robust estimation of parameter for fractal inverse problem in this paper some similarity measures for fractal image compression fic are introduced which are robust against noises in the proposed methods robust estimation technique from statistics is embedded into the encoding procedure of the fractal inverse problem to find the parameters when the original image is corrupted by noises we hope that the proposed scheme is insensitive to those noises presented in the corrupted image this leads to a new concept of robust estimation of fractal inverse problem the proposed least absolute derivation lad least trimmed squares lts and wilcoxon fic are the first attempt toward the design of robust fractal image compression which can remove the noises in the encoding process the main disadvantage of the robust fic is the computational cost to overcome this drawback particle swarm optimization pso technique is utilized to reduce the searching time simulation results show that the proposed fic is robust against the outliers in the image also the pso method can effectively reduce the encoding time while retaining the quality of the retrieved image

the fractal neighbor distance measure fractal image coding has been used successfully to compress and segment images and more recently utilized in a new distance measure to recognize objects this paper discusses how the process of decoding a set of region based contractive transformations has invariance properties that can be advantageous in object recognition we will show that the recognition ability of the proposed fractal neighbor classifier fnc utilizing the fractal neighbor distance fnd measure is a function of the contrast scaling factor and the illumination shift factor our investigation of the fnd required accurate control over the convergence of a fractal decoding process convergence can be determined by examining the contractivity and eventual contractivity factors we have derived theorems that allow these two factors to be calculated for a general class of fractal codes consisting of affine transformations with integral geometric scaling experiments were performed that verified our ability to control and modify these convergence properties furthermore experiments on human face recognition revealed that the performance of the fnc improved through the use of eventual convergence and the imposition of limits on the illumination shift factor

still image coding based on vector quantization and fractal approximation in this paper we propose a coding algorithm for still images using vector quantization vq and fractal approximation in which low frequency components of an input image are approximated by vq and its residual is coded by fractal mapping the conventional fractal coding algorithms indirectly used the gray patterns of an original image with contraction mapping whereas the proposed fractal coding method employs an approximated and then decimated image as a domain pool and uses its gray patterns thus the proposed algorithm utilizes fractal approximation without the constraint of contraction mapping for approximation of an original image we employ the discrete cosine transform dct rather than conventional polynomial based transforms in addition for variable blocksize segmentation we use the fractal dimension of a block that represents the roughness of the gray surface of a region computer simulations with several test images show that the proposed method shows better performance than the conventional fractal coding methods for encoding still pictures

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

the picard contraction mapping method for the parameter inversion of reaction diffusion systems an inverse problem is to determine unknown causes based on observation of their effects such problems often arise in scientific research and engineering practice in this paper we present a parameter inversion method for a class of reaction diffusion systems by the use of the picard contraction mapping we firstly establish an approximate differential equation model which corresponds to the given reaction diffusion system and discuss the contractivity of the picard mapping associated with the approximate model then we provide an algorithm for recovering parameters of the reaction diffusion system based on the collage theorem numerical tests show that the proposed method is efficient

classified vector quantization of images vector quantization vq provides many attractive features for image coding with high compression ratios however initial studies of image coding with vq have revealed several difficulties most notably edge degradation and high computational complexity we address these two problems and propose a new coding method classified vector quantization cvq which is based on a composite source model blocks with distinct perceptual features such as edges are generated from different subsources i e belong to different classes in cvq a classifier determines the class for each block and the block is then coded with a vector quantizer designed specifically for that class we obtain better perceptual quality with significantly lower complexity with cvq when compared to ordinary vq we demonstrate with cvq visual quality which is comparable to that produced by existing coders of similar complexity for rates in the range 0 6 1 0 bits pixel

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

a review of the fractal image coding literature fractal image compression is a technique based on the representation of an image by a contractive transform on the space of images for which the fixed point is close to the original image this broad principle encompasses a very wide variety of coding schemes many of which have been explored in the rapidly growing body of published research while certain theoretical aspects of this representation are well established relatively little attention has been given to the construction of a coherent underlying image model that would justify its use most purely fractal based schemes are not competitive with the current state of the art but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success this review represents a survey of the most significant advances both practical and theoretical since the publication of jacquin s 1990 original fractal coding scheme

an improved fractal image compression approach by using iterated function system and genetic algorithm abstract this paper presents an improved method of generating a binary image affine ifs iterated function system by using genetic algorithm we adopt a natural variable length genotype encoding to represent an individual the multiobject fitness function is also applied in this algorithm in addition a distributed version of the binary image compression algorithm is implemented both theoretical analysis and experimental results show a higher compression ratio with better quality images by using the proposed algorithm

fractal image denoising over the past decade there has been significant interest in fractal coding for the purpose of image compression however applications of fractal based coding to other aspects of image processing have received little attention we propose a fractal based method to enhance and restore a noisy image if the noisy image is simply fractally coded a significant amount of the noise is suppressed however one can go a step further and estimate the fractal code of the original noise free image from that of the noisy image based upon a knowledge or estimate of the variance of the noise assumed to be zero mean stationary and gaussian the resulting fractal code yields a significantly enhanced and restored representation of the original noisy image the enhancement is consistent with the human visual system where extra smoothing is performed in flat and low activity regions and a lower degree of smoothing is performed near high frequency components e g edges of the image we find that for significant noise variance spl sigma spl ges 20 the fractal based scheme yields results that are generally better than those obtained by the lee filter which uses a localized first order filtering process similar to fractal schemes we also show that the lee filter and the fractal method are closely related

