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

an analysis of a class of second order accurate godunov type schemes a general analysis including convergence results of second order godunov type schemes is proposed problems related to the entropy condition are discussed numerical experiments show the accuracy and the stability of the schemes

stochastic transport of particles in straining flows important features associated with the segregration of particles in turbulent flow are investigated by considering the statistical distribution phase space number density of particles subject to the combined effects of straining flow and stochastic forcing a fokker planck model is used to obtain results for the phase space distributions of particles that are entrained into straining flow fields the analysis shows that in marked contrast to the zero strain case nonsingular steady state distributions are generated and also confirms that the diffusional effect resulting from stochastic forcing is sufficient to offset the otherwise singular distributions that would result from the indefinite accumulation of particles along stagnation lines the influence of particle inertia stokes number on the form of the resulting distributions is considered and several significant results are observed the influence of strain rate on the attenuation of particle kinetic stresses is quantified and explained the development of large third order velocity moments is observed for stokes numbers above a critical value the mechanism underlying this phenomenon is seen to be a generic feature of particle transport in flows where vortex structures induce local counterflows of particles the system therefore provides an ideal test for closure models for third order moments of particle velocities and here the standard chapman enskog approximation is assessed

multiresolution registration of remote sensing imagery by optimization of mutual information using a stochastic gradient image registration is the process by which we determine a transformation that provides the most accurate match between two images the search for the matching transformation can be automated with the use of a suitable metric but it can be very time consuming and tedious we introduce a registration algorithm that combines a simple yet powerful search strategy based on a stochastic gradient with two similarity measures correlation and mutual information together with a wavelet based multiresolution pyramid we limit our study to pairs of images which are misaligned by rotation and or translation and present two main results first we demonstrate that in our application mutual information may be better suited for sub pixel registration as it produces consistently sharper optimum peaks than correlation then we show that the stochastic gradient search combined with either measure produces accurate results when applied to synthetic data as well as to multitemporal or multisensor collections of satellite data mutual information is generally found to optimize with one third the number of iterations required by correlation results also show that a multiresolution implementation of the algorithm yields significant improvements in terms of both speed and robustness over a single resolution implementation

a new evolutionary search strategy for global optimization of high dimensional problems global optimization of high dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation the weakness of randomization based evolutionary algorithms in searching high dimensional spaces is demonstrated in this paper a new strategy sp uci is developed to treat complexity caused by high dimensionalities this strategy features a slope based searching kernel and a scheme of maintaining the particle population s capability of searching over the full search space examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that sp uci surpasses two popular algorithms particle swarm optimizer pso and differential evolution de on high dimensional problems experimental results also corroborate the argument that in high dimensional optimization only problems with well formative fitness landscapes are solvable and slope based schemes are preferable to randomization based ones

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

a unified approach to fast image registration and a new curvature based registration technique abstract image registration is central to many challenges in medical imaging today it has a vast range of applications the purpose of this note is twofold first we review some of the most promising non linear registration strategies currently used in medical imaging we show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment second we introduce within the variational framework a new non linear registration model based on a curvature type smoother we show that affine linear transformations belong to the kernel of this regularizer as a result the approach becomes more robust against poor initializations of a pre registration step furthermore we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation we demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering mr mammography images

optimization of mutual information for multiresolution image registration we propose a new method for the intermodal registration of images using a criterion known as mutual information our main contribution is an optimizer that we specifically designed for this criterion we show that this new optimizer is well adapted to a multiresolution approach because it typically converges in fewer criterion evaluations than other optimizers we have built a multiresolution image pyramid along with an interpolation process an optimizer and the criterion itself around the unifying concept of spline processing this ensures coherence in the way we model data and yields good performance we have tested our approach in a variety of experimental conditions and report excellent results we claim an accuracy of about a hundredth of a pixel under ideal conditions we are also robust since the accuracy is still about a tenth of a pixel under very noisy conditions in addition a blind evaluation of our results compares very favorably to the work of several other researchers

