decision based order statistic filters the authors propose two adaptive order statistic filters which generate outputs based on the results of hypothesis tests to reduce edge shifting of the median filter a modified median filter mmf is proposed first a hypothesis test is applied to detect the edge location then whenever an edge is detected the mmf generates the output by modifying the median output based on a comparison of median value to the current input value the mmf can retain more fine details than the median filter with the same window size as well as reduce the output mean square error which is caused mainly by edge shifting to suppress nonimpulsive noise as well as impulsive noise an l type structure is combined with the mmf the proposed filter generates the output by using asymmetric alpha trimming on the mmf output in addition to noise suppression it can enhance the gradient of blurred edges provided that the size of the window is greater than the transition width of the blurred edges experimental results for one and two dimensional signals are presented

generalization of median root prior reconstruction penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions the penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood such that smooth images are favored attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself the previously introduced median root prior mrp favors locally monotonic images mrp preserves sharp edges while reducing locally nonmonotonic noise at the same time quantitative properties of mrp are good because differences in the neighboring pixel values are not penalized as such the median is used as an estimate for a penalty reference against which the pixel value is compared when setting the penalty in order to generalize the class of mrp type of priors the standard median was replaced by other order statistic operations the l and finite impulse response median hybrid fmh filters they allow for smoother appearance as they apply linear weighting together with robust nonlinear operations the images reconstructed using the new mrp l and mrp fmh priors are visually more conventional good quantitative properties of mrp are not significantly altered by the new priors

on the arithmetical complexity of sturmian words using the geometric dual technique by berstel and pocchiola we give a uniform o n 3 upper bound for the arithmetical complexity of a sturmian word we also give explicit expressions for the arithmetical complexity of sturmian words of slope between 1 3 and 2 3 in particular of the fibonacci word in this case the difference between the genuine arithmetical complexity function and our upper bound is bounded and ultimately 2 periodic in fact our formula is valid not only for sturmian words but for rotation words from a wider class

mathematical programming algorithms for regression based nonlinear filtering in r sup n this paper is concerned with regression under a sum of partial order constraints examples include locally monotonic piecewise monotonic runlength constrained and unimodal and oligomodal regression these are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis it is shown that under a least absolute error criterion these problems can be transformed into appropriate finite problems which can then be efficiently solved via dynamic programming techniques although the result does not carry over to least squares regression hybrid programming algorithms can be developed to solve least squares counterparts of certain problems in the class

improving gil werman algorithm for running min and max filters the current best bound on the number of comparison operations needed to compute the running maximum or minimum over a p element sliding data window is approximately three comparisons per output sample this bound is probabilistic for some algorithms and is derived for their complexities on the average for independent identically distributed i i d input signals the worst case complexities of these algorithms are o p the worst case complexity c sub r 3 4 p comparisons per output sample for 1d signals is achieved in the gil werman algorithm 1993 in this correspondence we propose a modification of the gil werman algorithm with the same worst case complexity but with a lower average complexity a theoretical analysis shows that using the proposed modification the complexities of sliding max or min 1d and 2d filters over i i d signals are reduced to c sub 1 2 5 3 5 p 1 p sup 2 and c sub 2 5 7 p 2 p sup 2 comparisons per output sample on the average respectively simulations confirm the theoretical results moreover experiments show that even for highly correlated data namely for real images the behavior of the algorithm remains the same as for i i d signals

multistage order statistic filters for image sequence processing the application of multistage order statistic filters mos to the task of noise suppression in time varying imagery is studied it is shown that mos filters efficiently preserve image structures under motion without motion compensation preprocessing in particular the families of multistage median and weighted median filters are considered motion preservation and statistical smoothing measures are derived it is shown that spatiotemporal filtering allows for a significant improvement over both spatial and temporal filtering in terms of output image resolution and noise suppression

a family of nonlinear filters with data dependent coefficients a new family of data dependent nonlinear filters ddnl is presented coefficients are computed locally and the absolute distance between signal samples is used to determine a rank order dependent weighting function the new filters have very good performance regarding noise suppression and impulse rejection and at the same time provide better edge preservation than the averager and other linear smoothers

