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

color texture analysis based on fractal descriptors color texture classification is an important step in image segmentation and recognition the color information is especially important in textures of natural scenes such as leaves surfaces terrains models etc in this paper we propose a novel approach based on the fractal dimension for color texture analysis the proposed approach investigates the complexity in r g and b color channels to characterize a texture sample we also propose to study all channels in combination taking into consideration the correlations between them both these approaches use the volumetric version of the bouligand minkowski fractal dimension method the results show a advantage of the proposed method over other color texture analysis methods

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

a comparison of estimators for 1 f noise abstract we use a monte carlo approach to investigate the performance of five different time series estimators of the exponent in 1 f noise we find that a maximum likelihood estimator is markedly superior to fourier regression methods and hurst exponent methods the results indicate that useful estimates of can be made from time series that are much shorter than generally presumed

determining the chromatic number of triangle free 2p3 free graphs in polynomial time let 2p 3 denote the disjoint union of two paths on three vertices a graph g that has no subgraph isomorphic to a graph h is called h free the vertex coloring problem is the problem to determine the chromatic number of a graph its computational complexity for triangle free h free graphs has been classified for every fixed graph h on at most 6 vertices except for the case h 2p 3 this remaining case is posed as an open problem by dabrowski lozin raman and ries we solve their open problem by showing polynomial time solvability

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

theoretical foundations of spatially variant mathematical morphology part i binary images we develop a general theory of spatially variant sv mathematical morphology for binary images in the euclidean space the basic sv morphological operators that is sv erosion sv dilation sv opening and sv closing are defined we demonstrate the ubiquity of sv morphological operators by providing an sv kernel representation of increasing operators the latter representation is a generalization of matheron s representation theorem of increasing and translation invariant operators the sv kernel representation is redundant in the sense that a smaller subset of the sv kernel is sufficient for the representation of increasing operators we provide sufficient conditions for the existence of the basis representation in terms of upper semicontinuity in the hit or miss topology the latter basis representation is a generalization of maragos basis representation for increasing and translation invariant operators moreover we investigate the upper semicontinuity property of the basic sv morphological operators several examples are used to demonstrate that the theory of spatially variant mathematical morphology provides a general framework for the unification of various morphological schemes based on spatially variant geometrical structuring elements for example circular affine and motion morphology simulation results illustrate the theory of the proposed spatially variant morphological framework and show its potential power in various image processing applications

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

information measures in scale spaces this article investigates renyi s 1976 generalized entropies under linear and nonlinear scale space evolutions of images scale spaces are useful computer vision concepts for both scale analysis and image restoration we regard images as densities and prove monotony and smoothness properties for the generalized entropies the scale space extended generalized entropies are applied to global scale selection and size estimations finally we introduce an entropy based fingerprint description for textures

secure semi blind watermarking based on iteration mapping and image features this paper presents a secure semi blind watermarking technique based on iteration mapping and image features an image gray or color is divided into blocks of fixed size that are analyzed using fractal dimension to determine their properties the feature blocks containing edges and textures are used to form a feature label the watermark is the fusion of image feature label and a binary copyright symbol arnold iteration transform is employed for constructing the watermark to increase the security the secure image adaptive watermark is then embedded in the feature blocks by modifying dct middle frequency coefficients the detection and extraction procedure is a semi blind i e it does not need the original image only those who have the original watermark and the key can detect and extract the right watermark which makes the approach have high security level experimental results demonstrate that this algorithm can achieve good perceptual invisibility adaptability and security it is also robust against spatial attacks including discarding scribbling luminance and contrast changing and other attacks including low or high pass filtering adding noise and jpeg processing

property testing and its connection to learning and approximation in this paper we consider the question of determining whether a function f has property p or is e far from any function with property p a property testing algorithm is given a sample of the value of f on instances drawn according to some distribution in some cases it is also allowed to query f on instances of its choice we study this question for different properties and establish some connections to problems in learning theory and approximation in particular we focus our attention on testing graph properties given access to a graph g in the form of being able to query whether an edge exists or not between a pair of vertices we devise algorithms to test whether the underlying graph has properties such as being bipartite k colorable or having a p clique clique of density p with respect to the vertex set our graph property testing algorithms are probabilistic and make assertions that are correct with high probability while making a number of queries that is independent of the size of the graph moreover the property testing algorithms can be used to efficiently i e in time linear in the number of vertices construct partitions of the graph that correspond to the property being tested if it holds for the input graph

