rondo rank order based nonlinear differential operator abstract a class of new differential filter that is a generalized version of the weighted median filter is proposed the weighted median filter is a generalization of the median filter that has weight coefficients in this paper we propose an extended version of the weighted median filter that has negative weight coefficients we call it the rank order based nonlinear differential operator rondo we show that rondo acts as an effective differential operator it detects edges in images degraded by impulsive noise effectively it also has clear selectivity of edge orientation

cylindrical smoothed particle hydrodynamics abstract smoothed particle hydrodynamics sph is formulated in two dimensional axisymmetric coordinates starting with a three dimensional cartesian representation of sph we integrate out the angular component and find a two dimensional cylindrical description a smoothed particle in this formulation becomes a smoothed torus the hoop stress resulting from interactions within the toroidal ring is a natural consequence of the derivation no pathological behavior is observed at the symmetry axis the formulation has been extended to include the entire stress tensor not just the pressure and is therefore applicable to a wide range of materials and flow speeds three calculations are presented and compared to known results

root properties and convergence rates of median filters median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to additional passes of the median filter in this paper the theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals

normalized sph with stress points smoothed particle hydrodynamics is extended to a normalized staggered particle formulation with boundary conditions a companion set of interpolation points is introduced that carry the stress velocity gradient and other derived field variables the method is stable linearly consistent and has an explicit treatment of boundary conditions also a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement test problems show that these improvements lead to increased accuracy and stability published in 2000 by john wiley sons ltd

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

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

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

order configuration functions mathematical characterizations and applications to digital signal and image processing we call a function f in n variables an order configuration function if for any x1 xn such that xi1 xin we have f x1 xn xt where t is determined by the n tuple i1 in corresponding to that ordering equivalently it is a function built as a minimum of maxima or a maximum of minima well known examples are the minimum the maximum the median and more generally rank functions or the composition of rank functions such types of functions are often used in nonlinear processing of digital signals or images for example in the median or separable median filter min max filters rank filters etc in this paper we study the mathematical properties of order configuration functions and of a wider class of functions that we call order subconfiguration functions we give several characterization theorems for them we show through various examples how our concepts can be used in the design of digital signal filters or image transformations based on order configuration functions

state description for the root signal set of median filters median filtering is a simple digital technique for smoothing signals one main characteristic of the filter is that it maps the input signal space into a root signal space where signals invariant to median filters are called roots of the signal in this paper we develop the theory for the root signal set of median filters a tree structure for the root signal set is obtained for binary signals the number of roots r n for a signal of length n and window size filter 2s 1 is exactly represented by the difference equation r n r n 1 r n s a general solution is obtained in a z domain approach finally a method for faster one dimensional median filter operation is introduced

projective clustering using neural networks with adaptive delay and signal transmission loss we develop a new neural network architecture for projective clustering of data sets that incorporates adaptive transmission delays and signal transmission information loss the resultant selective output signaling mechanism does not require the addition of multiple hidden layers but instead is based on the assumption that the signal transmission velocity between input processing neurons and clustering neurons is proportional to the similarity between the input pattern and the feature vector the top down weights of the clustering neuron the mathematical model governing the evolution of the signal transmission delay the short term memory traces and the long term memory traces represents a new class of large scale delay differential equations where the evolution of the delay is described by a nonlinear differential equation involving the similarity measure already noted we give a complete description of the computational performance of the network for a wide range of parameter values

an improved sph method towards higher order convergence this paper evaluates various formulations of the sph method for solving the euler equations convergence and stability aspects are discussed and tested taking into account subtleties induced by the presence of a free surface the coherence between continuity and momentum equations is considered using a variational study the use of renormalization to improve the accuracy of the simulations is investigated and discussed a new renormalization based formulation involving wide accuracy improvements of the scheme is introduced the classical sph and renormalized approaches are compared to the new method using simple test cases thus outlining the efficiency of this new improved sph method finally the so called tensile instability is shown to be prevented by this enhanced sph method through accuracy increases in the gradient approximations

