quasi fourier mellin transform for affine invariant features fourier mellin transform fmt has been widely used for the extraction of rotation and scale invariant features however affine transform is a more reasonable approximation model for real viewpoint change due to shearing the integral along the angular direction in the calculation of fmt cannot be used to extract the inherent features of an image undergoing affine transform to eliminate the effect of shearing whitening transform should be conducted on the integral along the radial direction fmt can hardly be modified by conventional whitening based methods with low computational cost due to additional processes in this paper two factors are constructed and embedded into fmt quasi fourier mellin transform qfmt is proposed the embedding of these factors is equivalent to whitening transform and can eliminate the effect of shearing in the affine transform in particular qfmt can also be calculated by integrating along the radial direction followed by integrating along the angular direction as in fmt based on qfmt the quasi fourier mellin descriptor qfmd is constructed for the extraction of affine invariant features some experiments have also been conducted to test the performance of the proposed method

real time affine global motion estimation using phase correlation and its application for digital image stabilization we propose a fast and robust 2d affine global motion estimation algorithm based on phase correlation in the fourier mellin domain and robust least square model fitting of sparse motion vector field and its application for digital image stabilization rotation scale translation rst approximation of affine parameters is obtained at the coarsest level of the image pyramid thus ensuring convergence for a much larger range of motions despite working at the coarsest resolution level using subpixel accurate phase correlation provides sufficiently accurate coarse estimates for the subsequent refinement stage of the algorithm the refinement stage consists of ransac based robust least square model fitting for sparse motion vector field estimated using block based subpixel accurate phase correlation at randomly selected high activity regions in finest level of image pyramid resulting algorithm is very robust to outliers such as foreground objects and flat regions we investigate the robustness of the proposed method for digital image stabilization application experimental results show that the proposed algorithm is capable of estimating larger range of motions as compared to another phase correlation method and optical flow algorithm

existence and stability of periodic solutions for parabolic systems with time delays this paper is concerned with the existence and stability time periodic solutions for a class of coupled parabolic equations with time delay and time delays may appear in the nonlinear reaction functions the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement our approach to the problem is by the method of upper and lower solution and using schauder fixed point theorem some methods for proving the stability of the periodic solution are also given the results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system finally a model arising from chemistry is used to illustrate the obtained results

local cohomology modules of a smooth z algebra have finitely many associated primes let r be a commutative noetherian ring that is a smooth mathbb z algebra for each ideal mathfrak a of r and integer k we prove that the local cohomology module h k mathfrak a r has finitely many associated prime ideals this settles a crucial outstanding case of a conjecture of lyubeznik asserting this finiteness for local cohomology modules of all regular rings

finiteness properties of local cohomology modules an application of d modules to commutative algebra the main goal of this paper is to establish finiteness properties of local cohomology modules in characteristic 0 that would be analogous to those proven by c huneke and r sharp in characteristicp 0 our method based on the theory of algebraicd modules seems to be the first application ofd modules to commutative algebra

an adaptable multilayer fractional fourier transform approach for image registration a novel adaptable accurate way for calculating polar fft and log polar fft is developed in this paper named multilayer fractional fourier transform mlfft mlfft is a necessary addition to the pseudo polar fft for the following reasons it has lower interpolation errors in both polar and log polar fourier transforms it reaches better accuracy with the nearly same computing complexity as the pseudo polar fft it provides a mechanism to increase the accuracy by increasing the user defined computing level this paper demonstrates both mlfft itself and its advantages theoretically and experimentally by emphasizing applications of mlfft in image registration with rotation and scaling our experiments suggest two major advantages of mlfft 1 scaling up to 5 and arbitrary rotation angles or scales up to 10 without rotation can be recovered by mlfft while currently the result recovered by the state of the art algorithms is the maximum scaling of 4 2 no iteration is needed to obtain large rotation and scaling values of images by mlfft hence it is more efficient than the pseudopolar based fft methods for image registration

periodic solutions of quasilinear parabolic systems with nonlinear boundary conditions abstract this paper is concerned with the existence of maximal and minimal periodic solutions of a class of quasilinear parabolic systems with nonlinear boundary conditions our approach to the problem is based on the method of upper and lower solutions and its associated monotone iterations an application is also made to the reaction diffusion system of lotka volterra competition model

