traditional approaches in some cases their runtime is orders of magnitude smaller this result allowed us to implement a real time estimation of the holder exponent on a live video signal the first such implementation in current literature moreover the evolved estimators are used to generate local descriptors of salient image regions a task for which a stable and robust matching is achieved comparable with state of the art methods in conclusion the evolved estimators produced by gp could help expand the application domain of holder regularity within the fields of image analysis and signal processing

the gleason prange theorem the gleason prange theorem describes a nontrivial automorphism of an extended quadratic residue code by using the fourier transform in an appropriate extension field methods of digital signal processing are used to make the proof transparent and the automorphism intuitive the theorem is proved both in a field of characteristic tow and in an arbitrary field and is stated simply as a general property of the discrete fourier transform

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

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

variational depth from focus reconstruction this paper deals with the problem of reconstructing a depth map from a sequence of differently focused images also known as depth from focus dff or shape from focus we propose to state the dff problem as a variational problem including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization which makes the method robust to noise and leads to more realistic depth maps in addition we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers allowing to minimize the energy very efficiently a numerical comparison to classical methods on simulated as well as on real data is presented

amalgamation and interpolation in ordered algebras the first part of this paper provides a comprehensive and self contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations in particular proofs are given of known equivalences between the amalgamation property and the robinson property the congruence extension property and the extension property and the flat amalgamation property and the deductive interpolation property as well as various dependencies between these properties these relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice ordered abelian groups and mv algebras and to determine important subvarieties of residuated lattices where these properties hold or fail in particular a full description is given of all subvarieties of commutative gmv algebras possessing the amalgamation property

tunable halfband pair wavelet filter banks and application to multifocus image fusion traditional maximally flat wavelet filters are highly regular but suffer from poor frequency selectivity because of their wide transition band in this paper an efficient method is proposed for the design of biorthogonal perfect reconstruction wavelet filter banks known as halfband pair filter banks hpfb to be used in several applications in image processing and pattern recognition the formulation is based on representation of a general halfband polynomial in the variable x we first derive filter coefficients in the polynomial domain in the variable x in terms of the coefficients of the corresponding function in z domain using convex optimization techniques and due to the simple structure of a parametric polynomial in general we can impose some free parameters to provide a tuning opportunity to optimize and control the wavelet filter characteristics perfect reconstruction and desired number of vanishing moments nvm are incorporated into the design procedure the method is systematic renders a reasonable optimization problem and it offers wavelet filters ranging from the maximally flat to the sharpest transition band therefore it can provide a useful design tool with a fine tuning option which is required in many applications such as watermarking detection segmentation fusion denoising and feature extraction the application of the wavelet pairs which have sharper transition band and better frequency selectivity is shown in multifocus imaging to obtain a fully focused image from a set of registered input images at varying foci by employing the distance transform and exponentially decaying function on the subbands in the wavelet domain various images are tested and experimental results compare favorably to the results in the literature

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

the category of linear codes slepian 1960 introduced a structure theory for linear binary codes and proved that every such code was uniquely the sum of indecomposable codes he had hoped to produce a canonical form for the generator matrix of an indecomposable code so that he might read off the properties of the code from such a matrix but such a program proved impossible we here work over an arbitrary field and define a restricted class of indecomposable codes which we call critical for these codes there is a quasicanonical form for the generator matrix every indecomposable code has a generator matrix that is obtained from the generator matrix of a critical indecomposable code by augmentation as an application of the this quasicanonical form we illuminate the perfect linear codes giving for example a canonical form for the generator matrix of the ternary golay 1949 code

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

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

ensemble strategies with adaptive evolutionary programming mutation operators such as gaussian levy and cauchy have been used with evolutionary programming ep according to the no free lunch theorem it is impossible for ep with a single mutation operator to outperform always for example classical ep cep with gaussian mutation is better at searching in a local neighborhood while the fast ep fep with the cauchy mutation performs better over a larger neighborhood motivated by these observations we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call this approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process in addition the recently proposed adaptive ep aep using gaussian acep and cauchy afep mutations is also evaluated in the aep the strategy parameter values are adapted based on the search performance in the previous few generations the performance of ensemble is compared with a mixed mutation strategy which integrates several mutation operators into a single algorithm as well as against the aep with a single mutation operator improved performance of the ensemble over the single mutation based algorithms and mixed mutation algorithm is verified using statistical tests

