eigenvalue distribution of some fractal semi elliptic differential operators we consider differential operators of type au x u x 1 t 1 frac partial 2t 1 u x partial x 1 2t 1 1 t 2 frac partial 2t 2 u x partial x 2 2t 2 x x 1 x 2 in r 2 and sierpinski carpets g subset r 2 the aim of the paper is to investigate spectral properties of the fractal differential operator a 1 circ tr gamma acting in the anisotropic sobolev space w t 1 t 2 2 bbb r 2 where tr gamma is closely related to the trace operator tr gamma

sharing a verifiable secret image using two shadows in this paper we propose a novel 2 2 verifiable secret sharing vss scheme which not only protects a secret image but also allows users to verify the restored secret image in the revealing and verifying phase for all binary grayscale and color images error diffusion and image clustering techniques are adopted to achieve our objective experimental results and discussions show that the proposed scheme with its smaller shadow size and lower computational complexity obviously outperforms previous vss schemes designed either with or without the cheating prevention mechanism moreover the use of a halftone logo gives an efficient solution to verifying whether the restored secret image is correct by using a halftone logo

inverse halftoning algorithm using edge based lookup table approach the inverse halftoning algorithm is used to reconstruct a gray image from an input halftone image based on the recently published lookup table lut technique this paper presents a novel edge based lut method for inverse halftoning which improves the quality of the reconstructed gray image the proposed method first uses the lut based inverse halftoning method as a preprocessing step to transform the given halftone image to a base gray image and then the edges are extracted and classified from the base gray image according to these classified edges a novel edge based lut is built up to reconstruct the gray image based on a set of 30 real training images with both low and high frequency contents experimental results demonstrated that the proposed method achieves a better image quality when compared to the currently published two methods by chang et al and mes 80e and vaidyanathan

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

distributions of localized eigenvalues of laplacians on post critically finite self similar sets abstract in this paper we study distributions of eigenvalues corresponding to localized eigenfunctions of laplacians on p c f self similar sets precisely we divide the eigenvalue counting function x of a laplacian into two parts w x and f x where w x is the counting function of localized eigenvalues and f x is the counting function of non localized global eigenvalues we study asymptotic behaviors of w x and f x as x it is shown that w x x d s 2 where d s is the spectral exponent on the other hand for a class of laplacians including the standard laplacian on the sierpinski gasket f x x f for some f d s 2 so localized eigenfunctions dominate global eigenfunctions in such cases

inverse halftoning and kernel estimation for error diffusion two different approaches in the inverse halftoning of error diffused images are considered the first approach uses linear filtering and statistical smoothing that reconstructs a gray scale image from a given error diffused image the second approach can be viewed as a projection operation where one assumes the error diffusion kernel is known and finds a gray scale image that will be halftoned into the same binary image two projection algorithms viz minimum mean square error mmse projection and maximum a posteriori probability map projection that differ on the way an inverse quantization step is performed are developed among the filtering and the two projection algorithms map projection provides the best performance for inverse halftoning using techniques from adaptive signal processing we suggest a method for estimating the error diffusion kernel from the given halftone this means that the projection algorithms can be applied in the inverse halftoning of any error diffused image without requiring any a priori information on the error diffusion kernel it is shown that the kernel estimation algorithm combined with map projection provide the same performance in inverse halftoning compared to the case where the error diffusion kernel is known

a linear time combinatorial algorithm to find the orthogonal hull of an object on the digital plane a combinatorial algorithm to compute the orthogonal hull of a digital object imposed on a background grid is presented in this paper the resolution and complexity of the orthogonal hull can be controlled by varying the grid size which may be used for a multiresolution analysis of a given object existing algorithms on finding the convex hull are based on divide and conquer strategy sweepline approach etc whereas the proposed algorithm is combinatorial in nature whose time complexity is linear on the object perimeter instead of the object area for a larger grid size the perimeter of an object decreases in length in terms of grid units and hence the runtime of the algorithm reduces significantly the algorithm uses only comparison and addition in the integer domain thereby making it amenable to usage in real world applications where speed is a prime factor experimental results including the cpu time demonstrate the elegance and efficacy of the proposed algorithm

a robust technique for image descreening based on the wavelet transform in this correspondence a novel wavelet based approach to recover continuous tone contone images from halftone images is presented wavelet decomposition of the halftone image facilitates a series of spatial and frequency selective processing to preserve most of the original image contents while eliminating the halftone noise furthermore optional nonlinear filtering can be applied as a postprocessing stage to create the final aesthetic contone image this approach lends itself to practical applications since it is independent of parameter estimation and hence universal to all types of halftoned images including those obtained by scanning printed halftones

application of statistical mechanics to np complete problems in combinatorial optimisation recently developed techniques of the statistical mechanics of random systems are applied to the graph partitioning problem the averaged cost function is calculated and agrees well with numerical results the problem bears close resemblance to that of spin glasses the authors find a spin glass transition in the system and the low temperature phase space has an ultrametric structure this sheds light on the nature of hard computation problems

local times for brownian motion on the sierpinski carpet jointly continuous local times are constructed for brownian motion on the sierpinski carpet a consequence is that the brownian motion hits points the method used is to analyze a sequence of eigenvalue problems