associated primes of local cohomology of flat extensions with regular fibers and σ finite d modules abstract in this manuscript we study the following question raised by mel hochster let r m k be a local ring and s be a flat extension with regular closed fiber is v m s ass s h i i s finite for every ideal i s and i n we prove that the answer is positive when s is either a polynomial or a power series ring over r and dim r i r 1 in addition we analyze when this question can be reduced to the case where s is a power series ring over r an important tool for our proof is the use of finite d modules which are not necessarily finitely generated as d modules but whose associated primes are finite we give examples of this class of d modules and applications to local cohomology

some results on local cohomology of polynomial and formal power series rings the one dimensional case abstract in this paper we prove several results on the finiteness of local cohomology of polynomial and formal power series rings in particular we give a partial affirmative answer for a question of l nunez betancourt 2014 14

on certain rings of differentiable type and finiteness properties of local cohomology abstract let r be a commutative f algebra where f is a field of characteristic 0 satisfying the following conditions r is equidimensional of dimension n every residual field with respect to a maximal ideal is an algebraic extension of f and der f r is a finitely generated projective r module of rank n such that r m r der f r der f r m we show that the associated graded ring of the ring of differential operators d r f is a commutative noetherian regular with unity and pure graded dimension equal to 2 dim r moreover we prove that d r f has weak global dimension equal to dim r and that its bernstein class is closed under localization at one element using these properties of d r f we show that the set of associated primes of every local cohomology module h i i r is finite if s m k is a complete regular local ring of mixed characteristic p 0 we show that the localization of s at p s p is such a ring as a consequence the set of associated primes of h i i s that does not contain p is finite moreover we prove this finiteness property for a larger class of functors

asymptotic behavior of solutions of a periodic diffusion system this paper deals with a periodic reaction diffusion system of plankton allelopathy under homogeneous neumann boundary conditions based on the result of ahmad and lazer we show some estimates and nonexistence results for the positive solutions of the system furthermore we investigate the asymptotic behavior of the solutions of the system that is one species dies out and the other exists as time t tends to infinity

video orbits of the projective group a simple approach to featureless estimation of parameters we present direct featureless methods for estimating the eight parameters of an exact projective homographic coordinate transformation to register pairs of images together with the application of seamlessly combining a plurality of images of the same scene resulting in a single image or new image sequence of greater resolution or spatial extent the approach is exact for two cases of static scenes 1 images taken from the same location of an arbitrary three dimensional 3 d scene with a camera that is free to pan tilt rotate about its optical axis and zoom or 2 images of a flat scene taken from arbitrary locations the featureless projective approach generalizes interframe camera motion estimation methods that have previously used a camera model which lacks the degrees of freedom to exactly characterize such phenomena as camera pan and tilt and or which have relied upon finding points of correspondence between the image frames the featureless projective approach which operates directly on the image pixels is shown to be superior in accuracy and the ability to enhance the resolution the proposed methods work well on image data collected from both good quality and poor quality video under a wide variety of conditions sunny cloudy day night these new fully automatic methods are also shown to be robust to deviations from the assumptions of static scene and no parallax

stability and attractivity of periodic solutions of parabolic systems with time delays abstract this paper is concerned with the existence stability and global attractivity of time periodic solutions for a class of coupled parabolic equations in a bounded domain the problem under consideration includes coupled system of parabolic and ordinary differential equations and time delays may appear in the nonlinear reaction functions our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement using schauder fixed point theorem while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme the results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system applications are also given to three lotka volterra reaction diffusion model problems and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions

bass numbers of local cohomology modules let a be a regular local ring of positive characteristic this paper is concerned with the local cohomology modules of a itself but with respect to an arbitrary ideal of a the results include that all the bass numbers of all such local cohomology modules are finite that each such local cohomology module has finite set of associated prime ideals and that whenever such a local cohomology module is artinian then it must be injective this last result had been proved earlier by hartshorne and speiser under the additional assumptions that a is complete and contains its residue field which is perfect the paper ends with some low dimensional evidence related to questions about whether the analogous statements for regular local rings of characteristic 0 are true

cohomological dimension lyubeznik numbers and connectedness in mixed characteristic abstract we establish a second vanishing theorem for local cohomology modules over regular rings of unramified mixed characteristic which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology applying this and new results on the mixed characteristic lyubeznik numbers we further study connectedness properties of the spectra of a certain class of rings