dimension estimation of discrete time fractional brownian motion with applications to image texture classification fractional brownian motion fbm is a suitable description model for a large number of natural shapes and phenomena in applications it is imperative to estimate the fractal dimension from sampled data namely discrete time fbm dfbm to this aim the increment of dfbm referred to as discrete time fractional gaussian noise dfgn is invoked as an auxiliary tool the regular part of dfgn is first filtered out via levinson s algorithm the power spectral density of the regular process is found to satisfy a power law that its exponent can be well fitted by a quadratic function of fractal dimension a new method is then proposed to estimate the fractal dimension of dfbm from the given data set the computational complexity and statistical properties are investigated moreover the proposed algorithm is robust with respect to amplitude scaling and shifting as well as time shifting on the data finally the effectiveness of this estimator is demonstrated via a classification problem of natural texture images

on the calculation of fractal features from images fractal geometry is becoming increasingly more important in the study of image characteristics there are numerous methods available to estimate parameters from images of fractal surfaces a very general technique to calculate numerous fractal features involves the estimation of the mass density function by box counting the authors analyze the box counting method establish a lower bound for the box size and indicate how algorithms can be improved to give better estimates of fractal features of images this provides a theoretical basis for a heuristic approach used by c a pickover and a l khorasani 1986

segmentation of color textures this paper describes an approach to perceptual segmentation of color image textures a multiscale representation of the texture image generated by a multiband smoothing algorithm based on human psychophysical measurements of color appearance is used as the input initial segmentation is achieved by applying a clustering algorithm to the image at the coarsest level of smoothing the segmented clusters are then restructured in order to isolate core clusters i e patches in which the pixels are definitely associated with the same region the image pixels representing the core clusters are used to form 3d color histograms which are then used for probabilistic assignment of all other pixels to the core clusters to form larger clusters and categorise the rest of the image the process of setting up color histograms and probabilistic reassignment of the pixels to the clusters is then propagated through finer levels of smoothing until a full segmentation is achieved at the highest level of resolution

mirror symmetry for closed open and unoriented gromov witten invariants abstract in the first part of this paper we obtain mirror formulas for twisted genus 0 two point gromov witten gw invariants of projective spaces and for the genus 0 two point gw invariants of fano and calabi yau complete intersections this extends previous results for projective hypersurfaces following the same approach but we also completely describe the structure coefficients in both cases and obtain relations between these coefficients that are vital to the applications to mirror symmetry in the rest of this paper in the second and third parts of this paper we confirm walcher s mirror symmetry conjectures for the annulus and klein bottle gw invariants of calabi yau complete intersection threefolds these applications are the main results of this paper in a separate paper the genus 0 two point formulas are used to obtain mirror formulas for the genus 1 gw invariants of all calabi yau complete intersections

updating the complexity status of coloring graphs without a fixed induced linear forest a graph is h free if it does not contain an induced subgraph isomorphic to the graph h the graph p k denotes a path on k vertices the coloring problem is the problem to decide whether a graph can be colored with at most colors such that adjacent vertices receive different colors we show that 4 coloring is np complete for p 8 free graphs this improves a result of le randerath and schiermeyer who showed that 4 coloring is np complete for p 9 free graphs and a result of woeginger and sgall who showed that 5 coloring is np complete for p 8 free graphs additionally we prove that the precoloring extension version of 4 coloring is np complete for p 7 free graphs but that the precoloring extension version of 3 coloring can be solved in polynomial time for p 2 p 4 free graphs a subclass of p 7 free graphs here p 2 p 4 denotes the disjoint union of a p 2 and a p 4 we denote the disjoint union of s copies of a p 3 by sp 3 and involve ramsey numbers to prove that the precoloring extension version of 3 coloring can be solved in polynomial time for sp 3 free graphs for any fixed s combining our last two results with known results yields a complete complexity classification of precoloring extension of 3 coloring for h free graphs when h is a fixed graph on at most 6 vertices the problem is polynomial time solvable if h is a linear forest otherwise it is np complete

counting h colorings of partial k trees the problem of counting all h colorings of a graph g with n vertices is considered while the problem is in general p complete we give linear time algorithms that solve the main variants of this problem when the input graph g is a k tree or in the case where g is directed when the underlying graph of g is a k tree our algorithms remain polynomial even in the case where k o logn or in the case where the size of h is o n our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k trees such as core checking and chromatic polynomial computation

signal detection in fractional gaussian noise several results related to the reproducing kernel hilbert space of fractional brownian motion are presented to facilitate the study of signal detection in additive fractional gaussian noise this hilbert space is completely characterized and an alternative characterization for the restriction of this class of functions to a compact interval 0 t is given infinite and finite interval whitening filters for fractional brownian motion are also developed the application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional gaussian noise a formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed

parameterized coloring problems on chordal graphs in the precoloring extension problem prext a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper coloring of the graph with the given number of colors two parameterized versions of the problem are studied in the paper either the number of precolored vertices or the number of colors used in the precoloring is restricted to be at most k we show that for chordal graphs these problems are polynomial time solvable for every fixed k but w 1 hard if k is the parameter for a graph class f let f ke resp f kv denote those graphs that can be made to be a member of f by deleting at most k edges resp vertices we investigate the connection between prext in f with the two parameters defined above and the coloring of f ke f kv graphs with k being the parameter answering an open question of leizhen cai parameterized complexity of vertex colouring discrete appl math 127 2003 415 429 we show that coloring chordal ke graphs is fixed parameter tractable

localization computation of one point disk invariants of projective calabi yau complete intersections we define one point disk invariants of a smooth projective calabi yau complete intersection in the presence of an anti holomorphic involution via localization we show that these invariants are rational numbers and obtain a formula for them which confirms in particular a conjecture by jinzenji shimizu int j geom method m 11 1 1456005 2014 conjecture 1

can the fractal dimension of images be measured abstract fractal dimension is a popular parameter for explaining certain phenomena and for describing natural textures the problem of estimating the fractal dimension of a profile or an image is more difficult and devious than theory suggests this paper studies the accuracy and robustness of two common estimators of fractal dimension box counting and the variation method using two types of data brownian and takagi poor results are demonstrated from applying theory directly called naive estimation data is then interpreted in the most optimistic way possible by matching the estimator to the known fractal dimension experiments quantify the effects of resolution or fineness of sampling and quantization or rounding of sampled values increasing resolution enhances the estimators when true dimension d is large but may possibly due to quantization effect degrade estimators when d is small quantization simply causes shifts in estimates the results suggest that one should not place much reliance in the absolute value of a fractal estimate but that the estimates do vary monotonically with d and might be useful descriptors in tasks such as image segmentation and description

maximum regular induced subgraphs in 2p3 free graphs finding maximum regular induced subgraphs is a family of algorithmic graph problems containing several important representatives such as maximum independent set maximum clique and maximum induced matching these problems are generally np hard on the other hand each of them may become polynomially solvable when restricted to graphs in special classes however polynomial time solutions are available only for very few monogenic classes i e classes defined by a single forbidden induced subgraph only three such results are available for the maximum independent set and maximum clique problems and only two for the maximum induced matching problem in the present paper we extend this restricted list of results by exploring the complexity of the problems in the class of 2p 3 free graphs which recently attracted considerable attention in the literature by elaborating a polynomial time solution to the maximum independent set problem in the class of 2k 2 free graphs proposed by farber in 16 we show that both maximum independent set 0 regular induced subgraph and maximum induced matching 1 regular induced subgraph are solvable in polynomial time for 2p 3 free graphs we also conjecture that the same is true for finding maximum k regular induced subgraphs for each value of k on the other hand we conjecture that finding a maximum subset of vertices inducing the complement of a k regular induced subgraph is np hard for 2p 3 free graphs and verify the conjecture for k 0 maximum clique k 1 maximum induced co matching and k 2

the reduced genus 1 gromov witten invariants of calabi yau hypersurfaces 0 introduction 691 0 1 mirror symmetry predictions for a quintic threefold 691 0 2 computing gw invariants of hypersurfaces 693 0 3 mirror symmetry formulas for projective cy hypersurfaces 695 1 equivariant cohomology and stable maps 698 1 1 definitions and notation 698 1 2 setup for localization computation on m1 1 p d 701 1 3 contributions from fixed loci i 704 1 4 contributions from fixed loci ii 708 2 localization computations 712 2 1 regularizable power series in rational functions 712 2 2 regularizability of gw generating functions 714 2 3 proofs of propositions 1 1 and 1 2 717 3 algebraic computations 721 3 1 linear independence in symmetric rational functions 722 3 2 the genus 0 generating functions 723 3 3 proof of theorem 3 725 appendix a some combinatorics 730 appendix b comparison of mirror symmetry formulations 733 acknowledgments 736 references 736

reduced genus one gromov witten invariants in a previous paper we described a natural closed subset m 0 1 k x a j of the moduli space m1 k x a j of stable genus one j holomorphic maps into a symplectic manifold x in this paper we generalize the definition of the main component to moduli spaces of perturbed in a restricted way j holomorphic maps this generalization implies that m 0 1 k x a j just like m1 k x a j carries a virtual fundamental class and can be used to define symplectic invariants these truly genus one invariants constitute part of the standard genus one gromovwitten invariants which arise from the entire moduli space m1 k x a j the new invariants are more geometric and can be used to compute the genus one gw invariants of complete intersections as shown in a separate paper