what is not in the domain of the laplacian on sierpinski gasket type fractals abstract we consider the analog of the laplacian on the sierpinski gasket and related fractals constructed by kigami a function f is said to belong to the domain of if f is continuous and f is defined as a continuous function we show that if f is a nonconstant function in the domain of then f2 is not in the domain of we give two proofs of this fact the first is based on the analog of the pointwise identity f2 2f f f 2 where we show that f 2 does not exist as a continuous function in fact the correct interpretation of f2 is as a singular measure a result due to kusuoka we give a new proof of this fact the second is based on a dichotomy for the local behavior of a function in the domain of at a junction point x0 of the fractal in the typical case nonvanishing of the normal derivative we have upper and lower bounds for f x f x0 in terms of d x x0 for a certain value and in the nontypical case vanishing normal derivative we have an upper bound with an exponent greater than 2 this method allows us to show that general nonlinear functions do not operate on the domain of

on the resistance of the sierpinski carpet let f text n be the nth stage in the construction of the sierpinski carpet let r text n be the electrical resistance of f text n when the left and right sides are each short circuited and a voltage is applied between them we prove that there exists a constant rho such that textstyle frac 1 4 rho n leq r n leq 4 rho n the motivation for this result came from the problem of establishing a the existence and b the value of the spectral dimension of the sierpinski carpet in this and a subsequent paper we settle a and give bounds for b

the zeta function of the laplacian on certain fractals we prove that the zeta function of the laplacian a on self similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane we characterise the poles compute their residues and give expressions for some special values of the zeta function furthermore we discuss the presence of oscillations in the eigenvalue counting function thereby answering a question posed by j kigami and m lapidus for this class of fractals

an adaptive inverse halftoning algorithm a class of inverse halftoning algorithms that recovers grayscale continuous tone images from halftone images is proposed the basic structure is an optimized linear filter then a properly designed adaptive postprocessor is employed to enhance the recovered image quality finally a multistage space varying algorithm is developed that uses the basic linear filter structure as before but with spatially adaptive parameters

fourier asymptotics of fractal measures abstract a measure on r n will be called locally uniformly dimensional if br x cr for all r 1 and all x where br x denotes the ball of radius r about x for l 2 d the measure d is in i so d is well defined we show it is locally in l2 and sup r 1 r n b r y f d 2 d c f 2 under additional hypotheses we show that lim r r n b r y f d 2 2 d is comparable in size to 2 2 a number of other related results are established the special case when is an integer and is the surface measure on a c1 manifold was treated by s agmon and l hormander j analyse math 30 1976 1 38

relaxation in graph coloring and satisfiability problems using t 0 monte carlo simulation we study the relaxation of graph coloring k col and satisfiability k sat two hard problems that have recently been shown to possess a phase transition in solvability as a parameter is varied a change from exponentially fast to power law relaxation and a transition to freezing behavior are found these changes take place for smaller values of the parameter than the solvability transition results for the coloring problem for colorable and clustered graphs and for the fraction of persistent spins for satisfiability are also presented

dirac operators and spectral triples for some fractal sets built on curves abstract we construct spectral triples and in particular dirac operators for the algebra of continuous functions on certain compact metric spaces the triples are countable sums of triples where each summand is based on a curve in the space several fractals like a finitely summable infinite tree and the sierpinski gasket fit naturally within our framework in these cases we show that our spectral triples do describe the geodesic distance and the minkowski dimension as well as more generally the complex fractal dimensions of the space furthermore in the case of the sierpinski gasket the associated dixmier type trace coincides with the normalized hausdorff measure of dimension log 3 log 2

inverse halftoning based on the bayesian theorem this study proposes a method which can generate high quality inverse halftone images from halftone images this method can be employed prior to any signal processing over a halftone image or the inverse halftoning used in jbig2 the proposed method utilizes the least mean square lms algorithm to establish a relationship between the current processing position and its corresponding neighboring positions in each type of halftone image including direct binary search error diffusion dot diffusion and ordered dithering after which a referenced region called a support region sr is used to extract features the sr can be obtained by relabeling the lms trained filters with the order of importance moreover the probability of black pixel occurrence is considered as a feature in this work according to this feature the probabilities of all possible grayscale values at the current processing position can be obtained by the bayesian theorem consequently the final output at this position is the grayscale value with the highest probability experimental results show that the proposed method offers better visual quality than that of mese vaidyanathan s and chang s methods in terms of human visual peak signal to noise ratio hpsnr in addition the memory consumption is also superior to mese vaidyanathan s method

singularly continuous spectrum of a self similar laplacian on the half line we investigate the spectrum of the self similar laplacian which generates the so called pq random walk on the integer half line using the method of spectral decimation we prove that the spectral type of the laplacian is singularly continuous whenever p 12 this serves as a toy model for generating singularly continuous spectrum which can be generalized to more complicated settings we hope it will provide more insight into fibonacci type and other weakly self similar models

comments on probability estimation in arithmetic and adaptive huffman entropy coders this comment points out some omissions in the work of duttweiler and chazmas see ibid vol 4 p 237 1995 on credit related to scaled count estimators that perform count scaling when the count of the less probable symbol lps reaches a limiting value