data driven affine deformation estimation and correction in cone beam computed tomography in computed tomography ct motion and deformation during the acquisition lead to streak artefacts and blurring in the reconstructed images to remedy these artefacts we introduce an efficient algorithm to estimate and correct for global affine deformations directly on the cone beam projections the proposed technique is data driven and thus removes the need for markers and or a tracking system a relationship between affine transformations and the cone beam transform is proved and used to correct the projections the deformation parameters that describe deformation perpendicular to the projection direction are estimated for each projection by minimizing a plane based inconsistency criterion the criterion compares each projection of the main scan with all projections of a fast reference scan which is acquired prior or posterior to the main scan experiments with simulated and experimental data show that the proposed affine deformation estimation method is able to substantially reduce motion artefacts in cone beam ct images

an example of an infinite set of associated primes of a local cohomology module let r m be a local noetherian ring let i subset r be any ideal and let m be a finitely generated r module in 1990 craig huneke conjectured that the local cohomology modules h i i m have finitely many associated primes for all i in this paper i settle this conjecture by constructing a local cohomology module of a local k algebra with an infinite set of associated primes and i do this for any field k

discrete infinite dimensional type k monotone dynamical systems and time periodic reaction diffusion systems abstract the asymptotic behavior of discrete type k monotone dynamical systems and reaction diffusion equations is investigated the studying content includes the index theory for fixed points permanence global stability convergence everywhere and coexistence it is shown that the system has a globally asymptotically stable fixed point if every fixed point is locally asymptotically stable with respect to the face it belongs to and at this point the principal eigenvalue of the diagonal partial derivative about any component not belonging to the face is not one a nice result presented is the sufficient and necessary conditions for the system to have a globally asymptotically stable positive fixed point it can be used to establish the sufficient conditions for the system to persist uniformly and the convergent result for all orbits applications are made to time periodic lotka volterra systems with diffusion and sufficient conditions for such systems to have a unique positive periodic solution attracting all positive initial value functions are given for more general time periodic type k monotone reaction diffusion systems with spatial homogeneity a simple condition is given to guarantee the convergence of all positive solutions

one dimensional mapping for estimating projective transformations in this paper the 1 d mapping is studied for estimating a general projective transformation between images first a ray model of image patches is proposed to convert a complex projective deformation of a patch in the cartesian space into two simple rigid shifts of radial lines in the log polar inverse polar space to capture these shifts via direct search two types of radial image line matching viz 1 d log polar mapping and 1 d inverse polar mapping are formally defined also the unique features of these shifts are analyzed then a novel two step mathematical framework is devised for transformation estimation in the first step the 1 d log polar mapping is applied to estimating four affine parameters via two alternative methods for simulated real images in the second step the 1 d inverse polar mapping is applied to estimating two projective parameters by a direct search combined with the two step line matching two translational parameters are also determined finally the performance of the framework is evaluated first in estimating a variety of projective transformations by comparing the estimates with their ground truths and between the two proposed methods and second in registering a wide range of challenging image pairs by comparing with a state of the art feature based method

toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic let r k x 1 dots x n be a ring of polynomials over a field k of characteristic p 0 there is an algorithm due to lyubeznik for deciding the vanishing of local cohomology modules h i i r where i subset r is an ideal this algorithm has not been implemented because its complexity grows very rapidly with the growth of p which makes it impractical in this paper we produce a modification of this algorithm that consumes a modest amount of memory

on positive solutions of the lotka volterra cooperating models with diffusion abstract in this paper using the existence and comparison conclusion for the time periodic quasimonotone nondecreasing systems given by pao c v and iterative method we investigate the time periodic lotka volterra cooperating model and present some existence uniqueness and nonexistence results we also use similar methods to treat the corresponding stationary system to give parallel results

periodic solutions of parabolic systems with nonlinear boundary conditions this paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions the approach to the problem is by the method of upper and lower solutions and its associated monotone iterations this method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial boundary value problems a sufficient condition for the stability of a periodic solution is also given these results are applied to three model problems arising from chemical kinetics ecology and population biology

linearly estimating all parameters of affine motion using radon transform fast and accurate motion estimation takes an important place in many fields of computer vision and image processing using radon transform to compute projections of the images along specified directions is an effective way to show the relationship between the 2d image object and its projections and estimate motions between the images all existing projection based motion estimation methods without the use of iteration have a severe defect that only five of the six affine parameters can be estimated there are some other methods that can estimate the six parameters but most of them are usually based on a certain iterative framework which is computationally intensive and sensitively dependent on the initial values in this paper a novel method based on radon transform is proposed to estimate all the six affine parameters directly the relationship in the projection domain between a pair of images connected by an affine motion is studied and a linear model is established by which all the six affine parameters can be directively found the employment of a hierarchical framework can produce more accurate results the experimental results reveal that the proposed method has a much better performance than the state of the art methods in this field