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

soft decision decoding of reed muller codes recursive lists recursive list decoding is considered for reed muller rm codes the algorithm repeatedly relegates itself to the shorter rm codes by recalculating the posterior probabilities of their symbols intermediate decodings are only performed when these recalculations reach the trivial rm codes in turn the updated lists of most plausible codewords are used in subsequent decodings the algorithm is further improved by using permutation techniques on code positions and by eliminating the most error prone information bits simulation results show that for all rm codes of length 256 and many subcodes of length 512 these algorithms approach maximum likelihood ml performance within a margin of 0 1 db as a result we present tight experimental bounds on ml performance for these codes

iterative decoding threshold analysis for ldpc convolutional codes an iterative decoding threshold analysis for terminated regular ldpc convolutional ldpcc codes is presented using density evolution techniques the convergence behavior of an iterative belief propagation decoder is analyzed for the binary erasure channel and the awgn channel with binary inputs it is shown that for a terminated ldpcc code ensemble the thresholds are better than for corresponding regular and irregular ldpc block codes

any code of which we cannot think is good a central paradox of coding theory concerns the existence and construction of the best codes virtually every linear code is good in the sense that it meets the gilbert varshamov bound on distance versus redundancy despite the sophisticated constructions for codes derived over the years however no one has succeeded in demonstrating a constructive procedure that yields such codes over arbitrary symbol fields using the theory of kolmogorov complexity it is shown that this statement holds true in a rigorous mathematical sense any linear code that is truly random in the sense that there is no concise way of specifying the code is good furthermore random selection of a code that does contain some constructive pattern results with probability bounded away from zero in a code that does not meet the gilbert varshamov bound regardless of the block length of the code in contrast to the situation for linear codes it is shown that there are effectively random nonlinear codes which have no guarantee on distance in addition it is shown that the techniques of kolmogorov complexity can be used to derive typical properties of classes of codes in a novel way

universal impulse noise filter based on genetic programming in this paper we present a novel method for impulse noise filter construction based on the switching scheme with two cascaded detectors and two corresponding estimators genetic programming as a supervised learning algorithm is employed for building two detectors with complementary characteristics the first detector identifies the majority of noisy pixels the second detector searches for the remaining noise missed by the first detector usually hidden in image details or with amplitudes close to its local neighborhood both detectors are based on the robust estimators of location and scale median and mad the filter made by the proposed method is capable of effectively suppressing all kinds of impulse noise in contrast to many existing filters which are specialized only for a particular noise model in addition we propose the usage of a new impulse noise model the mixed impulse noise which is more realistic and harder to treat than existing impulse noise models the proposed model is the combination of commonly used noise models salt and pepper and uniform impulse noise models simulation results show that the proposed two stage gp filter produces excellent results and outperforms existing state of the art filters

generation of all in focus images by noise robust selective fusion of limited depth of field images the limited depth of field of some cameras prevents them from capturing perfectly focused images when the imaged scene covers a large distance range in order to compensate for this problem image fusion has been exploited for combining images captured with different camera settings thus yielding a higher quality all in focus image since most current approaches for image fusion rely on maximizing the spatial frequency of the composed image the fusion process is sensitive to noise in this paper a new algorithm for computing the all in focus image from a sequence of images captured with a low depth of field camera is presented the proposed approach adaptively fuses the different frames of the focus sequence in order to reduce noise while preserving image features the algorithm consists of three stages 1 focus measure 2 selectivity measure 3 and image fusion an extensive set of experimental tests has been carried out in order to compare the proposed algorithm with state of the art all in focus methods using both synthetic and real sequences the obtained results show the advantages of the proposed scheme even for high levels of noise

soft decision decoding of reed muller codes a simplified algorithm soft decision decoding is considered for general reed muller rm codes of length n and distance d used over a memoryless channel a recursive decoding algorithm is designed and its decoding threshold is derived for long rm codes the algorithm has complexity of order nlnn and corrects most error patterns of the euclidean weight of order radicn lnn instead of the decoding threshold radicd 2 of the bounded distance decoding also for long rm codes of fixed rate r the new algorithm increases 4 pi times the decoding threshold of its hard decision counterpart