application of partition based median type filters for suppressing noise in images an adaptive median based filter is proposed for removing noise from images specifically the observed sample vector at each pixel location is classified into one of m mutually exclusive partitions each of which has a particular filtering operation the observation signal space is partitioned based an the differences defined between the current pixel value and the outputs of cwm center weighted median filters with variable center weights the estimate at each location is formed as a linear combination of the outputs of those cwm filters and the current pixel value to control the dynamic range of filter outputs a location invariance constraint is imposed upon each weighting vector the weights are optimized using the constrained lms least mean square algorithm recursive implementation of the new filter is then addressed the new technique consistently outperforms other median based filters in suppressing both random valued and fixed valued impulses and it also works satisfactorily in reducing gaussian noise as well as mixed gaussian and impulse noise

the wmmr filters a class of robust edge enhancers the authors develop a class of filters called weighted majority of m values with minimum range wmmr sup m that have the same impulse rejection properties as the median they demonstrate a subclass of these filters wmmr that may be optimized for edge enhancement in one dimension in that their output converges to the closest perfect edge one of these filters is shown to restore a class of noisy edges to the closest perfect edge on one pass applications in one and two dimensions are discussed and a two dimensional simulation is provided comparing the wmmr to other filters for smoothing and edge enhancement

asymptotic subword complexity of fixed points of group substitutions the subword complexity of fixed points of some types of substitutions was studied by various authors here we introduce a family of substitutions arising from multiplication tables of finite groups and other similar structures and analyze their subword complexity

generalized mean median filtering for robust frequency selective applications huber proposed the pepsi family of epsi contaminated normal distributions to model environments characterized by heavy tailed distributions based on this two component mixture distribution mean median mem filters were proposed the mem filter output is a combination of the sample mean and the sample median where observation samples are weighted uniformly this property of mem filters constrains them to the class of smoothers lacking frequency selective filtering capabilities this paper extends mem filtering to the weighted sum median wsm filtering structure admitting real valued weights thereby enabling more general filtering characteristics i e bandpass and high pass filtering the proposed filter structure is also well motivated from a presented maximum likelihood ml estimate analysis under epsi contaminated statistics the ml analysis demonstrates the need for a combination of weighted sum ws and weighted median wm type filters for processing of signals corrupted by epsi contaminated noise the wsm filter is statistically analyzed through the determination of filter output variance and breakdown probability the combination parameter alpha is optimized to minimize the filter output variance which is a measure of noise attenuation capability moreover filter design procedures that yield a desired spectral response are detailed finally the proposed wsm filter structure is tested utilizing signal processing applications including low pass bandpass and high pass filtering and image processing applications including image sharpening and denoising evaluating and comparing the wsm filter performance to that of the ws wm and mem filters

a class of rank order smoothers smoothers or nonlinear filters that make estimates purely on the basis of rank and temporal order determinations among members of the input data are inherently robust and compatible with vlsi implementations the classic example is the moving median smoother but it is possible to define others which have significantly different attributes both in relation to the statistical estimation problem and in relation to hardware implications attributes offered in the latter category which are especially desirable in systolic vlsi include essentially recursive operation and elimination of the interactions between rank and temporal ordering requirements which are a feature of median smoothers experimental results indicate significantly improved response to noisy steps for these smoothers in comparison to median smoothers of comparable rectangular pulse detection capabilities

repetiveness of languages generated by morphisms abstract we study the repetition of subwords in languages generated by morphisms fundamental to our approach is the notion of quasi repetitive elements using these elements we present a new characterization for repetitive morphisms from which we derive a simple proof for the fact that a d0l language is repetitive if and only if it is strongly repetitive ehrenfeucht and rozenberg inform and control 59 1983 13 35 from this proof we obtain a structurally simple polynomial time algorithm for deciding whether such a language is repetitive from further results on quasi repetitive elements we obtain as a consequence a complete characterization for all those morphisms on a two letter alphabet that are repetitive a result which is closely related to a result of seebold bull eatcs 36 1988 137 151 on the d0l periodicity problem finally we characterize those morphisms f on a two letter alphabet for which the language l f generated by f or the language sl f of subwords of l f are context free or even regular

line fitting in a noisy image the conventional least squared distance method of fitting a line to a set of data points is unreliable when the amount of random noise in the input such as an image is significant compared with the amount of data correlated to the line itself points which are far away from the line outliers are usually just noise but they contribute the most to the distance averaging skewing the line from its correct position the author presents a statistical method of separating the data of interest from random noise using a maximum likelihood principle

