intraclass rank tests for independence summary an intraclass rank test of spearman type is proposed to test for independence in a bivariate population the test is useful when there is prior information that the population has the same marginal distributions it is shown that the proposed test is asymptotically equivalent to spearman s test under the null hypothesis of independence and its contiguous alternatives and is empirically better than that in the case of small sample sizes

structure preserving smoothing of biomedical images smoothing of biomedical images should preserve gray level transitions between adjacent tissues while restoring contours consistent with anatomical structures anisotropic diffusion operators are based on image appearance discontinuities either local or contextual and might fail at weak inter tissue transitions meanwhile the output of block wise and morphological operations is prone to present a block structure due to the shape and size of the considered pixel neighborhood in this contribution we use differential geometry concepts to define a diffusion operator that restricts to image consistent level sets in this manner the final state is a non uniform intensity image presenting homogeneous inter tissue transitions along anatomical structures while smoothing intra structure texture experiments on different types of medical images magnetic resonance computerized tomography illustrate its benefit on a further process such as segmentation of images

the constant variation formulae for singular fractional differential systems with delay abstract this paper considers the caputo singular fractional differential systems with delay and the riemann liouville singular fractional differential systems with delay a new function is defined by the d inverse matrix and function two fundamental solutions are given the constant variation formulae for singular fractional differential systems with delay are obtained

testing independence when the form of the bivariate distribution is unspecified we address the problem of testing for independence between x and y in two situations in the first we assume that the joint distribution of x and y is unknown but the observations on x and y are identifiable in the second case we assume that the distribution of x y is exchangeable here we consider both when x y are identifiable and when they are not we illustrate applications to the testing of independence in dna databases and in twin studies

eigenvalue and stability of singular differential delay systems the eigenvalue and the stability of singular differential systems with delay are considered firstly we investigate some properties of the eigenvalue then give the exact exponential estimation for the fundamental solution and finally discuss the necessary and sufficient condition of uniform asymptotic stability

a note on design transformation and binning in nonparametric curve estimation summary methods based on design transformation and equal number binning are shown to overcome problems of design sparseness while retaining excellent theoretical properties in company with local linear smoothing they produce optimal estimators although with optimality defined a little differently from in the nontransformed case when used in conjunction with wavelet techniques they overcome problems of stochastic design but unlike related techniques based on convolution and interpolation do not degrade features of the signal through prior smoothing or inflate the variance

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

a comparison of algorithms for connected set openings and closings the implementation of morphological connected set operators for image filtering and pattern recognition is discussed two earlier algorithms based on priority queues and hierarchical queues respectively are compared to a more recent union find approach unlike the earlier algorithms which process regional extrema in the image sequentially the union find method allows simultaneous processing of extrema in the context of area openings closings and pattern spectra the union find algorithm outperforms the previous methods on almost all natural and synthetic images tested finally extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms and memory usages are compared

artistic edge and corner enhancing smoothing two important visual properties of paintings and painting like images are the absence of texture details and the increased sharpness of edges as compared to photographic images painting like artistic effects can be achieved from photographic images by filters that smooth out texture details while preserving or enhancing edges and corners however not all edge preserving smoothers are suitable for this purpose we present a simple nonlinear local operator that generalizes both the well known kuwahara filter and the more general class of filters known in the literature as ldquocriterion and value filter structure rdquo this class of operators suffers from intrinsic theoretical limitations which give rise to a dramatic instability in presence of noise especially on shadowed areas such limitations are discussed in the paper and overcome by the proposed operator a large variety of experimental results shows that the output of the proposed operator is visually similar to a painting comparisons with existing techniques on a large set of natural images highlight conditions on which traditional edge preserving smoothers fail whereas our approach produces good results in particular unlike many other well established approaches the proposed operator is robust to degradations of the input image such as blurring and noise contamination

on the existence and uniqueness of solutions of a class of fractional differential equations abstract in this paper we investigate the existence and uniqueness of solutions for the following class of multi order fractional differential equations d 1 1 1 d n n n u t i 1 n d i i i u t d i n i i u t f t u t t 0 1 u 0 0 i 1 n i 1 i 0 i 0 1 i n where d i n i i denotes the generalized erdelyi kober operator of fractional derivative of order i moreover some properties concerning the positive maximal minimal and continuation of solutions are obtained

edge preserving and peak preserving smoothing an alternative procedure is developed to the smoothed linear fitting method of mcdonald and owen the procedure is based on the detection of discontinuities by comparing at any given position three smooth fits diagnostics are used to detect discontinuities in the regression function itself edge detection or in its first derivative peak detection an application in electron microscopy is discussed

the controllability of fractional control systems with control delay this paper discusses the controllability of fractional control systems with control delay we firstly give the solution expression for fractional control systems with control delay then give the necessary and sufficient conditions for the controllability of fractional control systems with control delay