gradient domain based enhancement of multi view depth video multi view depth is an emerging and attractive 3d representation in recent years which acts a significant role in rendering numerous viewing angles from a small number of given input views the performance of those depth based 3d video applications is strongly dependent on the quality of multi view depth however because of the limitations of depth acquisition and estimation the quality of multi view depth suffers from artifacts in spatial dimension and inconsistency in both the temporal and inter view dimensions in this paper we propose a gradient domain based enhancement method for multi view depth being different from the traditional enhancement methods which intended to process one or two above dimensions our proposal exploits the coherence of both temporal and inter view dimensions in addition of the spatial one it is very challenging to obtain the stable characteristics in multi dimensions to solve this problem we propose to investigate the characteristics in the gradient domain rather than the intensity domain the enhanced multi view depth is obtained through the minimization of energy function under the constraint of a joint gradient field jgf which is estimated from multiple dimensions through motion estimation and geometric mapping therefore the enhanced multi view depth is a global optimization in multiple dimensions that ensures the consistency in temporal inter view and spatial domains furthermore we also propose an enhancement structure to indicate the process order of depth frames the experimental results suggest that the proposed method can enhance multi view depth with desired sharpness and consistency

forward fourier wavelet regularized deconvolution for ill conditioned systems we propose an efficient hybrid fourier wavelet regularized deconvolution forward algorithm that performs noise regularization via scalar shrinkage in both the fourier and wavelet domains the fourier shrinkage exploits the fourier transform s economical representation of the colored noise inherent in deconvolution whereas the wavelet shrinkage exploits the wavelet domain s economical representation of piecewise smooth signals and images we derive the optimal balance between the amount of fourier and wavelet regularization by optimizing an approximate mean squared error mse metric and find that signals with more economical wavelet representations require less fourier shrinkage forward is applicable to all ill conditioned deconvolution problems unlike the purely wavelet based wavelet vaguelette deconvolution wvd moreover its estimate features minimal ringing unlike the purely fourier based wiener deconvolution even in problems for which the wvd was designed we prove that forward s mse decays with the optimal wvd rate as the number of samples increases further we demonstrate that over a wide range of practical sample lengths forward improves on wvd s performance

strictly join irreducible varieties of bl algebras the missing pieces abstract basic logic bl introduced by p hajek in 1998 is the logic of all continuous t norms and their residua the variety of bl algebras forms the algebraic semantics of bl let l be a variety of bl algebras and let l l be its lattice of subvarieties ordered by inclusion l is called strictly join irreducible sji if whenever l is the join of a set s of varieties of bl algebras then l s every variety in l l is obtained as join of sji varieties which may be considered as the building blocks of all the varieties in l l in a previous work by the second author a partial classification for the sji varieties of bl algebras has been found in this paper we provide a full classification of the sji varieties of bl algebras our main result is that a variety of bl algebras is sji iff it is generated by a bl chain with finitely many components each of them being a cancellative hoop or a wajsberg hoop with finite rank as an application we provide a characterization for the varieties of bl algebras having only finitely many subvarieties and we study some additional topics

reed muller codes achieve capacity on erasure channels we introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding rather than relying on the precise structure of the codes our method exploits code symmetry in particular the technique applies to any sequence of linear codes where the blocklengths are strictly increasing the code rates converge and the permutation group of each code is doubly transitive in other words we show that symmetry alone implies near optimal performance an important consequence of this result is that a sequence of reed muller codes with increasing blocklength and converging rate achieves capacity this possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1 moreover these results extend naturally to all affine invariant codes and thus to extended primitive narrow sense bch codes this also resolves in the affirmative the existence question for capacity achieving sequences of binary cyclic codes the primary tools used in the proof are the sharp threshold property for symmetric monotone boolean functions and the area theorem for extrinsic information transfer functions

