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

shape elongation from optimal encasing rectangles let s be a shape with a polygonal boundary we show that the boundary of the maximally elongated rectangle r s which encases the shape s contains at least one edge of the convex hull of s such a nice property enables a computationally efficient construction of r s in addition we define the elongation of a given shape s as the ratio of the length of r s determined by the longer edge of r s and the width of r s determined by the shorter edge of r s and show that a so defined shape elongation measure has several desirable properties several examples are given in order to illustrate the behavior of the new elongation measure as a by product of the method developed here we obtain a new method for the computation of the shape orientation where the orientation of a given shape s is defined by the direction of the longer edge of r s

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

arbitrary l state solutions of the rotating morse potential by the asymptotic iteration method for non zerovalues we present an analytical solution of the radial schr odinger equation for the rotating morse potential using the pekeris approximation within the framework of the asymptotic iteration method the bound state energy eigenvalues and corresponding wavefunctions are obtained for a number of diatomic molecules and the results are compared with the findings of the super symmetry the hypervirial perturbation the nikiforov uvarov the variational the shifted 1 n and the modified shifted 1 n expansion methods

deformed shape invariance and exactly solvable hamiltonians with position dependent effective mass known shape invariant potentials for the constant mass schrodinger equation are taken as effective potentials in a position dependent effective mass pdem one the corresponding shape invariance condition turns out to be deformed its solvability imposes the form of both the deformed superpotential and the pdem a lot of new exactly solvable potentials associated with a pdem background are generated in this way a novel and important condition restricting the existence of bound states whenever the pdem vanishes at an end point of the interval is identified in some cases the bound state spectrum results from a smooth deformation of that of the conventional shape invariant potential used in the construction in others one observes a generation or suppression of bound states depending on the mass parameter values the corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials

the klein gordon equation of generalized hulthen potential in complex quantum mechanics we have investigated the reality of exact bound states of complex and or pt symmetric non hermitian exponential type generalized hulthen potential the klein gordon equation has been solved by using the nikiforov uvarov method which is based on solving the second order linear differential equations by reduction to a generalized equation of hypergeometric type in many cases of interest negative and positive energy states have been discussed for different types of complex potentials

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

scattering and bound state green s functions on a plane via so 2 1 lie algebra we calculate the green s functions for the particle vortex system for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field these green s functions which describe scattering or bound states depending on the specific potential in each case are obtained exactly using an algebraic method related to the so 2 1 lie group from these green s functions we obtain the corresponding wave functions and for the bound states we also find the energy spectra

linearity measure for curve segments in this paper we consider linearity measure for a bounded length curves first we define a new linearity measure for open curve segments and then extend method to closed curves contours the derived measures for both open curve segments and closed curves are invariant with respect to similarity transformations the linearity measure for open curve segments picks the value 1 if and only if the measured open line segment is a perfect straight line segment while the established linearity measures for closed curves never reach 1 as preferred

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

artificial fractal dimension obtained by using perimeter area relationship on digitalized images perimeter area relation is a widely used method to obtain the perimeter fractal dimension of self similar shapes embedded into a 2 dimensional space in this short paper we would like to demonstrate that the orientation anisotropy of the shapes which cannot be excluded in a natural sample can cause an error in the calculation of the perimeters and areas of the digitalized images in this way one might obtain artificial fractal dimension therefore the applicability of the perimeter area method seems to be very limited mited

solutions of the spatially dependent mass dirac equation with the spin and pseudospin symmetry for the coulomb like potential we study the effect of spatially dependent mass function over the solution of the dirac equation with the coulomb potential in the 3 1 dimensions for any arbitrary spin orbit k state in the framework of the spin and pseudospin symmetry concept the analytic bound state energy eigenvalues and the corresponding upper and lower two component spinors of the two dirac particles are obtained by means of the nikiforov uvarov method in closed form this physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the dirac equation the special cases k 1 l l 0 i e s wave the constant mass and the non relativistic limits are briefly investigated

