multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

homoclinic orbits in the near integrable double discrete sine gordon equation we establish the existence of homoclinic orbits for the near integrable double discrete sine gordon ddsg equation under periodic boundary conditions the hyperbolic structure and homoclinic orbits are constructed through the backlund transformation and lax pair a geometric perturbation method based on mel nikov analysis is used to establish necessary criteria for the persistent of temporally homoclinic orbits for the class of ddsg equations with dissipative perturbations

numerical chaos symplectic integrators and exponentially small splitting distances two discrete versions of duffing s equation are derived as reductions of discretizations of the nonlinear schrodinger nls equation inheriting the properties of the nsl discretizations one is shown to be integrable and using a mel nikov type analysis the other discretization is shown to be nonintegrable arguments are given why it is possible for the nonintegrable scheme to restore the homoclinic orbit at an exponentially fast rate which is faster than the order of the approximation as h 0 this suggests why there can be fundamental differences between symplectic and nonsymplectic discretizations of certain continuous hamiltonian systems

perturbation of a hopf bifurcation by an external time periodic forcing contenrs i introduction ii the mathematical model iii dynamics of the poincark map in the non resonant and weakly resonant cases iv dynamics of the poincark map in the p l resonant case v dynamics of the poincart map in the p 2 resonant case vi dynamics of the poincark map in the p 3 resonant case

efficient registration of nonrigid 3 d bodies we present a novel method to perform an accurate registration of 3 d nonrigid bodies by using phase shift properties of the dual tree complex wavelet transform dt bbcwt since the phases of dt bbcwt coefficients change approximately linearly with the amount of feature displacement in the spatial domain motion can be estimated using the phase information from these coefficients the motion estimation is performed iteratively first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field we use a parametric affine model to describe the motion where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations from the estimated affine parameters the motion field between the sensed and the reference data sets can be generated and the sensed data set then can be shifted and interpolated spatially to align with the reference datafeature displacement set

motion estimation using a complex valued wavelet transform this paper describes a new motion estimation algorithm that is potentially useful for both computer vision and video compression applications it is hierarchical in structure using a separable two dimensional 2 d discrete wavelet transform dwt on each frame to efficiently construct a multiresolution pyramid of subimages the dwt is based on a complex valued pair of four tap fir filters with gabor like characteristics the resulting complex dwt cdwt effectively implements an analysis by an ensemble of gabor like filters with a variety of orientations and scales the phase difference between the subband coefficients of each frame at a given subpel bears a predictable relation to a local translation in the region of the reference frame subtended by that subpel that relation is used to estimate the displacement field at the coarsest scale of the multiresolution pyramid each estimate is accompanied by a directional confidence measure in the form of the parameters of a quadratic matching surface the initial estimate field is progressively refined by a coarse to fine strategy in which finer scale information is appropriately incorporated at each stage the accuracy efficiency and robustness of the new algorithm are demonstrated in comparison testing against hierarchical implementations of intensity gradient based and fractional precision block matching motion estimators

strong continuity of generalized feynman kac semigroups necessary and sufficient conditions let e d e be a strongly local quasi regular symmetric dirichlet form on l2 e m and xt t 0 px x e the diffusion process associated with e d e for u d e e u has a quasi continuous version u and u xt has fukushima s decomposition u xt u x0 mtu ntu where mtu is the martingale part and ntu is the zero energy part in this paper we study the strong continuity of the generalized feynman kac semigroup defined by ptuf x ex entuf xt t 0 two necessary and sufficient conditions for ptu t 0 to be strongly continuous are obtained by considering the quadratic form qu d e b where qu f f e f f e u f2 for f d e b and the energy measure u of u respectively an example is also given to show that ptu t 0 is strongly continuous when u is not a measure of the kato class but of the hardy class with the constant u e 12 cf definition 4 5