a focus fusion framework with anisotropic depth map smoothing focus fusion is the task of combining a set of images focused at different depths into a single image that is entirely in focus the crucial point of all focus fusion methods is the decision about the in focus areas to this end we present a general framework for focus fusion that introduces a modern regularisation strategy on these per pixel decisions we assume that neighbouring pixels in the fused image belong to similar depth layers following this assumption we smooth the depth map with a sophisticated anisotropic diffusion process combined with a robust data fidelity term the experiments with synthetic and real world data demonstrate that our new model yields a better quality than several existing focus fusion methods moreover our methodology is general and can be applied to improve many fusion approaches highlightswe show that depth map regularisation is an important tool for focus fusion we incorporate modern concepts such as a coupled anisotropic diffusion term we substantially improve the runtime with a fast gpu implementation we evaluate different in focus measures we compare the overall performance to several methods from the literature

linear time encodable and decodable error correcting codes we present a new class of asymptotically good linear error correcting codes these codes can be both encoded and decoded in linear time they can also be encoded by logarithmic depth circuits of linear size and decoded by logarithmic depth circuits of size o nlogn we present both randomized and explicit constructions of these codes

good codes can be produced by a few permutations our main result is that good codes even those meeting the random coding bound can be produced with relatively few linear in the block length permutations from a single codeword this cutdown in complexity may be of practical importance the motivation for looking at such codes came from ahlswede s covering lemma which makes it possible to build correlated source codes from channel codes via permutations in appendix i we show that the problem of finding the best error exponents for coding sources with full side information at the decoder which has received attention in the recent literature can easily be reduced to the familiar one for the discrete memoryless channel dmc finally in appendices ii and iii we give rather precise double exponentially small bounds on the probabilities that a randomly chosen code will fail to meet the random coding or expurgated bound for the dmc according to these results good codes are hard to miss if selected at random this also explains why good codes of a iow complexity such as those produced by

sharp thresholds of graph properties and the sat problem consider g n p to be the probability space of random graphs on n vertices with edge probability p we will be considering subsets of this space defined by monotone graph properties a monotone graph property p is a property of graphs such that a p is invariant under graph automorphisims b if graph h has property p then so does any graph g having h as a subgraph a monotone symmetric family of graphs is a family defined by such a property one of the first observations made about random graphs by erdos and renyi in their seminal work on random graph theory 12 was the existence of threshold phenomena the fact that for many interesting properties p the probability of p appearing in g n p exhibits a sharp increase at a certain critical value of the parameter p bollobas and thomason proved the existence of threshold functions for all monotone set properties 6 and in 14 it is shown that this behavior is quite general and that all monotone graph properties exhibit threshold behavior i e the probability of their appearance increases from values very close to 0 to values close to 1 in a very small interval more precise analysis of the size of the threshold interval is done in 7 this threshold behavior which occurs in various settings which arise in combinatorics and computer science is an instance of the phenomenon of phase transitions which is the subject of much interest in statistical physics one of the main questions that arises in studying phase transitions is how sharp is the transition for example one of the motivations for this paper arose from the question of the sharpness of the phase transition for the property of satisfiability of a random kcnf boolean formula nati linial who introduced me to this problem suggested that although much concrete analysis was being performed on this problem the best approach would be to find general conditions for sharpness of the phase transition answering the question posed in 14 as to the relation between the length of the threshold interval and the value of the critical probability in this paper we indeed introduce a simple condition and prove it is sufficient stated roughly in the setting of random graphs the main theorem states that if a property has a coarse threshold then it can be approximated by the property of having certain given graphs as a subgraph this condition can be applied in a more

selecting the optimal focus measure for autofocusing and depth from focus a method is described for selecting the optimal focus measure with respect to gray level noise from a given set of focus measures in passive autofocusing and depth from focus applications the method is based on two new metrics that have been defined for estimating the noise sensitivity of different focus measures the first metric the autofocusing uncertainty measure aum is useful in understanding the relation between gray level noise and the resulting error in lens position for autofocusing the second metric autofocusing root mean square error arms error is an improved metric closely related to aum aum and arms error metrics are based on a theoretical noise sensitivity analysis of focus measures and they are related by a monotonic expression the theoretical results are validated by actual and simulation experiments for a given camera the optimally accurate focus measure may change from one object to the other depending on their focused images therefore selecting the optimal focus measure from a given set involves computing all focus measures in the set