spin and pseudospin symmetry along with orbital dependency of the dirac hulthen problem abstract the role of the hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the dirac equation with attractive scalar s r and repulsive vector v r potentials the spin and pseudospin symmetry along with orbital dependency pseudospin orbit and spin orbit dependent couplings of the dirac equation are included to the solution by introducing the hulthen square approximation this effective approach is based on forming the spin and pseudo centrifugal kinetic energy term from the square of the hulthen potential the analytical solutions of the dirac equation for the hulthen potential with the spin orbit and pseudospin orbit dependent couplings are obtained by using the nikiforov uvarov nu method the energy eigenvalue equations and wave functions for various degenerate states are presented for several spin orbital pseudospin orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry

asymptotic iteration method solutions to the relativistic duffin kemmer petiau equation a simple exact analytical solution of the relativistic duffin kemmer petiau equation within the framework of the asymptotic iteration method is presented exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the coulomb potentials as a nontrivial example the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method

the remarkable properties of the associated romanovski functions for and with n m q 0 a non negative integer we introduce a differential equation for the associated romanovski functions r q n m x so that its form remains invariant under the transformation n 2q n 1 introducing the rodrigues formula for both regions and we obtain simultaneously and separately realization of the laddering equations with respect to the labels n and m by means of two pairs of ladder operators also the square integrability and orthogonality of the functions are considered in cases 0 and 0 with respect to the weight functions and 1 x2 1 q respectively exponential generating functions for the infinite sequences with the same n in both regions and as well as for the infinite ones with given even and odd values of n m q are separately calculated as an application to supersymmetric quantum mechanics we show that there exist four different methods for generating the spectrum of the noncentral hyperbolic scarf potential

partial volume bayesian classification of material mixtures in mr volume data using voxel histograms the authors present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with magnetic resonance imaging mri or computed tomography ct because the authors allow for mixtures of materials and treat voxels as regions their technique reduces errors that other classification techniques can create along boundaries between materials and is particularly useful for creating accurate geometric models and renderings from volume data it also has the potential to make volume measurements more accurately and classifies noisy low resolution data well there are two unusual aspects to the authors approach first they assume that due to partial volume effects or blurring voxels can contain more than one material e g both muscle and fat the authors compute the relative proportion of each material in the voxels second they incorporate information from neighboring voxels into the classification process by reconstructing a continuous function spl rho x from the samples and then looking at the distribution of values that spl rho x takes on within the region of a voxel this distribution of values is represented by a histogram taken over the region of the voxel the mixture of materials that those values measure is identified within the voxel using a probabilistic bayesian approach that matches the histogram by finding the mixture of materials within each voxel most likely to have created the histogram the size of regions that the authors classify is chosen to match the sparing of the samples because the spacing is intrinsically related to the minimum feature size that the reconstructed continuous function can represent

on shape of plane elastic curves we study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending stretching or compressing line segments non uniformly along their extensions shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape preserving transformations the elastic properties of the curves are encoded in riemannian metrics on these spaces geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques the shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated

a new convexity measure based on a probabilistic interpretation of images in this paper we present a novel convexity measure for object shape analysis the proposed method is based on the idea of generating pairs of points from a set and measuring the probability that a point dividing the corresponding line segments belongs to the same set the measure is directly applicable to image functions representing shapes and also to gray scale images which approximate image binarizations the approach introduced gives rise to a variety of convexity measures which make it possible to obtain more information about the object shape the proposed measure turns out to be easy to implement using the fast fourier transform and we would consider this in detail finally we illustrate the behavior of our measure in different situations and compare it to other similar ones

improved moment invariants for shape discrimination abstract moment invariants have been frequently used as features for shape recognition they are computed based on the information provided by both the shape boundary and its interior region although several fast algorithms for computing traditional moment invariants have been proposed none has ever shown the theoretical results of moment invariants computed based on the shape boundary only this paper proposes improved moment invariants computed using the shape boundary only which tremendously reduces computations the new moment invariants called improved moment invariants are mathematically proved to be invariant to scaling translation and rotation graphical plots of the first two improved moment invariants for six country maps and four industrial tools using improved moment invariants are also given the results suggest that improved moment invariants can be used as effective features for shape discrimination or recognition