fast fractal image block coding based on local variances in fractal image block coding most of the time is spent on finding a close match between a range block and a large pool of domain blocks for a large image this effect becomes aggravated as the domain pool increases exponentially we propose using the local variances of domain blocks to reduce the search space by sorting the contracted domain pool according to their local variances and defining an acceptance criterion for a close match we can confine all the potential close matches to a relatively small sized window to limit the search space the encoding time can hence be shortened with the decoded image quality as good as that using the full search method the speedup can be over ten times depending on the complexity of encoded images

conditional strategies in iterated quantum games abstract iterated bipartite quantum games are implemented in terms of the discrete time quantum walk on the line our proposal allows for conditional strategies as two rational agents make a choice from a restricted set of two qubit unitary operations we discuss how several classical strategies are related to families of quantum strategies a quantum version of the well known prisoner s dilemma bipartite game in which both players use mixed strategies is presented as a specific example

query evaluation in probabilistic relational databases abstract this paper describes a generalization of the relational model in order to capture and manipulate a type of probabilistic information probabilistic databases are formalized by means of logic theories based on a probabilistic first order language proposed by halpern a sound and complete method is described for evaluating queries in probabilistic theories the generalization proposed can be incorporated into existing relational systems with the addition of a component for manipulating propositional formulas

iteration free fractal image coding based on efficient domain pool design the domain pool design is one of the dominant issues which affect the coding performance of fractal image compression in this paper we employ the lbg algorithm and propose a block averaging method to design the efficient domain pools based on a proposed iteration free fractal image codec the redundancies between the generated domain blocks are reduced by the proposed methods therefore we can obtain the domain pools that are more efficient than those in the conventional fractal coding schemes and thus the coding performance is improved on the other hand the iteration process in the conventional fractal coding scheme not only requires a large size of memory and a high computation complexity but also prolongs the decoding process the proposed iteration free fractal codec can overcome the problems above in computer simulation both the lbg based and block averaging methods for the domain pool design in the proposed iteration free scheme achieve excellent performances for example based on the proposed block averaging method the decoded lena image has at least a 0 5 db higher psnr under the same bit rate and an eight time faster decoding speed than the conventional fractal coding schemes that require iterations

huber fractal image coding based on a fitting plane recently there has been significant interest in robust fractal image coding for the purpose of robustness against outliers however the known robust fractal coding methods hfic and lad fic etc are not optimal since besides the high computational cost they use the corrupted domain block as the independent variable in the robust regression model which may adversely affect the robust estimator to calculate the fractal parameters depending on the noise level this paper presents a huber fitting plane based fractal image coding hfpfic method this method builds huber fitting planes hfps for the domain and range blocks respectively ensuring the use of an uncorrupted independent variable in the robust model on this basis a new matching error function is introduced to robustly evaluate the best scaling factor meanwhile a median absolute deviation mad about the median decomposition criterion is proposed to achieve fast adaptive quadtree partitioning for the image corrupted by salt pepper noise in order to reduce computational cost the no search method is applied to speedup the encoding process experimental results show that the proposed hfpfic can yield superior performance over conventional robust fractal image coding methods in encoding speed and the quality of the restored image furthermore the no search method can significantly reduce encoding time and achieve less than 2 0 s for the hfpfic with acceptable image quality degradation in addition we show that combined with the mad decomposition scheme the hfp technique used as a robust method can further reduce the encoding time while maintaining image quality

fractal modeling and segmentation for the enhancement of microcalcifications in digital mammograms the objective of this research is to model the mammographic parenchymal and ductal patterns and enhance the microcalcifications using a deterministic fractal approach according to the theory of deterministic fractal geometry images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional 2 d affine transformations the iterated functions systems and the collage theorem are the mathematical foundations of fractal image modeling here a methodology based on fractal image modeling is developed to analyze and model breast background structures the authors show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations therefore microcalcifications can be enhanced by taking the difference between the original image and the modeled image the authors results are compared with those of the partial wavelet reconstruction and morphological operation approaches the results demonstrate that the fractal modeling method is an effective way to enhance microcalcifications it may also be able to improve the detection and classification of microcalcifications in a computer aided diagnosis system

efficient tests for equivalence of hidden markov processes and quantum random walks while two hidden markov process hmp resp quantum random walk qrw parametrizations can differ from one another the stochastic processes arising from them can be equivalent here a polynomial time algorithm is presented which can determine equivalence of two hmp parametrizations m1 m2 resp two qrw parametrizations q1 q2 in time o max n1 n2 4 where n1 n2 are the number of hidden states in m1 m2 resp the dimension of the state spaces associated with q1 q2 and is the set of output symbols previously avail able algorithms for testing equivalence of hmps were exponential in the number of hidden states in case of qrws algorithms for testing equivalence had not yet been presented the core subrou tines of this algorithm can also be used to efficiently test hidden markov processes and quantum random walks for ergodicity