restoration of error diffused images using projection onto convex sets a novel inverse halftoning method is proposed to restore a continuous tone image from a given half tone image a set theoretic formulation is used where three sets are defined using the prior information about the problem a new space domain projection is introduced assuming the halftoning is performed using error diffusion and the error diffusion filter kernel is known the space domain frequency domain and space scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution

semilinear equations on fractal blowups abstract the paper concerns existence of a ground state for a nonlinear scalar field equation on a blowup fractal where imbedding of the energy space into l p is not compact in absence of invariant transformations involved in conventional concentration compactness argument the paper develops convergence reasoning based on the fractal s self similarity

completeness of arbitrarily sampled discrete time wavelet transforms an arbitrarily sampled discrete time wavelet transform is said to be complete if it is uniquely invertible i e if the underlying signal can be uniquely recovered from the available samples of the wavelet transform we develop easy to compute necessary and sufficient conditions and necessary but not sufficient conditions for the completeness of an arbitrarily sampled dyadic discrete time wavelet transform of a periodic signal in particular we provide necessary and sufficient conditions for completeness of the sampled wavelet transform when the lowpass filter associated with the dyadic wavelet filter bank has no unit circle zeros other than those at z 1 we present necessary but not sufficient conditions for completeness when the lowpass filter associated with the dyadic wavelet filter bank has arbitrary unit circle zeros we also provide necessary and sufficient conditions for completeness of a set of samples of both the lowpass approximation to the signal and its wavelet transform all the conditions we derive use only information about the location of the retained samples and the analyzing wavelet filter bank they can easily be checked without explicitly computing of the rank of a matrix finally we present a simple signal reconstruction procedure that can be used once we have determined the arbitrarily sampled discrete time wavelet transform is complete

on discontinuity and tail behaviours of the integrated density of states for nested pre fractals we consider a general finitely ramified fractal set called a nested fractal which is determined byn number of similitudes basic properties of the integrated density of statesn x for the discrete laplacian on the associated nested prefractal are investigated in particulardn is shown to be purely discontinuous ifm n wherem is the number of branches of the inverse of the rational function involved in the spectral decimation method due to rammal toulouse sierpinski gaskets and the modified koch curve are special examples

taylor approximations on sierpinski gasket type fractals for a class of fractals that includes the familiar sierpinski gasket there is now a theory involving laplacians dirichlet forms normal derivatives green s functions and the gauss green integration formula analogous to the theory of analysis on manifolds this theory was originally developed as a by product of the construction of stochastic processes analogous to brownian motion but has been given by a direct analytic construction in the work of kigami until now this theory has not provided anything analogous to the gradient of a function or a local taylor approximation in this paper we construct a family of derivatives which includes the known normal derivative at vertex points in the graphs that approximate the fractal and obtain taylor approximations at these points we show that a function in the domain of n can be locally well approximated by an n harmonic function solution of nu 0 one novel feature of this result is that it requires several different estimates to describe the optimal rate of approximation

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

fractal snowflake domain diffusion with boundary and interior drifts abstract we study a parabolic ventsell problem for a second order differential operator in divergence form and with interior and boundary drift terms on the snowflake domain we prove that under standard conditions a related cauchy problem possesses a unique classical solution and explain in which sense it solves a rigorous formulation of the initial ventsell problem as a second result we prove that functions that are intrinsically lipschitz on the snowflake boundary admit euclidean lipschitz extensions to the closure of the entire domain our methods combine the fractal membrane analysis the vector analysis for local dirichlet forms and pde on fractals coercive closed forms and the analysis of lipschitz functions

energy and laplacian on hanoi type fractal quantum graphs this article studies potential theory and spectral analysis on compact metric spaces which we refer to as fractal quantum graphs these spaces can be represented as a possibly infinite union of one dimensional intervals and a totally disconnected possibly uncountable compact set which roughly speaking represents the set of junction points classical quantum graphs and fractal spaces such as the hanoi attractor are included among them we begin with proving the existence of a resistance form on the hanoi attractor and go on to establish heat kernel estimates and upper and lower bounds on the eigenvalue counting function of laplacians corresponding to weakly self similar measures on the hanoi attractor these estimates and bounds rely heavily on the relation between the length and volume scaling factors of the fractal we then state and prove a necessary and sufficient condition for the existence of a resistance form on a general fractal quantum graph finally we extend our spectral results to a large class of weakly self similar fractal quantum graphs

brownian motion on the sierpinski gasket we construct a brownian motion taking values in the sierpinski gasket a fractal subset of 2 and study its properties this is a diffusion process characterized by local isotropy and homogeneity properties we show for example that the process has a continuous symmetric transition density p t x y with respect to an appropriate hausdorff measure and obtain estimates on p t x y

can one hear the dimension of a fractal we consider the spectrum of the laplacian in a bounded open domain of n with a rough boundary i e with possibly non integer dimension and we discuss a conjecture by m v berry generalizing weyl s conjecture then using ideas mark kac developed in his famous study of the drum we give upper and lower bounds for the second term of the expansion of the partition function the main thesis of the paper is to show that the relevant measure of the roughness of the boundary should be based on minkowski dimensions and on minkowski measures rather than on haussdorff ones

