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

generalized overlap measures for evaluation and validation in medical image analysis measures of overlap of labelled regions of images such as the dice and tanimoto coefficients have been extensively used to evaluate image registration and segmentation algorithms modern studies can include multiple labels defined on multiple images yet most evaluation schemes report one overlap per labelled region simply averaged over multiple images in this paper common overlap measures are generalized to measure the total overlap of ensembles of labels defined on multiple test images and account for fractional labels using fuzzy set theory this framework allows a single figure of merit to be reported which summarises the results of a complex experiment by image pair by label or overall a complementary measure of error the overlap distance is defined which captures the spatial extent of the nonoverlapping part and is related to the hausdorff distance computed on grey level images the generalized overlap measures are validated on synthetic images for which the overlap can be computed analytically and used as similarity measures in nonrigid registration of three dimensional magnetic resonance imaging mri brain images finally a pragmatic segmentation ground truth is constructed by registering a magnetic resonance atlas brain to 20 individual scans and used with the overlap measures to evaluate publicly available brain segmentation algorithms

co registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization diffusion mri provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain echo planar imaging epi sequences which are frequently used for acquisition of diffusion images are sensitive to inhomogeneities in the primary magnetic b0 field that cause localized distortions in the reconstructed images we describe and evaluate a new method for correction of susceptibility induced distortion in diffusion images in the absence of an accurate b0 fieldmap in our method the distortion field is estimated using a constrained non rigid registration between an undistorted t1 weighted anatomical image and one of the distorted epi images from diffusion acquisition our registration framework is based on a new approach inversion inverse contrast normalization for very simple registration which exploits the inverted contrast relationship between t1 and t2 weighted brain images to define a simple and robust similarity measure we also describe how inversion can be used for rigid alignment of diffusion images and t1 weighted anatomical images our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters compared to other methods inversion shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non rigid distortion correction

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

improved estimates of partial volume coefficients from noisy brain mri using spatial context this paper addresses the problem of accurate voxel level estimation of tissue proportions in the human brain magnetic resonance imaging mri due to the finite resolution of acquisition systems mri voxels can contain contributions from more than a single tissue type the voxel level estimation of this fractional content is known as partial volume coefficient estimation in the present work two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods concretely a novel markov random field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation in addition a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes based on the obtained results the main conclusions are that 1 both markov random field modelling and non local means filtering improved the partial volume coefficient estimation results and 2 non local means filtering was the better of the two strategies for partial volume coefficient estimation

limited memory bfgs systems with diagonal updates abstract in this paper we investigate a formula to solve systems of the form b i x y where b is a limited memory bfgs quasi newton matrix and is a positive constant these types of systems arise naturally in large scale optimization such as trust region methods as well as doubly augmented lagrangian methods we show that provided a simple condition holds on b 0 and the system b i x y can be solved via a recursion formula that requires only vector inner products this formula has complexity m 2 n where m is the number of l bfgs updates and n m is the dimension of x

labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion mri whereas high angular resolution reconstruction methods for diffusion mri can estimate multiple dominant fibre orientations within a single imaging voxel they are fundamentally limited in certain cases of complex subvoxel fibre structures resulting in ambiguous local orientation distribution functions in this article we address the important problem of disambiguating such complex subvoxel fibre tract configurations with the purpose of improving the performance of fibre tractography we do so by extending a curve inference method to distinguish between the cases of curving and fanning fibre bundles using differential geometric estimates in a local neighbourhood the key benefit of this method is the inference of curves instead of only fibre orientations to model the underlying fibre bundles this in turn allows distinct fibre geometries that contain nearly identical sets of fibre orientations at a voxel to be distinguished from one another experimental results demonstrate the ability of the method to successfully label voxels into one of the above categories and improve the performance of a fibre tracking algorithm

using spanning graphs for efficient image registration we provide a detailed analysis of the use of minimal spanning graphs as an alignment method for registering multimodal images this yields an efficient graph theoretic algorithm that for the first time jointly estimates both an alignment measure and a viable descent direction with respect to a parameterized class of spatial transformations we also show how prior information about the interimage modality relationship from prealigned image pairs can be incorporated into the graph based algorithm a comparison of the graph theoretic alignment measure is provided with more traditional measures based on plug in entropy estimators this highlights previously unrecognized similarities between these two registration methods our analysis gives additional insight into the tradeoffs the graph based algorithm is making and how these will manifest themselves in the registration algorithm s performance