technique for fractal image compression using genetic algorithm a new method for fractal image compression is proposed using genetic algorithm ga with an elitist model the self transformation property of images is assumed and exploited in the fractal image compression technique the technique described utilizes the ga which greatly decreases the search space for finding the self similarities in the given image this article presents theory implementation and an analytical study of the proposed method along with a simple classification scheme a comparison with other fractal based image compression methods is also reported

an edge property based neighborhood region search strategy for fractal image compression abstract in this paper an edge property based neighborhood region search method is proposed to speedup the fractal encoder the method searches for the best matched solution in the frequency domain a coordinate system is constructed using the two lowest discrete cosine transformation dct coefficients of image blocks image blocks with similar edge shapes will be concentrated in some specific regions therefore the purpose of speedup can be reached by limiting the search space moreover embedding the edge property of block into the proposed search method the speedup rate can be lifted further experimental results show that under the condition of the same psnr the encoding time of the proposed method is only about two fifth of duh s classification method compared with tseng s method the proposed method is near or superior to the performance of their method moreover the encoding speed of the proposed method is about 120 times faster than that of the full search method while the penalty of retrieved image quality is only decaying 0 9 db

a hybrid fractal video compression method fractal image compression is a relatively recent image compression method its extension to a sequence of motion images is important in video compression applications there are two basic fractal compression methods namely the cube based and the frame based methods being commonly used in the industry however there are advantages and disadvantages in both methods this paper proposes a hybrid algorithm highlighting the advantages of the two methods in order to produce a good compression algorithm for video industry experimental results show the hybrid algorithm improves the compression ratio and the quality of decompressed images

approximate counting uniform generation and rapidly mixing markov chains the paper studies effective approximate solutions to combinatorial counting and uniform generation problems using a technique based on the simulation of ergodic markov chains it is shown that for self reducible structures almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time it follows that for self reducible structures polynomial time randomised algorithms for counting to within factors of the form 1 n are available either for all fl e r or for no fi e r a substantial part of the paper is devoted to investigating the rate of convergence of finite ergodic markov chains and a simple but powerful characterisation of rapid convergence for a broad class of chains based on a structural property of the underlying graph is established finally the general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods this in turn leads to randomised approximate counting algorithms for these graphs with very good

a nonlinear model for fractal image coding after a very promising start progress in fractal image coding has been relatively slow recently most improvements have been concentrating on better adaptive coding algorithms and on search strategies to reduce the encoding time very little has been done to challenge the linear model of the fractal transformations used so far in practical applications in this paper we explain why effective nonlinear transformations are not easy to find and propose a model based on conformal mappings in the geometric domain that are a natural extension of the affine model our compression results show improvements over the linear model and support the hope that a deeper understanding of the notion of self similarity would further advance fractal image coding

a fast fractal decoding algorithm based on the selection of an initial image in this correspondence we show that the number of iterations required for the convergence of the fractal image decoding algorithm can be reduced by selecting a suitable initial image we consider fractal decoding to have two components namely dc and ac our initial image is an approximation of the attractor of dc decoding which is a good estimation of the range averaged image i e the image obtained by replacing all pixel intensities in a given block by the mean value of the block from the simulation it is demonstrated that the decoding speed is greatly improved

image coding by block prediction of multiresolution subimages the redundancy of the multiresolution representation has been clearly demonstrated in the case of fractal images but it has not been fully recognized and exploited for general images fractal block coders have exploited the self similarity among blocks in images we devise an image coder in which the causal similarity among blocks of different subbands in a multiresolution decomposition of the image is exploited in a pyramid subband decomposition the image is decomposed into a set of subbands that are localized in scale orientation and space the proposed coding scheme consists of predicting blocks in one subimage from blocks in lower resolution subbands with the same orientation although our prediction maps are of the same kind of those used in fractal block coders which are based on an iterative mapping scheme our coding technique does not impose any contractivity constraint on the block maps this makes the decoding procedure very simple and allows a direct evaluation of the mean squared error mse between the original and the reconstructed image at coding time more importantly we show that the subband pyramid acts as an automatic block classifier thus making the block search simpler and the block matching more effective these advantages are confirmed by the experimental results which show that the performance of our scheme is superior for both visual quality and mse to that obtainable with standard fractal block coders and also to that of other popular image coders such as jpeg

a sound and sometimes complete query evaluation algorithm for relational databases with null values a sound and in certain cases complete method is described for evaluating queries in relational databases with null values where these nulls represent existing but unknown individuals the soundness and completeness results are proved relative to a formalization of such databases as suitable theories of first order logic because the algorithm conforms to the relational algebra it may easily be incorporated into existing relational systems

a technique for image magnification using partitioned iterative function system abstract a new technique for image magnification using the theory of fractals is proposed the technique is designed assuming self transformability property of images in particular the magnification task is performed using the fractal code of the image instead of the original one resulting in a reduction in memory requirement to generate the fractal codes genetic algorithm with elitist model is used which greatly decreases the search for finding self similarities in the given image the article presents both theory and implementation of the proposed method a simple distortion measure scheme and a similarity criterion based on just noticeable difference have also been proposed to judge the image quality of the magnified image comparison with one of the most popular magnification techniques the nearest neighbor technique is made