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

shape from fractal geometry abstract a novel method for the recovery of a planar surface orientation from its image using fractal measures is presented a fractal related feature the average holder constant is defined in the two dimensional topological space it is proven that the average holder constant is scale sensitive and the distance ratio from any two points on the fractal surface to the viewer can be calculated from their average holder constants by incorporating the distance ratio into the surface vanishing line formula in the geometric model a method for inferring planar surface shape is derived the novelty of this method is that the fractal related feature is used as a direct input in the shape recovery process experimental results showing the validity of applying this method to artificially rotated textured images and images of naturally textured surfaces are presented

feature selection in the pattern classification problem of digital chest radiograph segmentation in pattern classification problems the choice of variables to include in the feature vector is a difficult one the authors have investigated the use of stepwise discriminant analysis as a feature selection step in the problem of segmenting digital chest radiographs in this problem locally calculated features are used to classify pixels into one of several anatomic classes the feature selection step was used to choose a subset of features which gave performance equivalent to the entire set of candidate features while utilizing less computational resources the impact of using the reduced selected feature set on classifier performance is evaluated for two classifiers a linear discriminator and a neural network the results from the reduced selected feature set were compared to that of the full feature set as well as a randomly selected reduced feature set the results of the different feature sets were also compared after applying an additional postprocessing step which used a rule based spatial information heuristic to improve the classification results this work shows that in the authors pattern classification problem using a feature selection step reduced the number of features used reduced the processing time requirements and gave results comparable to the full set of features

semitotal domination new hardness results and a polynomial time algorithm for graphs of bounded mim width abstract a semitotal dominating set of a graph g with no isolated vertex is a dominating set d of g such that every vertex in d is within distance two of another vertex in d the minimum size t 2 g of a semitotal dominating set of g is squeezed between the domination number g and the total domination number t g semitotal dominating set is the problem of finding given a graph g a semitotal dominating set of g of size t 2 g in this paper we continue the systematic study on the computational complexity of this problem when restricted to special graph classes in particular we show that it is solvable in polynomial time for the class of graphs of bounded mim width by a reduction to total dominating set and we provide several approximation lower bounds for subclasses of subcubic graphs moreover we obtain complexity dichotomies in monogenic classes for the decision versions of semitotal dominating set and total dominating set finally we show that it is np complete to recognise the graphs such that t 2 g t g and those such that g t 2 g even if restricted to be planar and with maximum degree at most 4 and we provide forbidden induced subgraph characterisations for the graphs hereditarily satisfying either of these two equalities

texture roughness analysis and synthesis via extended self similar ess model the 2d fractional brownian motion fbm model provides a useful tool to model textured surfaces whose roughness is scale invariant to represent textures whose roughness is scale dependent we generalize the fbm model to the extended self similar ess model in this research we present an estimation algorithm to extract the model parameters from real texture data furthermore a new incremental fourier synthesis algorithm is proposed to generate the 2d realizations of the ess model finally the estimation and rendering methods are combined to synthesize real textured surfaces

the complexity of colouring problems on dense graphs abstract we consider the problem of deciding whether or not a graph has a vertex k colouring restricted to the class of graphs in which each vertex has degree at least n where is a fixed positive constant and n is the number of vertices of the graph we show that there is a deterministic polynomial time algorithm for this problem when k 3 k 2 and that this is best possible we also consider the corresponding enumeration problems

the 3 colorability problem on graphs with maximum degree four the 3 colorability problem is known to be np complete in the class of graphs with maximum degree four on the other hand due to the celebrated theorem of brooks the problem has a polynomial time solution for graphs with maximum degree three to make the complexity gap more precise we study a family of intermediate graph classes between these two extremes and classify all of them according to the computational complexity of the problem in particular we generalize brooks s theorem in the case of 3 colorability to a larger class by showing that every connected graph in that class is 3 colorable unless it is a complete graph on four vertices

bott s formula and enumerative geometry we outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of bott as an example gromov witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed the results are consistent with predictions made from mirror symmetry compu tations we also compute degrees of some loci in the linear system of plane curves of degrees less than 10 like those corresponding to sums of powers of linear forms and curves carrying inscribed polygons mathematical institute university of oslo p 0 box 1053 n 0316 oslo norway e mail address ellingsr0math uio no mathematical institute university of bergen alleg 55 n 5007 bergen norway e mail address strommeti i uib no this content downloaded from 157 55 39 29 on tue 12 apr 2016 10 23 14 utc all use subject to http about jstor org terms