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 penalized likelihood approach to image warping discussion a warping is a function that deforms images by mapping between image domains the choice of function is formulated statistically as maximum penalized likelihood where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping the paper addresses two issues simultaneously of how to choose the warping function and how to assess the alignment a new fourier von mises image model is identified with phase differences between fourier transformed images having von mises distributions also new null set distortion criteria are proposed with each criterion uniquely minimized by a particular set of polynomial functions a conjugate gradient algorithm is used to estimate the warping function which is numerically approximated by a piecewise bilinear function the method is motivated by and used to solve three applied problems to register a remotely sensed image with a map to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images

multisensor image registration via implicit similarity this paper presents an approach to the registration of significantly dissimilar images acquired by sensors of different modalities a robust matching criterion is derived by aligning the locations of gradient maxima the alignment is achieved by iteratively maximizing the magnitudes of the intensity gradients of a set of pixels in one of the images where the set is initialized by the gradient maxima locations of the second image no explicit similarity measure that uses the intensities of both images is used the computation utilizes the full spatial information of the first image and the accuracy and robustness of the registration depend only on it false matchings are detected and adaptively weighted using a directional similarity measure by embedding the scheme in a coarse to fine formulation we were able to estimate affine and projective global motions even when the images were characterized by complex space varying intensity transformations the scheme is especially suitable when one of the images is of considerably better quality than the other noise blur etc we demonstrate these properties via experiments on real multisensor image sets

learning to match deriving optimal template matching algorithms from probabilistic image models finding correspondences between images by template matching is a common problem in image understanding although a variety of solutions have been proposed most of them rely on the arbitrary choice of a template and a matching function often different cost functions lead to different results and the choice of a good cost for a specific application remains an art statistical models on the other hand allow us to derive optimal learning and matching algorithms from modeling assumptions using likelihood maximization principles the key contribution of this paper is the development of a statistical framework for learning what function to optimize from training examples we present a family of statistical models for grayscale images which allow us to derive optimal template matching algorithms the intensity at each pixel is described by a random variable whose distribution is encoded by a deformable template firstly we assume the intensity distribution to be gaussian and derive an intensity matching algorithm which is a generalization of the classical sum of squared differences then we introduce a hidden segmentation variable in the probabilistic model and derive a segmentation matching algorithm that can handle photometric variations both models are exemplified on the automatic detection of anatomical landmarks in brain magnetic resonance images

structural properties of context free sets of graphs generated by vertex replacement abstract we establish that a vertex replacement set of graphs i e a set of graphs generated by a c ednce or equivalently by a separated handle rewriting graph grammar is hyperedge replacement i e is generated by a hyperedge replacement graph grammar iff its graphs do not contain arbitrary large complete bipartite graphs kn n as subgraphs another equivalent condition is that its graphs have a number of edges that is linearly bounded in terms of the number of vertices these properties are decidable by means of an appropriate extension of the theorem by parikh that characterizes the commutative images of context free languages we extend these results to hypergraphs

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

intensity based 2 d 3 d registration of cerebral angiograms we propose a new method for aligning three dimensional 3 d magnetic resonance angiography mra with 2 d x ray digital subtraction angiograms dsa our method is developed from our algorithm to register computed tomography volumes to x ray images based on intensity matching of digitally reconstructed radiographs drrs to make the dsa and drr more similar we transform the mra images to images of the vasculature and set to zero the contralateral side of the mra to that imaged with dsa we initialize the search for a match on a user defined circular region of interest we have tested six similarity measures using both unsegmented mra and three segmentation variants of the mra registrations were carried out on images of a physical neuro vascular phantom and images obtained during four neuro vascular interventions the most accurate and robust registrations were obtained using the pattern intensity gradient difference and gradient correlation similarity measures when used in conjunction with the most sophisticated mra segmentations using these measures 95 of the phantom start positions and 82 of the clinical start positions were successfully registered the lowest root mean square reprojection errors were 1 3 mm standard deviation 0 6 for the phantom and 1 5 mm standard deviation 0 9 for the clinical data sets finally we present a novel method for the comparison of similarity measure performance using a technique borrowed from receiver operator characteristic analysis