strengths and weaknesses of quantum computing recently a great deal of attention has been focused on quantum computation following a sequence of results bernstein and vazirani in proc 25th annual acm symposium theory comput 1993 pp 11 20 siam j comput 26 1997 pp 1277 1339 simon in proc 35th annual ieee symposium foundations comput sci 1994 pp 116 123 siam j comput 26 1997 pp 1340 1349 shor in proc 35th annual ieee symposium foundations comput sci 1994 pp 124 134 suggesting that quantum computers are more powerful than classical probabilistic computers following shor s result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time it is natural to ask whether all of np can be efficiently solved in quantum polynomial time in this paper we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class np cannot be solved on a quantum turing machine qtm in time o 2 n 2 we also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class np cap conp cannot be solved on a qtm in time o 2 n 3 the former bound is tight since recent work of grover in it proc 28 th annual acm symposium theory comput 1996 shows how to accept the class np relative to any oracle on a quantum computer in time o 2 n 2

a fractal vector quantizer for image coding we investigate the relation between vq vector quantization and fractal image coding techniques and propose a novel algorithm for still image coding based on fractal vector quantization fvq in fvq the source image is approximated coarsely by fixed basis blocks and the codebook is self trained from the coarsely approximated image rather than from an outside training set or the source image itself therefore fvq is capable of eliminating the redundancy in the codebook without any side information in addition to exploiting the self similarity in real images effectively the computer simulation results demonstrate that the proposed algorithm provides better peak signal to noise ratio psnr performance than most other fractal based coders

discrete quantum walks hit exponentially faster this paper addresses the question what processes take polynomial time on a quantum computer that require exponential time classically we show that the hitting time of the discrete time quantum walk on the n bit hypercube from one corner to its opposite is polynomial in n this gives the first exponential quantum classical gap in the hitting time of discrete quantum walks we provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs we outline a possible application to sequential packet routing

quantum repeated games revisited we present a scheme for playing quantum repeated 2 2 games based on marinatto and weber s approach to quantum games as a potential application we study the twice repeated prisoner s dilemma game we show that results not available in the classical game can be obtained when the game is played in the quantum way before we present our idea we comment on the previous scheme of playing quantum repeated games proposed by iqbal and toor we point out the drawbacks that make their results unacceptable

iterated function systems and the global construction of fractals iterated function systems i f ss are introduced as a unified way of generating a broad class of fractals these fractals are often attractors for i f ss and occur as the supports of probability measures associated with functional equations the existence of certain p balanced measures for i f ss is established and these measures are uniquely characterized for hyperbolic i f ss the hausdorff besicovitch dimension for some attrac tors of hyperbolic i f ss is estimated with the aid of p balanced measures what appears to be the broadest framework for the exactly computable moment theory of p balanced measures that of linear i f ss and of probabilistic mixtures of iterated riemann surfaces is presented this extensively generalizes earlier work on orthogonal polynomials on julia sets an example is given of fractal reconstruction with the use of linear i f ss and moment theory

a fast fractal image coding based on kick out and zero contrast conditions a fast algorithm for fractal image coding based on a single kick out condition and the zero contrast prediction is proposed in this paper the single kick out condition can avoid a large number of range domain block matches when finding the best matched domain block an efficient method for zero contrast prediction is also proposed which can determine whether the contrast factor for a domain block is zero or not and compute the corresponding difference between the range block and the transformed domain block efficiently and exactly the proposed algorithm can achieve the same reconstructed image quality as the exhaustive search and can greatly reduce the required computation or runtime in addition this algorithm does not need any pre processing step or additional memory for its implementation and can combine with other fast fractal algorithms to further improve the speed experimental results show that the runtime is reduced by about 50 of that of the exhaustive search method when combined with the dct inner product algorithm the required runtime for the algorithm can be further reduced by about 50 the proposed algorithm was also compared to two other fast fractal algorithms experimental results also show that our algorithm achieves a better efficiency and requires a much smaller amount of memory for implementation

combining fractal image compression and vector quantization in fractal image compression the code is an efficient binary representation of a contractive mapping whose unique fixed point approximates the original image the mapping is typically composed of affine transformations each approximating a block of the image by another block called domain block selected from the same image the search for a suitable domain block is time consuming moreover the rate distortion performance of most fractal image coders is not satisfactory we show how a few fixed vectors designed from a set of training images by a clustering algorithm accelerates the search for the domain blocks and improves both the rate distortion performance and the decoding speed of a pure fractal coder when they are used as a supplementary vector quantization codebook we implemented two quadtree based schemes a fast top down heuristic technique and one optimized with a lagrange multiplier method for the 8 bits per pixel bpp luminance part of the 512 spl kappa 512 lena image our best scheme achieved a peak signal to noise ratio of 32 50 db at 0 25 bpp

histogram thresholding by minimizing graylevel fuzziness the problem of histogram sharpening and thresholding by minimizing greyness ambiguity using the measures of fuzziness in a set is considered this work provides a complete mathematical formulation of the said problem in order that both fuzzy and crisp segmentation result the criteria regarding the choices of membership functions and the window sizes are established they involve symmetry in ambiguity around the crossover point and bound functions for restricting the variation of membership function values the segmentation thus obtained provides not only flexibility in methodology but also effective results experimental results further establish the same conclusions