an improved box counting method for image fractal dimension estimation fractal dimension fd is a useful feature for texture segmentation shape classification and graphic analysis in many fields the box counting approach is one of the frequently used techniques to estimate the fd of an image this paper presents an efficient box counting based method for the improvement of fd estimation accuracy a new model is proposed to assign the smallest number of boxes to cover the entire image surface at each selected scale as required thereby yielding more accurate estimates the experiments using synthesized fractional brownian motion images real texture images and remote sensing images demonstrate this new method can outperform the well known differential boxing counting dbc method

min max operators in texture analysis a signature is generated for a given picture by operating on it with different masks the operations are gray level generalizations of shrink and expand for binary pictures using serra s morphological methods 10 the signature is a set of numbers each corresponding to an application of an operator at a certain scale and direction and can be used to analyze the discriminate textures it is shown that this family of signatures includes as special cases several currently used texture descriptors

colouring of graphs with ramsey type forbidden subgraphs a colouring of a graph g v e is a mapping c v 1 2 such that c u c v if email protected e if c v

representing curves at their natural scales abstract the shapes of curves generally contain several structures at different scales an expressive curve representation should explicitly describe each structure at its appropriate scale this greatly simplifies any reasoning processes e g matching applied to the curve rather than exhaustively represent the curve over a full range of scales just the most significant ones should be retained for a compact and useful representation a technique is presented that identifies the significant or natural scales in a curve

local fractal and multifractal features for volumic texture characterization for texture analysis several features such as co occurrence matrices gabor filters and the wavelet transform are used recently fractal geometry appeared to be an effective feature to analyze texture but it is often restricted to 2d images while 3d information can be very important especially in medical image processing moreover applications are limited to the use of fractal dimension this study focuses on the benefits of fractal geometry in a classification method based on volumic texture analysis the proposed methods make use of fractal and multifractal features for a 3d texture analysis of a voxel neighborhood they are validated with synthetic data before being applied on real images their efficiencies are proved by comparison to some other texture features in supervised classification processes adaboost and support vector machine classifiers the results showed that features based on fractal geometry by combining fractal and multifractal features contributed to new texture characterization information on new features was useful and complementary for a classification method this study suggests that fractal geometry can provide a new useful information in 3d texture analysis especially in medical imaging

viewpoint invariant texture description using fractal analysis image texture provides a rich visual description of the surfaces in the scene many texture signatures based on various statistical descriptions and various local measurements have been developed existing signatures in general are not invariant to 3d geometric transformations which is a serious limitation for many applications in this paper we introduce a new texture signature called the multifractal spectrum mfs the mfs is invariant under the bi lipschitz map which includes view point changes and non rigid deformations of the texture surface as well as local affine illumination changes it provides an efficient framework combining global spatial invariance and local robust measurements intuitively the mfs could be viewed as a better histogram with greater robustness to various environmental changes and the advantage of capturing some geometrical distribution information encoded in the texture experiments demonstrate that the mfs codes the essential structure of textures with very low dimension and thus represents an useful tool for texture classification

fractal feature analysis and classification in medical imaging following b b mandelbrot s fractal theory 1982 it was found that the fractal dimension could be obtained in medical images by the concept of fractional brownian motion an estimation concept for determination of the fractal dimension based upon the concept of fractional brownian motion is discussed two applications are found 1 classification 2 edge enhancement and detection for the purpose of classification a normalized fractional brownian motion feature vector is defined from this estimation concept it represented the normalized average absolute intensity difference of pixel pairs on a surface of different scales the feature vector uses relatively few data items to represent the statistical characteristics of the medial image surface and is invariant to linear intensity transformation for edge enhancement and detection application a transformed image is obtained by calculating the fractal dimension of each pixel over the whole medical image the fractal dimension value of each pixel is obtained by calculating the fractal dimension of 7 7 pixel block centered on this pixel

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

on the complexity of 4 coloring graphs without long induced paths we show that deciding if a graph without induced paths on nine vertices can be colored with 4 colors is an np complete problem improving a previous np completeness result proved by woeginger and sgall in 2001 the complexity of 4 coloring graphs without induced paths on five vertices remains open we show that deciding if a graph without induced paths or cycles on five vertices can be colored with 4 colors can be done in polynomial time a step in our algorithm uses the well known and deep fact due to grotschel lovasz and schrijver stating that perfect graphs can be optimally colored in polynomial time

