nonrigid registration of 2 d and 3 d dynamic cell nuclei images for improved classification of subcellular particle motion the observed motion of subcellular particles in fluorescence microscopy image sequences of live cells is generally a superposition of the motion and deformation of the cell and the motion of the particles decoupling the two types of movements to enable accurate classification of the particle motion requires the application of registration algorithms we have developed an intensity based approach for nonrigid registration of multichannel microscopy image sequences of cell nuclei first based on 3 d synthetic images we demonstrate that cell nucleus deformations change the observed motion types of particles and that our approach allows to recover the original motion second we have successfully applied our approach to register 2 d and 3 d real microscopy image sequences a quantitative experimental comparison with previous approaches for nonrigid registration of cell microscopy has also been performed

particularities of newton s method in space frame force determination utilising eigenpair functions abstract redundant space frame dynamics are modelled through the structural eigenproblem which is formulated to account for the geometric stiffness due to self equilibrating membrane forces the resulting mathematical eigenvalues and eigenvectors respectively indicative of natural frequencies and modes of oscillation are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium newton s method or sensitivity analysis provides a means for minimising the difference between mathematical and physically observed eigenvalues whereupon the axial forces are inferred from the model issues of convergence and root uniqueness are anticipated eigenvalue coalescence in which eigenvalues transitorily coalesce to permute their arbitrarily numerical ordering is seen to define non smooth eigenvalue functions and hence encumber newton s method mode tracing strategies to overcome this are discussed the existence of various degrees of eigenvalue degeneracy owing to frame cyclic symmetry or otherwise is anticipated in terms of the influence upon newton s method if the degree of frame static redundancy is greater than one and there exist a number of linearly independent force distributions then the required force determination is a multidimensional newton method problems encountered in these manifold dimensions including those arising from frame spatial periodicity and the adversity of newton s method are overcome emphasis is placed upon minimising the dimensionality of newton s method through enforcement of equilibrium constraints illustrative numerical simulations are given and some applications of the method are proposed

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

some experiments in relaxation image matching using corner features abstract a relaxation method based on patterns of local features is used to find matches between pairs of images or subimages that differ in position or orientation a local operator is applied to the two images to detect two sets of corners c1 cm and d1 dn each of them characterized by position orientation contrast and sharpness of the angle for each pair ci dj a figure of merit is computed and a relaxation process is used to iteratively adjust these figures of merit based on the merits of other pairs in approximately corresponding positions after a few iterations of this process good matches pairs having much better merit than their next best choices are clustered yielding sets of transformation parameters shift vectors or rotation angles under which many corners correspond this method has yielded good results for tv images of objects such as tools and industrial parts as well as for aerial images of terrain

mom volume integral equation solution for an isolated metal dielectric resonator with the edge based basis functions the objective of the present study is to show that the method of volume integral used in conjunction with the zeroth order edge based basis functions de carvalho and de souza mendes 1999 gives an accurate and stable solution for a metal dielectric resonator when the number of the basis functions remains relatively small special attention is paid to the resonator in the form of a thin dielectric layer backed by two metal sheets the metal surface is described in terms of the rao wilton glisson rwg basis functions

on the determination of resonant modes of dielectric objects using surface integral equations although surface integral equations have been extensively used for solving the scattering problem of arbitrarily shaped dielectric objects when applied to the resonance problem there are still some issues not fully addressed by the literature in this paper the method of moments with rao wilton glisson basis functions is applied to the electric field integral equation efie for solving the resonance problem of dielectric objects the resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane and the modal field distribution is obtained through singular value decomposition svd the determinant of the impedance matrix is not used since it is difficult to find its roots for the exterior efie the original basis functions are used as testing functions for the interior efie the basis functions rotated by 90 spl deg are used as testing functions to obtain an accurate modal field solution the impedance matrix needs to be reduced by half before svd is applied to it numerical results are given and compared with those obtained by using the volume integral equation

fuzzy cognitive maps for stereovision matching this paper outlines a method for solving the stereovision matching problem using edge segments as the primitives in stereovision matching the following constraints are commonly used epipolar similarity smoothness ordering and uniqueness we propose a new matching strategy under a fuzzy context in which such constraints are mapped the fuzzy context integrates both fuzzy clustering and fuzzy cognitive maps with such purpose a network of concepts nodes is designed each concept represents a pair of primitives to be matched each concept has associated a fuzzy value which determines the degree of the correspondence the goal is to achieve high performance in terms of correct matches the main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped initially each concept value is loaded via the fuzzy clustering and then updated by the fuzzy cognitive maps framework this updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved under this fuzzy approach we gain quantitative and qualitative matching correspondences this method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods

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

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

efficient simulation of rectangular dielectric resonators using volume mpie mom formulation with combined entire domain and subdomain basis functions an efficient method of moments mom formulation using combined entire domain and subdomain basis functions is proposed for simulating the resonant modes of a rectangular dielectric resonator in free space an approximate analytical solution for the resonant mode of the dr is used as the entire domain basis function while a set of tetrahedral basis functions are used as subdomain basis functions since the main profile of the resonant mode can be well represented by the entire domain basis function only small number of subdomain basis functions are needed for further refinement of the representation compared with the mom formulations using only subdomain or entire domain basis functions this method is much faster for the same accuracy numerical results are given and compared with other methods

method of moments solution for a printed patch slot antenna on a thin finite dielectric substrate using the volume integral equation in this paper a volume integral equation vie based modeling method suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and tested two new key features of the method are the use of proper dielectric basis functions and proper vie conditioning close to the metal surface where the surface boundary condition of the zero tangential e component must be extended into adjacent tetrahedra the extended boundary condition is the exact result for the piecewise constant dielectric basis functions the latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost the use of low order basis functions also implies the use of low order integration schemes and faster filling of the impedance matrix for some common patch slot antennas the vie based modeling approach is found to give an error of about 1 or less in the resonant frequency for one layer tetrahedral meshes with a relatively small number of unknowns this error is obtained by comparison with fine finite element method fem simulations or with measurements or with the analytical mode matching approach hence it is competitive with both the method of moments surface integral equation approach and with the fem approach for the printed antennas on thin dielectric substrates

fast point based 3 d alignment of live cells typical time intervals between acquisitions of three dimensional 3 d images of the same cell in live cell imaging are in the orders of minutes in the meantime the live cell can move in a water basin on the stage this movement can hamper the studies of intranuclear processes we propose a fast point based image registration method for the suppression of the movement of a cell as a whole in the image data first centroids of certain intracellular objects are computed for each image in a time lapse series then a matching between the centroids which have the maximal number of pairs is sought between consecutive point sets by a 3 d extension of a two dimensional fast point pattern matching method which is invariant to rotation translation local distortion and extra missing points the proposed 3 d extension assumes rotations only around the z axis to retain the complexity of the original method the final step involves computing the optimal fully 3 d transformation between images from corresponding points in the least squares manner the robustness of the method was evaluated on generated data the results of the simulations show that the method is very precise and its correctness can be estimated this article also presents two practical application examples namely the registration of images of hp1 domains and the registration of images of telomeres more than 97 of time consecutive images were successfully registered the results show that the method is very well suited to live cell imaging

segmentation and shape tracking of whole fluorescent cells based on the chan vese model we present a fast and robust approach to tracking the evolving shape of whole fluorescent cells in time lapse series the proposed tracking scheme involves two steps first coherence enhancing diffusion filtering is applied on each frame to reduce the amount of noise and enhance flow like structures second the cell boundaries are detected by minimizing the chan vese model in the fast level set like and graph cut frameworks to allow simultaneous tracking of multiple cells over time both frameworks have been integrated with a topological prior exploiting the object indication function the potential of the proposed tracking scheme and the advantages and disadvantages of both frameworks are demonstrated on 2 d and 3 d time lapse series of rat adipose derived mesenchymal stem cells and human lung squamous cell carcinoma cells respectively