high capacity data hiding for error diffused block truncation coding block truncation coding btc is an efficient compression technique with extremely low computational complexity however the blocking and false contour effects are two major deficiencies in btc which cause severe perceptual artifacts the former scheme error diffused btc edbtc can significantly improve the above issues through the visual low pass compensation on the bitmap which thus widens its possible application market yet the corresponding security issue may limit its value in this paper a method namely complementary hiding edbtc is developed to cope the above issue this paper is managed by firstly discussing when a single watermark is embedded and then multiple watermarks are employed to test the limitation of the proposed scheme herein an adaptive external bias factor is employed to control the watermark embedding and this factor also affects the image quality and robustness simultaneously experimental results demonstrate that the proposed method only requires an extremely small external bias factor to carry watermarks which enables a high capacity scenario without significantly damaging image quality

statistical mechanics of socio economic systems with heterogeneous agents we review the statistical mechanics approach to the study of the emerging collective behaviour of systems of heterogeneous interacting agents the general framework is presented through examples in such contexts as ecosystem dynamics and traffic modelling we then focus on the analysis of the optimal properties of large random resource allocation problems and on minority games and related models of speculative trading in financial markets discussing a number of extensions including multi asset models majority games and models with asymmetric information finally we summarize the main conclusions and outline the major open problems and limitations of the approach

resistance and spectral dimension of sierpinski carpets the authors announce results which prove the existence of the spectral dimension ds for sierpinski carpets in two dimensions their method employs the einstein relation zeta d omega df using this numerical calculations of the resistance of approximations to the sierpinski carpet yield an accurate estimate for ds

a novel classification method of halftone image via statistics matrices existing classification methods tend not to work well on various error diffusion patterns thus a novel classification method for halftone image via statistics matrices is proposed the statistics matrix descriptor of halftone image is constructed according to the characteristic of error diffusion filters on this basis an extraction algorithm is developed based on halftone image patches the feature modeling is formulated as an optimization problem and then a gradient descent method is used to seek optimum class feature matrices by minimizing the total square error a maximum likelihood method is proposed according to priori knowledge of training samples in experiments the performance evaluation method is provided and comparisons of performance between our method and seven similar methods are made then the influence of parameters performance under various attacks computational time complexity and the limitations are discussed from our experimental study it is observed that our method has lower classification error rate when compared with other similar methods in addition it is robust against usual attacks

weak uncertainty principle for fractals graphs and metric measure spaces we develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by okoudjou and strichartz we assume either an appropriate measure growth condition with respect to the effective resistance metric or in the absence of such a metric we assume the poincare inequality and reverse volume doubling property we also consider the weak uncertainty inequality in the context of nash type inequalities our results can be applied to a wide variety of metric measure spaces including graphs fractals and manifolds

pure point spectrum for the laplacian on unbounded nested fractals abstract we prove for the class of nested fractals introduced by t lindstrom 1990 memoirs amer math soc 420 that the integrated density of states is completely created by the so called neuman dirichlet eigenvalues the corresponding eigenfunctions lead to eigenfunctions with compact support on the unbounded set and we prove that for a large class of blow ups the set of neuman dirichlet eigenfunctions is complete leading to a pure point spectrum with compactly supported eigenfunctions this generalizes previous results of h teplyaev 1998 j funct anal 159 537 567 on the sierpinski gasket our methods are elementary and use only symmetry arguments via the representations of the symmetry group of the set

tree structured method for lut inverse halftoning and for image halftoning the authors previously proposed a look up table lut based method for inverse halftoning of images the lut for inverse halftoning is obtained from the histogram gathered from a few sample halftone images and corresponding original images many of the entries in the lut are unused because the corresponding binary patterns hardly occur in commonly encountered halftones these are called nonexistent patterns in this paper we propose a tree structure which will reduce the storage requirements of an lut by avoiding nonexistent patterns we demonstrate the performance on error diffused images and ordered dither images then we introduce lut based halftoning and tree structured lut tlut halftoning even though the tlut method is more complex than lut halftoning it produces better halftones and requires much less storage than lut halftoning we demonstrate how the error diffusion characteristics can be achieved with this method afterwards our algorithm is trained on halftones obtained by direct binary search dbs the complexity of tlut halftoning is higher than the error diffusion algorithm but much lower than the dbs algorithm also the halftone quality of tlut halftoning increases if the size of the tlut gets bigger thus the halftone image quality between error diffusion and dbs will be achieved depending on the size of the tree structure in the tlut algorithm

modeling and quality assessment of halftoning by error diffusion digital halftoning quantizes a graylevel image to one bit per pixel halftoning by error diffusion reduces local quantization error by filtering the quantization error in a feedback loop in this paper we linearize error diffusion algorithms by modeling the quantizer as a linear gain plus additive noise we confirm the accuracy of the linear model in three independent ways using the linear model we quantify the two primary effects of error diffusion edge sharpening and noise shaping for each effect we develop an objective measure of its impact on the subjective quality of the halftone edge sharpening is proportional to the linear gain and we give a formula to estimate the gain from a given error filter in quantifying the noise we modify the input image to compensate for the sharpening distortion and apply a perceptually weighted signal to noise ratio to the residual of the halftone and modified input image we compute the correlation between the residual and the original image to show when the residual can be considered signal independent we also compute a tonality measure similar to total harmonic distortion we use the proposed measures for edge sharpening noise shaping and tonality to evaluate the quality of error diffusion algorithms