stack filters the median and other rank order operators possess two properties called the threshold decomposition and the stacking properties the first is a limited superposition property which leads to a new architecture for these filters the second is an ordering property which allows an efficient vlsi implementation of the threshold decomposition architecture motivated by the success of rank order filters in a wide variety of applications and by the ease with which they can now be implemented we consider in this paper a new class of filters called stack filters they share the threshold decomposition and stacking properties of rank order filters but are otherwise unconstrained they are shown to form a very large class of easily implemented nonlinear filters which includes the rank order operators as well as all compositions of morphological operators the convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters the results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals the output distribution for these filters is also found all the stack filters of window width 3 are determined along with their convergence properties among these filters are found two which we have named asymmetric median filters they share all the properties of median filters except that they remove impulses of one sign only that is one removes only positive going edges the other removes only negative going edges while the median filter removes impulses of both signs this investigation of the properties of stack filters thus produces several new useful and easily implemented filters

repetition free words abstract we give a systematical treatment of repetition free words and repetition free homomorphisms we study the global structure of the set of repetition free infinite words and the behaviour of the density function of repetition free words generally we consider finite or infinite words which do not contain given words as subwords

a nonparametric method for fitting a straight line to a noisy image in fitting a straight line to a noisy image the least squares method becomes highly unreliable either when the noise distribution is nonnormal or when it is contaminated by outliers the authors propose a nonparametric method the median of the intercepts to overcome these difficulties this method is free of assumptions about the noise distribution and insensitive to outliers and it does not require quantization of the parameter space thus unlike the hough transform its outcome does not depend on the bin size the method is efficient and its implementation does not involve practical difficulties such as local minima or poor convergence of iterative procedures

discretization errors in the hough transform abstract straight line segments in a two dimensional image can be detected with the hough transform by searching peaks in a parameter space the influence on the hough transform of the quantization of the parameter space the quantization of the image and the width of the line segment is investigated in this paper the hough transform was improved by o gorman and clowes by taking into account the gradient direction the resulting scatter of the peaks can be reduced by using a weighting function in the transform examples of asbestos preparations are given

robust image modeling techniques with an image restoration application a robust parameter estimation algorithm for a nonsymmetric half plane nshp autoregressive model where the driving noise is a mixture of a gaussian and an outlier process is presented the convergence of the estimation algorithm is proved an algorithm to estimate parameters and original image intensity simultaneously from the impulse noise corrupted image where the model governing the image is not available is also presented the robustness of the parameter estimates is demonstrated by simulation finally an algorithm to restore realistic images is presented the entire image generally does not obey a simple image model but a small portion e g 8 8 of the image is assumed to obey an nshp model the original image is divided into windows and the robust estimation algorithm is applied for each window the restoration algorithm is tested by comparing it to traditional methods on several different images

robust detection of straight and circular road segments in noisy aerial images this paper treats the problem of detecting straight or circular pieces of road in noisy low resolution aerial images it first uses a local operator to detect pixels whose neighborhoods are line like and then applies robust estimation techniques to find sets of such pixels that lie on or near straight or circular loci an unbiased ordinary least squares estimator cannot handle outlying data even for straight loci on the other hand conventional robust techniques for fitting circular arcs are severely affected by digitization effects and the fact that circular road segments are typically short and shallow we therefore introduce an estimator that is both robust and statistically efficient we also present a simple ad hoc technique that achieves comparable results and can handle road segments that are either straight or circular

on the joint subword complexity of automatic sequences let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m denotes the number of distinct blocks u n u n m 1 of size m in u in this paper we study the complexity of u n u 1 n u r n n 0 when each u i u i n n 0 i 1 r is a q i automatic sequence over a finite set s i and q 1 q r 2 are pairwise coprime integers as an application we answer a question of allouche and shallit regarding morphic real numbers

an analytic theory for power law detection of bursty targets in multiplicative noise a detection problem is formulated for a bursty target in multiplicative noise a power law detector is considered for this problem with the detector exponent matched to the burstiness of the target a simple analytic theory is related for the detector exponent a theory applicable in particular to the family of gamma weibull multiplicative noise models

repetition of subwords in dol languages a language k is repetitive if for each positive integer n there exists a word w such that w n is a subword of k language k is called strongly repetitive if there exists a word w such that for each positive integer n w n is a subword of k it is shown that it is decidable whether an arbitrary dol language is repetitive it is also shown that if a dol language is repetitive then it is strongly repetitive

threshold superposition in morphological image analysis systems it is shown that four composite morphological systems namely morphological edge detection peak valley extraction skeletonization and shape size distributions obey a weak linear superposition called threshold linear superposition the output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray level image at all levels these results are generalized to a vector space formulation e g to any finite linear combination of simple morphological systems thus many such systems processing gray level images are reduced to corresponding binary image processing systems which are easier to analyze and implement

deterministic properties of analog median filters two key deterministic properties of analog median filters are established the first is that root signals are characterized by a special class of locally monotone functions and the second is that the repeated application of a median filter produces a root signal which retains significant features in the original data both results are extensions of well known facts for discrete median filters in addition it is shown that these properties do not extend to a natural multidimensional version of the median filter