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

maximum likelihood estimation of the parameters of discrete fractionally differenced gaussian noise process a maximum likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced gaussian noise from an observation set of finite size n the procedure does not involve the computation of any matrix inverse or determinant it requires n sup 2 2 o n operations the expected value of the loglikelihood function for estimating the parameter d of fractionally differenced gaussian noise which corresponds to a parameter of the equivalent continuous time fractional brownian motion related to its fractal dimension is shown to have a unique maximum that occurs at the true value of d a cramer rao bound on the variance of any unbiased estimate of d obtained from a finite sized observation set is derived it is shown experimentally that the maximum likelihood estimate of d is unbiased and efficient when finite size data sets are used in the estimation procedure the proposed procedure is extended to deal with noisy observations of discrete fractionally differenced gaussian noise

measuring the fractal dimension of signals morphological covers and iterative optimization fractals can model many classes of time series data the fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales the covering methods are a class of efficient approaches to measure the fractal dimension of an arbitrary fractal signal by creating multiscale covers around the signal s graph in this paper we develop a general method that uses multiscale morphological operations with varying structuring elements to unify and extend the theory and digital implementations of covering methods it is theoretically estab lished that for the fractal dimension computation covering one dimensional signals with planar sets is equivalent to mor phologically transforming the signal by one dimensional func tions which reduces the computational complexity from quad ratic in the signal s length to linear then a morphological covering algorithm is developed and applied to discrete time signals synthesized from weierstrass functions fractal inter polation functions and fractional brownian motion further for deterministic parametric fractals depending on a single pa rameter related to their dimension we develop an optimization method that starts from an initial estimate and iteratively con verges to the true fractal dimension by searching in the param eter space and minimizing a distance between the original sig nal and all such signals from the same class experimental results are also provided to demonstrate the good performance of the developed methods

evaluating the fractal dimension of surfaces fractal objects derive from many interface phenomena as they arise in for example materials science chemistry and geology hence the problem of estimating fractal dimension becomes of both theoretical and practical importance existing algorithms implement the standard definitions of fractal dimension directly but as we show often give unreliable results when applied to digitized and quantized data we present a new algorithm for estimating the fractal dimension of surfaces the variation method that is more reliable and robust than the standard ones it is based on a new definition of fractal dimension particularly suited for graphs of functions the variation method is validated with both fractional brownian surfaces and takagi surfaces two classes of mathematical objects with known fractal dimension and is shown to give more accurate results than the classical algorithms finally our new algorithm is applied to data from sand blasted metal surfaces

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

boundary classes for graph problems involving non local properties abstract we continue the study of boundary classes for np hard problems and focus on seven np hard graph problems involving non local properties hamiltonian cycle hamiltonian cycle through specified edge hamiltonian path feedback vertex set connected vertex cover connected dominating set and graph vc con dimension our main result is the determination of the first boundary class for feedback vertex set we also determine boundary classes for hamiltonian cycle through specified edge and hamiltonian path and give some insights on the structure of some boundary classes for the remaining problems

nonlinear operator for oriented texture texture is an important part of the visual world of animals and humans and their visual systems successfully detect discriminate and segment texture relatively recently progress was made concerning structures in the brain that are presumably responsible for texture processing neurophysiologists reported on the discovery of a new type of orientation selective neuron in areas v1 and v2 of the visual cortex of monkeys which they called grating cells such cells respond vigorously to a grating of bars of appropriate orientation position and periodicity in contrast to other orientation selective cells grating cells respond very weakly or not at all to single bars which do not make part of a grating elsewhere we proposed a nonlinear model of this type of cell and demonstrated the advantages of grating cells with respect to the separation of texture and form information in this paper we use grating cell operators to obtain features and compare these operators in texture analysis tasks with commonly used feature extracting operators such as gabor energy and co occurrence matrix operators for a quantitative comparison of the discrimination properties of the concerned operators a new method is proposed which is based on the fisher 1923 linear discriminant and the fisher criterion the operators are also qualitatively compared with respect to their ability to separate texture from form information and their suitability for texture segmentation

on the genus one gromov witten invariants of complete intersections we state and prove a long elusive relation between genus one gromov witten of a complete intersection and twisted gromov witten invariants of the ambient projective space as shown in a previous paper certain naturally arising cones of holomorphic vector bundle sections over the main component m 0 1 k p d of the moduli space of stable genus one holomorphic maps into p have a well defined euler class in this paper we extend this result to moduli spaces of perturbed in a restricted way j holomorphic maps this extension is used to show that these cones are the correct genus one analogues of the vector bundles relating genus zero gromov witten invariants of a complete intersection to those of the ambient projective space a relationship for highergenus invariants is conjectured as well