group theory of the smorodinsky winternitz system the three degrees of freedom smorodinsky winternitz system is a degenerate or super integrable hamiltonian that possesses five functionally independent globally defined and single valued integrals of the motion in both classical and quantum mechanics this is explained in terms of a forced degeneracy imposed as a consequence of the invariance of the hamiltonian under a group of symmetry transformations isomorphic to the three dimensional unitary unimodular group su 3 in turn this degeneracy group is embedded in a larger group of transformations that maps all the bound energy levels among each other the so called dynamical group all the bound state eigenfunctions act as basis functions for a single irreducible representation of the dynamical group so in common with the hydrogen atom and the harmonic oscillator the quantum mechanics of the smorodinsky winternitz system may be completely solved within the framework of group theory alone

dynamical invariance algebra of the hartmann potential the accidental degeneracy occurring in the quantum mechanical treatment of the ring shaped potential v eta sigma 2r 1 1 2q eta 2 sigma 2 r sin theta 2 is explained by constructing an su 2 dynamical invariance algebra the schrodinger equation is solved in parabolic coordinates written in the framework of the kustaanheimo stiefel transformation and the hamilton jacobi equations are solved in ordinary parabolic coordinates all finite trajectories are found to be periodic

path integral solutions for deformed poschl teller like and conditionally solvable potentials i discuss in this paper the behaviour of the solutions of the so called q hyperbolic potentials i e poschl teller like and conditionally solvable potentials in terms of the path integral formalism the differences in comparison to the usual poschl teller like potentials are investigated including the discrete energy spectra and the bound state wavefunctions we also point out the relation of the q deformation with curvature on hyperboloids

exact solution for a noncentral electric dipole ring shaped potential in the tridiagonal representation the schrodinger equation with noncentral electric dipole ring shaped potential is investigated by working in a complete square integrable basis that supports an infinite tridiagonal matrix representation of the wave operator the three term recursion relations for the expansion coefficients of both the angular and radial wavefunctions are presented the discrete spectrum for the bound states is obtained by the diagonalization of the radial recursion relation some potential applications of this system in different fields are discussed

bound state solutions of the dirac equation for the trigonometric and hyperbolic scarf grosche potentials using the nikiforov uvarov method the relativistic dirac equation with equal trigonometric and hyperbolic scarf grosche scalar and vector potentials in 3 1 and 1 1 space time dimension are solved by using the nikiforov uvarov method the exact energy equations and the spinor wave functions are obtained for these sets of potentials the bound states energy are calculated numerically also with appropriate transformations solutions of the fourth potential v4 can be deduced from the solutions of the third potential v3

hidden symmetry algebra and overlap coefficients for two ring shaped potentials a new approach is proposed to general systems possessing su 1 1 su 1 1 dynamical symmetry on the base of this approach the quadratic hahn algebra qh 3 is shown to serve as a hidden symmetry in both quantum and classical pictures for two potentials generalizing the hartmann and the oscillator ring shaped potentials the overlap coefficients between wavefunctions in spherical and parabolic cylindrical coordinates are shown to coincide with clebsch gordan coefficients for su 1 1 algebra

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

radial basis functions and level set method for image segmentation using partial differential equation combining nonlinear evolution equations which arise from image segmentation using partial differential equation based level set method using radial basis functions a meshless numerical algorithm is presented for image segmentation in this paper both globally supported and compactly supported radial basis functions are used to interpolate the level set function of the evolution equation with a high level of accuracy and smoothness the nonlinear evolution equation is finally cast into ordinary differential equations and euler s scheme is employed compared with traditional level set approaches the presented algorithm is robust to initialization or even free of manual initialization and avoids the complex and costly re initialization of the level set function the capability of the presented algorithm is demonstrated through some numerical experiments

measuring linearity of planar point sets our goal is to design algorithms that give a linearity measure for planar point sets there is no explicit discussion on linearity in literature although some existing shape measures may be adapted we are interested in linearity measures which are invariant to rotation scaling and translation these linearity measures should also be calculated very quickly and be resistant to protrusions in the data set the measures of eccentricity and contour smoothness were adapted from literature the other five being triangle heights triangle perimeters rotation correlation average orientations and ellipse axis ratio the algorithms are tested on 30 sample curves and the results are compared against the linear classifications of these curves by human subjects it is found that humans and computers typically easily identify sets of points that are clearly linear and sets of points that are clearly not linear they have trouble measuring sets of points which are in the gray area in between although they appear to be conceptually very different approaches we prove theoretically and experimentally that eccentricity and rotation correlation yield exactly the same linearity measurements they however provide results which are furthest from human measurements the average orientations method provides the closest results to human perception while the other algorithms proved themselves to be very competitive