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

complexity for finite factors of infinite sequences abstract we define several notions of language complexity for finite words and use them to define and compute some new complexity functions for infinite sequences in particular they give a new characterization of sturmian sequences and discriminate between sturmian sequences with bounded or unbounded partial quotients

edge detection in ultrasound imagery using the instantaneous coefficient of variation the instantaneous coefficient of variation icov edge detector based on normalized gradient and laplacian operators has been proposed for edge detection in ultrasound images in this paper the edge detection and localization performance of the icov squared icovs detector are examined first a simplified version of the icovs detector the normalized gradient magnitude squared is scrutinized in order to reveal the statistical performance of edge detection and localization in speckled ultrasound imagery both the probability of detection and the probability of false alarm are evaluated for the detector edge localization is characterized by the position of the peak and the 3 db width of the detector response then the speckle edge response of the icovs as applied to a realistic edge model is studied through theoretical analysis we reveal the compensatory effects of the normalized laplacian operator in the icov edge detector for edge localization error an icov based edge detection algorithm is implemented in which the icov detector is embedded in a diffusion coefficient in an anisotropic diffusion process experiments with real ultrasound images have shown that the proposed algorithm is effective in extracting edges in the presence of speckle quantitatively the icovs provides a lower localization error and qualitatively a dramatic improvement in edge detection performance over an existing edge detection method for speckled imagery

robust line estimation with errors in both variables abstract the estimator holding the central place in the theory of the multivariate errors in the variables ev model results from performing orthogonal regression on variables rescaled according to the covariance matrix of the errors our simulations on the univariate model essentially relegate this estimator to use only in large samples on data with no trace of outlier contamination a modification requiring a robust preliminary slope is proposed that essentially sets out the generalization to ev of the robust w estimator in regression it is demonstrated that the modification is robust to outlier contamination even in small samples given a sufficiently good preliminary estimator candidates for a preliminary slope estimator based on the data are discussed and the performance of one under simulation is examined

algorithms for subsequence combinatorics a subsequence is obtained from a string by deleting any number of characters thus in contrast to a substring a subsequence is not necessarily a contiguous part of the string counting subsequences under various constraints has become relevant to biological sequence analysis to machine learning to coding theory to the analysis of categorical time series in the social sciences and to the theory of word complexity we present theorems that lead to efficient dynamic programming algorithms to count 1 distinct subsequences in a string 2 distinct common subsequences of two strings 3 matching joint embeddings in two strings 4 distinct subsequences with a given minimum span and 5 sequences generated by a string allowing characters to come in runs of a length that is bounded from above

a new class of detail preserving filters for image processing a new class of median type filters for image processing is proposed in the filters linear fir substructures are used in conjunction with the median operation the root signals and noise attenuation properties of the fir median hybrid filters are analyzed and compared to representative edge preserving filtering operations the concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the fir median hybrid filters in the multilevel filters there exists a tradeoff between noise attenuation and detail preservation the analysis and examples indicate that fir median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the k nearest neighbor averaging filters

an edge gradient enhancing adaptive order statistic filter we consider an adaptive order statistic os filter that can enhance gradients of edges while suppressing impulsive and some nonimpulsive noise components in particular comparison and selection cs filters are introduced in which the output is determined by comparing the sample mean and median values inside each window it is shown theoretically that cs filters can enhance gradients of a variety of edges including noisy blurred ones some root properties of cs filters are also shown finally experimental results are presented to illustrate the performance characteristics of these filters

analytic line fitting in the presence of uniform random noise abstract one of the most fundamental tasks in pattern recognition involves fitting a curve such as a line segment to a given set of data points using the conventional ordinary least squares ols method of fitting a line to a set of data points is notoriously unreliable when the data contain points coming from two different populations i randomly distributed points random noise ii points correlated with the line itself e g obtained by perturbing the line with zero mean gaussian noise points which lie far away from the line i e outliers usually belong to the random noise population since they contribute the most to the squared distances they skew the line estimate from its correct position in this paper we present an analytic method of separating the components of the mixture unlike previous methods we derive a closed form solution applying a variant of the method of moments mom to the assumed mixture model yields an analytic estimate of the desired line finally we provide experimental results obtained by our method

subword complexity of uniform d0l words over finite groups we deal with the subword complexity of uniform d0l words obtained from group substitutions our main interest is whether the subword complexity is almost proportional to the length of the factor we find necessary and sufficient conditions for that for some cases we show that this is impossible

