unitary rotation of square pixellated images the unitary rotation of square pixellated images is based on the finite su 2 oscillator model which describes systems whose values for position momentum and energy are discrete and finite in a two dimensional position space this allows the construction of angular momentum states orthonormal and complete for which rotations are defined as multiplication by phases that carry the rotation angle the decomposition of a digital square images in terms of these angular momentum states determines a unitary hence invertible rotation of the image whose kernel can be computed as a four dimensional array of real numbers

simulation of confined magnetohydrodynamic flows with dirichlet boundary conditions using a pseudo spectral method with volume penalization a volume penalization approach to simulate magnetohydrodynamic mhd flows in confined domains is presented here the incompressible visco resistive mhd equations are solved using parallel pseudo spectral solvers in cartesian geometries the volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow in the present case it allows to use other than periodic boundary conditions in a fourier pseudo spectral approach the numerical method is validated and its convergence is assessed for two and three dimensional hydrodynamic hd and mhd flows by comparing the numerical results with results from literature and analytical solutions the test cases considered are two dimensional taylor couette flow the z pinch configuration three dimensional orszag tang flow ohmic decay in a periodic cylinder three dimensional taylor couette flow with and without axial magnetic field and three dimensional hartmann instabilities in a cylinder with an imposed helical magnetic field finally we present a magnetohydrodynamic flow simulation in toroidal geometry with non symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

accurate computation of zernike moments in polar coordinates an algorithm for high precision numerical computation of zernike moments is presented the algorithm based on the introduced polar pixel tiling scheme does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on cartesian coordinates this yields a dramatic improvement of the zernike moments accuracy in terms of their reconstruction and invariance properties the introduced image tiling requires an interpolation algorithm which turns out to be of the second order importance compared to the discretization error various comparisons are made between the accuracy of the proposed method and that of commonly used techniques the results reveal the great advantage of our approach

on the approximation power of convolution based least squares versus interpolation there are many signal processing tasks for which convolution based continuous signal representations such as splines and wavelets provide an interesting and practical alternative to the more traditional sine based methods the coefficients of the corresponding signal approximations are typically obtained by direct sampling interpolation or quasi interpolation or by using least squares techniques that apply a prefilter prior to sampling we compare the performance of these approaches and provide quantitative error estimates that can be used for the appropriate selection of the sampling step h specifically we review several results in approximation theory with a special emphasis on the strang fix 1971 conditions which relate the general o h sup l behavior of the error to the ability of the representation to reproduce polynomials of degree n l 1 we use this theory to derive pointwise error estimates for the various algorithms and to obtain the asymptotic limit of the l sub 2 error as h tends to zero we also propose a new improved l sub 2 error bound for the least squares case in the process we provide all the relevant bound constants for polynomial splines some of our results suggest the existence of an intermediate range of sampling steps where the least squares method is roughly equivalent to an interpolator with twice the order we present experimental examples that illustrate the theory and confirm the adequacy of our various bound and limit determinations

efficient implementation of accurate geometric transformations for 2 d and 3 d image processing this paper proposes the use of a polynomial interpolator structure based on horner s scheme which is efficiently realizable in hardware for high quality geometric transformation of two and three dimensional images polynomial based interpolators such as cubic b splines and optimal interpolators of shortest support are shown to be exactly implementable in the horner structure framework this structure suggests a hardware software partition which can lead to efficient implementations for multidimensional interpolation

pseudopolar based estimation of large translations rotations and scalings in images one of the major challenges related to image registration is the estimation of large motions without prior knowledge this work presents a fourier based approach that estimates large translations scalings and rotations the algorithm uses the pseudopolar pp fourier transform to achieve substantial improved approximations of the polar and log polar fourier transforms of an image thus rotations and scalings are reduced to translations which are estimated using phase correlation by utilizing the pp grid we increase the performance accuracy speed and robustness of the registration algorithms scales up to 4 and arbitrary rotation angles can be robustly recovered compared to a maximum scaling of 2 recovered by state of the art algorithms the algorithm only utilizes one dimensional fast fourier transform computations whose overall complexity is significantly lower than prior works experimental results demonstrate the applicability of the proposed algorithms

krylov methods for the incompressible navier stokes equations methods are presented for time evolution steady state solving and linear stability analysis for the incompressible navier stokes equations at low to moderate reynolds numbers the methods use krylov subspaces constructed by the arnoldi process from actions of the explicit navier stokes right hand side and of its jacobian without inversion of the viscous operator time evolution is performed by a nonlinear extension of the method of exponential propagation steady states are calculated by inexact krylov newton iteration using orthores and gmres linear stability analysis is carried out using an implicitly restarted arnoldi process with implicit polynomial filters a detailed implementation is described for a pseudospectral calculation of the stability of taylor vortices with respect to wavy vortices in the couette taylor problem 9 1994 academic press inc