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

on the periodic lotka volterra competition model abstract we analyze the existence stability and multiplicity of t periodic coexistence states for the classical nonautonomous periodic lotka volterra competing species model this is done by treating the average values of the birth rates of species as parameters and studying the global structure of the set of coexistence states as these parameters vary as a result of this analysis we can explain the interesting differences between the results for the periodic case and the associated autonomous model

extension of phase correlation to subpixel registration in this paper we have derived analytic expressions for the phase correlation of downsampled images we have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak but rather in several coherent peaks mostly adjacent to each other these coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration the analytic results provide a closed form solution to subpixel translation estimation and are used for detailed error analysis excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands

bockstein homomorphisms in local cohomology let r be a polynomial ring in finitely many variables over the integers fix an ideal a of r we prove that for all but finitely prime integers p the bockstein homomorphisms on local cohomology h a r pr h k 1 a r pr are zero this vanishing of bockstein homomorphisms is predicted by lyubeznik s conjecture which states that when r is a regular ring the modules h a r have finitely many associated prime ideals we further show that when r is replaced by a hypersurface ring the vanishing of bockstein homomorphisms as well as the analogue of lyubeznik s conjecture need not hold bockstein homomorphisms have their origins in algebraic topology we establish a connection between algebraic and topological bockstein homomorphisms through stanley reisner theory

a model of the effect of image motion in the radon transform domain one of the most fundamental properties of the radon projection transform is that shifting of the image results in shifted projections this useful property relates translational motion in the image to simple displacement in the projections it is far from clear however how more general types of motion in the image domain will be manifested in the projections in this paper we present a model for this phenomenon in the general case namely we develop a generalization of the shift property of the radon transform we study various properties of the apparent projected motion implied by the model and study the case of affine motion in particular we also present illustrative examples and briefly discuss the inverse problem implied by the forward model developed herein along with some possible applications

asymptotic behaviour of solutions of periodic competition diffusion system on considere le systeme d equations de reaction diffusion u t k 1 u a bu cv v t k 2 v v d eu fv ou k 1 k 2 a b f sont des fonctions suffisamment lisses definies sur un cylindre ou est un domaine borne lisse de r n

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

asymptotic behavior of solutions of a periodic reaction diffusion system of a three species of competition model this paper concerns a three species periodic competition system which subjects to homogeneous neumann boundary conditions using a result obtained by ahmad and lazer we give some estimates and nonexistence results for the positive solutions of the system furthermore we investigate the asymptotic behavior of the solutions of the system definitely we refer to that one species dies out and the other two coexist as time t tends to infinity

coexistence and stability of a competition diffusion system in population dynamics abstract the coexistence and stability of the population densities of two competing species in a bounded habitat are investigated in the present paper where the effect of dispersion transportation is taken into consideration the mathematical problem involves a coupled system of lotka volterra type reaction diffusion equations together with some initial and boundary conditions including the dirichlet neumann and third type necessary and sufficient conditions for the coexistence and competitive exclusion are established and the effect of diffusion is explicitly given for the stability problem general criteria for the stability and instability of a steady state solution are established and then applied to various situations depending on the relative magnitude among the physical parameters also given are necessary and sufficient conditions for the existence of multiple steady state solutions and the stability or instability of each of these solutions special attention is given to the neumann boundary condition with respect to which some threshold results for the coexistence and stability or instability of the four uniform steady states are characterized it is shown in this situation that only one of the four constant steady states is asymptotically stable while the remaining three are unstable the stability or instability of these states depends solely on the relative magnitude among the various rate constants and is independent of the diffusion coefficients

constructing arbitrary torsion elements for a local cohomology module local cohomology modules are in general not finitely generated over the ambient ring towards a better understanding of the structure of these modules huneke 1992 hu asked if they have finitely many associated prime ideals the answer is negative several authors have constructed a ring whose local cohomology module has infinitely many associated primes in certain situations one can prove that a local cohomology module has infinitely many associated primes by showing that z pz embeds into the local cohomology module for each prime integer p we show that in fact each finitely generated abelian group embeds into a local cohomology module