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

arithmetical complexity of symmetric d0l words we characterize and count words which occur in arithmetical subsequences of fixed points of symmetric morphisms

on the subword complexity of square free dol languages abstract the subword complexity of a language k is the function which to every positive integer n assigns the number of different subwords of length n occuring in words of k a language k is square free if no word in it contains a subword of the form xx where x is a nonempty word the best upper and lower bounds on the subword complexity of infinite square free dol languages are established

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

on the subword complexity of thue morse polynomial extractions let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m is the number of distinct blocks of length m in u let t t n n 0 denote the thue morse sequence in this paper we study the complexity of the sequences t h t h n n 0 when h n q n is a polynomial with h n n in particular we solve an open problem of allouche and shallit regarding t n 2 n 0 we also study the vector space over z 2z spanned by the sequences t h

an optimal nonlinear extension of linear filters based on distributed arithmetic distributed arithmetic da based implementation of linear filters relies on the linear nature of this operation and has been suggested as a multiplication free solution in this work we introduce a nonlinear extension of linear filters optimizing under mean square error criterion the memory function mf multivariate boolean function with not only binary output which is in the core of da based implementation such an extension will improve the filtering of noise which may contain non gaussian components without increasing the complexity of implementation experiments on real images have shown the superiority of the proposed filters over the optimal linear filters different versions of these filters are also considered for an impulsive noise removal faster processing and filtering using large input data windows

streaking in median filtered images this paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions the effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate for one dimensional discrete iid random signals with continuous input probability densities the probability of a streak of length l occurring is computed and shown to be independent of the input probability distribution expressions for the first and second moments of the streak length are also derived and certain asymptotic results are given as the analysis and definition of the analogous effect in two dimensions is less tractable the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries the analytic results are supported by examples using both one and two dimensional signals

a class of order statistic lms algorithms conventional gradient based adaptive filters as typified by the well known lms algorithm use an instantaneous estimate of the error surface gradient to update the filter coefficients such a strategy leaves the algorithm extremely vulnerable to impulsive interference a class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented these algorithms dubbed order statistic least mean squares oslms are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from gaussian to highly impulsive three specific oslms filters are defined the median lms the average lms and the trimmed mean lms the properties of these algorithms are investigated and the potential for improvement demonstrated finally a general adaptive oslms scheme in which the nature of the order statistic operator is also adapted in response to the statistics of the input signal is presented it is shown that this can facilitate performance gains over a wide range of input data types

palindrome complexity we study the palindrome complexity of infinite sequences on finite alphabets i e the number of palindromic factors blocks of given length occurring in a given sequence we survey the known results and obtain new results for some sequences in particular for rote sequences and for fixed points of primitive morphisms of constant length belonging to class p of hof knill simon we also give an upper bound for the palindrome complexity of a sequence in terms of its block complexity

robust techniques for edge detection in multiplicative weibull image noise abstract recent studies of the approximately multiplicative noise present in images from coherent radar systems suggest that the first order statistics can be broadly modeled by the two parameter weibull probability density function w y y 1 exp y this paper defines and compares some novel techniques for the robust detection of sustained image irradiance changes or edges in images immersed in multiplicative weibull noise it is shown that edge detection in multiplicative noise is accomplished effectively by comparing ratios of locally adjacent image irradiance estimates to an appropriate threshold several such estimates are considered local irradiance averages optimal single order statistics and best linear unbiased estimates using order statistics the results of a statistical monte carlo performance analysis suggest that edge detection using ratios of single order statistics ros detector offers the best compromise among computational convenience edge localization and robust performance while the ratio of blues detector rob detector yields the best overall statistical and empirical noise suppression the ratio of averages detector roa detector while statistically optimal in some cases often yields inferior edge localization relative to the other schemes images corrupted by synthetically generated weibull noise are used to support the analysis