inverse halftoning using wavelets this work introduces a new approach to inverse halftoning using nonorthogonal wavelets the distinct features of this wavelet based approach are 1 edge information in the highpass wavelet images of a halftone image is extracted and used to assist inverse halftoning 2 cross scale correlations in the multiscale wavelet decomposition are used for removing background halftoning noise while preserving important edges in the wavelet lowpass image and 3 experiments show that our simple wavelet based approach outperforms the best results obtained from inverse halftoning methods published in the literature which are iterative in nature

new spatial measure for dispersed dot halftoning assuring good point distribution in any density as a core component of dispersed dot halftoning this paper focuses on the definition of new measures for giving or measuring good point distributions in a plane by defining good point distributions from a purely geometric viewpoint of circle packing it is shown that the energy defined by a certain strong convex function satisfies the necessary conditions for obtaining good point distributions in any point density by minimizing the energy the energy with such the conditions are mathematically plain and there are no obscure parameters the theory is also significantly motivated by a requirement of the adjustability to discrete spaces and it is shown that the conditions actually work well also in the spaces as an application by using technically simple methods dispersed dot halftone masks are designed and goodness of point distributions of masks are estimated

harmonic calculus on fractals a measure geometric approach ii differentiation of functions w r t finite atomless measures with compact support on the real line is introduced the related harmonic calculus is similar to that of the classical lebesgue case as an application we obtain the weyl exponent for the spectral asymptotics of the laplacians w r t linear cantor type measures with arbitrary weights

hardware friendly descreening conventional electrophotographic printers tend to produce moire artifacts when used for printing images scanned from printed material such as books and magazines we propose a novel noniterative nonlinear and space variant descreening filter that removes a wide range of moire causing screen frequencies in a scanned document while preserving image sharpness and edge detail this filter is inspired by perona malik s anisotropic diffusion equation the amount of diffusion of the image intensity resulting from applying the filter is governed by an edge intensity estimate that is robust under halftone noise more precisely the filter extracts a spatial feature vector comprising local intensity gradients estimated from a local window in a presmoothed version of the noisy input image tunable nonlinear polynomial functions of this feature vector are then used to perform one iteration of a discrete diffusion controlled by the intensity gradient the polynomial functions and feature extraction kernels are selected empirically in order to minimize computation while ensuring robust performance across a wide range of test images on a target imaging platform the algorithm uses integer arithmetic mostly relying on low cost bit wise shift and addition operations and uses a strictly sequential architecture to provide a cost effective and robust descreening solution in practical imaging devices including copiers and multifunction printers we compare the performance of the proposed algorithm to other descreening solutions and demonstrate that the new algorithm improves quality over the existing methods while reducing computation

look up table lut method for inverse halftoning in this paper we propose look up table lut based methods for inverse halftoning of images the lut for inverse halftoning is obtained from the histogram gathered from a few sample halftone images and corresponding original images the method is extremely fast no filtering is required and the psnr and visual image quality achieved is comparable to the best methods known for inverse halftoning the lut inverse halftoning method does not depend on the specific properties of the halftoning method and can be applied to any halftoning method then an algorithm for template selection for lut inverse halftoning is introduced we demonstrate the performance of the lut inverse halftoning algorithm on error diffused images and ordered dithered images we also extend lut inverse halftoning to color halftones

improved block truncation coding using optimized dot diffusion block truncation coding btc has been considered a highly efficient compression technique for decades however its inherent artifacts blocking effect and false contour caused by low bit rate configuration are the key problems to deal with these an improved btc namely dot diffused btc ddbtc is proposed in this paper moreover this method can provide excellent processing efficiency by exploiting the nature parallelism advantage of the dot diffusion and excellent image quality can also be offered through co optimizing the class matrix and diffused matrix of the dot diffusion according to the experimental results the proposed ddbtc is superior to the former error diffused btc in terms of various objective image quality assessment methods as well as processing efficiency in addition the ddbtc also shows a significant image quality improvement comparing with that of the former ordered dither btc

error diffused image compression using a binary to gray scale decoder and predictive pruned tree structured vector quantization the authors consider data compression of binary error diffused images the original contribution is using nonlinear filters to decode error diffused images to compress them in the gray scale domain this gives better image quality than directly compressing the binary images their method is of low computational complexity and can work with any halftoning algorithm

permutation filter lattices a general order statistic filtering framework a general nonlinear filtering framework permutation order statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination permutation filters much like polynomial filters are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions at the simplest level in the filter lattice permutation filters reduce to either a simple linear fir or to an order statistic os filter but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties in order to enhance the robustness of permutation fitters we develop spl alpha trimmed permutation indicators and their associated filter lattices we conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system this paper thus extends the potential of order statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems

transition density estimates for brownian motion on affine nested fractals a class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals for these fractals estimates on the transition density for the brownian motion are obtained using the associated dirichlet form an upper bound for the diagonal can be found using a nash type inequality then probabilistic techniques are used to obtain the off diagonal bound the approach differs from previous treatments as it uses only the dirichlet form and no estimates on the resolvent the bounds obtained are expressed in terms of an intrinsic metric on the fractal

signal recovery from wavelet transform maxima the paper presents an iterative algorithm for signal recovery from discrete time wavelet transform maxima the signal recovery algorithm is developed by using the method of projections onto convex sets convergence of the algorithm is assured

