finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

numerical verification of solutions for a simplified signorini problem abstract we proposed some numerical methods for the automatic proof of existence of solutions for variational inequalities i e obstacle problems and elastoplastic torsion problems it is based on nakao s method by using finite element approximation and its explicit error estimates for the problem in this paper we present a numerical verification algorithm of exact solutions for a simplified signorini problem in a computer a numerical example for the signorini problem is presented

a moving grid framework for geometric deformable models geometric deformable models based on the level set method have become very popular in the last decade to overcome an inherent limitation in accuracy while maintaining computational efficiency adaptive grid techniques using local grid refinement have been developed for use with these models this strategy however requires a very complex data structure yields large numbers of contour points and is inconsistent with the implementation of topology preserving geometric deformable models tgdms in this paper we investigate the use of an alternative adaptive grid technique called the moving grid method with geometric deformable models in addition to the development of a consistent moving grid geometric deformable model framework our main contributions include the introduction of a new grid nondegeneracy constraint the design of a new grid adaptation criterion and the development of novel numerical methods and an efficient implementation scheme the overall method is simpler to implement than using grid refinement requiring no large complex hierarchical data structures it also offers an extra benefit of automatically reducing the number of contour vertices in the final results after presenting the algorithm we demonstrate its performance using both simulated and real images

numerical verification of solutions for some unilateral boundary value problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for some unilateral boundary value problems using the finite element approximations and explicit a priori error estimates we construct in a computer a set of solutions which satisfies the hypothesis of schauder s fixed point theorem for a compact map on a certain sobolev space further the conditions of verifiability by this method are considered and some numerical examples are presented

efficient visual tracking using particle filter with incremental likelihood calculation in this paper we propose a particle filter that determines the weight of each particle employing the incremental likelihood calculation since there is usually a large overlap region between the two particles that are sequentially generated determining the weight of the particle has only a small time cost therefore the real time performance of the proposed tracker can be dramatically improved extensive experimental results for single object and multiple object tracking scenarios are presented to demonstrate the efficiency of the proposed approach finally an interesting color based active vision system is developed for a free floating space robot testbed to facilitate teleoperation

a new feature extractor invariant to intensity rotation and scaling of color images this paper proposes a new method for extracting the invariant features of an image based on the concept of principal component analysis and a competitive learning algorithm the proposed algorithm can be applied to binary gray level or colored texture images with a size greater than 256x256 pixels in addition to translation scaling and rotation invariant extraction the extraction of a feature invariant to color intensity can be implemented by using this method in our experiment the proposed method shows the capability to differentiate images having the same shape but different colored textures the experimental results report the effectiveness of this technique and its performance as measured by recognition accuracy rate and computational time these results are also compared with those obtained by classical techniques

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

an active contour model and its algorithms with local and global gaussian distribution fitting energies in this paper we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation in the proposed model the local and global region fitting energies are described by the combination of the local and global gaussian distributions with different means and variances respectively in this combination we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies then we present an algorithm for implementing the proposed model directly considering that in practice the selection of the weighting coefficient is troublesome we present a modified algorithm in order to overcome this problem and increase the flexibility by adaptively updating the weighting coefficient and the time step with the contour evolution this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate besides it is robust to the noise and can be used to extract the desired objects experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real world images

coping with discontinuities in computer vision their detection classification and measurement the general principles of detection classification and measurement of discontinuities are studied the following issues are discussed detecting the location of discontinuities classifying discontinuities by their degrees measuring the size of discontinuities and coping with the random noise and designing optimal discontinuity detectors an algorithm is proposed for discontinuity detection from an input signal s for degree k discontinuity detection and measurement a detector p phi is used where p is the pattern and phi is the corresponding filter if there is a degree k discontinuity at location t sub 0 then in the filter response there is a scaled pattern alpha p at t sub 0 where alpha is the size of the discontinuity this reduces the problem to searching for the scaled pattern in the filter response a statistical method is proposed for the approximate pattern matching to cope with the random noise a study is made of optimal detectors which minimize the effects of noise