unveiling and exemplifying the unitary equivalence of discrete time quantum walk models the two major discrete time formulations for quantum walks coined and scattering are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology andrade et al 2009 phys rev a 80 052301 although the proof explicitly describes the mapping obtention its high technicality may hinder relevant physical aspects involved in the equivalence discussing concrete examples the most general constructions for the line square and honeycomb lattices here we unveil the similarities and differences of these two versions of quantum walks we moreover show how to derive the dynamics of one from the other by means of proper projections we perform calculations for different probability amplitudes such as hadamard grover discrete fourier transform and the uncommon in the area but interesting discrete hartley transform comparing the evolutions our study illustrates the models interplay an important issue for implementations and applications of such systems

a fuzzy image metric with application to fractal coding image quality assessment is an important issue addressed in various image processing applications such as image video compression and image reconstruction the peak signal to noise ratio psnr with the l sup 2 metric is commonly used in objective image quality assessment however the measure does not agree very well with the human visual perception in many cases a fuzzy image metric fim is defined based on sugeno s 1977 fuzzy integral this new objective image metric which is to some extent a proper evaluation from the viewpoint of the judgment procedure is closely approximates the subjective mean opinion score mos with a correlation coefficient of about 0 94 as compared to 0 82 obtained using the psnr compared to the l sup 2 metric we demonstrate that a better performance can be achieved in fractal coding by using the proposed fim

fast fractal image encoding based on adaptive search this paper presents a new adaptive search approach to reduce the computational complexity of fractal encoding a simple but very efficient adaptive necessary condition is introduced to exclude a large number of unqualified domain blocks so as to speed up fractal image compression furthermore we analyzed an unconventional affine parameter that has better properties than the conventional luminance offset specifically we formulated an optimal bit allocation scheme for the simultaneous quantizations of the usual scaling and the aforementioned unconventional affine parameter experiments on standard images showed that our adaptive search method yields superior performance over conventional fractal encoding

mathematical framework to show the existence of attractor of partitioned iterative function systems abstract the technique of image compression using iterative function system ifs is known as fractal image compression an extension of ifs theory is partitioned or local iterative function system pifs for coding the gray level images several techniques of pifs based image compression have already been proposed by many researchers the theory of pifs appears to be different from the theory of ifs in the sense of application domain the present article discusses some basic differences between ifs and pifs and provides a separate mathematical formulation for the existence of attractor of partitioned ifs in particular it has been shown that the attractor exists and it is an approximation of the given target image the experimental results have also been presented in support of the theory the experimental results have been obtained by using a ga based pifs technique proposed by mitra et al ieee trans image process 7 4 1998 586 593

ifs imaging beyond compression abstract historically most research in fractal image coding focused on its compression capabilities seeking to obtain the best domain range block matching with the minimal amount of fractal code in the course of these investigations it was implicitly known yet perhaps not fully investigated that a number of domain image subblocks will approximate a given range image subblock almost as well as the optimal domain subblock selected by collage coding recently we have presented a simple mathematical model of image self similarity and a series of computer experiments that examine the self similarity of natural images under contractive affine greyscale maps s alexander e vrscay s tsurumi a simple general model for the affine self similarity of images in a campilho m karnel eds iciar in lecture notes in computer science vol 5112 springer verlag 2008 pp 192 203 s alexander multiscale methods in image modelling and image processing ph d thesis dept of applied mathematics university of waterloo 2005 we demonstrated that typical natural images have large numbers of such maps that closely approximate all areas i e range subblock of the image in the present work some implications of this are explored a novel ifs type fractal operator with overlapping maps ifsom is presented application of this technique in a multiscale manner is demonstrated to have denoising performance comparable to current state of the art methods extensions of this preliminary work are discussed

hybrid vector quantization for multiresolution image coding in this correspondence we propose a coding scheme that exploits the redundancy of the multiresolution representation of images in that blocks in one subimage are predicted from blocks of the adjacent lower resolution subimage with the same orientation the pool of blocks used for prediction of a given subband plays the role of a codebook that is built from vectors of coefficients inside the subband decomposition itself whenever the prediction procedure does not give satisfactory results with respect to a target quality the block coefficients are quantized using a geometric vector quantizer for a laplacian source

fractal block coding a functional approach for image and signal processing in this paper we show how the generalized self similarity model introduced by cabrelli et al in 1 can be used for the coding and reconstruction of digital signals and images we also prove how the block coding techniques introduced by jacquin 2 for measures flt naturally into this functional model allowing us to take advantage of local redundancy of the images as well as to fully automate the encoding and decoding process c

application of the eisert wilkens lewenstein quantum game scheme to decision problems with imperfect recall we investigate implementations of the eisert wilkens lewenstein ewl scheme of playing quantum games beyond strategic games the scope of our research is decision problems i e one player extensive games the research is based on the examination of their features when the decision problems are carried out via the ewl protocol we prove that unitary operators can be adapted to play the role of strategies in decision problems with imperfect recall furthermore we prove that unitary operators provide the decision maker with possibilities that are inaccessible for classical strategies