a general fictitious domain method with immersed jumps and multilevel nested structured meshes this study addresses a new fictitious domain method for elliptic problems in order to handle general and possibly mixed embedded boundary conditions e b c robin neumann and dirichlet conditions on an immersed interface the main interest of this fictitious domain method is to use simple structured meshes possibly uniform cartesian nested grids which do not generally fit the interface but define an approximate one a cell centered finite volume scheme with a non conforming structured mesh is derived to solve the set of equations with additional algebraic transmission conditions linking both flux and solution jumps through the immersed approximate interface hence a local correction is devised to take account of the relative surface ratios in each control volume for the robin or neumann boundary condition then the numerical scheme conserves the first order accuracy with respect to the mesh step this opens the way to combine the e b c method with a multilevel mesh refinement solver to increase the precision in the vicinity of the interface such a fictitious domain method is very efficient the l 2 and l norm errors vary like o h l where h l is the grid step of the finest refinement level around the interface until the residual first order discretization error of the non refined zone is reached the numerical results reported here for convection diffusion problems with dirichlet robin and mixed dirichlet and robin boundary conditions confirm the expected accuracy as well as the performances of the present method

some new results on the blaszak marciniak lattice backlund transformation and nonlinear superposition formula the so called blaszak marciniak lattice is considered by the dependent variable transformation the blaszak marciniak lattice is transformed into a quart linear form by introducing an auxiliary variable we further transform it into the bilinear form a corresponding backlund transformation is obtained furthermore a nonlinear superposition formula is proved rigorously as an application of the obtained results soliton solutions are derived

rank and select revisited and extended the deep connection between the burrows wheeler transform bwt and the so called rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text indexing rank of a symbol at a given position equals the number of times the symbol appears in the corresponding prefix of the sequence select is the inverse retrieving the positions of the symbol occurrences it has been shown that improvements to rank select algorithms in combination with the bwt turn into improved compressed text indexes this paper is devoted to alternative implementations and extensions of rank and select data structures first we show that one can use gap encoding techniques to obtain constant time rank and select queries in essentially the same space as what is achieved by the best current direct solution and sometimes less second we extend symbol rank and select to substring rank and select giving several space time trade offs for the problem an application of these queries is in position restricted substring searching where one can specify the range in the text where the search is restricted to and only occurrences residing in that range are to be reported in addition arbitrary occurrences are reported in text position order several byproducts of our results display connections with searchable partial sums chazelle s two dimensional data structures and grossi et al s wavelet trees

numerical simulation of fluid structure interaction with the volume penalization method we present a novel scheme for the numerical simulation of fluid structure interaction problems it extends the volume penalization method a member of the family of immersed boundary methods to take into account flexible obstacles we show how the introduction of a smoothing layer physically interpreted as surface roughness allows for arbitrary motion of the deformable obstacle the approach is carefully validated and good agreement with various results in the literature is found a simple one dimensional solid model is derived capable of modeling arbitrarily large deformations and imposed motion at the leading edge as it is required for the simulation of simplified models for insect flight the model error is shown to be small while the one dimensional character of the model features a reasonably easy implementation the coupled fluid solid interaction solver is shown not to introduce artificial energy in the numerical coupling and validated using a widely used benchmark we conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections

convolution based interpolation for fast high quality rotation of images this paper focuses on the design of fast algorithms for rotating images and preserving high quality the basis for the approach is a decomposition of a rotation into a sequence of one dimensional translations as the accuracy of these operations is critical we introduce a general theoretical framework that addresses their design and performance we also investigate the issue of optimality and present an improved least square formulation of the problem this approach leads to a separable three pass implementation of a rotation using one dimensional convolutions only we provide explicit filter formulas for several continuous signal models including spline and bandlimited representations finally we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm our results indicate that the present algorithm in its higher order versions outperforms all standard high accuracy methods of which we are aware both in terms of speed and quality its computational complexity increases linearly with the order of accuracy the best quality results are obtained with the sine based algorithm which can be implemented using simple one dimensional ffts

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

backlund transformation and solutions of a 3 1 dimensional nonlinear evolution equation in this paper bell polynomial method is used to study the integrability of a 3 1 dimensional nonlinear evolution equation we get the bilinear representation and backlund transformation of the equation the exact solutions are obtained by means of linear superposition principle and homoclinic test approach

on the optimality of ideal filters for pyramid and wavelet signal approximation the reconstructed lowpass component in a quadrature mirror filter qmf bank provides a coarser resolution approximation of the input signal since the outputs of the two qmf branches are orthogonal the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error this property is used as a common strategy for the optimization of qmf banks orthogonal wavelet transforms and least squares pyramids a general solution is derived for the qmf bank that provides the optimal decomposition of an arbitrary wide sense stationary process this approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate in particular it is shown that the sine wavelet transform is optimal for the representation at all scales of signals with non increasing spectral density

comparison of interpolating methods for image resampling when resampling an image to a new set of coordinates for example when rotating an image there is often a noticeable loss in image quality to preserve image quality the interpolating function used for the resampling should be an ideal low pass filter to determine which limited extent convolving functions would provide the best interpolation five functions were compared a nearest neighbor b linear c cubic b spline d high resolution cubic spline with edge enhancement a 1 and e high resolution cubic spline a 0 5 the functions which extend over four picture elements c d e were shown to have a better frequency response than those which extend over one a or two b pixels the nearest neighbor function shifted the image up to one half a pixel linear and cubic b spline interpolation tended to smooth the image the best response was obtained with the high resolution cubic spline functions the location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned and the response has the most smoothing when the resampled points are equidistant from the original coordinate points thus at the expense of some increase in computing time image quality can be improved by resampled using the high resolution cubic spline function as compared to the nearest neighbor linear or cubic b spline functions