two projection methods for the solution of signorini problems abstract two iterative methods based on projection and boundary element methods are considered for signorini problems the regularized problem with the projection boundary condition is first deduced from the signorini problem by using the equivalence between the signorini boundary condition and the projection fixed point problem our methods formulate the signorini boundary condition into a sequence of robin boundary conditions in the new boundary condition there is a penalty parameter the convergence speed of the first method is greatly influenced by the value of which is difficult to choose for individual problems to improve the performance of this method we present a self adaptive projection method which adjusts the parameter automatically per iteration based on the iterative data the main result of this work is to provide the convergence of the methods under mild assumptions as the iteration process is given by the potential and its derivative on the boundary of the domain the unknowns of the problem are computed explicitly by using the boundary element method both theoretical results and numerical experiments indicate efficiency of the methods proposed

orthogonal variant moments features in image analysis moments are statistical measures used to obtain relevant information about a certain object under study e g signals images or waveforms e g to describe the shape of an object to be recognized by a pattern recognition system invariant moments e g the hu invariant set are a special kind of these statistical measures designed to remain constant after some transformations such as object rotation scaling translation or image illumination changes in order to e g improve the reliability of a pattern recognition system the classical moment invariants methodology is based on the determination of a set of transformations or perturbations for which the system must remain unaltered although very well established the classical moment invariants theory has been mainly used for processing single static images i e snapshots and the use of image moments to analyze images sequences or video from a dynamic point of view has not been sufficiently explored and is a subject of much interest nowadays in this paper we propose the use of variant moments as an alternative to the classical approach this approach presents clear differences compared to the classical moment invariants approach that in specific domains have important advantages the difference between the classical invariant and the proposed variant approach is mainly but not solely conceptual invariants are sensitive to any image change or perturbation for which they are not invariant so any unexpected perturbation will affect the measurements i e is subject to uncertainty on the contrary a variant moment is designed to be sensitive to a specific perturbation i e to measure a transformation not to be invariant to it and thus if the specific perturbation occurs it will be measured hence any unexpected disturbance will not affect the objective of the measurement confronting thus uncertainty furthermore given the fact that the proposed variant moments are orthogonal i e uncorrelated it is possible to considerably reduce the total inherent uncertainty the presented approach has been applied to interesting open problems in computer vision such as shape analysis image segmentation tracking object deformations and object motion tracking obtaining encouraging results and proving the effectiveness of the proposed approach

an intensive restraint topology adaptive snake model and its application in tracking dynamic image sequence the aim of this work is to propose an improved intensive restraint topology adaptive snake model for detecting and tracking target contours with complex topological morphology from dynamic gray scale image sequences the image is discretized by orthogonal equidistant grid lines and snake nodes are constrained to move only from one grid vertex to another along grid lines thus the computation is much simpler than those of other t snakes since complicated calculation of intersection points of snake curve and grid lines is not required topological transformation is implemented through splitting snake nodes as well as automatically detecting and eliminating topological collision an adaptive weighted expansion energy term is introduced into snake s energy function driving the model to pass across the region with non uniform intensity distribution inside the target region the required manual interaction is reduced to only select a random point within the target region in the first frame of the image sequence for subsequent frames the detection result in the previous frame is regarded as the initial model in the current frame through experiments on simulated image data and clinical x ray coronary angiographic sequences the model s topological flexibility and lower computation cost compared with other t snakes are demonstrated also the sensitivity of the model to weights of the energy terms and grid size as well as the initial plan of the model is discussed based on experimental results

adaptive multilevel rough entropy evolutionary thresholding abstract in this study comprehensive research into rough set entropy based thresholding image segmentation techniques has been performed producing new and robust algorithmic schemes segmentation is the low level image transformation routine that partitions an input image into distinct disjoint and homogenous regions using thresholding algorithms most often applied in practical situations especially when there is pressing need for algorithm implementation simplicity high segmentation quality and robustness combining entropy based thresholding with rough set results in the rough entropy thresholding algorithm the authors propose a new algorithm based on granular multilevel rough entropy evolutionary thresholding that operates on a multilevel domain the mret algorithm performance has been compared to the iterative ret algorithm and standard k means clustering methods on the basis of index as a representative validation measure performance in experimental assessment suggests that granular multilevel rough entropy threshold based segmentations mret present high quality comparable with and often better than k means clustering based segmentations in this context the rough entropy evolutionary thresholding mret algorithm is suitable for specific segmentation tasks when seeking solutions that incorporate spatial data features with particular characteristics