least squares halftoning via human vision system and markov gradient descent ls mgd algorithm and analysis halftoning is the core algorithm governing most digital printing or imaging devices by which images of continuous tones are converted to ensembles of discrete or quantum dots it is through the human vision system hvs that such fields of quantum dots can be perceived to be almost identical to the original continuous images in the current work we propose a least squares based halftoning model with a substantial contribution from the hvs model and we design a robust computational algorithm based on markov random walks furthermore we discuss and quantify the important role of spatial smoothing by the hvs and rigorously prove the gradient descent property of the markov stochastic algorithm computational results on typical test images further confirm the performance of the new approach the proposed algorithm and its mathematical analysis are generically applicable to similar discrete or nonlinear programming problems

hybrid lms mmse inverse halftoning technique the objective of this work is to reconstruct high quality gray level images from bilevel halftone images we develop optimal inverse halftoning methods for several commonly used halftone techniques which include dispersed dot ordered dither clustered dot ordered dither and error diffusion at first the least mean square lms adaptive filtering algorithm is applied in the training of inverse halftone filters the resultant optimal mask shapes are significantly different for various halftone techniques and these mask shapes are also quite different from the square shape that was frequently used in the literature in the next step we further reduce the computational complexity by using lookup tables designed by the minimum mean square error mmse method the optimal masks obtained from the lms method are used as the default filter masks finally we propose the hybrid lms mmse inverse halftone algorithm it normally uses the mmse table lookup method for its fast speed when an empty cell is referred the lms method is used to reconstruct the gray level value consequently the hybrid method has the advantages of both excellent reconstructed quality and fast speed in the experiments the error diffusion yields the best reconstruction quality among all three halftone techniques

the riemann zeta function and the one dimensional weyl berry conjecture for fractal drums based on his earlier work on the vibrations of drums with fractal boundary the first author has refined m v berry s conjecture that extended from the smooth to the fractal case h weyl s conjecture for the asymptotics of the eigenvalues of the laplacian on a bounded open subset of w see 16 we solve here in the one dimensional case that is when n 1 this modified weyl berry conjecture we discover in the process some unexpected and intriguing connections between spectral geometry fractal geometry and the riemann zeta function we therefore show that one can hear that is recover from the spectrum not only the minkowski fractal dimension of the boundary as was established previously by the first author but also under the stronger assumptions of the conjecture its minkowski content a fractal analogue of its length we also prove still in dimension one a related conjecture of the first author as well as its converse which characterizes the situation when the error estimates of the aforementioned paper are sharp

self similarity of volume measures for laplacians on p c f self similar fractals our main goal in this paper is to obtain a precise analogue of weyl s asymptotic formula for the eigenvalue distribution of laplacians on a certain class of finitely ramified or p c f self similar fractals building in particular on the work of 7 9 22 24 our main result consists in precisely identifying for the class of decimable fractals the volume measures constructed by the second author in 24 for general p c f fractals and showing that they are self similar

a fast high quality inverse halftoning algorithm for error diffused halftones halftones and other binary images are difficult to process with causing several degradation degradation is greatly reduced if the halftone is inverse halftoned converted to grayscale before scaling sharpening rotating or other processing for error diffused halftones we present 1 a fast inverse halftoning algorithm and 2 a new multiscale gradient estimator the inverse halftoning algorithm is based on anisotropic diffusion it uses the new multiscale gradient estimator to vary the tradeoff between spatial resolution and grayscale resolution at each pixel to obtain a sharp image with a low perceived noise level because the algorithm requires fewer than 300 arithmetic operations per pixel and processes 7 spl times 7 neighborhoods of halftone pixels it is well suited for implementation in vlsi and embedded software we compare the implementation cost peak signal to noise ratio and visual quality with other inverse halftoning algorithms

harmonic calculus on p c f self similar sets the main object of this paper is the laplace operator on a class of fractals first we establish the concept of the renormalization of difference operators on post critically finite p c f for short self similar sets which are large enough to include finitely ramified self similar sets and extend the results for sierpinski gasket given in 10 to this class under each invariant operator for renormalization the laplace operator green function dirichlet form and neumann derivatives are explicitly constructed as the natural limits of those on finite pre self similar sets which approximate the p c f self similar sets also harmonic functions are shown to be finite dimensional and they are characterized by the solution of an infinite system of finite difference equations

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

halftone image classification using lms algorithm and naive bayes former research on inverse halftoning most focus on developing a general purpose method for all types of halftone patterns such as error diffusion ordered dithering etc while fail to consider the natural discrepancies among various halftoning methods to achieve optimal image quality for each halftoning method the classification of halftone images is highly demanded this study employed the least mean square filter for improving the robustness of the extracted features and employed the naive bayes classifier to verify all the extracted features for classification nine of the most well known halftoning methods were involved for testing the experimental results demonstrated that the classification performance can achieve a 100 accuracy rate and the number of distinguishable halftoning methods is more than that of a former method established by chang and yu

spectral dimension and bohr s formula for schrodinger operators on unbounded fractal spaces we establish an asymptotic formula for the eigenvalue counting function of the schrodinger operator for some unbounded potentials v on several types of unbounded fractal spaces we give sufficient conditions for bohr s formula to hold on metric measure spaces which admit a cellular decomposition and then verify these conditions for fractafolds and fractal fields based on nested fractals in particular we partially answer a question of fan khandker and strichartz regarding the spectral asymptotics of the harmonic oscillator potential on the infinite blow up of a sierpinski gasket