feature based statistical analysis of structural mr data for automatic detection of focal cortical dysplastic lesions this paper presents a method for fully automated detection and localization of focal cortical dysplastic fcd lesions from anatomical magnetic resonance mr images of the human brain model based tissue classification of the image under study was applied first such that a gray matter gm segmentation map is obtained of which we demonstrate that it also includes possible fcd lesions cortical thickness was estimated at each voxel using an appropriate distance transform applied to the binarized gm object and an fcd specific feature map was constructed by computing the ratio of cortical thickness over absolute image intensity gradient at each voxel in absence of any prior anatomical hypothesis on the spatial location of the lesion a statistical parameter map was constructed by evaluating the evidence for each gray matter voxel against the null hypothesis of no difference in the feature map of the patient versus similar maps obtained for a group of normal controls voxel clusters for which the null hypothesis was found to be improbable at optimally selected thresholds for cluster height and extent were reported as lesions the method was applied to a surgical series of 17 fcd patient images that were compared against a group of 64 neurologically normal controls the method correctly detected and located the fcd lesion in 9 out of 17 fcd cases 53 using a threshold that minimized false positives and 12 of 17 71 using a threshold that allowed more false positive results the detected lesions had a median volume of 7 2 cm3 versus 2 9 cm3 for the non detected lesions the detected lesions more often had an increased cortical thickness on t1 than the non detected lesions p 0 015 fisher s exact test due to a high variance of the feature maps in the temporal lobes and insula detection of fcd lesions in these regions appeared more difficult than in other brain regions with lower variance

the complexity of the kn n problem for node replacement graph languages the bounded kn n problem is the question whether or not a graph language of a given graph grammar contains arbitrarily large complete bipartite subgraphs kn n in this paper we investigate the complexity of this problem for all relevant classes of node replacement graph grammers our main result states that the bounded kn n problem is nl complete for reduced nonblocking ence graph grammars and for reduced linear nce graph grammars as an application our results settle the complexity of the problems whether or not the graph language of a given confluent boundary or linear graph grammar has bounded tree width and whether or not it is an hr graph language

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

the monadic second order logic of graphs xiv uniformly sparse graphs and edge set quantifications we consider the class usk of uniformly k sparse simple graphs i e the class of finite or countable simple graphs every finite subgraph of which has a number of edges bounded by k times the number of vertices we prove that for each k every monadic second order formula intended to express a graph property that uses variables denoting sets of edges can be effectively translated into a monadic second order formula where all set variables denote sets of vertices and that expresses the same property of the graphs in usk this result extends to the class of uniformly k sparse simple hypergraphs of rank at most m for any k and m it follows that every subclass of usk consisting of finite graphs of bounded clique width has bounded tree width clique width is a graph complexity measure similar to tree width and relevant to the construction of polynomial algorithms for np complete problems on special classes of graphs

trees grids and mso decidability from graphs to matroids monadic second order mso logic has proved to be a useful tool in many areas of application reaching flom decidability and complexity to picture processing correctness of programs and parallel processes to characterize the structural borderline between decidability and undecidability is a classical research problem here this problem is related to questions in computational complexity especially to the model checking problem for which many tools developed in the area of decidability have proved to be useful for more than two decades it was conjectured in d seese the structure of the models of decidable monadic theories of graphs ann pure appl logic 53 1991 169 195 that decidability of monadic theories of countable structures implies that the theory can be reduced via interpretability to a theory of trees it is one of the main goals of this article to prove a variant of this conjecture for matroids representable over a finite field matroids can be viewed as a wide generalization of graphs and they seem to capture some second order properties in a more suitable way than graphs themselves cf the recent development in matroid structure theory j f geelen a h m gerards g p whittle branch width and well quasi ordering in matroids and graphs j combin theory ser b 84 2002 270 290 j f geelen a h m gerards n robertson g p whittle excluding a planar graph from a gf q representable matroid manuscript 2003 more exactly we prove for every finite field f that any class of f representable matroids with a decidable mso theory must have uniformly bounded branch width moreover we show that bounding the branch width of all matroids in general is not sufficient to obtain a decidable mso theory our paper gives a rather detailed introduction to these different subjects and shows that a blend of ideas and methods from logic together with structural matroid theory can lead to new tools and algorithms and can shed light on some old open problems