on removing interpolation and resampling artifacts in rigid image registration we show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts these artifacts negatively affect the accuracy of registration by producing local optima altering the gradient shifting the global optimum and making rigid registration asymmetric in this paper after an extensive literature review we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically we show the sum of squared differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration we then discuss aliasing that occurs in rotation which is due to the fact that an image represented in the cartesian grid is sampled with different rates in different directions and propose the use of oscillatory isotropic interpolation kernels which allow better recovery of true global optima by overcoming this type of aliasing through our experiments on brain fingerprint and white noise images we illustrate the superior performance of the integral registration cost function in both the cartesian and spherical coordinates and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration

a fast finite volume method for conservative space fractional diffusion equations in convex domains we develop a fast finite volume method for variable coefficient conservative space fractional diffusion equations in convex domains via a volume penalization approach the method has an optimal storage and an almost linear computational complexity the method retains second order accuracy without requiring a richardson extrapolation numerical results are presented to show the utility of the method

the affix array data structure and its applications to rna secondary structure analysis efficient string processing in large data sets like complete genomes is strongly connected to the suffix tree and similar index data structures with respect to complex structural string analysis like the search for rna secondary structure patterns unidirectional suffix tree algorithms are inferior to bidirectional algorithms based on the affix tree data structure the affix tree incorporates the suffix tree and the suffix tree of the reverse text in one tree structure but suffers from its large memory requirements in this paper i present a new data structure denoted affix array which is equivalent to the affix tree with respect to its algorithmic functionality but with smaller memory requirements and improved performance i will show a linear time construction of the affix array without making use of the linear time construction of the affix tree i will also show how bidirectional affix tree traversals can be transferred to the affix array and present the impressive results of large scale rna secondary structure analysis based on the new data structure

a fast computation technique for the direct numerical simulation of rigid particulate flows in this paper we present a computation technique for the direct numerical simulation of freely moving rigid bodies in fluids we solve three dimensional laminar flow problems using a control volume approach the key feature of this approach is that the computational overhead relative to a pure fluid solver to solve for the motion of rigid particle is very small the formulation is convenient for handling irregular geometries we present results for the sedimentation of particles of different shapes convergence tests are presented to assess the order of accuracy of the numerical scheme various test cases are considered and the numerical results are compared with experimental values to validate the code due to the ability to perform fast computations this method has been used for animations and its application to the direct numerical simulation of turbulent particulate flows merits investigation the technique is not restricted to any constitutive model of the suspending fluid hence it may potentially be used in large eddy simulations les or reynolds averaged navier stokes rans type simulations

dynamic denoising of tracking sequences in this paper we describe an approach to the problem of simultaneously enhancing image sequences and tracking the objects of interest represented by the latter the enhancement part of the algorithm is based on bayesian wavelet denoising which has been chosen due to its exceptional ability to incorporate diverse a priori information into the process of image recovery in particular we demonstrate that in dynamic settings useful statistical priors can come both from some reasonable assumptions on the properties of the image to be enhanced as well as from the images that have already been observed before the current scene using such priors forms the main contribution of the present paper which is the proposal of the dynamic denoising as a tool for simultaneously enhancing and tracking image sequences within the proposed framework the previous observations of a dynamic scene are employed to enhance its present observation the mechanism that allows the fusion of the information within successive image frames is bayesian estimation while transferring the useful information between the images is governed by a kalman filter that is used for both prediction and estimation of the dynamics of tracked objects therefore in this methodology the processes of target tracking and image enhancement collaborate in an interlacing manner rather than being applied separately the dynamic denoising is demonstrated on several examples of sar imagery the results demonstrated in this paper indicate a number of advantages of the proposed dynamic denoising over static approaches in which the tracking images are enhanced independently of each other

a cartesian grid embedded boundary method for the heat equation and poisson s equation in three dimensions we present an algorithm for solving poisson s equation and the heat equation on irregular domains in three dimensions our work uses the cartesian grid embedded boundary algorithm for 2d problems of johansen and colella a cartesian grid embedded boundary method for poisson s equation on irregular domains j comput phys 147 2 1998 60 85 and extends work of mccorquodale colella and johansen a cartesian grid embedded boundary method for the heat equation on irregular domains j comput phys 173 2001 620 635 our method is based on a finite volume discretization of the operator on the control volumes formed by intersecting the cartesian grid cells with the domain combined with a second order accurate discretization of the fluxes the resulting method provides uniformly second order accurate solutions and gradients and is amenable to geometric multigrid solvers

bidirectional search in a string with wavelet trees and bidirectional matching statistics searching for genes encoding micrornas mirnas is an important task in genome analysis because the secondary structure of mirna but not the sequence is highly conserved the genes encoding it can be determined by finding regions in a genomic dna sequence that match the structure it is known that algorithms using a bidirectional search on the dna sequence for this task outperform algorithms based on unidirectional search the data structures supporting a bidirectional search affix trees and affix arrays however are rather complex and suffer from their large space consumption here we present a new data structure called bidirectional wavelet index that supports bidirectional search with much less space with this data structure it is possible to search for candidates of rna secondary structural patterns in large genomes for example the complete human genome another important application of this data structure is short read alignment as a second contribution we show how bidirectional matching statistics can be computed in linear time