general potentials described by so 2 1 dynamical algebra in parabolic coordinate systems the authors propose general three dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the so 2 1 dynamical group then they construct their green functions algebraically and find their spectra particular cases of these potentials which appear in the literature are also briefly discussed

exact solutions of the schrodinger equation with non central potential by the nikiforov uvarov method the general solutions of the schrodinger equation for a non central potential are obtained by using the nikiforov uvarov method the schrodinger equation with general non central potential is separated into radial and angular parts and energy eigenvalues and eigenfunctions are derived analytically by making special selections the non central potential is reduced to coulomb and hartmann ring shaped potentials and the obtained results are compared with the solutions of coulomb and hartmann potentials given in the literature

on the number of lattice animals embeddable in the square lattice enumeration of lattice animals embeddable in a square lattice has been extended to 24 cell animals by redelmeier 1981 it is shown that the number of animals per site an approximately 0 317 4 0626 nn 1 exp 0 465 n 0 87 to a high degree of accuracy

exact solution of the schrodinger equation for a potential well with a barrier and other potentials a method is described with which exactly solvable one dimensional stationary schrodinger equations can be derived from solved differential equations the procedure is illustrated by the example of a schrodinger equation for a potential well with a barrier of the form u z v q2 tanh2 z q1 tanhz coshz q0 the eigenvalues and eigenfunctions of this potential are calculated exactly the results are explicit analytical expressions in closed form for the whole eigenvalue spectrum as well as for all the eigenfunctions

measuring linearity of curves in 2d and 3d in this paper we define a new linearity measure for open curve segments in 2d and 3d the measure considers the distance of the curve end points to the curve centroid it is simple to compute and has the basic properties that should be satisfied by any linearity measure the new measure ranges over the interval 0 1 and produces the value 1 if and only if the measured curve is a perfect straight line segment also the new linearity measure is invariant with respect to translations rotations and scaling transformations the new measure is theoretically well founded and because of this its behaviour can be well understood and predicted to some extent this is always beneficial because it indicates the suitability of the new measure to the desired application several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure highlightsa new linearity measure is developed for open curve segments in 2d and 3d the measure is based on the curve end points and the curve centroid the measure is simple to compute the measure ranges over the interval 0 1 the measure is invariant with respect to translations rotations and scalings

generating random percolation clusters a fortran 77 program generator f is presented to generate random percolation clusters cluster sizes up to n 500 pixels can be generated random numbers are generated using the manly random number generator and clock time a second fortran 77 program cluster f enables the identification of the different clusters out of a set of randomly generated clusters using cluster f the 63 possible different clusters for n 5 are selected the percolation clusters are generated and presented using a matrix approach

the emerging discipline of computational functional anatomy computational functional anatomy cfa is the study of functional and physiological response variables in anatomical coordinates for this we focus on two things i the construction of bijections via diffeomorphisms between the coordinatized manifolds of human anatomy and ii the transfer group action and parallel transport of functional information into anatomical atlases via these bijections we review advances in the unification of the bijective comparison of anatomical submanifolds via point sets including points curves and surface triangulations as well as dense imagery we examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in dti as well as parallel transport of metric information across multiple templates which preserves the inner product

method to correct intensity inhomogeneity in mr images for atherosclerosis characterization we are developing methods to characterize atherosclerotic disease in human carotid arteries using multiple mr images having different contrast mechanisms t1w t2w pdw to enable the use of voxel gray values for interpretation of disease we created a new method local entropy minimization with a bicubic spline model lems to correct the severe spl ap 80 intensity inhomogeneity that arises from the surface coil array this entropy based method does not require classification and robustly addresses some problems that are more severe than those found in brain imaging including noise steep bias field sensitivity of artery wall voxels to edge artifacts and signal voids near the artery wall validation studies were performed on a synthetic digital phantom with realistic intensity inhomogeneity a physical phantom roughly mimicking the neck and patient carotid artery images we compared lems to a modified fuzzy c means segmentation based method mafcm and a linear filtering method linf following lems correction skeletal muscles in patient images were relatively isointense across the field of view in the physical phantom lems reduced the variation in the image to 1 9 and across the vessel wall region to 2 5 a value which should be sufficient to distinguish plaque tissue types based on literature measurements in conclusion we believe that the correction method shows promise for aiding human and computerized tissue classification from mr signal intensities