volume preserving nonrigid registration of mr breast images using free form deformation with an incompressibility constraint in this paper we extend a previously reported intensity based nonrigid registration algorithm by using a novel regularization term to constrain the deformation global motion is modeled by a rigid transformation while local motion is described by a free form deformation based on b splines an information theoretic measure normalized mutual information is used as an intensity based image similarity measure registration is performed by searching for the deformation that minimizes a cost function consisting of a weighted combination of the image similarity measure and a regularization term the novel regularization term is a local volume preservation incompressibility constraint which is motivated by the assumption that soft tissue is incompressible for small deformations and short time periods the incompressibility constraint is implemented by penalizing deviations of the jacobian determinant of the deformation from unity we apply the nonrigid registration algorithm with and without the incompressibility constraint to precontrast and postcontrast magnetic resonance mr breast images from 17 patients without using a constraint the volume of contrast enhancing lesions decreases by 1 78 mean 26 image improvement motion artifact reduction obtained using the new constraint is compared with that obtained using a smoothness constraint based on the bending energy of the coordinate grid by blinded visual assessment of maximum intensity projections of subtraction images for both constraints volume preservation improves and motion artifact correction worsens as the weight of the constraint penalty term increases for a given volume change of the contrast enhancing lesions 2 of the original volume the incompressibility constraint reduces motion artifacts better than or equal to the smoothness constraint in 13 out of 17 cases better in 9 equal in 4 worse in 4 the preliminary results suggest that incorporation of the incompressibility regularization term improves intensity based free form nonrigid registration of contrast enhanced mr breast images by greatly reducing the problem of shrinkage of contrast enhancing structures while simultaneously allowing motion artifacts to be substantially reduced

first and second order error estimates for the upwind source at interface method the upwind source at interface method for hyperbolic conservation laws with source term introduced in b perthame c simeoni convergence of the upwind interface source method for hyperbolic conservation laws hyperbolic problems theory numerics applications t hou and e tadmor eds springer 2003 is essentially first order accurate under appropriate hypotheses of consistency on the finite volume discretization of the source term we prove l p error estimates 1 le p infty in the case of a uniform spatial mesh for which an optimal result can be obtained we thus conclude that the same convergence rates hold as for the corresponding homogeneous problem to improve the numerical accuracy we develop two different approaches of dealing with the source term and we discuss the question of deriving second order error estimates numerical evidence shows that those techniques produce high resolution schemes compatible with the upwind source at interface method

an explicit asymptotic preserving low froude scheme for the multilayer shallow water model with density stratification we present an explicit scheme for a two dimensional multilayer shallow water model with density stratification for general meshes and collocated variables the proposed strategy is based on a regularized model where the transport velocity in the advective fluxes is shifted proportionally to the pressure potential gradient using a similar strategy for the potential forces we show the stability of the method in the sense of a discrete dissipation of the mechanical energy in general multilayer and non linear frames these results are obtained at first order in space and time and extended using a simple second order muscl extension with the objective of minimizing the diffusive losses in realistic contexts sufficient conditions are exhibited on the regularizing terms to ensure the scheme s linear stability at first and second order in time and space the other main result stands in the consistency with respect to the asymptotics reached at small and large time scales in low froude regimes which governs large scale oceanic circulation additionally robustness and well balanced results for motionless steady states are also ensured these stability properties tend to provide a very robust and efficient approach easy to implement and particularly well suited for large scale simulations some numerical experiments are proposed to highlight the scheme efficiency an experiment of fast gravitational modes a smooth surface wave propagation an initial propagating surface water elevation jump considering a non trivial topography and a last experiment of slow rossby modes simulating the displacement of a baroclinic vortex subject to the coriolis force

consistent image registration presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another this approach produces a consistent set of transformations that have less pairwise registration error i e better correspondence than traditional methods that estimate the forward and reverse transformations independently the transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics the transformations are parameterized by a fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation results using a linear elastic material constraint are presented using both magnetic resonance and x ray computed tomography image data the results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear elasticity give better registration results than using either constraint alone or none at all

convergence results for the 1 λ sa es using the theory of ϕ irreducible markov chains this paper investigates theoretically the 1 sa es on the well known sphere function we prove sufficient conditions on the parameters of the algorithm ensuring the convergence of 1 n ln xn where xn is the parent at generation n this in turn guarantees the asymptotic log linear convergence or divergence of the algorithm the technique used for this analysis calls upon the theory of markov chains on a continuous state space and on the so called foster lyapunov drift conditions those conditions enable us to derive practical conditions that prove stability properties of markov chains

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

a generalized fokker planck equation for particle transport in random media abstract a transport equation is derived for the probability density function pdf that gives the phase space distribution of a particle moving in a random medium the motion of the particle is determined by a general second order stochastic differential equation that models transport in a medium exhibiting correlated fluctuations in both space and time the derivation makes use of cumulant expansions and functional calculus the most general form of the transport equation requires closure and a simple closure approximation is discussed no closure approximation is necessary when the stochastic component of the particle equation of motion is a correlated gaussian process and results for transport in an unbounded medium are derived for this exact case these results are consistent with other studies and serve to validate the model