on cryptographic properties of the cosets of r 1 m we introduce a new approach for the study of weight distributions of cosets of the reed muller code of order 1 our approach is based on the method introduced by kasami 1968 using pless 1963 identities by interpreting some equations we obtain a necessary condition for a coset to have a high minimum weight most notably we are able to distinguish such cosets which have three weights only we then apply our results to the problem of the nonlinearity of boolean functions we particularly study the links between this criterion and the propagation characteristics of a function

a new upper bound on the block error probability after decoding over the erasure channel motivated by cryptographic applications we derive a new upper bound on the block error probability after decoding over the erasure channel the bound works for all linear codes and is in terms of the generalized hamming weights it turns out to be quite useful for reed muller codes for which all the generalized hamming weights are known whereas the full weight distribution is only partially known for these codes the error probability is related to the cryptographic notion of algebraic immunity we use our bound to show that the algebraic immunity of a random balanced m variable boolean function is of order m 2 1 o 1 with probability tending to 1 as m goes to infinity

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

the permutation group of affine invariant extended cyclic codes the extended cyclic codes of length p sup m p is a prime which are invariant under the affine group acting on f sub pm are called affine invariant codes following results of berger 1996 1994 we present the formal expression of the permutation group of these codes afterwards we give several tools in order to determine effectively the group of a given code or of some infinite class of codes we next prove by studying some examples that our tools are efficient in the end we give our main application the permutation group of primitive bch codes defined on any prime field

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

intelligent reversible watermarking and authentication hiding depth map information for 3d cameras in this paper we propose an application for 3d cameras by reversibly hiding the depth map in the corresponding 2d images the proposed technique is prospective in cameras capable of capturing simultaneously the 2d image and resultant depth map of an object 3d cameras equipped with self embedding capability can serve two additional purposes protection of the captured image and secure transmission of its depth map the reversible watermarking in addition to other features guarantees the lossless recovery of an original image and separation of its depth map when required for this purpose a reversible watermarking scheme based on genetic algorithm ga has been proposed which computes suitable threshold for each block of coefficients in the wavelet domain thus a tradeoff is made between watermark imperceptibility and capacity using ga the threshold map is embedded in addition to the actual payload and thus the proposed approach does not require histogram pre processing in order to avoid overflow underflow the same threshold map has been used for authentication purpose by correlating it with the low frequency coefficients of the 2d transformed image further to exploit the inherent redundancy in the depth map which is the actual payload in this case lossless compression has been employed before its embedding similarly besides secret key based permutation a cryptographic layer is overlaid on the watermarking layer for security purposes experiments conducted on images and depth maps obtained using a 3d camera and an optical microscopic system validate the proposed concept

free products in the category of abelian l groups with strong unit abstract we examine the structure of free products in the category a 1 of abelian l groups with strong unit we give several examples of free product computations with particular regard to l groups in a 1 corresponding via the functor k0 to af c algebras considered by glimm bratteli elliott pimsner voiculescu effros and others

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

the generalized area theorem and some of its consequences there is a fundamental relationship between belief propagation bp and maximum a posteriori decoding the case of transmission over the binary erasure channel was investigated in detail in a companion paper c meacuteasson a montanari and r urbanke maxwell s construction the hidden bridge between iterative and maximum a posteriori decoding ieee transactions on information theory submitted for publication this paper investigates the extension to general memoryless channels paying special attention to the binary case an area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed we show that this area theorem gives rise to an upper bound on the maximum a posteriori threshold for sparse graph codes in situations where this bound is tight the extrinsic soft bit estimates delivered by the bp decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold more generally it is conjectured that the fundamental relationship between the maximum a posteriori probability map and the bp decoder which was observed for transmission over the binary erasure channel carries over to the general case we finally demonstrate that in order for the design rate of an ensemble to approach the capacity under bp decoding the component codes have to be perfectly matched a statement which is well known for the special case of transmission over the binary erasure channel

on the hardness of approximating minimum vertex cover we prove the minimum vertex cover problem to be np hard to approximate to within a factor of 1 3606 extending on previous pcp and hardness of approximation technique to that end one needs to develop a new proof framework and to borrow and extend ideas from several fields