on an iteration method for eigenvalue problems we discuss a recently proposed asymptotic iteration method for eigenvalue problems we analyse its rate of convergence the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

high precision boundary length estimation by utilizing gray level information we present a novel method that provides an accurate and precise estimate of the length of the boundary perimeter of an object by taking into account gray levels on the boundary of the digitization of the same object assuming a model where pixel intensity is proportional to the coverage of a pixel we show that the presented method provides error free measurements of the length of straight boundary segments in the case of nonquantized pixel values for a more realistic situation where pixel values are quantized we derive optimal estimates that minimize the maximal estimation error we show that the estimate converges toward a correct value as the number of gray levels tends toward infinity the method is easy to implement we provide the complete pseudocode since the method utilizes only a small neighborhood it is very easy to parallelize we evaluate the estimator on a set of concave and convex shapes with known perimeters digitized at increasing resolution in addition we provide an example of applicability of the method on real images by suggesting appropriate preprocessing steps and presenting results of a comparison of the suggested method with other local approaches

exact solutions of deformed schrodinger equation with a class of non central physical potentials in this paper we present exact solutions of schrodinger equation for a class of non central physical potentials within the formalism of position dependent effective mass the energy eigenvalues and eigenfunctions of the bound states for the schrodinger equation are obtained analytically by means of asymptotic iteration method and easily calculated through a new generalized decomposition of the effective potential allowing easy separation of the coordinates our results are in excellent agreement with other works in the literature

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

fractal dimension of time indexed paths abstract measuring animal track or other trajectories for example the track of a flowing particle by divider method to obtain the fractal dimension without knowing the chronology of the points of the path one can obtain erroneous results the importance of time indexing of the track s point will be demonstrated by a simply geometrical example neglecting these indices the error can be high enough to mask relevant differences between various movement paths

an easy measure of compactness for 2d and 3d shapes an easy measure of compactness for 2d two dimensional and 3d three dimensional shapes composed of pixels and voxels respectively is presented the work proposed here is based on the two previous works of the measure of discrete compactness e bribiesca measuring 2 d shape compactness using the contact perimeter comput math appl 33 1997 1 9 e bribiesca a measure of compactness for 3d shapes comput math appl 40 2000 1275 1284 the measure of compactness proposed here improves and simplifies the previous measure of discrete compactness now using this proposed measure of compactness it is possible to compute measures for any kind of object including porous and fragmented objects also the computation of the measures is very simple by means of the use of only one equation the measure of compactness proposed here depends in large part on the sum of the contact perimeters of the side connected pixels for 2d shapes or on the sum of the contact surface areas of the face connected voxels for 3d shapes relations between the perimeter and the contact perimeter for 2d shapes and between the area of the surface enclosing the volume and the contact surface area are presented the measure presented here of compactness is invariant under translation rotation and scaling in this work the term of compactness does not refer to point set topology but is related to intrinsic properties of objects finally in order to prove our measure of compactness we calculate the measures of discrete compactness of different objects also we present an important application for brain structures quantification by means of the use of the new proposed measure of discrete compactness

computational models of mri characteristics of focal cortical dysplasia improve lesion detection abstract in many patients focal cortical dysplasia fcd is characterized by minor structural changes that may go unrecognized by standard radiological analysis we previously demonstrated that visual analysis of a composite map based on three simple models of mri features of fcd increased the sensitivity of fcd lesion detection compared to visual analysis of conventional mri here we report on the use of improved methods for characterizing fcd which improve contrast in the composite maps a laplacian based metric for measuring cortical thickness a convolutional kernel to model blurring of the gm wm interface and an operator to measure hyperintense t1 signal to validate these methods we processed the mris of 14 fcd patients with our original set of image processing operators and an improved set of image processing operators comparison of the composite maps associated with the two sets of operators revealed that contrast between lesional tissue and nonlesional cortex was significantly increased in the composite maps associated with the set of improved operators increasing this contrast is an important step toward the goal of automated fcd lesion detection