wavelet and finite element solutions for the neumann problem using fictitious domains this paper presents a new fictitious domain formulation for the solution of a strongly elliptic boundary value problem with neumann boundary conditions for a bounded domain in a finite dimensional euclidean space with a smooth possibly only lipschitz boundary this extends the domain to a larger rectangular domain with periodic boundary conditions for which fast solvers are available the extended solution converges on the original domain in the appropriate function spaces as the penalty parameter approaches zero both wavelet galerkin and finite elements numerical approximation schemes are developed using this methodology the convergence rates of both schemes are comparable and the use of finite elements requires a parameterization of the boundary while the wavelet galerkin method admits an implicit description of the boundary in terms of a wavelet representation of the boundary measure defined as the distributional gradient of the characteristic function of the interior the accuracy of both methods is investigated and compared both theoretically and for numerical test cases the conclusion is that the methods are comparable and that the wavelet method allows the use of more general boundaries which are not explicitly parametrized which would be of greater advantage in higher dimensions the numerical tests are carried out in two dimensions

moms maximal order interpolation of minimal support we consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly supported basis function spl phi z we first give the expression for the cases of spl phi that have minimal support for a given accuracy also known as approximation order this class of functions which we call maximal order minimal support functions moms is made of linear combinations of the b spline of the same order and of its derivatives we provide an explicit form of the moms that maximizes the approximation accuracy when the step size is small enough we compute the sampling gain obtained by using these optimal basis functions over the splines of the same order we show that it is already substantial for small orders and that it further increases with the approximation order l when l is large this sampling gain becomes linear more specifically its exact asymptotic expression is 2 spl pi e l since the optimal functions are continuous but not differentiable for even orders and even only piecewise continuous for odd orders our result implies that regularity has little to do with approximating performance these theoretical findings are corroborated by experimental evidence that involves compounded rotations of images

every unit matrix is a lulu abstract the four matrices l0u0l1u1 at the end of the title are triangular with ones on their main diagonals their product has determinant one following a question and theorem of toffoli we show that any matrix with determinant one can be factored in this way a transformation of the plane becomes a sequence of one dimensional shears with n2 1 free parameters

on bilinear representations and infinite conservation laws of a nonlinear variable coefficient equation the kdv equation for non uniform media with relaxation effects has extensive applications in mathematics and physics satsuma 1976 20 and hirota 1979 21 once investigated its algebraic properties in the paper we shall generalize it a more general integrable equation with variable coefficients and further discuss the corresponding bilinear representation backlund transformation lax pair and infinite conservation laws by making use of the bell polynomials

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

recursive regularization filters design properties and applications least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed for each problem there is a family of discrete regularization filters r filters which allow an efficient determination of the solutions these operators are stable symmetric lowpass filters with an adjustable scale factor two decomposition theorems for the z transform of such systems are presented one facilitates the determination of their impulse response while the other allows an efficient implementation through successive causal and anticausal recursive filtering a case of special interest is the design of r filters for the first and second order difference operators these results are extended for two dimensional signals and for illustration purposes are applied to the problem of edge detection this leads to a very efficient implementation 8 multiplies 10 adds per pixel of the optimal canny edge detector based on the use of a separable second order r filter

approximation of the laplace and stokes operators with dirichlet boundary conditions through volume penalization a spectral viewpoint we report the results of a study on the spectral properties of laplace and stokes operators modified with a volume penalization term designed to approximate dirichlet conditions in the limit when a penalization parameter eta tends to zero the eigenvalues and eigenfunctions are determined either analytically or numerically as functions of eta both in the continuous case and after applying fourier or finite difference discretization schemes for fixed eta we find that only the part of the spectrum corresponding to eigenvalues lambda lesssim eta 1 1 approaches dirichlet boundary conditions while the remainder of the spectrum is made of uncontrolled spurious wall modes the penalization error for the controlled eigenfunctions is estimated as a function of eta and lambda surprisingly in the stokes case we show that the eigenfunctions approximately satisfy with a precision o eta o navier slip boundary conditions with slip length equal to sqrt eta moreover for a given discretization we show that there exists a value of eta corresponding to a balance between penalization and discretization errors below which no further gain in precision is achieved these results shed light on the behavior of volume penalization schemes when solving the navier stokes equations outline the limitations of the method and give indications on how to choose the penalization parameter in practical cases

a fourier penalty method for solving the time dependent maxwell s equations in domains with curved boundaries we present a high order fourier penalty method for the maxwell s equations in the vicinity of perfect electric conductor boundary conditions the approach relies on extending the smooth non periodic domain of the equations to a periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain the forcing or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter which then allows for higher order numerical methods we present an efficient numerical method for constructing the penalty term and discretize the resulting equations using a fourier spectral method we demonstrate convergence orders of up to 3 5 for the one dimensional maxwell s equations and show that the numerical method does not suffer from dispersion or pollution errors we also illustrate the approach in two dimensions and demonstrate convergence orders of 2 5 for transverse magnetic modes and 1 5 for the transverse electric modes we conclude the paper with numerous test cases in dimensions two and three including waves traveling in a bent waveguide and scattering off of a windmill like geometry