threshold saturation via spatial coupling why convolutional ldpc ensembles perform so well over the bec convolutional low density parity check ldpc ensembles introduced by felstrom and zigangirov have excellent thresholds and these thresholds are rapidly increasing functions of the average degree several variations on the basic theme have been proposed to date all of which share the good performance characteristics of convolutional ldpc ensembles we describe the fundamental mechanism that explains why convolutional like or spatially coupled codes perform so well in essence the spatial coupling of individual codes increases the belief propagation bp threshold of the new ensemble to its maximum possible value namely the maximum a posteriori map threshold of the underlying ensemble for this reason we call this phenomenon threshold saturation this gives an entirely new way of approaching capacity one significant advantage of this construction is that one can create capacity approaching ensembles with an error correcting radius that is increasing in the blocklength although we prove the threshold saturation only for a specific ensemble and for the binary erasure channel bec empirically the phenomenon occurs for a wide class of ensembles and channels more generally we conjecture that for a large range of graphical systems a similar saturation of the dynamical threshold occurs once individual components are coupled sufficiently strongly this might give rise to improved algorithms and new techniques for analysis

automatic estimation and removal of noise from a single image image denoising algorithms often assume an additive white gaussian noise awgn process that is independent of the actual rgb values such approaches cannot effectively remove color noise produced by today s ccd digital camera in this paper we propose a unified framework for two tasks automatic estimation and removal of color noise from a single image using piecewise smooth image models we introduce the noise level function nlf which is a continuous function describing the noise level as a function of image brightness we then estimate an upper bound of the real nlf by fitting a lower envelope to the standard deviations of per segment image variances for denoising the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the rgb values in each segment then a gaussian conditional random field gcrf is constructed to obtain the underlying clean image from the noisy input extensive experiments are conducted to test the proposed algorithm which is shown to outperform state of the art denoising algorithms

reed muller codes for random erasures and errors this paper studies the parameters for which binary reed muller rm codes can be decoded successfully on the binary erasure channel and binary symmetry channel and in particular when can they achieve capacity for these two classical channels necessarily this paper also studies the properties of evaluations of multivariate gf 2 polynomials on the random sets of inputs for erasures we prove that rm codes achieve capacity both for very high rate and very low rate regimes for errors we prove that rm codes achieve capacity for very low rate regimes and for very high rates we show that they can uniquely decode at about the square root of the number of errors at capacity the proofs of these four results are based on different techniques which we find interesting in their own right in particular we study the following questions about e m r the matrix whose rows are the truth tables of all the monomials of degree leq r in m variables what is the most resp least number of random columns in e m r that define a submatrix having full column rank resp full row rank with high probability we obtain tight bounds for very small resp very large degrees r which we use to show that rm codes achieve capacity for erasures in these regimes our decoding from random errors follows from the following novel reduction for every linear code c of sufficiently high rate we construct a new code c obtained by tensorizing c such that for every subset s of coordinates if c can recover from erasures in s then c can recover from errors in s specializing this to the rm codes and using our results for erasures imply our result on the unique decoding of the rm codes at high rate finally two of our capacity achieving results require tight bounds on the weight distribution of rm codes we obtain such bounds extending the recent bounds from constant degree to linear degree polynomials

maxwell construction the hidden bridge between iterative and maximum a posteriori decoding there is a fundamental relationship between belief propagation and maximum a posteriori decoding a decoding algorithm which is called the maxwell decoder is introduced and provides a constructive description of this relationship both the algorithm itself and the analysis of the new decoder are reminiscent of the maxwell construction in thermodynamics this paper investigates in detail the case of transmission over the binary erasure channel while the extension to general binary memoryless channels is discussed in a companion paper

spatially coupled ensembles universally achieve capacity under belief propagation we investigate spatially coupled code ensembles for transmission over the binary erasure channel it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble this explains why convolutional ldpc ensembles originally introduced by felstrom and zigangirov perform so well over this channel we show that the equivalent result holds true for transmission over general binary input memoryless output symmetric channels more precisely given a desired error probability and a gap to capacity we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding in fact most codes in this ensemble have this property the quantifier universal refers to the single ensemble code that is good for all channels but we assume that the channel is known at the receiver the key technical result is a proof that under belief propagation decoding spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble we conclude by discussing some interesting open problems

on russo s approximate zero one law consider the product measure mu p on 0 1 n when 0 operatorname resp 1 is given weight 1 p operatorname resp p consider a monotone subset a of 0 1 n we give a precise quantitative form to the following statement if a does not depend much on any given coordinate d mu p a dp is large thus in that case there is a threshold effect and mu p a jumps from near 0 to near 1 in a small interval