skull stripping using graph cuts removal of non brain tissues particularly dura is an important step in enabling accurate measurement of brain structures many popular methods rely on iterative surface deformation to fit the brain boundary and tend to leave residual dura similar to other approaches the method proposed here uses intensity thresholding followed by removal of narrow connections to obtain a brain mask however instead of using morphological operations to remove narrow connections a graph theoretic image segmentation technique was used to position cuts that isolate and remove dura this approach performed well on both the standardized ibsr test data sets and empirically derived data compared to the hybrid watershed algorithm hwa segonne et al 2004 the novel approach achieved an additional 10 30 of dura removal without incurring further brain tissue erosion the proposed method is best used in conjunction with hwa as the errors produced by the two approaches often occur at different locations and cancel out when their masks are combined our experiments indicate that this combination can substantially decrease and often fully avoid cortical surface overestimation in subsequent segmentation

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

a unified curvature definition for regular polygonal and digital planar curves in this paper we propose a new definition of curvature called visual curvature it is based on statistics of the extreme points of the height functions computed over all directions by gradually ignoring relatively small heights a multi scale curvature is obtained the theoretical properties and the experiments presented demonstrate that multi scale visual curvature is stable even in the presence of significant noise to our best knowledge the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves moreover it yields stable curvature estimates of curves in digital images even under sever distortions we also show a relation between multi scale visual curvature and convexity of simple closed curves

solvable potentials associated with su 1 1 algebras a systematic study we consider a specific differential realization of the su 1 1 algebra and use it to explore such algebraic structures associated with shape invariant potentials our approach combines elements of various methods of solving the schrodinger equation such as supersymmetric quantum mechanics or the factorization method algebraic techniques and special function theory in fact it amounts to reformulating transformations mapping the schrodinger equation into the differential equation of orthogonal polynomials in group theoretical terms our systematic study recovers a number of earlier results in a natural unified way and also leads to new findings the procedure presented here implicitly contains a similar treatment of the compact su 2 algebra as well possible generalizations of this approach involving different realizations of the su 1 1 algebra other algebraic structures and larger classes of potentials are also outlined

an approximate κ state solutions of the dirac equation for the generalized morse potential under spin and pseudospin symmetry by using an improved approximation scheme to deal with the centrifugal pseudo centrifugal term we solve the dirac equation for the generalized morse potential with arbitrary spin orbit quantum number in the presence of spin and pseudospin symmetry the analytic bound state energy eigenvalues and the associated upper and lower spinor components of two dirac particles are found by using the basic concepts of the nikiforov uvarov method we study the special cases when 1 l l 0 s wave the non relativistic limit and the limit when becomes zero kratzer potential model the present solutions are compared with those obtained by other methods

solution of the dirac equation with pseudospin symmetry for a new harmonic oscillatory ring shaped noncentral potential a new harmonic oscillatory ring shaped noncentral potential is proposed in which the noncentral electric dipole and a novel angle dependent component are included the pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator the resulting three term recursion relation for the expansion coefficients of the wavefunctions both angular and radial is presented the angular radial wavefunction is written in terms of the jacobi laguerre polynomials the discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation

a new ring shaped potential and its dynamical invariance algebra a new ring shaped potential obtained by replacing the coulomb part of the hartmann potential by a harmonic oscillator term is investigated the schrodinger equation is solved in spherical circular cylindrical prolate and oblate spheroidal coordinates as in the case of the hartmann potential the accidental degeneracies occurring in the spectrum are shown to be due to an su 2 dynamical invariance algebra this establishes a close connection between both ring shaped potentials