some statistical properties of mathematical morphology analyzes the statistical properties of the basic binary and multilevel morphological operations with both 1 d and 2d structuring elements very simple expressions for the output distribution of erosion and opening are derived in the case of any independent identically or nonidentically distributed inputs the probability relations between erosion and dilation also between opening and closing are developed the output expectation bias and variances are analyzed and computed to show the efficiency of morphological operations for noise supression as applications of theoretical results the effects of the morphological operations on noisy signals are illustrated by several examples the study reveals certain interesting phenomena for example the output variances of opening for some input distributions are greater than those of erosion and morphological operations perform better than median filters in edge preservation

shape based invariant texture indexing this paper introduces a new texture analysis scheme which is invariant to local geometric and radiometric changes the proposed methodology relies on the topographic map of images obtained from the connected components of level sets this morphological tool providing a multi scale and contrast invariant representation of images is shown to be well suited to texture analysis we first make use of invariant moments to extract geometrical information from the topographic map this yields features that are invariant to local similarities or local affine transformations these features are invariant to any local contrast change we then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases the obtained experimental results outperform the current state of the art in locally invariant texture analysis

enumerative geometry of calabi yau 4 folds gromov witten theory is used to define an enumerative geometry of curves in calabi yau 4 folds the main technique is to find exact solutions to moving multiple cover integrals the resulting invariants are analogous to the bps counts of gopakumar and vafa for calabi yau 3 folds we conjecture the 4 fold invariants to be integers and expect a sheaf theoretic explanation

classification and segmentation of rotated and scaled textured images using texture tuned masks abstract a rotation and scale invariant texture classifier function is described for effective classification and segmentation of images involving textures of unknown rotation and scale changes the classifier used is the texture energy associated with a mask that has been tuned to be both discriminant between different textures and to be invariant to rotation and scale changes the mask tuning scheme utilized is based on task oriented criterion optimization via a guided random search procedure to incorporate the changes both a dynamic texture sample set using a two dimensional 2d linked list and a re ranking procedure are applied for training maximum feature dispersion of inter texture classes and high feature convergence of inner texture class samples associated with other statistical measures are suggested as key criteria in training in a study based on 15 distinct brodatz textures it is found that the tuning process although computationally intensive converges efficiently the mean classifier values of the classifier for a particular texture at different orientation and different scales are tightly clustered an objective measure of classification capability is determined by computing the standard deviation of the classifier over pure texture at definite orientation and scale examples are presented of the classifier function applied to the segmentation of collages of brodatz textures comprising regions of various orientation and scale

closing complexity gaps for coloring problems on h free graphs if a graph g contains no subgraph isomorphic to some graph h then g is called h free a coloring of a graph g v e is a mapping c v 1 2 such that no two adjacent vertices have the same color i e c u c v if email protected e if c v 0 the listk coloring problem is to decide whether a graph allows a coloring such that every vertex u receives a color from some given set l u that must be a subset of 1 k we show that list 4 coloring is np complete for p 6 free graphs where p 6 is the path on six vertices this completes the classification of listk coloring for p 6 free graphs

automatic classification for solitary pulmonary nodule in ct image by fractal analysis based on fractional brownian motion model perfusion computed tomography ct method has been used to differentiate malignant pulmonary nodules from benign nodules based on the assessment for the change of the ct attenuation value within the pulmonary nodules instead of using the change of the ct attenuation value a set of fractal features based on fractional brownian motion model is proposed in this paper to automatically distinguish malignant nodules from benign nodules in a set of 107 ct images from 107 different patients with each image containing a solitary pulmonary nodule our experimental results obtained from a support vector machine classifier show that the accuracy sensitivity specificity positive predictive value negative predictive value and the area under the roc curve are 83 11 90 92 71 70 80 05 87 52 and 0 8437 respectively by using the proposed fractal based feature set such a result outperforms the conventional method of using the change of the ct attenuation value as the feature for classification when combining this conventional method with our proposed fractal based method the accuracy sensitivity specificity positive predictive value negative predictive value and the area under the roc curve can be promoted to 88 82 93 92 82 90 87 30 90 20 and 0 9019 respectively in other words a high performance of pulmonary nodule classification can be achieved with a single post contrast ct scan

self similar anisotropic texture analysis the hyperbolic wavelet transform contribution textures in images can often be well modeled using self similar processes while they may simultaneously display anisotropy the present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of gaussian anisotropic selfsimilar processes it will be first shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2d discrete wavelet transform with the hyperbolic wavelet transform which permits the use of different dilation factors along the horizontal and vertical axes defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized this discrepancy defines a rotation angle second we show that this rotation angle can be jointly estimated third a nonparametric bootstrap based procedure is described which provides confidence intervals in addition to the estimates themselves and enables us to construct an isotropy test procedure which can be applied to a single texture image fourth the robustness and versatility of the proposed analysis are illustrated by being applied to a large variety of different isotropic and anisotropic self similar fields as an illustration we show that a true anisotropy built in self similarity can be disentangled from an isotropic self similarity to which an anisotropic trend has been superimposed