on the performance of fractal compression with clustering the paper investigates a technique to reduce the computational complexity of fractal image compression on gray scale images the technique uses a clustering process on image domain blocks with the clusters formed with the use of k d trees and the fast pairwise nearest neighbor algorithm of equitz 1984 results indicate the method is effective for smaller domain block sizes and generally shows improvement in terms of picture peak signal to noise ratio snr over the quadrant variance classification method

segmentation based compression for graylevel images abstract this paper presents a segmentation based lossy image compression slic algorithm the segmentation scheme biswas and pal pattern recog lett 21 2000 entropy based and hierarchical in nature provides sub images of homogeneous regions the compression algorithm encodes a graylevel image through global approximations of sub images by 2 d bezier bernstein polynomial along with corrections if needed over regions in sub images by local approximation contours by 1 d bezier bernstein polynomial and texture if present by huffman coding scheme using hilbert scan on texture blocks order of the 2 d polynomials has been computed with the help of an image quality index iqi the proposed compression algorithm also examines the compression result by encoding contours through their approximation based on stretching of discrete circular arcs stretching is done by affine transformation compression results in both the cases have been compared with jpeg results attempts have been made to evaluate the quality of reconstructed images through a fidelity vector whose components are different objective measures

image coding based on a fractal theory of iterated contractive image transformations the author proposes an independent and novel approach to image coding based on a fractal theory of iterated transformations the main characteristics of this approach are that i it relies on the assumption that image redundancy can be efficiently exploited through self transformability on a block wise basis and ii it approximates an original image by a fractal image the author refers to the approach as fractal block coding the coding decoding system is based on the construction for an original image to encode of a specific image transformation a fractal code which when iterated on any initial image produces a sequence of images that converges to a fractal approximation of the original it is shown how to design such a system for the coding of monochrome digital images at rates in the range of 0 5 1 0 b pixel the fractal block coder has performance comparable to state of the art vector quantizers

region based fractal image compression using heuristic search presents work carried out on fractal or attractor image compression the approach relies on the assumption that image redundancy can be efficiently exploited through self transformability the algorithms described utilize a novel region based partition of the image that greatly increases the compression ratios achieved over traditional block based partitionings due to the large search spaces involved heuristic algorithms are used to construct these region based transformations results for three different heuristic algorithms are given the results show that the region based system achieves almost double the compression ratio of the simple block based system at a similar decompressed image quality for the lena image compression ratios of 41 1 can be achieved at a psnr of 26 56 db

a fast and efficient hybrid fractal wavelet image coder the excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time this paper presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression fast fractal encoding using fisher s domain classification is applied to the lowpass subband of wavelet transformed image and a modified set partitioning in hierarchical trees spiht coding on the remaining coefficients furthermore image details and wavelet progressive transmission characteristics are maintained no blocking effects from fractal techniques are introduced and the encoding fidelity problem common in fractal wavelet hybrid coders is solved the proposed scheme promotes an average of 94 reduction in encoding decoding time comparing to the pure accelerated fractal coding results the simulations also compare the results to the spiht wavelet coding in both cases the new scheme improves the subjective quality of pictures for high medium low bitrates

quantum dating market abstract we consider the dating market decision problem under the quantum mechanics point of view quantum states whose associated amplitudes are modified by men strategies are used to represent women the grover quantum search algorithm is used as a playing strategy success is more frequently obtained by playing quantum than playing classic

a fast encoding algorithm for fractal image compression using the dct inner product in this paper a fast encoding algorithm is developed for fractal image compression at each search entry in the domain pool the mean square error mse calculations of the given range block and the eight dihedral symmetries of the domain block are obtained simultaneously in the frequency domain in which the redundant computations are all eliminated in the new encoding algorithm it is shown in software simulation that the encoding time is about six times faster than that of the baseline method with almost the same psnr for the retrieved image the fast algorithm is performed to deal with the eight dihedral symmetries at each search entry therefore it can be applied to various enhanced algorithms which are equipped with quadtree classification and other mechanisms

a random polynomial time algorithm for approximating the volume of convex bodies a randomized polynomial time algorithm for approximating the volume of a convex body k in n dimensional euclidean space is presented the proof of correctness of the algorithm relies on recent theory of rapidly mixing markov chains and isoperimetric inequalities to show that a certain random walk can be used to sample nearly uniformly from within k

a simple class of fractal transforms for hyperspectral images a complete metric space of function valued mappings appropriate for the representation of hyperspectral images is introduced a class of fractal transforms is then formulated on this space under certain conditions the fractal transform t can be contractive implying the existence of a unique fixed point we then formulate a simple class of block transforms for the fractal coding of digital hyperspectral images and illustrate with an example

a novel fractal image compression scheme with block classification and sorting based on pearson s correlation coefficient fractal image compression fic is an image coding technology based on the local similarity of image structure it is widely used in many fields such as image retrieval image denoising image authentication and encryption fic however suffers from the high computational complexity in encoding although many schemes are published to speed up encoding they do not easily satisfy the encoding time or the reconstructed image quality requirements in this paper a new fic scheme is proposed based on the fact that the affine similarity between two blocks in fic is equivalent to the absolute value of pearson s correlation coefficient apcc between them first all blocks in the range and domain pools are chosen and classified using an apcc based block classification method to increase the matching probability second by sorting the domain blocks with respect to apccs between these domain blocks and a preset block in each class the matching domain block for a range block can be searched in the selected domain set in which these apccs are closer to apcc between the range block and the preset block experimental results show that the proposed scheme can significantly speed up the encoding process in fic while preserving the reconstructed image quality well