parabolic type equations associated with the dirichlet form on the sierpinski gasket by using analytic tools from stochastic analysis we initiate a study of some non linear parabolic equations on sierpinski gasket motivated by modellings of fluid flows along fractals which can be considered as models of simplified rough porous media unlike the regular space case such parabolic type equations involving non linear convection terms must take a different form due to the fact that convection terms must be singular to the linear part which defines the heat semigroup in order to study these parabolic type equations a new kind of sobolev inequalities for the dirichlet form on the gasket will be established these sobolev inequalities which are interesting on their own and in contrast to the case of euclidean spaces involve two l p norms with respect to two mutually singular measures by examining properties of singular convolutions of the associated heat semigroup we derive the space time regularity of solutions to these parabolic equations under a few technical conditions the burgers equations on the sierpinski gasket are also studied for which a maximum principle for solutions is derived using techniques from backward stochastic differential equations and the existence uniqueness and regularity of its solutions are obtained

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

on the asymptotics of the eigenvalue counting function for random recursive sierpinski gaskets we consider natural laplace operators on random recursive affine nested fractals based on the sierpinski gasket and prove an analogue of weyl s classical result on their eigenvalue asymptotics the eigenvalue counting function n is shown to be of order ds 2 as where we can explicitly compute the spectral dimension d s moreover the limit n ds 2 will typically exist and can be expressed as a deterministic constant multiplied by a random variable this random variable is a power of the limiting random variable in a suitable general branching process and has an interpretation as the volume of the fractal

inverse halftoning via map estimation there has been a tremendous amount of research in the area of image halftoning where the goal has been to find the most visually accurate representation given a limited palette of gray levels often just two black and white this paper focuses on the inverse problem that of finding efficient techniques for reconstructing high quality continuous tone images from their halftoned versions the proposed algorithms are based on a maximum a posteriori map estimation criteria using a markov random field mrf model for the prior image distribution image estimates obtained with the proposed model accurately reconstruct both the smooth regions of the image and the discontinuities along image edges algorithms are developed and example gray level reconstructions are presented generated from both dithered and error diffused halftone originals application of the technique to the problems of rescreening and the processing of halftone images are shown

statistical mechanics of the mixed majority minority game with random external information we study the asymptotic macroscopic properties of the mixed majority minority game modelling a population in which two types of heterogeneous adaptive agents namely fundamentalists driven by differentiation and trend followers driven by imitation interact the presence of a fraction f of trend followers is shown to induce a a significant loss of informational efficiency with respect to a pure minority game in particular an efficient unpredictable phase exists only for f 1 2 we solve the model by means of an approximate static replica theory and by a direct dynamical generating functional technique the two approaches coincide and match numerical results convincingly

halftone to continuous tone conversion of error diffusion coded images considers the problem of reconstructing a continuous tone contone image from its halftoned version where the halftoning process is done by error diffusion the authors present an iterative nonlinear decoding algorithm for halftone to contone conversion and show simulation results that compare the performance of the algorithm to that of conventional linear low pass filtering they find that the new technique results in subjectively superior reconstruction as there is a natural relationship between error diffusion and spl sigma spl delta modulation the reconstruction algorithm can also be applied to the decoding problem for spl sigma spl delta modulators

exact spectrum of the laplacian on a domain in the sierpinski gasket abstract for a certain domain in the sierpinski gasket sg whose boundary is a line segment a complete description of the eigenvalues of the laplacian with an exact count of dimensions of eigenspaces under the dirichlet and neumann boundary conditions is presented the method developed in this paper is a weak version of the spectral decimation method due to fukushima and shima since for a lot of bad eigenvalues the spectral decimation method can not be used directly let 0 x x be the eigenvalue counting functions of the laplacian associated to sg and respectively we prove a comparison between 0 x and x says that 0 0 x x c x log 2 log 5 log x for sufficiently large x for some positive constant c as a consequence x g log x x log 3 log 5 o x log 2 log 5 log x as x for some right continuous discontinuous log 5 periodic function g r r with 0 inf r g sup r g moreover we explain that the asymptotic expansion of x should admit a second term of the order log 2 log 5 that becomes apparent from the experimental data this is very analogous to the conjectures of weyl and berry

spectral analysis on infinite sierpinski gaskets we study the spectral properties of the laplacian on infinite sierpin ski gaskets we prove that the laplacian with the neumann boundary condition has pure point spectrum moreover the set of eigenfunctions with compact support is complete the same is true if the infinite sierpin ski gasket has no boundary but is false for the laplacian with the dirichlet boundary condition in all these cases we describe the spectrum of the laplacian and all the eigenfunctions with compact support to obtain these results first we prove certain new formulas for eigenprojectors of the laplacian on finite sierpin ski pre gaskets then we prove that the spectrum of the discrete laplacian on a sierpin ski lattice is pure point and the eigenfunctions are localized 1998 academic press