diffeomorphic multi frame non rigid registration of cell nuclei in 2d and 3d live cell images to gain a better understanding of cellular and molecular processes it is important to quantitatively analyze the motion of subcellular particles in live cell microscopy image sequences since generally the subcellular particles move and cell nuclei move as well as deform it is important to decouple the movement of particles from that of the cell nuclei using non rigid registration methods we have developed a diffeomorphic multi frame approach for non rigid registration of cell nuclei in 2d and 3d live cell fluorescence microscopy images our non rigid registration approach is based on local optic flow estimation exploits information from multiple consecutive image frames and determines diffeomorphic transformations in the log domain which allows efficient computation of the inverse transformations to register single images of an image sequence to a reference image we use a temporally weighted mean image which is constructed based on inverse transformations and multiple consecutive frames using multiple consecutive frames improves the registration accuracy compared to pairwise registration and using a temporally weighted mean image significantly reduces the computation time compared with previous work in addition we use a flow boundary preserving method for regularization of computed deformation vector fields which prevents from over smoothing compared to standard gaussian filtering our approach has been successfully applied to 2d and 3d synthetic as well as real live cell microscopy image sequences and an experimental comparison with non rigid pairwise multi frame and temporal groupwise registration has been carried out

fast algorithm for point pattern matching invariant to translations rotations and scale changes abstract based on 2 d cluster approach a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters scaling s and rotation on a two parameter space s experiments are conducted both on real and synthetic data the experimental results show that the proposed matching algorithm can handle translation rotation and scaling differences under noisy or distorted condition the computational time is just about 0 5 s for 50 to 50 point matching on sun 4 workstation

apparently first closed form solutions for inhomogeneous vibrating beams under axial loading closed form solutions are presented for fundamental natural frequencies of inhomogeneous vibrating beams under axially distributed loading the mode shape is postulated as coinciding with the static deflection of the associated homogeneous beam without distributed axial loading then the inverse problem of determining the stiffness and mass density distributions producing the above mode shape is solved to describe these variations the family of polynomial functions is used several sets of boundary conditions are considered it is shown that the natural frequency vanishes when the intensity of the axially distributed loading equals the critical buckling value a linear relationship is established between the square of the natural frequency and the load ratio for all reported sets of boundary conditions in contrast to uniform beams where the exact linear relationship holds for columns with simply supported and or sliding ends

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

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

separation of horizontal and vertical dependencies in a surface volume integral equation approach to model quasi 3 d structures in multilayered media a new and efficient integral equation approach is presented to model heterogeneous dielectric volumes in a multilayered environment the dielectric volumes can be vertically large they can cross dielectric interfaces and they should be quasi 3 d which means that the contour faces should be placed either horizontally or vertically in the multilayered environment in this way a perpendicular prismatic mesh can be fitted on the volumes and the 3 d displacement currents can be expanded in generalized rooftop functions with separated horizontal x y and vertical z dependencies this makes it possible to evaluate all z z reaction integrals fully analytically in the spectral domain and ensures an efficient implementation the formulation of the source field relations is adapted to the quasi 3 d geometries as a hybrid dyadic mixed potential form additionally the electromagnetic coupling between dielectric volumes and metal sheets is included using a coupled volume surface formulation this turns the implementation into a complete full wave solver for planar antennas containing both finite and infinite dielectric regions in order to illustrate and validate the presented approach two patch antennas with a local volumetric inhomogeneity under the patch are numerically analyzed in a multilayered environment eventually a matrix fill time comparison is used to demonstrate the improvement in computation efficiency

a markov random field model based approach to image interpretation an image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph and image interpretation is achieved through assigning object labels or interpretations to the segmented regions or nodes using domain knowledge extracted feature measurements and spatial relationships between the various regions the interpretation labels are modeled as a markov random field mrf on the corresponding adjacency graph and the image interpretation problem is then formulated as a maximum a posteriori map estimation rule given domain knowledge and region based measurements simulated annealing is used to find this best realization or optimal map interpretation this approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the gibbs distribution representing the pdf of the underlying mrf a general methodology is provided for the design of the clique functions results of image interpretation experiments on synthetic and real world images are described