alternative area perimeter ratios for measurement of 2d shape compactness of habitats area perimeter ratios are often used to quantify 2d shape compactness shape compactness is of main importance to evaluate the effect of external disturbance on natural habitats reference values a m i n p a m a x p p m i n a p m a x a for area a and perimeter p are defined and proven the calculation of these reference values is based on the characteristics of the object studied and on pixel geometry the cases for 4 and 8 connectivity are discussed using these references alternative area perimeter ratios are composed examples are elaborated to illustrate the use of the indices and their performance

pseudospin symmetry for a new oscillatory ring shaped noncentral potential a new oscillatory ring shaped noncentral potential is proposed and the pseudospin symmetry for this potential is investigated by solving the dirac equation with equally mixed scalar and vector potentials with opposite signs the spinor wave functions and the energy spectrum for the bound states are obtained by using the nikiforov uvarov method the effect of angle dependent part on the radial solutions and the algebraic property of the energy equation are discussed

path integral quantization of certain noncentral systems with dynamical symmetries path integral quantization is done for the five classes of potentials appearing in the systematic search for nonrelativistic systems with dynamical symmetries done by makarov smorodinsky valiev and winternitz nuovo cimento a 52 1061 1967 by an iterated application of bateman s series formula to the polar coordinate path integral an expansion is obtained of the feynman kernel or the green s function whichever is possible in terms of hypergeometric functions of the polar and azimuthal parts and a radial path integral is obtained whose evaluation yields the energy eigenvalues and the normalized wave functions special cases include the hartmann potential and the ring shaped oscillator

the pseudospin symmetric solution of the morse potential for any κ state in this paper the energy eigenvalues and the corresponding spinors of the dirac particles are obtained and the pseudospin symmetric solution of the attractive scalar and repulsive vector morse potential for any spin orbit quantum number is provided by using the pekeris approximation within the framework of the asymptotic iteration method

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

the potential group approach and hypergeometric differential equations this paper proposes a generalized realization of the potential groups so 2 1 and so 2 2 to describe the confluent hypergeometric and the hypergeometric equations respectively it implies that the classes of schrodinger equations with solvable potentials whose analytical solutions are related to the confluent hypergeometric and the hypergeometric functions can be realized in terms of the above group structure

3d brain tumor segmentation in mri using fuzzy classification symmetry analysis and spatially constrained deformable models we propose a new general method for segmenting brain tumors in 3d magnetic resonance images our method is applicable to different types of tumors first the brain is segmented using a new approach robust to the presence of tumors then a first tumor detection is performed based on selecting asymmetric areas with respect to the approximate brain symmetry plane and fuzzy classification its result constitutes the initialization of a segmentation method based on a combination of a deformable model and spatial relations leading to a precise segmentation of the tumors imprecision and variability are taken into account at all levels using appropriate fuzzy models the results obtained on different types of tumors have been evaluated by comparison with manual segmentations

segmentation of focal cortical dysplasia lesions on mri using level set evolution focal cortical dysplasia fcd is the most frequent malformation of cortical development in patients with medically intractable epilepsy on mri fcd lesions are not easily differentiable from the normal cortex and defining their spatial extent is challenging in this paper we introduce a method to segment fcd lesions on t1 weighted mri it relies on two successive three dimensional deformable models whose evolutions are based on the level set framework the first deformable model is driven by probability maps obtained from three mri features cortical thickness relative intensity and gradient these features correspond to the visual characteristics of fcd and allow discriminating lesions and normal tissues in a second stage the previous result is expanded towards the underlying and overlying cortical boundaries throughout the whole cortical section the method was quantitatively evaluated by comparison with manually traced labels in 18 patients with fcd the automated segmentations achieved a strong agreement with the manuals labels demonstrating the applicability of the method to assist the delineation of fcd lesions on mri this new approach may become a useful tool for the presurgical evaluation of patients with intractable epilepsy related to cortical dysplasia

quantification of mr brain images by mixture density and partial volume modeling the problem of automatic quantification of brain tissue by utilizing single valued single echo magnetic resonance imaging mri brain scans is addressed it is shown that this problem can be solved without classification or segmentation a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap the general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues the quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture this problem is solved by tree annealing with and without partial volume utilized the results compared and the sensitivity of the tree annealing algorithm to various parameters is exhibited the actual quantification is performed by two methods a classification based method called bayes quantification and parameter estimation results from each method are presented for synthetic and actual data

measuring 2 d shape compactness using the contact perimeter a new perimeter for shapes composed of cells is defined this perimeter is called the contact perimeter which corresponds to the sum of the boundaries of neighboring cells of the shape also a relation between the perimeter of the shape and the contact perimeter is presented the contact perimeter corresponds to the measure of compactness proposed here called discrete compactness in this case the term compactness does not refer to point set topology but is related to intrinsic properties of objects