sparse low energy decomposition for viscous conservation laws for viscous conservation laws solutions contain smooth but high contrast features which require the use of fine grids to properly resolve on coarse grids these high contrast jumps resemble shocks rather than their true viscous profiles which could lead to issues in the numerical approximation of their underlying dynamics in many cases the equations of motion emit traveling wave solutions which can be used to represent the viscous profiles analytically the traveling wave solutions can be thought of as a lower dimensional representation of the motion since they contain information from the evolution equation but are constant along certain time space curves using a parameterized basis involving the traveling waves along with the sparse low energy decompositions found in imaging sciences we propose an approximation to viscous conservation laws which separates the coarse smooth component from the sharp fine one our method provides an appropriate approximation to the solution on a coarse grid thereby accurately under resolving the viscous profile this is similar to the philosophy of shock capturing methods in the sense that we want to capture the viscous front without needing to resolve the profile theoretical results on the consistency of our method are shown in general we provide several computational examples for convex and non convex fluxes

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

shear based fast hierarchical backprojection for parallel beam tomography we introduce a family of fast algorithms for 2 d parallel beam tomographic backprojection they aggregate the projections in a hierarchical structure involving the shearing and addition of sparsely sampled images the algorithms achieve a computational cost of o n2 logp when backprojecting an ntimesn pixel image from p projections the algorithms provide a systematic means guided by a fourier domain interpretation to adjust and optimize the tradeoff between computational cost and accuracy in an example with n 512 and p 1458 the algorithms provide high accuracy with more than an order of magnitude reduction in operation counts

a fourier spectral method for the navier stokes equations with volume penalization for moving solid obstacles an efficient numerical scheme to compute flows past rigid solid bodies moving through viscous incompressible fluid is presented solid obstacles of arbitrary shape are taken into account using the volume penalization method to impose no slip boundary condition the 2d navier stokes equations written in the vorticity streamfunction formulation are discretized using a fourier pseudo spectral scheme four different time discretization schemes of the penalization term are proposed and compared the originality of the present work lies in the implementation of time dependent penalization which makes the above method capable of solving problems where the obstacle follows an arbitrary motion fluid solid coupling for freely falling bodies is also implemented the numerical method is validated for different test cases the flow past a cylinder couette flow between rotating cylinders sedimentation of a cylinder and a falling leaf with elliptical shape

addendum b spline interpolation in medical image processing analyzes b spline interpolation techniques of degree 2 4 and 5 with respect to all criteria that have been applied to evaluate various interpolation schemes in a recently published survey on image interpolation in medical imaging lehmann et al 1999 it is shown that high degree b spline interpolation has superior fourier properties smallest interpolation error and reasonable computing times therefore high degree b splines are preferable interpolators for numerous applications in medical image processing particularly if high precision is required if no aliasing occurs this result neither depends on the geometric transform applied for the tests nor the actual content of images

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

immersed interface methods for neumann and related problems in two and three dimensions we develop and apply a finite difference method to discretize the laplacian operator with neumann boundary conditions on an irregular domain using a regular cartesian grid the method is an extension of the immersed interface method developed by leveque and li siam j numer anal 31 1994 1019 1044 with careful selection of stencils the method is second order accurate and produces a matrix that is stable diagonally semidominant the method is illustrated on several two dimensional problems and one three dimensional problem

a volume penalization method for incompressible flows and scalar advection diffusion with moving obstacles a volume penalization method for imposing homogeneous neumann boundary conditions in advection diffusion equations is presented thus complex geometries which even may vary in time can be treated efficiently using discretizations on a cartesian grid a mathematical analysis of the method is conducted first for the one dimensional heat equation which yields estimates of the penalization error the results are then confirmed numerically in one and two space dimensions simulations of two dimensional incompressible flows with passive scalars using a classical fourier pseudo spectral method validate the approach for moving obstacles the potential of the method for real world applications is illustrated by simulating a simplified dynamical mixer where for the fluid flow and the scalar transport no slip and no flux boundary conditions are imposed respectively

suffix arrays a new method for on line string searches a new and conceptually simple data structure called a suffix array for on line string searches is introduced in this paper constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms the main advantage of suffix arrays over suffix trees is that in practice they use three to five times less space from a complexity standpoint suffix arrays permit on line string searches of the type is w a substring of a to be answered in time o p log n where p is the length of w and n is the length of a which is competitive with and in some cases slightly better than suffix trees the only drawback is that in those instances where the underlying alphabet is finite and small suffix trees can be constructed in o n time in the worst case versus o n log n time for suffix arrays however an augmented algorithm is given that regardless of the alphabet size constructs suffix arrays in o n expected time albeit with lesser space efficiency it is