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

triangular norm based measures and their markov kernel representation abstract we approach the problem whether left continuous triangular norm based valuations called t measures or t probability measures defined on triangular normbased tribes of the unit cube can be disintegrated by markov kernels we prove that each t measure based on a fundamental triangular norm these triangular norms t together with their corresponding triangular conorms s satisfy the functional equation t x y s x y x y can be uniquely represented as a sum of a disintegrable t measure and a hard core which is either identically zero or which is monotonically irreducible i e cannot be disintegrated

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

a variety containing emv algebras and pierce sheaves of emv algebras abstract according to 11 we know that the class of all emv algebras emv is not a variety since it is not closed under the subalgebra operator the main aim of this work is to find the least variety containing emv for this reason we introduced the variety wemv of wemv algebras of type 2 2 2 2 0 induced by some identities we show that adding a derived binary operation to each emv algebra m 0 we extend its language so that m 0 called an associated wemv algebra belongs to wemv then using the congruence relations induced by the prime ideals of a wemv algebra we prove that each wemv algebra can be embedded into an associated wemv algebra we show that wemv is the least subvariety of the variety of wemv algebras containing emv finally we study pierce sheaves of proper emv algebras

channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels a method is proposed called channel polarization to construct code sequences that achieve the symmetric capacity i w of any given binary input discrete memoryless channel b dmc w the symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability channel polarization refers to the fact that it is possible to synthesize out of n independent copies of a given b dmc w a second set of n binary input channels wn i 1 les i les n such that as n becomes large the fraction of indices i for which i wn i is near 1 approaches i w and the fraction for which i wn i is near 0 approaches 1 i w the polarized channels wn i are well conditioned for channel coding one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining codes constructed on the basis of this idea are called polar codes the paper proves that given any b dmc w with i w 0 and any target rate r i w there exists a sequence of polar codes cfrn nges1 such that cfrn has block length n 2n rate ges r and probability of block error under successive cancellation decoding bounded as pe n r les o n 1 4 independently of the code rate this performance is achievable by encoders and decoders with complexity o n logn for each

algebraic immunity for cryptographically significant boolean functions analysis and construction recently algebraic attacks have received a lot of attention in the cryptographic literature it has been observed that a boolean function f used as a cryptographic primitive and interpreted as a multivariate polynomial over f sub 2 should not have low degree multiples obtained by multiplication with low degree nonzero functions in this paper we show that a boolean function having low nonlinearity is also weak against algebraic attacks and we extend this result to higher order nonlinearities next we present enumeration results on linearly independent annihilators we also study certain classes of highly nonlinear resilient boolean functions for their algebraic immunity we identify that functions having low degree subfunctions are weak in terms of algebraic immunity and we analyze some existing constructions from this viewpoint further we present a construction method to generate boolean functions on n variables with highest possible algebraic immunity spl lceil n 2 spl rceil this construction first presented at the 2005 workshop on fast software encryption fse 2005 has been the first one producing such functions these functions are obtained through a doubly indexed recursive relation we calculate their hamming weights and deduce their nonlinearities we show that they have very high algebraic degrees we express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables we deduce a very fast way of computing the output to these functions given their input

efficient focus sampling through depth of field calibration due to the limited depth of field dof of conventional digital cameras only the objects within a certain distance range from the camera are in focus objects outside the dof are observed with different amounts of defocus depending on their position focus sampling consists of capturing different images of the same scene by changing the focus configuration of the camera in order to alternately bring objects at different depths into focus focus sampling is an important part of different focus related applications such as autofocus focus stacking and depth estimation this work proposes a calibration procedure for modeling the depth of field of conventional cameras in order to perform an efficient focus sampling the method is simple in terms of repeatability and can be easily implemented in different imaging devices experimental tests are presented in order to illustrate the effectiveness of the proposed approach in autofocus results demonstrate that a significant reduction in the number of frames required to capture during autofocusing can be achieved by means of the proposed methodology