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

improving consistency and reducing ambiguity in stochastic labeling an optimization approach we approach the problem of labeling a set of objects from a quantitative standpoint we define a world model in terms of transition probabilities and propose a definition of a class of global criteria that combine both ambiguity and consistency a projected gradient algorithm is developed to minimize the criterion we show that the minimization procedure can be implemented in a highly parallel manner results are shown on several examples and comparisons are made with relaxation labeling techniques

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

nonrigid registration of 3 d multichannel microscopy images of cell nuclei we present an intensity based nonrigid registration approach for the normalization of 3 d multichannel microscopy images of cell nuclei a main problem with cell nuclei images is that the intensity structure of different nuclei differs very much thus an intensity based registration scheme cannot be used directly instead we first perform a segmentation of the images from the cell nucleus channel smooth the resulting images by a gaussian filter and then apply an intensity based registration algorithm the obtained transformation is applied to the images from the nucleus channel as well as to the images from the other channels to improve the convergence rate of the algorithm we propose an adaptive step length optimization scheme and also employ a multiresolution scheme our approach has been successfully applied using 2 d cell like synthetic images 3 d phantom images as well as 3 d multichannel microscopy images representing different chromosome territories and gene regions we also describe an extension of our approach which is applied for the registration of 4 d image series of moving cell nuclei

comparison of two sets of low order basis functions for tetrahedral vie modeling a convergence study is made for the two types of low order basis functions for the volume integral equation vie both functions impose the continuity of the normal component of the electric flux through the faces the one basis function is that of schaubert wilton and glisson 1984 and is face based another basis function was first introduced by de carvalho and de souza mendes 1999 and is edge based the exact number of unknowns for the edge based functions is determined in this study the study demonstrates a better performance of the edge based basis functions compared to the face based bases first the edge based basis functions have nearly the same or a faster convergence rate for equal tetrahedral meshes they also show a high numerical stability second for the same tetrahedral mesh the number of unknowns for the edge based functions is considerably smaller the ratio of unknowns edge based versus face based ranges from 0 6 for rough plate meshes to approximately 0 5 for large volumetric meshes third the edge based functions are piecewise constant and are easily implemented into the method of moments their disadvantage is a preliminary condition operation which implies the elimination of the nullspace of the basis set

natural frequencies of beams under tensile axial loads abstract the effect of a constant axial tensile force on natural frequencies and mode shapes of a uniform single span beam with different combinations of end conditions is presented numerical observations indicate that the variation of normalized natural frequency parameter with normalized tension parameter is almost the same for clamped pinned and pinned free and similarly for clamped clamped and clamped sliding beams the variation of the sliding free beam is only slightly different from that of the latter pair and the free free beam for pinned pinned pinned sliding and sliding sliding beams this variation may exactly be expressed as 1 u this formula may be used for beams with other types of end constraints when the beam vibrates in a third mode or higher it also gives the upper bound approximation to the fundamental natural frequency of a pinned free beam for beams with other types of boundary conditions this approximation may be expressed as 1 u where the coefficient depends only on the type of the end constraints it is found that when the dimensionless tension parameter u is greater than about 12 then u can be expressed as an analytical function of u where is the dimensionless natural frequency parameter for such a beam in the first few modes the natural frequency is independent of the flexural rigidity and the beam behaves like a string the string solution gives a lower bound approximation to the natural frequency

non rigid contour based registration of cell nuclei in 2 d live cell microscopy images using a dynamic elasticity model the analysis of the pure motion of subnuclear structures without influence of the cell nucleus motion and deformation is essential in live cell imaging in this paper we propose a 2 d contour based image registration approach for compensation of nucleus motion and deformation in fluorescence microscopy time lapse sequences the proposed approach extends our previous approach which uses a static elasticity model to register cell images compared with that scheme the new approach employs a dynamic elasticity model for the forward simulation of nucleus motion and deformation based on the motion of its contours the contour matching process is embedded as a constraint into the system of equations describing the elastic behavior of the nucleus this results in better performance in terms of the registration accuracy our approach was successfully applied to real live cell microscopy image sequences of different types of cells including image data that was specifically designed and acquired for evaluation of cell image registration methods an experimental comparison with the existing contour based registration methods and an intensity based registration method has been performed we also studied the dependence of the results on the choice of method parameters