absolute continuity of symmetric markov processes we study girsanov s theorem in the context of symmetric markov processes extending earlier work of fukushima takeda and fitzsimmons on girsanov transformations of gradient type we investigate the most general girsanov transformation leading to another symmetric markov process this investigation requires an extension of the forward backward martingale method of lyons zheng to cover the case of processes with jumps

non integrability and continuation of fixed points of 2 n dimensional perturbed twist maps abstract in this paper a simple criterion to prove non integrability of symplectic perturbed twist mappings in 2 n dimensions is developed for sufficiently small perturbations in addition an upper bound for the number of isolating integrals the system can possess is provided a criterion for the analytic continuation of isolated periodic orbits in case of a small nonzero perturbation of twist maps is found the evaluation of their linear stability character by obtaining a simplified expression of the eigenvalues of the jacobian matrix concludes the theoretical part the theory is finally applied to a twist map perturbed by the suris potential and also a four dimensional map with physical interest

mel nikov s function for two dimensional mappings this paper calculates explicitly the mel nikov function for general perturbations of two dimensional maps possessing a saddle connection this result may be considered as the discrete analogue of ziglin s calculation of the mel nikov function for time periodic perturbations of two dimensional continuous flows key words integrable planar maps perturbations homoclinic orbits mel nikov s function poisson summation formula

absolute continuity of symmetric diffusions let x and y be symmetric diffusion processes with a common state space and let p m resp q be the law of x resp y with its symmetry measure m resp as initial distribution we study the consequences of the absolute continuity condition q t 1 t the density p also serves to link the dirichlet forms of x and y in a simple way our identification of l relies on notions of even and odd for additive functionals these notions complement fukushima s decomposition and the forward backward martingale decomposition of lyons and zheng

perturbation of dirichlet forms lower semiboundedness closability and form cores we study perturbations e e qu of dirichlet forms e on some l2 space l2 m given by quadratic forms q g g d with a signed borel measure whose positive and negative parts are smooth measures with respect to the given dirichlet form we give necessary and sufficient conditions for e to be a lower semibounded closed quadratic form with a unique associated continuous semigroup pt on l2 m we also study the associated resolvent semigroup as well as the relation between e and the largest closed quadratic form which is smaller than e in particular we exhibit form cores

on the singularity analysis of intersecting separatrices in near integrable dynamical systems abstract it has been recently proved by s l ziglin that transversal intersections of separatrices invariant manifolds in near integrable hamiltonian systems of two degrees of freedom imply the existence of multi valued solutions with infinitely many riemann sheets ziglin s theorem is illustrated here on a simple example and then extended and applied to non hamiltonian analytic flows x f x eg x t with x x y and g x t g x t 2 which for e 0 possess the painleve property on the other hand the theoretically expected logarithmic singularities for e 0 are obtained explicitly in solutions near the intersecting separatrices thus we conjecture that dynamical systems with the painleve property can have no separatrix intersections and hence no strange attractors etc these singularities are then numerically located and found to form certain very interesting chimney patterns in the complex t plane on which they accumulate densely the upper part of the chimneys away from the re t axis is asymptotically quite insensitive to changes in parameter values or initial conditions the singularity pattern itself however becomes denser and each chimney is seen to gradually collapse towards the re t axis as the amplitude of the driving term increases and the motion becomes more chaotic

existence of nontrivial homoclinic orbits for fourth order difference equations we obtain a sufficient condition for the existence of nontrivial homoclinic orbits for fourth order difference equations by using mountain pass theorem a weak convergence argument and a discrete version of lieb s lemma

hardy s inequality for dirichlet forms abstract we prove an abstract form of hardy s l2 inequality in which the dirichlet integral is replaced by the dirichlet form of a general symmetric markov process a number of examples are provided