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

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

macro tree translations of linear size increase are mso definable the first main result is that if a macro tree translation is of linear size increase i e if the size of every output tree is linearly bounded by the size of the corresponding input tree then the translation is mso definable i e definable in monadic second order logic this gives a new characterization of the mso definable tree translations in terms of macro tree transducers they are exactly the macro tree translations of linear size increase the second main result is that given a macro tree transducer it can be decided whether or not its translation is mso definable and if it is then an equivalent mso transducer can be constructed similar results hold for attribute grammars which define a subclass of the macro tree translations

rapid elastic image registration for 3 d ultrasound a subvolume based algorithm for elastic ultrasound registration sure was developed and evaluated designed primarily to improve spatial resolution in three dimensional compound imaging the algorithm registers individual image volumes nonlinearly before combination into compound volumes sure works in one or two stages optionally using miami fuse spl copy software first to determine a global affine registration before iteratively dividing the volume into subvolumes and computing local rigid registrations in the second stage connectivity of the entire volume is ensured by global interpolation using thin plate splines after each iteration the performance of sure was quantified in 20 synthetically deformed in vivo ultrasound volumes and in two phantom scans one of which was distorted at acquisition by placing an aberrating layer in the sound path the aberrating layer was designed to induce beam aberrations reported for the female breast synthetic deformations of 1 5 2 5 mm were reduced by over 85 when sure was applied to register the distorted image volumes with the original ones registration times were below 5 min on a 500 mhz cpu for an average data set size of 13mb in the aberrated phantom scans sure reduced the average deformation between the two volumes from 1 01 to 0 30mm this was a statistically significant p 0 01 improvement over rigid and affine registration transformations which produced reductions to 0 59 and 0 50 mm respectively

the monadic second order logic of graphs x linear orderings graphs are finite and handled as relational structures we give some answers to the following general questions 1 1 for which classes of graphs c is it possible to specify a linear ordering of the set of vertices of each graph of c by fixed monadic second order formulas 2 2 for which classes of graphs c does there exist an extension l of monadic second order logic such that a subclass l of c is recognizable if and only if it is the class of graphs in c that satisfy a formula of l in this paper recognizability is understood in an algebraic sense relative to a finite set of graph operations and basic graphs that generate all graphs of c 3 3 for which classes of graphs c is it possible to construct in every graph of the class and by fixed formulas of a suitable extension of monadic second order logic its hierarchichal structure i e a finite term written with the operations and basic graphs of 2 that defines the considered graph applications concern dependency graphs of partially commutative words partial k paths cographs and graphs the modular decomposition of which uses prime graphs of bounded size

image registration by compression abstract image registration consists in finding the transformation that brings one image into the best possible spatial correspondence with another image in this paper we present a new framework for image registration based on compression the basic idea underlying our approach is the conjecture that two images are correctly registered when we can maximally compress one image given the information in the other the contribution of this paper is twofold first we show that image registration can be formulated as a compression problem second we demonstrate the good performance of the similarity metric introduced by li et al in image registration two different approaches for the computation of this similarity metric are described the kolmogorov version computed using standard real world compressors and the shannon version calculated from an estimation of the entropy rate of the images

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

computation of the mid sagittal plane in 3 d brain images we present a new method to automatically compute reorient and recenter the mid sagittal plane in anatomical and functional three dimensional 3 d brain images this iterative approach is composed of two steps at first given an initial guess of the mid sagittal plane generally the central plane of the image grid the computation of local similarity measures between the two sides of the head allows to identify homologous anatomical structures or functional areas by way of a block matching procedure the output is a set of point to point correspondences the centers of homologous blocks subsequently we define the mid sagittal plane as the one best superposing the points on one side and their counterparts on the other side by reflective symmetry practically the computation of the parameters characterizing the plane is performed by a least trimmed squares estimation then the estimated plane is aligned with the center of the image grid and the whole process is iterated until convergence the robust estimation technique we use allows normal or abnormal asymmetrical structures or areas to be treated as outliers and the plane to be mainly computed from the underlying gross symmetry of the brain the algorithm is fast and accurate even for strongly tilted heads and even in presence of high acquisition noise and bias field as shown on a large set of synthetic data the algorithm has also been visually evaluated on a large set of real magnetic resonance mr images we present a few results on isotropic as well as anisotropic anatomical mr and computed tomography and functional single photon emission computed tomography and positron emission tomography real images for normal and pathological subjects