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

enlargement or reduction of digital images with minimum loss of information the purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary noninteger scaling factors in our formulation the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and spl delta respectively the change of scale is achieved by determining the spline with step size spl delta that provides the closest approximation of the original signal in the l sub 2 norm we show that this approximation can be computed in three steps i a digital prefilter that provides the b spline coefficients of the input signal ii a resampling using an expansion formula with a modified sampling kernel that depends explicitly on spl delta and iii a digital postfilter that maps the result back into the signal domain we provide explicit formulas for n 0 1 and 3 and propose solutions for the efficient implementation of these algorithms we consider image processing examples and show that the present method compares favorably with standard interpolation techniques finally we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

reversible resampling of integer signals except some extremely special cases signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation in this paper we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals i e the original signal can be reconstructed losslessly from the resampled data by using matrix factorization we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling the new factorization yields three elementary integer reversible matrices the method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices it can be applied to integer signals by in place integer reversible computation which needs no auxiliary memory to keep the original sample data for the transformation during the process or for ldquoundordquo recovery after the process some examples of low order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling

two and three dimensional image rotation using the fft techniques for rotating two and three dimensional 2 d and 3 d images using fast fourier transforms ffts are presented the methods are applications of the multidimensional chirp algorithm in the 2 d case one chirp transformation is sufficient requiring four 2 d ffts in the 3 d case two successive chirp transformations are required needing six 3 d ffts

on the combinatorics of the hirota d operators a generic formula is presented which relates the hirota d operators to simple combinatorics particular classes of partition polynomials bell polynomials and generalizations are found to play an important role in the characterization of bilinearizable equations as a consequence it is shown that bilinear backlund transformations for single field bilinearizable equations linearize systematically into corresponding laxpairs

double line image rotation this paper proposes a fast algorithm for rotating images while preserving their quality the new approach rotates images based on vertical or horizontal lines in the original image and their rotated equation in the target image the proposed method is a one pass method that determines a based line equation in the target image and extracts all corresponding pixels on the base line floating point multiplications are performed to calculate the base line in the target image and other line coordinates are calculated using integer addition or subtraction and logical justifications from the base line pixel coordinates in the target image to avoid a heterogeneous distance between rotated pixels in the target image each line rotates to two adjacent lines the proposed method yields good performance in terms of speed and quality according to the results of an analysis of the computation speed and accuracy

a new formula for bivariate hermite interpolation on variable step grids and its application to image interpolation in this paper we present a novel formula of the bivariate hermite interpolating bhi polynomial in the case of support points arranged on a grid with variable step this expression is applicable when interpolation of a bivariate function is required given its value and the values of its partial derivatives of arbitrarily high order at the support points the proposed formula is a generalization of an existing formula for the bivariate hermite polynomial it is also algebraically much simpler thus can be computed more efficiently in order to apply hermite interpolation to image interpolation we simplify the proposed bhi to handle support points on a regular unit step grid the values of image partial derivatives are arithmetically approximated using compact finite differences the proposed method is being assessed in a number of image interpolation experiments that include a synthetic image for which the values of the partial derivatives are computed analytically as well as a collection of images from different medical modalities the proposed bhi with up to second order image partial derivatives outperforms the convolution based interpolation methods as well as generalized interpolation methods with the same number of support points that was compared with in the majority of image interpolation experiments the computational load of the proposed bhi is calculated and its behaviour with respect to its controlling parameters is investigated

flusi a novel parallel simulation tool for flapping insect flight using a fourier method with volume penalization we introduce flusi a fully parallel open source software package for pseudospectral simulations of three dimensional flapping flight in viscous flows it is freely available for noncommercial use from github https github com pseudospectators flusi the computational framework runs on high performance computers with distributed memory architectures the discretization of the three dimensional incompressible navier stokes equations is based on a fourier pseudospectral method with adaptive time stepping the complex time varying geometry of insects with rigid flapping wings is handled using the volume penalization method the modules characterizing the insect geometry flight mechanics and wing kinematics are described validation tests for different benchmarks illustrate the efficiency and precision of the approach finally computations for a model insect in the turbulent regime demonstrate the versatility of the software

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

darboux covariant lax pairs and infinite conservation laws of the 2 1 dimensional breaking soliton equation in this paper the binary bell polynomials are applied to succinctly construct bilinear formulism bilinear backlund transformations lax pairs and darboux covariant lax pairs for the 2 1 dimensional breaking soliton equation an extra auxiliary variable is introduced to get the bilinear formulism the infinitely local conservation laws of the equation are found by virtue of its lax equation and a generalized miura transformation all conserved densities and fluxes are given with explicit recursion formulas

polynomial spline signal approximations filter design and asymptotic equivalence with shannon s sampling theorem the least squares polynomial spline approximation of a signal g t in l sub 2 r is obtained by projecting g t on s sup n r the space of polynomial splines of order n it is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g t with a b spline of order n more specifically the coefficients of the b spline interpolation of order 2n 1 of the sampled filtered sequence are identical to the coefficients of the least squares approximation of g t of order n it is shown that this approximation can be obtained from a succession of three basic operations prefiltering sampling and postfiltering which confirms the parallel with the classical sampling reconstruction procedure for bandlimited signals the frequency responses of these filters are determined for three equivalent spline representations using alternative sets of shift invariant basis functions of s sup n r the standard expansion in terms of b spline coefficients a representation in terms of sampled signal values and a representation using orthogonal basis functions