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

non symmetric perturbations of symmetric dirichlet forms abstract we provide a path space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local dirichlet form the representation is a combination of feynman kac and girsanov formulas and extends previously known results in the framework of symmetric diffusion processes through the use of the hardy class of smooth measures which contains the kato class of smooth measures

melnikov potential for exact symplectic maps the splitting of separatrices of hyperbolic fixed points for exact symplectic maps of n degrees of freedom is considered the non degenerate critical points of a real valued function called the melnikov potential are associated to transverse homo clinic orbits and an asymptotic expression for the symplectic area between homoclinic orbits is given moreover if the unperturbed invariant manifolds are completely dou bled it is shown that there exist in general at least 4 primary homoclinic orbits 4 n in antisymmetric maps both lower bounds are optimal two examples are presented a 2n dimensional central standard like map and the hamiltonian map associated to a magnetized spherical pendulum several topics are studied about these examples existence of splitting explicit computations of melnikov potentials transverse homoclinic orbits exponentially small splitting etc

the mel nikov technique for highly dissipative systems we present explicit calculations that extend the applicability of the mel nikov technique to include a general class of highly dissipative systems in particular the dissipation may be in the form of large positive or negative damping the only required assumption is that each system of this class possesses a homoclinic or a heteroclinic orbit we also show that sufficiently small time sinusoidal perturbation of these systems results in nonempty transversal intersection of stable and unstable manifolds for all but at most discretely many frequencies the results are then demonstrated via computer simulation of the highly damped pendulum with constant plus small time sinusoidal forcing

discrete dichotomies and bifurcations from critical homoclinic orbits abstract perturbed discrete systems likexn 1 f xn g xn xn r n n z when the associated unperturbed map 0 is not invertible and has acriticalorbit n homoclinic to a hyperbolic fixed pointpare studied bycriticalwe mean that thef n are invertible for any integern 0 butf 0 is not invertible the main goal is to give sufficient conditions for a bifurcationfrom zero to many homoclinicswhen the parameter crosses zero we also give a melnikov like result assuring thepersistence of homoclinicsin a complete neighborhood of 0 this result is similar to the ones obtained for diffeomorphisms and flows

on the potential theory of symmetric markov processes on reprend des resultats de dynkin et on considere un processus de markov fort symetrique continu a droite on etudie la relation existant entre le cone de mesures positives d energie finie et la capacite

a mel nikov approach to soliton like solutions of systems of discretized nonlinear schro dinger equations we investigate a class of n coupled discretized nonlinear schrodinger equations of interacting chains in a nonlinear lattice which in the limit of zero coupling become integrable ablowitz ladik differential difference equations we study the existence of stationary localized excitations in the form of soliton like time periodic states by reducing the system to a perturbed 2n dimensional symplectic map whose homoclinic orbits are obtained by a recently developed mel nikov analysis we find that depending on the perturbation homoclinic orbits can be accurately located from the simple zeros of a mel nikov vector and illustrate our results in the cases n 2 and 3

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

splitting of a small separatrix loop near the saddle center bifurcation in area preserving maps abstract when the saddle center bifurcation occurs in an analytic family of area preserving maps a parabolic fixed point first appears at the origin and then this point bifurcates creating an elliptic fixed point and a hyperbolic one separatrices of the hyperbolic fixed point form a small loop around the elliptic point in general the separatrices intersect transversely and the splitting is exponentially small with respect to the perturbation parameter we derive an asymptotic formula which describes the splitting and study the properties of the pre exponential factor

quadratic forms corresponding to the generalized schrodinger semigroups suppose that xt is the standard brownian motion in rd d 3 that h1 rd is a bounded continuous function such that 2 belongs to the kato class and is a measure belonging to the kato class let a t be defined as a t xt x0 t0 xs dxs and let a t be the continuous additive functional with as its revuz measure define at as the sum of the two additive functionals above then the semigroup defined as ttf x ex eatf xt is called a generalized schrodinger semigroup in this paper we identify the quadratic form corresponding to tt as e h1 rd with e u v 12 u x v x dx rd uv x x dx rdu x v x dx