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

qn like variable storage conjugate gradients both conjugate gradient and quasi newton methods are quite successful at minimizing smooth nonlinear functions of several variables and each has its advantages in particular conjugate gradient methods require much less storage to implement than a quasi newton code and therefore find application when storage limitations occur they are however slower so there have recently been attempts to combine cg and qn algorithms so as to obtain an algorithm with good convergence properties and low storage requirements one such method is the code conmin due to shanno and phua it has proven quite successful but it has one limitation it has no middle ground in that it either operates as a quasi newton code using o n 2 storage locations or as a conjugate gradient code using 7n locations but it cannot take advantage of the not unusual situation where more than 7n locations are available but a quasi newton code requires an excessive amount of storage

robust voxel similarity metrics for the registration of dissimilar single and multimodal images in this paper we develop data driven registration algorithms relying on pixel similarity metrics that enable an accurate subpixel rigid registration of dissimilar single or multimodal 2d 3d images gross dissimilarities are handled by considering similarity measures related to robust m estimators in particular a novel robust similarity metric is proposed for comparing multimodal images the proposed robust similarity metrics are compared to the most popular standard similarity metrics on synthetic as well as on real world image pairs showing gross dissimilarities three case studies are considered the registration of single modal and multimodal 3d medical images the matching of multispectral remotely sensed images and the registration of intensity and range images the proposed robust similarity measures compare favourably with the standard non robust techniques

limited memory reduced hessian methods for large scale unconstrained optimization limited memory bfgs quasi newton methods approximate the hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank one matrices these methods are particularly effective for large problems in which the approximate hessian cannot be stored explicitly it can be shown that the conventional bfgs method accumulates approximate curvature in a sequence of expanding subspaces this allows an approximate hessian to be represented using a smaller reduced matrix that increases in dimension at each iteration when the number of variables is large this feature may be used to define limited memory reduced hessian methods in which the dimension of the reduced hessian is limited to save storage limited memory reduced hessian methods have the benefit of requiring half the storage of conventional limited memory methods in this paper we propose a particular reduced hessian method with substantial computational advantages compared to previous reduced hessian methods numerical results from a set of unconstrained problems in the cute test collection indicate that our implementation is competitive with the limited memory codes l bfgs and l bfgs b

reduced storage quasi newton trust region approaches to function optimization in this paper we consider several algorithms for reducing the storage when using a quasi newton method in a dogleg trust region setting for minimizing functions of many variables secant methods require o n2 locations to store an approximate hessian and o n2 operations per iteration when minimizing a function of n variables this storage requirement becomes impractical when n becomes large our algorithms use a bfgs update and require kn storage and 4kn o k2 operations per iteration but they may require more iterations than the standard trust region techniques typically k is between 10 and 100 our dogleg trust region strategies involve expressions with matrix products with both the inverse of this hessian and with the hessian itself our techniques for updating expressions for the hessian and its inverse can be used to improve the performance of line search limited memory algorithms

the bounded degree problem for ence graph grammars the complexity of the bounded degree problem is analyzed for graph languages generated by ence graph grammars in particular the bounded degree problem is shown to be undecidable for ence graph grammars dexptime complete for confluent boundary ence graph grammars pspace complete for linear ence graph grammars and p complete for non blocking ence graph grammars in our main theorem we show that the bounded degree problem is nl complete for reduced non blocking ence graph grammars many of the shown results carry over to other types of graph grammars

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 limited memory quasi newton trust region method for box constrained optimization by means of wolfe conditions strategy we propose a quasi newton trust region method to solve box constrained optimization problems this method is an adequate combination of the compact limited memory bfgs and the trust region direction while the generated point satisfies the wolfe conditions and therefore maintains a positive definite approximation to the hessian of the objective function the global convergence and the quadratic convergence of this method are established under suitable conditions finally we compare our algorithms iwtral and ibwtral with an active set trust region algorithm astral xu and burke 2007 on the cutest box constrained test problems presented by gould et al 2015 numerical results show that the presented method is competitive and totally interesting for solving box constrained optimization

further analysis of interpolation effects in mutual information based image registration this paper presents an analysis of the mutual information mi metric in rigid body registration of two digital images in particular local fluctuations of the mi value due to interpolation in contrast to existing work in this area this paper starts with two hypothetical continuous images based on which both sampling and interpolation effects are analyzed this analysis indicates that an ideal interpolator may not be able to completely suppress the undesirable local minima of the mi metric if the sampling effect is not negligible several preprocessing methods are discussed for reducing the interpolation effects

mutual information aspects of scale space images in image registration mutual information is a well performing measure based on principles of uncertainty similarly in image analysis the gaussian scale space based on minimal assumptions of the image is used to derive intrinsic properties of an image this paper starts an investigation of a combination of both methods this combination results in a double parameterized mutual information measure using local information of the image for single modality matching best response is found for coinciding parameters then critical values are found for which the parameterized mutual information has extrema first results on multi modality matching show that different parameter values instead of coinciding values yield the best response for the parameterized mutual information