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

on the analysis of finite volume methods for evolutionary problems finite volume or finite element methods now dominate the modeling of steady flows because of their natural handling of complex configurations they should have a similar advantage for unsteady flows however their error analysis on nonuniform meshes has met a number of difficulties in this paper a new approach is adopted which makes greater use of a godunov formulation it opens the way for a fuller comparison of characteristic based methods with semidiscrete methods

automatic lung segmentation for accurate quantitation of volumetric x ray ct images segmentation of pulmonary x ray computed tomography ct images is a precursor to most pulmonary image analysis applications this paper presents a fully automatic method for identifying the lungs in three dimensional 3 d pulmonary x ray ct images the method has three main steps first the lung region is extracted from the ct images by gray level thresholding then the left and right lungs are separated by identifying the anterior and posterior junctions by dynamic programming finally a sequence of morphological operations is used to smooth the irregular boundary along the mediastinum in order to obtain results consistent with these obtained by manual analysis in which only the most central pulmonary arteries are excluded from the lung region the method has been tested by processing 3 d ct data sets from eight normal subjects each imaged three times at biweekly intervals with lungs at 90 vital capacity the authors present results by comparing their automatic method to manually traced borders from two image analysts averaged over all volumes the root mean square difference between the computer and human analysis is 0 8 pixels 0 54 mm the mean intrasubject change in tissue content over the three scans was 2 75 spl plusmn 2 29 mean spl plusmn standard deviation

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

spline based hybrid image registration using landmark and intensity information based on matrix valued non radial basis functions we introduce a new approach for spline based elastic image registration using both point landmarks and intensity information with this approach both types of information as well as a regularization based on the navier equation are directly integrated in a single energy minimizing functional for this functional we have derived an analytic solution which is based on matrix valued non radial basis functions with our approach the full 3d intensity information is exploited i e all voxels are considered and subsampling using a grid is not required a special case of our hybrid approach is obtained by disregarding the landmark information which results in a pure intensity based elastic registration approach we have successfully applied our approach to 3d synthetic images 2d mr images of the human brain 2d gel electrophoresis images and 3d ct lung images

simultaneous multiresolution strategies for nonrigid image registration multiresolution strategies are commonly used in the nonrigid registration to avoid local minima in the optimization space generally a step by step hierarchical approach is adopted in which the registration starts on a level with reduced complexity downsampled images global transformations then continuing to levels with increased complexity until the finest level is reached in this paper we propose two alternative multiresolution strategies for both the data and transformation models in which different resolution levels are considered simultaneously instead of subsequently through combining the different strategies for data and transformation we systematically define 3 3 multiresolution schemes including both existing and novel methods experiments on 10 pairs of computed tomography lung data sets showed that the best performing strategy resulted in a reduction of the upper quartile of the mean target registration error from 2 to 1 5 mm compared with the conventionally hierarchical multiresolution method while achieving smoother deformations experiments with intersubject registration of 18 3d t1 weighted mri brain scans confirmed that simultaneous multiresolution strategies produce more accurate registration results median of mean overlap increased from 0 55 to 0 57 and smoother deformation fields than the traditionally hierarchical method evaluation of robustness indicated that the largest differences in accuracy between methods are observed for structures with a relatively large initial misalignment

evaluation of optimization methods for nonrigid medical image registration using mutual information and b splines a popular technique for nonrigid registration of medical images is based on the maximization of their mutual information in combination with a deformation field parameterized by cubic b splines the coordinate mapping that relates the two images is found using an iterative optimization procedure this work compares the performance of eight optimization methods gradient descent with two different step size selection algorithms quasi newton nonlinear conjugate gradient kiefer wolfowitz simultaneous perturbation robbins monro and evolution strategy special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives the optimization methods are tested on manually deformed ct images of the heart on follow up ct chest scans and on mr scans of the prostate acquired using a bffe tl and t2 protocol registration accuracy is assessed by computing the overlap of segmented edges precision and convergence properties are studied by comparing deformation fields the results show that the robbins monro method is the best choice in most applications with this approach the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image randomly selected in every iteration to compute the derivative of the mutual information from the other methods the quasi newton and the nonlinear conjugate gradient method achieve a slightly higher precision at the price of larger computation times

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

pet ct image registration in the chest using free form deformations we have implemented and validated an algorithm for three dimensional positron emission tomography transmission to computed tomography registration in the chest using mutual information as a similarity criterion inherent differences in the two imaging protocols produce significant nonrigid motion between the two acquisitions a rigid body deformation combined with localized cubic b splines is used to capture this motion the deformation is defined on a regular grid and is parameterized by potentially several thousand coefficients together with a spline based continuous representation of images and parzen histogram estimates our deformation model allows closed form expressions for the criterion and its gradient a limited memory quasi newton optimization algorithm is used in a hierarchical multiresolution framework to automatically align the images to characterize the performance of the method 27 scans from patients involved in routine lung cancer staging were used in a validation study the registrations were assessed visually by two expert observers in specific anatomic locations using a split window validation technique the visually reported errors are in the 0 to 6 mm range and the average computation time is 100 min on a moderate performance workstation