stochastic analysis for the recursive median filter process vector probability measure functions density function for recursively median filtered signals are found when the underlying input binary sequences are either independent identically distributed i i d or markov chains the results are parametric in the window size of the filter and in the probability distribution of the input sequence using statistical threshold decomposition the same results are found for discrete alphabet random sequences that are either i i d or markov chains some examples illustrating the efficacy of the recursive median filter relative to the nonrecursive implementation are presented in particular the breakdown probabilities are tabulated for both recursive and nonrecursive median filters

the concave convex procedure the concave convex procedure cccp is a way to construct discrete time iterative dynamical systems that are guaranteed to decrease global optimization and energy functions monotonically this procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted in terms of it in particular we prove that all expectation maximization algorithms and classes of legendre minimization and variational bounding algorithms can be reexpressed in terms of cccp we show that many existing neural network and mean field theory algorithms are also examples of cccp the generalized iterative scaling algorithm and sinkhorn s algorithm can also be expressed as cccp by changing variables cccp can be used both as a new way to understand and prove the convergence of existing optimization algorithms and as a procedure for generating new algorithms

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

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

reformulation of smoothed particle hydrodynamics with riemann solver smoothed particle hydrodynamics is reformulated in terms of the convolution of the original hydrodynamics equations and the new evolution equations for the particles are derived the same evolution equation of motion is also derived using a new action principle the force acting on each particle is determined by solving the riemann problem the use of the riemann solver strengthens the method making it accurate for the study of phenomena with strong shocks the prescription for the variable smoothing length is shown these techniques are implemented in strict conservation form the results of a few test problems are also shown

a separable median filter for image noise smoothing this paper investigates some properties of the separable filter resulting from successive applications of a one dimensional median filter on the rows and columns of an image although the output of this separable filter is not identical to the corresponding nonseparable two dimensional median filter with a square window its performance in image noise smoothing is close in particular its effectiveness in smoothing noise and its behavior with edges are characterized and compared with those of the two dimensional median filter it is shown that the separable filter has a much simpler implementation in real time hardware at video rates for example

the nearest neighbor median filter some deterministic properties and implementations abstract further analysis of the nearest neighbor median filter nnmf is carried out it is proved that the nnmf has the threshold decomposition property and the stacking property using these properties it is formally shown that the nnmf is a subclass of the weighted median filter wmf and the weight coefficients of the equivalent wmf are derived it is shown that the nnmf is more efficient than the equivalent wmf from the viewpoint of computational complexity two theorems about the effect of repeated operations of nnmf are proved these theorems are described in the style of dealing with local configurations of image moreover hardware implementations of the nnmf are presented

a constant density approach for incompressible multi phase sph a constant density approach which corrects intermediate density errors by adjusting the half time step velocity with exact projection is proposed for the multi phase sph method developed in our previous work x y hu n a adams an incompressible multi phase sph method j comput phys 227 2007 264 278 as no prescribed reference pressure is required the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection sph method numerical examples for taylor green flow capillary waves and for rayleigh taylor instability are presented and compared to theoretical solutions or references from the literature

detail preserving ranked order based filters for image processing the theoretical analysis of multistage median filters is developed it is shown that multistage median filters are a combination of max median and min median filters since multistage median filters belong to the class of two dimensional stack filters they have threshold decomposition attributes making their theoretical analysis simple statistical threshold decomposition is applied to derive the statistical characteristics of these filters and the results are used to evaluate the performance of these two types of multistage filters finally a quantitative and qualitative comparison of the multistage filters and of other efficient detail preserving filters is presented the comparisons are made using the mean squared error and the mean absolute error criteria

a new clustering approach on the basis of dynamical neural field in this letter we present a new hierarchical clustering approach based on the evolutionary process of amari s dynamical neural field model dynamical neural field theory provides a theoretical framework macroscopically describing the activity of neuron ensemble based on it our clustering approach is essentially close to the neurophysiological nature of perception it is also computationally stable insensitive to noise flexible and tractable for data with complex structure some examples are given to show the feasibility