three dimensional nonrigid mr trus registration using dual optimization in this study we proposed an efficient nonrigid magnetic resonance mr to transrectal ultrasound trus deformable registration method in order to improve the accuracy of targeting suspicious regions during a three dimensional 3 d trus guided prostate biopsy the proposed deformable registration approach employs the multi channel modality independent neighborhood descriptor mind as the local similarity feature across the two modalities of mr and trus and a novel and efficient duality based convex optimization based algorithmic scheme was introduced to extract the deformations and align the two mind descriptors the registration accuracy was evaluated using 20 patient images by calculating the tre using manually identified corresponding intrinsic fiducials in the whole gland and peripheral zone additional performance metrics dice similarity coefficient dsc mean absolute surface distance mad and maximum absolute surface distance maxd were also calculated by comparing the mr and trus manually segmented prostate surfaces in the registered images experimental results showed that the proposed method yielded an overall median tre of 1 76 mm the results obtained in terms of dsc showed an average of 80 8 pm7 8 hbox for the apex of the prostate 92 0 pm3 4 hbox for the mid gland 81 7 pm6 4 hbox for the base and 85 7 pm4 7 hbox for the whole gland the surface distance calculations showed an overall average of 1 84 pm0 52 mm for mad and 6 90 pm2 07 mm for maxd

anomalous local coordination density fluctuations and void statistics in disordered hyperuniform many particle ground states we provide numerical constructions of one dimensional hyperuniform many particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but faster than the surface area hyperuniformity defined by vanishing infinite wavelength local density fluctuations provides a quantitative metric of global order within a many particle configuration and signals the onset of an inverted critical point in which the direct correlation function becomes long ranged by targeting a specified form of the structure factor at small wavenumbers s k k for 0 1 using collective density variables we are able to tailor the form of asymptotic local density fluctuations while simultaneously measuring the effect of imposing weak and strong constraints on the available degrees of freedom within the system this procedure is equivalent to finding the possibly disordered classical ground state of an interacting many particle system with up to four body interactions even in one dimension the long range effective interactions induce clustering and nontrivial phase transitions in the resulting ground state configurations we provide an analytical connection between the fraction of constrained degrees of freedom within the system and the disorder order phase transition for a class of target structure factors by examining the realizability of the constrained contribution to the pair correlation function our results explicitly demonstrate that disordered hyperuniform many particle ground states and therefore also point distributions with substantial clustering can be constructed we directly relate the local coordination structure of our point patterns to the distribution of the void space external to the particles and we provide a scaling argument for the configurational entropy analogous to spin frustated system of the disordered ground states by emphasizing the intimate connection between geometrical constraints on the particle distribution and structural regularity our work has direct implications for higher dimensional systems including an understanding of the appearance of hyperuniformity and quasi long range pair correlations in maximally random strictly jammed packings of hard spheres

volume image registration by cross entropy optimization cross entropy ce an information theoretic measure quantifies the difference between two probability density functions this measure is applied to volume image registration when a good prior estimation of the joint distribution of the voxel values of two images in registration is available the ce can be minimized to find an optimal registration if such a prior estimation is not available one seeks the registration which gives a joint distribution different from unlikely ones as much as possible i e the ce is maximized to find an optimal registration when the unlikely distribution is a uniform one ce maximization reduces to joint entropy minimization when the unlikely distribution is proportional to one of the marginal distributions it reduces to conditional entropy minimization when the unlikely distribution is the product of two marginal distributions it degenerates to mutual information maximization these different ces are added together and are used as criteria for image registration the accuracy and robustness of this new approach are tested and compared using a likely joint distribution and various unlikely joint distributions and their combinations

image registration using the walsh transform this paper presents a new algorithm which can be used to register images of the same or different modalities e g images with multiple channels such as x rays temperature or elevation or simply images of different spectral bands in particular a correlation based scheme is used but instead of gray values it correlates numbers formulated by different combinations of the extracted local walsh coefficients of the images each image patch is expanded in terms of walsh basis functions each walsh basis function can be thought of as measuring a different aspect of local structure e g horizontal edge corner etc the coefficients of the expansion therefore can be thought of as dense local features estimating at each point the degree of presence of for example a horizontal edge a corner with contrast of a certain type etc these coefficients are normalized and used as digits in a chosen number system which allows one to create a unique number for each type of local structure the choice of the basis of the number system allows one to give different emphasis to different types of local feature e g corners versus edges and thus the method we present forms a unified framework in terms of which several feature matching methods may be interpreted the algorithm is compared with wavelet and contour based approaches using simulated and real images the two images are assumed to differ from each other by a rotation and a translation only