joint compression watermarking scheme using majority parity guidance and halftoning based block truncation coding in this paper a watermarking scheme called majority parity guided error diffused block truncation coding mpg edbtc is proposed to achieve high image quality and embedding capacity edbtc exploits the error diffusion to effectively reduce blocking effect and false contour which inherently exhibit in traditional btc in addition the coding efficiency is significantly improved by replacing high and low means evaluation with extreme values substitution the proposed mpg edbtc embeds a watermark simultaneously during compression by evaluating the parity value in a predefined parity check region pcr as documented in the experimental results the proposed scheme can provide good robustness image quality and processing efficiency finally the proposed mpg edbtc is extended to embed multiple watermarks and achieves excellent image quality robustness and capacity nowadays most multimedia is compressed before it is stored it is more appropriate to embed information such as watermarks during compression the proposed method has been proved to solve effectively the inherent problems in traditional btc and provide excellent performance in watermark embedding

a pocs based restoration algorithm for restoring halftoned color quantized images this paper studies the restoration of images which are color quantized with error diffusion though there are many reported algorithms proposed for restoring noisy blurred color images and inverse halftoning restoration of color quantized images is rarely addressed in the literature especially when the images are color quantized with halftoning direct application of existing restoration techniques are generally inadequate to deal with this problem in this paper a restoration algorithm based on projection onto convex sets is proposed this algorithm makes use of the available color palette and the mechanism of a halftoning process to derive useful a priori information for restoration simulation results showed that it could improve the quality of a halftoned color quantized image remarkably in terms of both snr and cielab color difference metric

image restoration by the method of convex projections part 2 applications and numerical results the image restoration theory discussed in a previous paper by youla and webb 1 is applied to a simulated image and the results compared with the well known method known as the gerchberg papoulis algorithm the results show that the method of image restoration by projection onto convex sets by providing a convenient technique for utilizing a priori information performs significantly better than the gerchberg papoulis method

optimized halftoning using dot diffusion and methods for inverse halftoning unlike the error diffusion method the dot diffusion method for digital halftoning has the advantage of pixel level parallelism however the image quality offered by error diffusion is still regarded as superior to most of the other known methods we show how the dot diffusion method can be improved by optimization of the so called class matrix by taking the human visual characteristics into account we show that such optimization consistently results in images comparable to error diffusion without sacrificing the pixel level parallelism adaptive dot diffusion is also introduced and then a mathematical description of dot diffusion is derived furthermore inverse halftoning of dot diffused images is discussed and two methods are proposed the first one uses projection onto convex sets pocs and the second one uses wavelets of these methods the wavelet method does not make use of the knowledge of the class matrix embedded multiresolution dot diffusion is also discussed which is useful for rendering at different resolutions and transmitting images progressively

transition densities for brownian motion on the sierpinski carpet upper and lower bounds are obtained for the transition densitiesp t x y of brownian motion on the sierpinski carpet these are of the same form as those which hold for the sierpinski gasket in addition the joint continuity ofp t x y is proved the existence of the spectral dimension is established and the einstein relation connecting the spectral dimension the hausdorff dimension and the resistance exponent is shown to hold

weyl s problem for the spectral distribution of laplacians on p c f self similar fractals we establish an analogue of weyl s classical theorem for the asymptotics of eigenvalues of laplacians on a finitely ramified i e p c f self similar fractalk such as for example the sierpinski gasket we consider both dirichlet and neumann boundary conditions as well as laplacians associated with bernoulli type multifractal measures onk from a physical point of view we study the density of states for diffusions or for wave propagation in fractal media more precisely let x be the number of eigenvalues less thanx then we show that x is of the order ofxds 2 asx where the spectral exponent ds is computed in terms of the geometric as well as analytic structures ofk further we give an effective condition that guarantees the existence of the limit ofx ds 2 x asx this condition is in some sense generic in addition we define in terms of the above spectral exponents and calculate explicitly the spectral dimension ofk

inverse halftoning using binary permutation filters the problem of reconstructing a continuous tone image given its ordered dithered halftone or its error diffused halftone image is considered we develop a modular class of nonlinear filters that can reconstruct the continuous tone information preserving image details and edges that provide important visual cues the proposed nonlinear reconstruction algorithms denoted as binary permutation filters are based on the space and rank orderings of the halftone samples provided by the multiset permutation of the on pixels in a halftone observation window for a given window size we obtain a wide range of filters by varying the amount of space rank ordering information utilized in the estimate for image reconstructions from ordered dithered halftones we develop periodically space varying filters that can account for the periodical nature of the underlying screening process a class of suboptimal but simpler space invariant reconstruction filters are also proposed and tested constrained lms type algorithms are employed for the design of reconstruction filters that minimize the reconstruction mean squared error we present simulations showing that binary permutation filters are modular robust to image source characteristics and that they produce high visual quality image reconstruction

analysis of ordered dither for arbitrary sampling lattices and screen periodicities ordered dither is considered a simple and effective method of image binarization for rectangular lattices it has been shown that this method of spatially periodic quantization causes aliasing in the frequency domain resulting in a degradation of halftone image quality this result is extended by deriving an expression for the spectrum of the halftoned image generalized for any sampling lattice and any screen periodicity this expression will show the explicit relationship between screen function and halftone image quality using this expression the nonlinearities associated with four optimized screens are analyzed to determine which screens are best suited to halftone rectangularly and hexagonally sampled images