a fictitious domain approach with spread interface for elliptic problems with general boundary conditions the aim of this article is to solve second order elliptic problems in an original physical domain using a fictitious domain method with a spread interface approach the main idea of the fictitious domain approach consists in immersing the original domain of study into a geometrically bigger and simpler one called fictitious domain as the spatial discretization is being performed in the fictitious domain this method allows the use of structured meshes the discretization is not boundary fitted to the original physical domain this paper describes several ways to impose dirichlet robin or neumann boundary conditions on a spread immersed interface without locally modifying the numerical scheme and without using lagrange multipliers the numerical applications focus on difiusion and convection problems in the unit disk with dirichlet or robin boundary conditions for such problems analytical solutions can be determined for a correctly chosen source term the numerical resolution is performed using a q1 finite element scheme the spread interface approach is then combined with a local adaptive mesh refinement algorithm in order to increase the precision in the vinicity of the immersed boundary the l2 norm of the errors is computed in order to evaluate the capability of the method immersed boundaries are found in many industrial applications like two phase flow simulations fluid structure interaction etc this article represents a first step towards the simulation of these kinds of applications

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

fourier spectral and wavelet solvers for the incompressible navier stokes equations with volume penalization convergence of a dipole wall collision in this study we use volume penalization to mimic the presence of obstacles in a flow or a domain with no slip boundaries this allows in principle the use of fast fourier spectral methods and coherent vortex simulation techniques based on wavelet decomposition of the flow variables to compute turbulent wall bounded flow or flows around solid obstacles by simply adding one term in the equation convergence checks are reported using a recently revived and unexpectedly difficult dipole wall collision as a benchmark computation several quantities like the vorticity isolines truncation error kinetic energy and enstrophy are inspected for a collision of a dipole with a no slip wall and compared with available benchmark data obtained with a standard chebyshev pseudospectral method we quantify the possible deteriorating effects of the gibbs phenomenon present in the fourier based schemes due to continuity restrictions of the penalized navier stokes equations on the wall it is found that gibbs oscillations have a negligible effect on the flow evolution allowing higher order recovery of the accuracy on a fourier basis by means of postprocessing an advantage of coherent vortex simulations on the other hand is that the degrees of freedom of the flow computation can strongly be reduced in this study we quantify the possible reduction of degrees of freedom while keeping the accuracy for an optimal convergence scenario the penalization parameter has to scale with the number of fourier and wavelet modes in addition an implicit treatment of the darcy drag term in the penalized navier stokes equations is beneficial since this allows one to set the time step independent from the penalization parameter without additional computational or memory requirements

a cartesian grid embedded boundary method for the heat equation on irregular domains we present an algorithm for solving the heat equation on irregular time dependent domains it is based on the cartesian grid embedded boundary algorithm of johansen and colella j comput phys 147 2 60 85 for discretizing poisson s equation combined with a second order accurate discretization of the time derivative this leads to a method that is second order accurate in space and time for the case where the boundary is moving we convert the moving boundary problem to a sequence of fixed boundary problems combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves we find that in the moving boundary case the use of crank nicolson time discretization is unstable requiring us to use the l sub 0 stable implicit runge kutta method of twizell gumel and arigu

quantitative fourier analysis of approximation techniques i interpolators and projectors we present a general fourier based method that provides an accurate prediction of the approximation error as a function of the sampling step t our formalism applies to an extended class of convolution based signal approximation techniques which includes interpolation generalized sampling with prefiltering and the projectors encountered in wavelet theory we claim that we can predict the l sup 2 approximation error by integrating the spectrum of the function to approximate not necessarily bandlimited against a frequency kernel e spl omega that characterizes the approximation operator this prediction is easier yet more precise than was previously available our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function our error prediction is exact for stationary processes as well as for bandlimited signals we apply this method to the comparison of standard interpolation and approximation techniques our method has interesting implications for approximation theory in particular we use our results to obtain some new asymptotic expansions of the error as t spl rarr 0 as well as to derive improved upper bounds of the kind found in the strang fix 1971 theory we finally show how we can design quasi interpolators that are near optimal in the least squares sense

on the kdv type equation with variable coefficients in this paper the kdv type equations with variable coefficients appearing a lot in the literature are discussed generally the explicit transformations which transform various kdv mkdv and kp type nonlinear evolution equations into their canonical forms with constant coefficients are given the results presented here tie up many of the investigations scattered in the literature

reversible fast and high quality grid conversions a new grid conversion method is proposed to resample between two 2 d periodic lattices with the same sampling density the main feature of our approach is the symmetric reversibility which means that when using the same algorithm for the converse operation then the initial data is recovered exactly to that purpose we decompose the lattice conversion process into at most three successive shear operations the translations along the shear directions are implemented by 1 d fractional delay operators which revert to simple 1 d convolutions with appropriate filters that yield the property of symmetric reversibility we show that the method is fast and provides high quality resampled images applications of our approach can be found in various settings such as grid conversion between the hexagonal and the cartesian lattice or fast implementation of affine transformations such as rotations