sequences of linear arithmetical complexity arithmetical complexity of infinite sequences is the number of all words of a given length whose symbols occur in the sequence at positions which constitute arithmetical progressions we show that uniformly recurrent sequences whose arithmetical complexity grows linearly are precisely toeplitz words of a specific form

edge preserving filtering by combining nonlinear mean and median filters a very general class of nonlinear filters called mapping order statistics filters mosfs is introduced a subclass of the mosfs called l sub p mean median filters l sub p mmfs is discussed the l sub p mmf shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters in the analysis of the deterministic properties of the l sub p mmf the concept of a monotonic trend region is introduced a necessary condition for a signal to be a root signal is given this necessary condition is also valid for the known finite impulse response median hybrid filter

what s in a set of points straight line fitting the problem of fitting a straight line to a planar set of points is reconsidered a parameter space computational approach capable of fitting one or more lines to a set of points is presented the suggested algorithm handles errors in both coordinates of the data points even when the error variances vary between coordinates and among points and can be readily made robust to outliers the algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework it is observed that certain extensions of the hough transform can be turned to be equivalent to well known m estimators thus allowing computationally efficient approximate m estimation

computing abelian complexity of binary uniform morphic words although a lot of research has been done on the factor complexity also called subword complexity of morphic words obtained as fixed points of iterated morphisms there has been little development in exploring algorithms that can efficiently compute their abelian complexity the factor complexity counts the number of factors of a given length n while the abelian complexity counts that number up to letter permutation we propose and analyze a simple o n algorithm for quickly computing the exact abelian complexities for all indices from 1 up to n when considering binary uniform morphisms using our algorithm we also analyze the structure in the abelian complexity for that class of morphisms our main result implies in particular that the infinite word over the alphabet 1 0 1 constructed from the consecutive forward differences of the abelian complexity of a fixed point of a binary uniform morphism is in fact an automatic sequence with the same morphic length since the proof produces morphisms that typically contain many redundant letters we present an efficient algorithm to eliminate them in order to simplify the morphisms and to see the patterns produced more clearly

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

noise reduction of image sequences using motion compensation and signal decomposition in this paper a new spatio temporal filtering method for removing noise from image sequences is proposed this method combines the use of motion compensation and signal decomposition to account for the effects of object motion because of object motion image sequences are temporally nonstationary which requires the use of adaptive filters by motion compensating the sequence prior to filtering nonstationarities i e parts of the signal that are momentarily not stationary can be reduced significantly however since not all nonstationarities can be accounted for by motion a motion compensated signal still contains nonstationarities an adaptive algorithm based on order statistics is described that decomposes the motion compensated signal into a noise free nonstationary part and a noisy stationary part an rls filter is then used to filter the noise from the stationary signal our new method is experimentally compared with various noise filtering approaches from literature

uniformly growing k th power free homomorphisms a string is called kth power free if it does not have xk as a nonempty substring for all nonnegative rational numbers k kth power free strings and kth power free homomorphisms are investigated and the shortest uniformly growing square free k 2 and cube free k 3 homomorphisms mapping into least alphabets with three and two letters are introduced it is shown that there exist exponentially many square free and cube free strings of each length over these alphabets sharpening the kth power freeness to the repetitive threshold rt n of n letter alphabets we provide arguments for the nonexistence of various rt n th power free homomorphisms

on the combinatorics of finite words in this paper we consider a combinatorial method for the analysis of finite words recently introduced in colosimo and de luca special factors in biological strings preprint 97 42 dipt matematica univ di roma for the study of biological macromolecules the method is based on the analysis of right special factors of a given word a factor u of a word w is special if there exist at least two occurrences of the factor u in w followed on the right by two distinct letters we show that in the combinatorics of finite words two parameters play an essential role the first denoted by r represents the minimal integer such that there do not exist special factors of w of length r the second that we denote by k is the minimal length of a factor of w which cannot be extended on the right in a factor of w some new results are proved in particular a new characterization in terms of special factors and of r and k is given for the set per of all words w having two periods p and q which are coprimes and such that w p q 2

hierarchical structures in sturmian dynamical systems the paper is concerned with hierarchical stuctures in subshifis over a finite alphabet in particular we present a hierarchy based approach to sturmian systems this approach is then used to characterize the linearly repetitive sturmian systems among the sturmian systems by uniform positivity of certain weights more generally we discuss various bounds on weights and their relationship finally we combine hierarchies and bounds on a weights to study a thermodynamic formalism for lattice gas models associated to arbitrary linearly repetitive subshifts