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

bartlett adjustment of empirical discrepancy statistics summary we introduce two classes of empirical discrepancy statistics that extend empirical likelihood and establish simple conditions under which they admit bartlett adjustment

constrained controllability of fractional linear systems with delays in control abstract the paper presents finite dimensional dynamical control systems described by linear fractional order state equations with multiple delays in control the constrained controls are considered the set of admissible control values is assumed to be a compact set containing 0 a convex and compact set containing 0 in its interior a cone with vertex at zero and a nonempty interior or a convex and close cone with nonempty interior and vertex at zero the definitions of various types of constrained controllability of the linear fractional systems with delays in control are formulated new necessary and sufficient conditions for constrained relative controllability of fractional order control systems with delayed controls are established and proved numerical examples are provided to illustrate the obtained theoretical results

almost automorphic mild solutions to fractional differential equations abstract we introduce the concept of resolvent families to prove the existence of almost automorphic mild solutions to the differential equation d t u t a u t t n f t 1 2 n z considered in a banach space x where f r x is almost automorphic we also prove the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t 1 2 assuming f t x is almost automorphic in t for each x x satisfies a global lipschitz condition and takes values on x finally we prove also the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t u t 1 2 under analogous conditions as in the previous case

outlier robust corner preserving methods for reconstructing noisy images the ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother unfortunately they usually seem to be at odds with each other one can only improve one property at the cost of the other by combining m smoothing and least squares trimming the tm smoother is introduced as a means to unify corner preserving properties and outlier robustness to identify edge and corner preserving properties a new theory based on differential geometry is developed further robustness concepts are transferred to image processing in two examples the tm smoother outperforms other corner preserving smoothers a software package containing both the tm and the m smoother can be downloaded from the internet

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

close form solution and parameter selection for convex minimization based edge preserving smoothing this work presents a new approach for the analysis of convex minimization based edge preserving image smoothing and the parameter selection therein the global solution that is the response of a convex smoothing model to the ideal step edge is derived in close form by analyzing the close form solution insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution based on this a scheme is proposed for selecting parameters to achieve desirable responses at edges the theoretic results are substantiated by experiments

revisiting the relationship between adaptive smoothing and anisotropic diffusion with modified filters anisotropic diffusion has been known to be closely related to adaptive smoothing and discretized in a similar manner this paper revisits a fundamental relationship between two approaches it is shown that adaptive smoothing and anisotropic diffusion have different theoretical backgrounds by exploring their characteristics with the perspective of normalization evolution step size and energy flow based on this principle adaptive smoothing is derived from a second order partial differential equation pde not a conventional anisotropic diffusion via the coupling of fick s law with a generalized continuity equation where a source or sink exists which has not been extensively exploited we show that the source or sink is closely related to the asymmetry of energy flow as well as the normalization term of adaptive smoothing it enables us to analyze behaviors of adaptive smoothing such as the maximum principle and stability with a perspective of a pde ultimately this relationship provides new insights into application specific filtering algorithm design by modeling the source or sink in the pde we introduce two specific diffusion filters the robust anisotropic diffusion and the robust coherence enhancing diffusion as novel instantiations which are more robust against the outliers than the conventional filters

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

fast bilateral filtering for denoising large 3d images a fast implementation of bilateral filtering is presented which is based on an optimal expansion of the filter kernel into a sum of factorized terms these terms are computed by minimizing the expansion error in the mean square error sense this leads to a simple and elegant solution in terms of eigenvectors of a square matrix in this way the bilateral filter is applied through computing a few gaussian convolutions for which very efficient algorithms are readily available moreover the expansion functions are optimized for the histogram of the input image leading to improved accuracy it is shown that this further optimization it made possible by removing the commonly deployed constrain of shiftability of the basis functions experimental validation is carried out in the context of digital rock imaging results on large 3d images of rock samples show the superiority of the proposed method with respect to other fast approximations of bilateral filtering

on systems of linear fractional differential equations with constant coefficients abstract this paper deals with the study of linear systems of fractional differential equations such as the following system 1 y a x y b x where y is the riemann liouville or the caputo fractional derivative of order 0 2 a x a 11 x a 1 n x a n 1 x a nn x b x b 1 x b n x are matrices of known real functions in a way analogous to the usual case we show how a generalized matrix exponential function and certain fractional green function in connection with the mittag leffler type functions would allow us to obtain an explicit representation of the general solution to the system 1 when a is a constant matrix

fractional order nonlinear systems with delay in iterative learning control in this paper we discuss a p type iterative learning control ilc scheme for a class of fractional order nonlinear systems with delay by introducing the norm and using gronwall inequality the sufficient condition for the robust convergence of the tracking errors is obtained based on this convergence the p type ilc updating laws can be determined