a versatile sharp interface immersed boundary method for incompressible flows with complex boundaries a sharp interface immersed boundary method for simulating incompressible viscous flow past three dimensional immersed bodies is described the method employs a multi dimensional ghost cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three dimensional stationary moving and or deforming bodies the complex immersed surfaces are represented by grids consisting of unstructured triangular elements while the flow is computed on non uniform cartesian grids the paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries simulations of a number of canonical two and three dimensional flows are used to verify the accuracy and fidelity of the solver over a range of reynolds numbers flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems finally two cases inspired from biology with highly complex three dimensional bodies are simulated in order to demonstrate the versatility of the method

rectification for cone beam projection and backprojection the purpose of this paper is to derive a technique for accelerating the computation of cone beam forward and backward projections that are the basic steps of tomographic reconstruction the cone beam geometry of c arm systems is commonly described with projection matrices such matrices provide a continuous framework for analyzing the flow of operations needed to compute backprojection for analytical reconstruction as well as the combination of forward and backward projections for iterative reconstruction the proposed rectification technique resamples the original data to planes that are aligned with two of the reconstructed volume main axes so that the original cone beam geometry can be replaced by a simpler geometry where succession of plane magnifications are involved only rectification generalizes previous independent results to the cone beam backprojection of preprocessed data as well as to cone beam iterative reconstruction the memory access pattern of simple magnifications provides superior predictability and is therefore easier to optimize independently of the choice of the interpolation technique rectification is also shown to provide control over interpolation errors through oversampling allowing tradeoffs between computation speed and precision to be set experimental results are provided for linear and nearest neighbor interpolations based on simulations as well as phantom and patient data acquired on a digital c arm system

approximate string matching using a bidirectional index we study strategies of approximate pattern matching that exploit bidirectional text indexes extending and generalizing ideas of 9 we introduce a formalism called search schemes to specify search strategies of this type then develop a probabilistic measure for the efficiency of a search scheme prove several combinatorial results on efficient search schemes and finally provide experimental computations supporting the superiority of our strategies

convergence analysis of the q1 finite element method for elliptic problems with non boundary fitted meshes summary the aim of this paper is to derive a priori error estimates when the mesh does not fit the original domain s boundary this problematic of the last century e g the finite difference methodology returns to topical studies with the huge development of domain embedding fictitious domain or cartesiangrid methods these methods use regular structured meshes most often cartesian for non aligned domains although non boundary fitted approaches become more and more applied very few studies are devoted to theoretical error estimates in this paper the convergence of a q1 nonconforming finite element method is analyzed for secondorder elliptic problems with dirichlet robin or neumann boundary conditions the finite element method uses standard q1 rectangular finite elements as the finite element approximate space is not contained in the original solution space this method is referred to as nonconforming a stairstep boundary defined from the cartesian mesh approximates the original domain s boundary the convergence analysis of the finite element method for such a kind of non boundary fitted stairstepped approximation is no treated in the literature the study of dirichlet problems is based on similar techniques as those classically used with boundary fitted linear triangular finite elements the estimates obtained for robin problems are novel and use some more technical arguments the rate of convergence is proved to be in o h 1 2 for the h 1 norm for all general boundary conditions and classical duality arguments allow to obtain an o h error estimate in the l 2 norm for dirichlet problems numerical results obtained with fictitious domain techniques that impose original boundary conditions on a non boundary fitted approximate immersed interface are presented these results confirm the theoretical rates of convergence copyright c 2007 john wiley sons ltd

accurate image rotation using hermite expansions in this paper we propose an approach for the accurate rotation of a digital image using hermite expansions this exploits the fact that if a 2 d continuous bandlimited hermite expansion is rotated the resulting function can be expressed as a hermite expansion with the same bandlimit furthermore the hermite coefficients of the initial 2 d expansion and the rotated expansion are mapped through an invertible linear relationship two efficient methods to compute the mapping between hermite coefficients during rotation are proposed we also propose a method for connecting the hermite expansion and a discrete image using this method we can obtain the hermite expansion from a discrete image and vice versa combining these techniques we propose new methods for the rotation of discrete images we assess the accuracy of our methods and compare them with an existing fft based method implementing three shears we find that the method proposed here consistently has better accuracy than the fft based method

discussion on integrable properties for higher dimensional variable coefficient nonlinear partial differential equations in this paper we introduce two new higher dimensional variable coefficient partial differential equations one is a 2 1 dimensional equation which can be reduced to the well known kp equation which first occurs to the paper b b kadomtsev and v i petviashvili on the stability of solitary waves in weakly dispersive media sov phys dokl 15 539 1970 whose bilinear representation lax pairs backlund transformations and infinite conservation laws are obtained respectively by using the bell polynomials another one is a 3 1 dimensional equation whose integrability is also investigated by us and whose lax pairs backlund transformations and infinite conservation laws are obtained respectively

interpolation artifacts in sub pixel image registration we consider the problem of registering aligning two images to sub pixel accuracy by optimization of objective functions constructed from the images intensity values we show that some widely used interpolation methods can introduce multiple local optima in the energy of the interpolated image which if not counter balanced by other terms can cause local optima in registration objective functions including the sum of squared differences cross correlation and mutual information we discuss different solutions to address the problem based on high degree b spline interpolation low pass filtering the images and stochastic integration numerical examples using synthetic and real signals and images are shown