best neighborhood matching an information loss restoration technique for block based image coding systems imperfect transmission of block coded images often results in lost blocks a novel error concealment method called best neighborhood matching bnm is presented by using a special kind of information redundancy blockwise similarity within the image the proposed algorithm can utilize the information of not only neighboring pixels but also remote regions in the image very good restoration results are obtained by experiments

bounds for mixing time of quantum walks on finite graphs several inequalities are proved for the mixing time of discrete time quantum walks on finite graphs the mixing time is defined differently than in aharonov et al 2002 proc 33rd stoc 2001 new york acm pp 50 9 arxiv quant ph 0012090v2 and it is found that for particular examples of walks on a cycle a hypercube and a complete graph quantum walks provide no speedup in mixing over the classical counterparts in addition non unitary quantum walks i e walks with decoherence are considered and a criterion for their convergence to the unique stationary distribution is derived

fractal image compression with region based functionality region based functionality offered by the mpeg 4 video compression standard is also appealing for still images for example to permit object based queries of a still image database a popular method for still image compression is fractal coding however traditional fractal image coding uses rectangular range and domain blocks although new schemes have been proposed that merge small blocks into irregular shapes the merging process does not in general produce semantically meaningful regions we propose a new approach to fractal image coding that permits region based functionalities images are coded region by region according to a previously computed segmentation map we use rectangular range and domain blocks but divide boundary blocks into segments belonging to different regions since this prevents the use of standard dissimilarity measure we propose a new measure adapted to segment shape we propose two approaches one in the spatial and one in the transform domain while providing additional functionality the proposed methods perform similarly to other tested methods in terms of psnr but often result in images that are subjectively better due to the limited domain block codebook size the new methods are faster than other fractal coding methods tested the results are very encouraging and show the potential of this approach for various internet and still image database applications

a wavelet based analysis of fractal image compression why does fractal image compression work what is the implicit image model underlying fractal block coding how can we characterize the types of images for which fractal block coders will work well these are the central issues we address we introduce a new wavelet based framework for analyzing block based fractal compression schemes within this framework we are able to draw upon insights from the well established transform coder paradigm in order to address the issue of why fractal block coders work we show that fractal block coders of the form introduced by jacquin 1992 are haar wavelet subtree quantization schemes we examine a generalization of the schemes to smooth wavelets with additional vanishing moments the performance of our generalized coder is comparable to the best results in the literature for a jacquin style coding scheme our wavelet framework gives new insight into the convergence properties of fractal block coders and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm our experiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zero trees finally our framework reveals some of the fundamental limitations of current fractal compression schemes

recurrence and polya number of quantum walks we analyze the recurrence probability polya number for d dimensional unbiased quantum walks a sufficient condition for a quantum walk to be recurrent is derived as a by product we find a simple criterion for localization of quantum walks in contrast with classical walks where the polya number is characteristic for the given dimension the recurrence probability of a quantum walk depends in general on the topology of the walk choice of the coin and the initial state this allows us to change the character of the quantum walk from recurrent to transient by altering the initial state

image compression with a hybrid wavelet fractal coder a hybrid wavelet fractal coder wfc for image compression is proposed the wfc uses the fractal contractive mapping to predict the wavelet coefficients of the higher resolution from those of the lower resolution and then encode the prediction residue with a bitplane wavelet coder the fractal prediction is adaptively applied only to regions where the rate saving offered by fractal prediction justifies its overhead a rate distortion criterion is derived to evaluate the fractal rate saving and used to select the optimal fractal parameter set for wfc the superior performance of the wfc is demonstrated with extensive experimental results

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

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

incomplete information in relational databases abstract this paper concerns the semantics of codd s relational model of data formulated are precise conditions that should be satisfied in a semantically meaningful extension of the usual relational operators such as projection selection union and join from operators on relations to operators on tables with null values of various kinds allowed these conditions require that the system be safe in the sense that no incorrect conclusion is derivable by using a specified subset of the relational operators and that it be complete in the sense that all valid conclusions expressible by relational expressions using operators in are in fact derivable in this system two such systems of practical interest are shown the first based on the usual codd s null values supports projection and selection the second based on many different marked null values or variables allowed to appear in a table is shown to correctly support projection positive selection with no negation occurring in the selection condition union and renaming of attributes which allows for processing arbitrary conjunctive queries a very desirable property enjoyed by this system is that all relational operators on tables are performed in exactly the same way as in the case of the usual relations a third system mainly of theoretical interest supporting projection selection union join and renaming is also discussed under a so called closed world assumption it can also handle the operator of difference it is based on a device called a conditional table and is crucial to the proof of the correctness of the second system all systems considered allow for relational expressions containing arbitrarily many different relation symbols and no form of the universal relation assumption is required categories and subject descriptors h 2 3 database management languages query languages h 2 4 database management systems query processing general terms theory