probabilistic segmentation of brain tissue in mr imaging a new method has been developed for probabilistic segmentation of five different types of brain structures white matter gray matter cerebro spinal fluid without ventricles ventricles and white matter lesion in cranial mr imaging the algorithm is based on information from t1 weighted t1 w inversion recovery ir proton density weighted pd t2 weighted t2 w and fluid attenuation inversion recovery flair scans it uses the k nearest neighbor classification technique that builds a feature space from spatial information and voxel intensities the technique generates for each tissue type an image representing the probability per voxel being part of it by application of thresholds on these probability maps binary segmentations can be obtained a similarity index si and a probabilistic si psi were calculated for quantitative evaluation of the results the influence of each image type on the performance was investigated by alternately leaving out one of the five scan types this procedure showed that the incorporation of the t1 w pd or t2 w did not significantly improve the segmentation results further investigation indicated that the combination of ir and flair was optimal for segmentation of the five brain tissue types evaluation with respect to the gold standard showed that the si values for all tissues exceeded 0 8 and all psi values exceeded 0 7 implying an excellent agreement

computation of image spatial entropy using quadrilateral markov random field shannon entropy is a powerful tool in image analysis but its reliable computation from image data faces an inherent dimensionality problem that calls for a low dimensional and closed form model for the pixel value distributions the most promising such models are markovian however the conventional markov random field is hampered by noncausality and its causal versions are also not free of difficulties for example the markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system a new model named quadrilateral markov random field qmrf is introduced in this paper in order to overcome these limitations a property of qmrf with neighboring size of 2 is then used to decompose an image prior into a product of 2 d joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption in addition the paper includes an extension of the introduced method to the computation of image spatial mutual information comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones

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

robust gradient based 3 d 2 d registration of ct and mr to x ray images one of the most important technical challenges in image guided intervention is to obtain a precise transformation between the intrainterventional patient s anatomy and corresponding preinterventional 3 d image on which the intervention was planned this goal can be achieved by acquiring intrainterventional 2 d images and matching them to the preinterventional 3 d image via 3 d 2 d image registration a novel 3 d 2 d registration method is proposed in this paper the method is based on robustly matching 3 d preinterventional image gradients and coarsely reconstructed 3 d gradients from the intrainterventional 2 d images to improve the robustness of finding the correspondences between the two sets of gradients hypothetical correspondences are searched for along normals to anatomical structures in 3 d images while the final correspondences are established in an iterative process combining the robust random sample consensus algorithm ransac and a special gradient matching criterion function the proposed method was evaluated using the publicly available standardized evaluation methodology for 3 d 2 d registration consisting of 3 d rotational x ray computed tomography magnetic resonance mr and 2 d x ray images of two spine segments and standardized evaluation criteria in this way the proposed method could be objectively compared to the intensity gradient and reconstruction based registration methods the obtained results indicate that the proposed method performs favorably both in terms of registration accuracy and robustness the method is especially superior when just a few x ray images and when mr preinterventional images are used for registration which are important advantages for many clinical applications

a model based on local graphs for colour images and its application for gaussian noise smoothing in this paper a new model for processing colour images is presented a graph is built for each image pixel taking into account some constraints on links each pixel is characterized depending on the features of its related graph which allows to process it appropriately as an example we provide a characterization of each pixel based on the link cardinality of its connected component this feature enables us to properly distinguish flat image regions respect to edge and detail regions according to this we have designed a hybrid filter for colour image smoothing it combines a filter able to properly process flat image regions with another one that is more appropriate for details and texture experimental results show that our model performs appropriately we also see that our proposed filter is competitive with respect to state of the art methods it is close closer to the corresponding optimal switching filter respect to other analogous hybrid method