axis symmetrical riemann problem solved with standard sph method development of a polar formulation with artificial viscosity abstract this paper presents the development of a cylindrical sph formulation based on previous study of the literature petschek et al with an explicit formulation for the artificial viscosity the entire development is explained to propose a formulation adapted to solve euler equations in the case of a riemann problem with axis symmetric conditions thus the artificial viscosity is constructed to find smooth solutions of well known riemann problems such as sod noh and sedov problems numerical results are compared to exact solutions and observations are made on numerical parameters influence this study contributes to validate the axis symmetrical formulation for pure hydrodynamics tests

sph in spherical and cylindrical coordinates new kernel functions for spherically planar and cylindrically symmetric problems are developed based on the fundamental interpolation theory of sph the lagrangian formalism is used to derive the corresponding set of modified sph equations of motion the results show good agreement both with analytical and numerical results in the case of the sod shock tube test the noh infinite shock problem and the sedov point explosion test the formulation has also been included in a 3d cylindrically symmetric problem of two colliding spherical shocks for this latter problem the results are presented allowing both a constant and a variable resolution the results clearly demonstrate the capability of the new formulation to solve the singularity problem at the symmetry axis

morphological filters part ii their relations to median order statistic and stack filters this paper extends the theory of median order statistic os and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions dilations openings closings and open closings that commute with thresholding the max min representation of os filters is introduced by showing that any median or other os filter is equal to a maximum of erosions moving local minima and also to a minimum of dilations moving local maxima thus os filters can be computed by a closed formula that involves a max min on prespecified sets of numbers and no sorting stack filters are established as the class of filters that are composed exactly of a finite number of max min operations the kernels of median os and stack filters are collections of input signals that uniquely represent these filters due to their translation invariance the max min functional definitions of these nonlinear iliters is shown to be equivalent to a maximum of erosions by minimal with respect to a signal ordering kernel elements and also to a minimum of dilations by minimal kernel elements of dual filters the representation of stack filters based on their minimal kernel elements is proven to be equivalent to their representation based on irreducible sum of products expressions of boolean functions it is also shown that median filtering and its iterations of any signal by convex 1 d windows is bounded below by openings and above by closings a signal is a root fixed point of the median iff it is a root of both an opening and a closing the open closing and clos opening yield median roots in one pass suppress impulse noise similarly to the median can discriminate between positive and negative noise impulses and are computationally less complex than the median some similar results are obtained for 2 d median filtering

primitive cellular automata threshold decomposition and ranked order operations a connection between ranked filters and primitive cellular automata is discussed primitive cellular automata are those whose nodes comprise a single bit of state information it is shown that these structures can perform ranked order operations on one dimensional k level signals by virtue of threshold decomposition extensions to the case of multidimensional signals are also possible

spontaneous clustering via minimum gamma divergence we propose a new method for clustering based on local minimization of the gamma divergence which we call spontaneous clustering the greatest advantage of the proposed method is that it automatically detects the number of clusters that adequately reflect the data structure in contrast existing methods such as k means fuzzy c means or model based clustering need to prescribe the number of clusters we detect all the local minimum points of the gamma divergence by which we define the cluster centers a necessary and sufficient condition for the gamma divergence to have local minimum points is also derived in a simple setting applications to simulated and real data are presented to compare the proposed method with existing ones

estimating the number of clusters in a data set via the gap statistic we propose a method the gap statistic for estimating the number of clusters groups in a set of data the technique uses the output of any clustering algorithm e g k means or hierarchical comparing the change in within cluster dispersion with that expected under an appropriate reference null distribution some theory is developed for the proposal and a simulation study shows that the gap statistic usually outperforms other methods that have been proposed in the literature

median filtering by threshold decomposition median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to further passes of the median filter in this paper it is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals filtering each binary signal to a root with a binary median filter and then reversing the decomposition this equivalence allows problems in the analysis and the implementation of median filters for arbitrary level signals to be reduced to the equivalent problems for binary signals since the effects of median filters on binary signals are well understood this technique is a powerful new tool