constructing the highest degree subgraph for dense graphs in ncal abstract in this paper we first show that the highest degree subgraph problem remains p complete for dense graphs i e when m n 2 poly log n this hardness result gives a clear motivation in studying the approximability of the highest degree problem even for this restricted case we then provide an n b approximation scheme computing approximate solutions for dense graphs thus proving that in this case the problem belongs to the n b a s class

morphology based multifractal estimation for texture segmentation multifractal analysis is becoming more and more popular in image segmentation community in which the box counting based multifractal dimension estimations are most commonly used however in spite of its computational efficiency the regular partition scheme used by various box counting methods intrinsically produces less accurate results in this paper a novel multifractal estimation algorithm based on mathematical morphology is proposed and a set of new multifractal descriptors namely the local morphological multifractal exponents is defined to characterize the local scaling properties of textures a series of cubic structure elements and an iterative dilation scheme are utilized so that the computational complexity of the morphological operations can be tremendously reduced both the proposed algorithm and the box counting based methods have been applied to the segmentation of texture mosaics and real images the comparison results demonstrate that the morphological multifractal estimation can differentiate texture images more effectively and provide more robust segmentations

texture segmentation using fractal dimension this paper deals with the problem of recognizing and segmenting textures in images for this purpose the authors employ a technique based on the fractal dimension fd and the multi fractal concept six fd features are based on the original image the above average high gray level image the below average low gray level image the horizontally smoothed image the vertically smoothed image and the multi fractal dimension of order two a modified box counting approach is proposed to estimate the fd in combination with feature smoothing in order to reduce spurious regions to segment a scene into the desired number of classes an unsupervised k means like clustering approach is used mosaics of various natural textures from the brodatz album as well as microphotographs of thin sections of natural rocks are considered and the segmentation results to show the efficiency of the technique supervised techniques such as minimum distance and k nearest neighbor classification are also considered the results are compared with other techniques

parallel construction of perfect matchings and hamiltonian cycles on dense graphs the intensive study of fast parallel and distributed algorithms for various routing and communications problems on graphs with good expanding properties ref pu1 ref pu2 ref ss is being carried out recently the parallel solutions for expanders that already exist ref pu 2 required an extensive randomization and an application of a randomized subroutine for the maximum matching problem in this paper we attack the problem of fast parallel algorithms for constructing perfect matchings and hamiltonian cycles on dense graph networks undirected graphs of minimal degree v over 2 somewhat surprisingly we design fast deterministic parallel algorithms for constructing both the perfect matchings and the hamiltonian cycles on the dense graphs the algorithm for constructing perfect matchings on dense graphs works in o log 2 n parallel time and o n 8 processors or o log 4 n parallel time and o n 4 processors on a crew pram the algorithm for constructing hamiltonian cycles on dense graphs works in o log 5 n parallel time and o n 4 processors on a crew pram our method of the parallel solution involves a development of new dense graph combinatorics suitable for fast parallelization

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

a fuzzy approach for modelling visual texture properties abstract in this paper we address the problem of simulating the human perception of texture properties in images in particular we have focused our study on the properties of coarseness contrast and directionality that play a fundamental role in the human perception of texture the objective is not to precisely identify classify or discriminate between different textures as a whole but to be able to assess the presence of each texture property in the image for this purpose fuzzy sets defined on the domain of different groups of measures are employed in order to model each property by using parametric membership functions the corresponding parameters are obtained by learning a functional relationship between the computational values given by the measures and the human perception the performance of each fuzzy set is analyzed and tested with the human assessments and a ranking of subsets of measures is obtained according to their ability to represent the perception of the property allowing us to identify the most suitable combination of measures

on the structure of certain natural cones over moduli spaces of genus one holomorphic maps we show that certain naturally arising cones over the main component of a moduli space of j0 holomorphic maps into pn have a well defined euler class we also prove that this is the case if the standard complex structure j0 on pn is replaced by a nearby almost complex structure j the genus zero analogue of the cone considered in this paper is a vector bundle the genus zero gromov witten invariant of a projective complete intersection can be viewed as the euler class of such a vector bundle as shown in a separate paper this is also the case for the genus one part of the genus one gw invariant the remaining part is a multiple of the genus zero gw invariant

a multi scale morphologic edge detector in this paper we present a morphologic edge detection methods using multi scale approach for detecting edges of various fineness under noisy condition it is shown that the proposed edge detector has the desirable properties that a good edge detector should have comparative study reveals its superiority over other morphologic edge detectors