a family of hybrid conjugate gradient methods for unconstrained optimization conjugate gradient methods are an important class of methods for unconstrained optimization especially for large scale problems recently they have been much studied this paper proposes a three parameter family of hybrid conjugate gradient methods two important features of the family are that i it can avoid the propensity of small steps namely if a small step is generated away from the solution point the next search direction will be close to the negative gradient direction and ii its descent property and global convergence are likely to be achieved provided that the line search satisfies the wolfe conditions some numerical results with the family are also presented

randomly perturbed b splines for nonrigid image registration b splines are commonly utilized to construct the transformation model in free form deformation ffd based registration b splines become smoother with increasing spline order however a higher order b spline requires a larger support region involving more control points which means higher computational cost in general the third order b spline is considered as a good compromise between spline smoothness and computational cost a lower order function is seldom used to construct the transformation model for registration since it is less smooth in this research we investigated whether lower order b spline functions can be utilized for more efficient registration while preserving smoothness of the deformation by using a novel random perturbation technique with the proposed perturbation technique the expected value of the cost function given probability density function pdf of the perturbation is minimized by a stochastic gradient descent optimization extensive experiments on 2d synthetically deformed brain images and real 3d lung and brain scans demonstrated that the novel randomly perturbed free form deformation rpffd approach improves the registration accuracy and transformation smoothness meanwhile lower order rpffd methods reduce the computational cost substantially

registration of cervical mri using multifeature mutual information radiation therapy for cervical cancer can benefit from image registration in several ways for example by studying the motion of organs or by partially automating the delineation of the target volume and other structures of interest in this paper the registration of cervical data is addressed using mutual information mi of not only image intensity but also features that describe local image structure three aspects of the registration are addressed to make this approach feasible first instead of relying on a histogram based estimation of mutual information which poses problems for a larger number of features a graph based implementation of alpha mutual information alpha mi is employed second the analytical derivative of alpha mi is derived this makes it possible to use a stochastic gradient descent method to solve the registration problem which is substantially faster than non derivative based methods third the feature space is reduced by means of a principal component analysis which also decreases the registration time the proposed technique is compared to a standard approach based on the mutual information of image intensity only experiments are performed on 93 t2 weighted mr clinical data sets acquired from 19 patients with cervical cancer several characteristics of the proposed algorithm are studied on a subset of 19 image pairs one pair per patient on the remaining data 36 image pairs one or two pairs per patient the median overlap is shown to improve significantly compared to standard mi from 0 85 to 0 86 for the clinical target volume ctv p 2 ldr10 2 from 0 75 to 0 81 for the bladder p 8 ldr 10 6 and from 0 76 to 0 77 for the rectum p 2 ldr 10 4 the registration error is improved at important tissue interfaces such as that of the bladder with the ctv and the interface of the rectum with the uterus and cervix

simplified godunov schemes for 2 x 2 systems of conservation laws some godunov type schemes for solving isentropic gas dynamic equations are presented after analyzing a one intermediary state scheme and its properties we prove consistency with entropy condition for time continuous limit solutions of a simplified godunov scheme by techniques due to osher we prove also similar results for high order versions of these numerical schemes

constructing diffeomorphic representations for the groupwise analysis of nonrigid registrations of medical images groupwise nonrigid registrations of medical images define dense correspondences across a set of images defined by a continuous deformation field that relates each target image in the group to some reference image these registrations can be automatic or based on the interpolation of a set of user defined landmarks but in both cases quantifying the normal and abnormal structural variation across the group of imaged structures implies analysis of the set of deformation fields we contend that the choice of representation of the deformation fields is an integral part of this analysis this paper presents methods for constructing a general class of multi dimensional diffeomorphic representations of deformations we demonstrate for the particular case of the polyharmonic clamped plate splines that these representations are suitable for the description of deformations of medical images in both two and three dimensions using a set of two dimensional annotated mri brain slices and a set of three dimensional segmented hippocampi with optimized correspondences the class of diffeomorphic representations also defines a non euclidean metric on the space of patterns and for the case of compactly supported deformations on the corresponding diffeomorphism group in an experimental study we show that this non euclidean metric is superior to the usual ad hoc euclidean metrics in that it enables more accurate classification of legal and illegal variations

probabilistic models for particle and scalar transport in fluctuating flows an evaluation of simple closure approximations abstract a generalized fokker planck equation is used to describe the transport of discrete particles and fluid points in fluctuating flows simple closure approximations for this equation are considered which allow free field analytic solutions to be constructed results based on these solutions are compared with those obtained from simulation of the underlying non markovian particle and fluid point trajectories the work validates the form of the generalized fokker planck equation and demonstrates the effectiveness of using models based on this equation to study such transport