fire fractal indexing with robust extensions for image databases as already documented in the literature fractal image encoding is a family of techniques that achieves a good compromise between compression and perceived quality by exploiting the self similarities present in an image furthermore because of its compactness and stability the fractal approach can be used to produce a unique signature thus obtaining a practical image indexing system since fractal based indexing systems are able to deal with the images in compressed form they are suitable for use with large databases we propose a system called fire which is then proven to be invariant under three classes of pixel intensity transformations and under geometrical isometries such as rotations by multiples of spl pi 2 and reflections this property makes the system robust with respect to a large class of image transformations that can happen in practical applications the images can be retrieved even in the presence of illumination and or color alterations additionally the experimental results show the effectiveness of fire in terms of both compression and retrieval accuracy

study on huber fractal image compression in this paper a new similarity measure for fractal image compression fic is introduced in the proposed huber fractal image compression hfic the linear huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression when the original image is corrupted by noises we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image this leads to a new concept of robust fractal image compression the proposed hfic is one of our attempts toward the design of robust fractal image compression the main disadvantage of hfic is the high computational cost to overcome this drawback particle swarm optimization pso technique is utilized to reduce the searching time simulation results show that the proposed hfic is robust against outliers in the image also the pso method can effectively reduce the encoding time while retaining the quality of the retrieved image

n person quantum russian roulette abstract we generalize the concept of quantum russian roulette introduced in schmidt and da silva 2013 our model coincides with the previous one in the case of the game with two players and gives the suitable quantum description for any finite number of players as an example we provide a detailed study of the three and four person case

image compression by b tree triangular coding this paper describes an algorithm for still image compression called b tree triangular coding bttc the coding scheme is based on the recursive decomposition of the image domain into right angled triangles arranged in a binary tree the method is attractive because of its fast encoding o n log n and decoding spl theta n where n is the number of pixels and because it is easy to implement and to parallelize experimental studies indicate that bttc produces images of satisfactory quality from a subjective and objective point of view one advantage of bttc over jpeg is its shorter execution time

disordered quantum walks in one lattice dimension we study a spin 12 particle moving on a one dimensional lattice subject to disorder induced by a random space dependent quantum coin the discrete time evolution is given by a family of random unitary quantum walk operators where the shift operation is assumed to be deterministic each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices we derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization put differently the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance our findings imply that this effect takes place if the coin is chosen at random from the haar measure or some measure continuous with respect to it but also for a class of discrete probability measures which support consists of two coins one of them being the hadamard coin

shape recognition using fractal geometry within this paper fractal transformations are presented as a powerful new shape recognition technique the motivation behind using fractal transformations is to develop a high speed shape recognition technique which will be scale invariant a review is given of the most popular existing shape recognition techniques there then follows a full mathematical analysis of the new technique together with a proof of the authors fractal invariance theorem the new theorem at the centre of the recognition technique through the mathematical analysis it becomes apparent that the fractal recognition technique possesses the remarkable property that it is able to distinguish between similar objects details are then given of the practical implementation of the technique together with an algorithm for making the technique rotationally invariant the technique is then applied to a selection of real world objects and a comparison made with the popular moment invariants technique this shows that the fractal technique is faster than the technique of moment invariants and also requires less initial information to be effective finally conclusions are drawn and further work detailed

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

solution of an inverse problem for fractals and other sets abstract the problem of providing succinct approximate descriptions of given bounded subsets of rn can be solved by application of the contraction mapping principle

region based fractal image compression a fractal coder partitions an image into blocks that are coded via self references to other parts of the image itself we present a fractal coder that derives highly image adaptive partitions and corresponding fractal codes in a time efficient manner using a region merging approach the proposed merging strategy leads to improved rate distortion performance compared to previously reported pure fractal coders and it is faster than other state of the art fractal coding methods

adaptive partition and hybrid method in fractal video compression fractal image compression is a relatively recent image compression method which is simple to use and often leads to a high compression ratio these advantages make it suitable for the situation of a single encoding and many decoding as required in video on demand archive compression etc there are two fundamental fractal compression methods namely the cube based and the frame based methods being commonly studied however there are advantages and disadvantages in both methods this paper gives an extension of the fundamental compression methods based on the concept of adaptive partition experimental results show that the algorithms based on adaptive partition may obtain a much higher compression ratio compared to algorithms based on fixed partition while maintaining the quality of decompressed images

a perceptually motivated three component image model part i description of the model some psychovisual properties of the human visual system are discussed and interpreted in a mathematical framework the formation of perception is described by appropriate minimization problems and the edge information is found to be of primary importance in visual perception having introduced the concept of edge strength it is demonstrated that strong edges are of higher perceptual importance than weaker edges textures we have also found that smooth areas of an image influence our perception together with the edge information and that this influence can be mathematically described via a minimization problem based on this study we have proposed to decompose the image into three components i primary ii smooth and iii texture which contain respectively the strong edges the background and the textures an algorithm is developed to generate the three component image model and an example is provided in which the resulting three components demonstrate the specific properties as expected finally it is shown that the primary component provides a superior representation of the strong edge information as compared with the popular laplacian gaussian operator edge extraction scheme