probabilistic segmentation of white matter lesions in mr imaging a new method has been developed for fully automated segmentation of white matter lesions wmls in cranial mr imaging the algorithm uses information from t1 weighted t1 w inversion recovery ir proton density weighted pd t2 weighted t2 w and fluid attenuation inversion recovery flair scans it is based on the k nearest neighbor knn classification technique that builds a feature space from voxel intensities and spatial information the technique generates images representing the probability per voxel being part of a wml by application of thresholds on these probability maps binary segmentations can be obtained roc curves show that the segmentations achieve both high sensitivity and specificity a similarity index si overlap fraction of and extra fraction ef are calculated for additional quantitative analysis of the result the si is also used for determination of the optimal probability threshold for generation of the binary segmentation using probabilistic equivalents of the si of and ef the probability maps can be evaluated directly providing a powerful tool for comparison of different classification results this method for automated wml segmentation reaches an accuracy that is comparable to methods for multiple sclerosis ms lesion segmentation and is suitable for detection of wmls in large and longitudinal population studies

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

rism single modal image registration via rank induced similarity measure similarity measure is an important block in image registration most traditional intensity based similarity measures e g sum of squared difference correlation coefficient and mutual information assume a stationary image and pixel by pixel independence these similarity measures ignore the correlation between pixel intensities hence perfect image registration cannot be achieved especially in the presence of spatially varying intensity distortions here we assume that spatially varying intensity distortion such as bias field is a low rank matrix based on this assumption we formulate the image registration problem as a nonlinear and low rank matrix decomposition nllrmd therefore image registration and correction of spatially varying intensity distortion are simultaneously achieved we illustrate the uniqueness of nllrmd and therefore we propose the rank of difference image as a robust similarity in the presence of spatially varying intensity distortion finally by incorporating the gaussian noise we introduce rank induced similarity measure based on the singular values of the difference image this measure produces clinically acceptable registration results on both simulated and real world problems examined in this paper and outperforms other state of the art measures such as the residual complexity approach

a new divergence measure for medical image registration a new type of divergence measure for the registration of medical images is introduced that exploits the properties of the modified bessel functions of the second kind the properties of the proposed divergence coefficient are analysed and compared with those of the classic measures including kullback leibler renyi and ialpha divergences to ensure its effectiveness and widespread applicability to any arbitrary set of data types the performance of the new measure is analysed for gaussian exponential and other advanced probability density functions the results verify its robustness finally the new divergence measure is used in the registration of ct to mr medical images to validate the improvement in registration accuracy

automatic registration of ct and mr brain images using correlation of geometrical features describes an automated approach to register ct and mr brain images differential operators in scale space are applied to each type of image data so as to produce feature images depicting ridgeness the resulting ct and mr feature images show similarities which can be used for matching no segmentation is needed and the method is devoid of human interaction the matching is accomplished by hierarchical correlation techniques results of 2 d and 3 d matching experiments are presented the correlation function ensures an accurate match even if the scanned volumes to be matched do not completely overlap or if some of the features in the images are not similar

magnetic resonance image tissue classification using a partial volume model abstract we describe a sequence of low level operations to isolate and classify brain tissue within t1 weighted magnetic resonance images mri our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering edge detection and mathematical morphology we compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic b spline gain field to local estimates of the image nonuniformity spaced throughout the mri volume the local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point the measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit voxels in the intensity normalized image are then classified into six tissue types using a maximum a posteriori classifier this classifier combines the partial volume tissue measurement model with a gibbs prior that models the spatial properties of the brain we validate each stage of our algorithm on real and phantom data using data from the 20 normal mri brain data sets of the internet brain segmentation repository our method achieved average indices of 0 746 0 114 for gray matter gm and 0 798 0 089 for white matter wm compared to expert labeled data our method achieved average indices 0 893 0 041 for gm and 0 928 0 039 for wm compared to the ground truth labeling on 12 volumes from the montreal neurological institute s brainweb phantom

image comparison by compound disjoint information with applications to perceptual visual quality assessment image registration and tracking in this paper we study normalized disjoint information as a metric for image comparison and its applications to perceptual image quality assessment image registration and video tracking disjoint information is the joint entropy of random variables excluding the mutual information this measure of statistical dependence and information redundancy satisfies more rigorous metric conditions than mutual information including self similarity minimality symmetry and triangle inequality it is applicable to two or more random variables and can be computed by vector histogramming vector parzen window density approximation and upper bound approximation involving fewer variables we show such a theoretic advantage does have implications in practice in the domain of digital image and video multiple visual features are extracted and normalized compound disjoint information is derived from a set of marginal densities of the image distributions thus enriching the vocabulary of content representation the proposed metric matching functions are applied to several domain applications to demonstrate their efficacy