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

on the connection between the hydrogen atom and the harmonic oscillator the continuum case the connection between a three dimensional nonrelativistic hydrogen atom with positive energy and a four dimensional isotropic harmonic oscillator with repulsive potential is established by applying jordan schwinger boson calculus to the algebra of the laplace runge lenz pauli vector the spectrum generating group so 4 2 both for the bound and free states of the three dimensional hydrogen atom arises as a quotient of the group sp 8 r associated to four dimensional isotropic harmonic oscillator with constraint

spatial aggregation of two dimensional objects in raster data structures raster data structures are characterized by pixel geometry and resolution a method is proposed to reduce resolution to a minimum using spatial aggregation without information loss the method is based on a matrix approach and developed for a two dimensional spatial object perimeter measures and fractal dimension are shown not to be invariant to spatial aggregation

measuring cubeness in the limit cases abstract in this paper we show that the recently introduced family of the cubeness measures c s 0 satisfy the following desirable property lim c s 0 for any given 3d shape s different from a cube the result implies that the behaviour of cubeness measures changes depending on the selected value of and the cubeness measure can be arbitrarily close to zero for a suitably large value of this also implies that for a suitable value of the measure c s can be used for detecting small deviations of a shape from a perfect cube some examples are given to illustrate these properties

dynamical potential algebras for gendenshtein and morse potentials a differential realization of so 2 1 is shown to be the potential algebra for the one dimensional systems with the morse or gendenshtein potentials this shows that two classes of gendenshtein potentials will support the same eigenvalues as the morse potential and that the three sets of eigenfunctions may be derived in a common formalism the potential algebra is then extended to a dynamical potential algebra with operators connecting states both in different potentials and with different energies giving new dynamical algebras for the gendenshtein problem the matrix elements of certain corresponding operators in the three types of system may then be given by a single formula involving so 2 1 wigner coefficients the authors also give ladder operators connecting the gendenshtein potential eigenstates

the distance between shape centroids is less than a quarter of the shape perimeter in this paper we consider the distance between the shape centroid computed from the shape interior points and the shape centroid computed from the shape boundary points we show that the distance between those centroids is upper bounded by the quarter of the perimeter of the shape considered the obtained upper bound is sharp and cannot be improved next we introduce the shape centredness as a new shape descriptor which informally speaking should indicate to which degree a shape has a uniquely defined centre by exploiting the result mentioned above we give a formula for the computation of the shape centredness such a computed centredness is invariant with respect to translation rotation and scaling transformations

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

application of the exact quantization rule to the relativistic solution of the rotational morse potential with pseudospin symmetry we present an analytical solution of the radial dirac equation for the rotational morse potential through the pekeris approximation the bound state energy eigenvalues are obtained by using an exact quantization rule for non zero values of the dirac equation as an application of the rule we give the numerical solutions of the results for special values of the potential parameters

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

shape ellipticity from hu moment invariants in this paper we derive an explicit formula which uses the first two hu moment invariants to compute a shape ellipticity measure i e to evaluate how much a planar shape differs from an ellipse the ellipticity measure computed by this formula is invariant with respect to translation rotation and scaling transformations also the highest possible value is obtained if and only if the shape considered is an ellipse several experiments are also provided to confirm the theoretical observations a by product of the derivations made in this paper is an implicit interpretation of geometric shape meaning of the second hu moment invariant a formula which connects the shape ellipticity and the first hu moment invariant both having a well understood behavior and the second hu moment invariant is derived

asymptotic iteration method for eigenvalue problems an asymptotic iteration method for solving second order homogeneous linear differential equations of the form y 0 x y s0 x y is introduced where 0 x 0 and s0 x are c functions applications to schrodinger type problems including some with highly singular potentials are presented