concordance assisted learning for estimating optimal individualized treatment regimes in this article we propose a new concordance assisted learning for estimating optimal individualized treatment regimes we first introduce a type of concordance function for prescribing treatment and propose a robust rank regression method for estimating the concordance function we then find treatment regimes up to a threshold to maximize the concordance function named prescriptive index finally within the class of treatment regimes that maximize the concordance function we find the optimal threshold to maximize the value function we establish the convergence rate and asymptotic normality of the proposed estimator for parameters in the prescriptive index an induced smoothing method is developed to estimate the asymptotic variance of the proposed estimator we also establish the n1 3 consistency of the estimated optimal threshold and its limiting distribution in addition a doubly robust estimator of parameters in the prescriptive index is developed under a class of monotonic index models the practical use and effectiveness of the proposed methodology are demonstrated by simulation studies and an application to an aids data

numerical verification of solutions for variational inequalities in this paper we consider a numerical technique that enables us to verify the existence of solutions for variational inequalities this technique is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations using the finite element approximations and explicit a priori error estimates for obstacle problems we present an effective verification procedure that through numerical computation generates a set which includes the exact solution further a numerical example for an obstacle problem is presented

a method of moments estimator for random effect multivariate meta analysis meta analysis is a powerful approach to combine evidence from multiple studies to make inference about one or more parameters of interest such as regression coefficients the validity of the fixed effect model meta analysis depends on the underlying assumption that all studies in the meta analysis share the same effect size in the presence of heterogeneity the fixed effect model incorrectly ignores the between study variance and may yield false positive results the random effect model takes into account both within study and between study variances it is more conservative than the fixed effect model and should be favored in the presence of heterogeneity in this paper we develop a noniterative method of moments estimator for the between study covariance matrix in the random effect model multivariate meta analysis to our knowledge it is the first such method of moments estimator in the matrix form we show that our estimator is a multivariate extension of dersimonian and laird s univariate method of moments estimator and it is invariant to linear transformations in the simulation study our method performs well when compared to existing random effect model multivariate meta analysis approaches we also apply our method in the analysis of a real data example

numerical verifications of solutions for elliptic equations in nonconvex polygonal domains in this paper methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied in order to verify solutions using computer it is necessary to determine some constants which appear in a priori error estimations we propose some methods for determination of these constants in numerical examples calculating these constants for anl shaped domain we verify the solution of a nonlinear elliptic equation

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element the verifications of solutions to weakly nonlinear elliptic equations by the method described e g by nakao 1988 1989 etc are sometimes hardly accomplished when the right hand sides of the equations are very large to overcome such difficulties a residual iteration technique with approximate solution was introduced by nakao 1993 in the present paper we propose an a posteriori method for the residual iteration and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element

maximin projection learning for optimal treatment decision with heterogeneous individualized treatment effects a saline feature of data from clinical trials and medical studies is inhomogeneity patients not only differ in baseline characteristics but also the way they respond to treatment optimal individualized treatment regimes are developed to select effective treatments based on patient s heterogeneity however the optimal treatment regime might also vary for patients across different subgroups in this paper we mainly consider patient s heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups we propose a new maximin projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation based on estimated optimal treatment regimes for all subgroups the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming qclp problem which can be efficiently computed by interior point methods consistency and asymptotic normality of the estimator is established numerical examples show the reliability of the proposed methodology

a numerical approach to the proof of existence of solutions for some generalized obstacle problems in 8 we proposed some numerical verification methods for automatic proof of the existence of solution for obstacle problems in this paper we propose a new iterative algorithm to automatically prove the existence of solutions for some generalized obstacle problems

new computational methods for full and subset zernike moments the computation of zernike radial polynomials contributes most of the computation time in computing the zernike moments due to the involvement of factorial terms the common approaches used in fast computation of zernike moments are kintner s prata s coefficient and q recursive methods in this paper we propose faster methods to derive the full set of zernike moments as well as a subset of zernike moments a hybrid algorithm that uses prata s simplified kintner s and coefficient methods is used to derive the full set of zernike moments in the computation of a subset of zernike moments we propose using the combination of prata s simplified kintner s coefficient and q recursive methods fast computation is achieved by using the recurrence relations between the zernike radial polynomials of successive order without any involvement of factorial terms in the first and second experiments we show both the hybrid algorithms take lesser computation time than the existing methods in computing the full set of zernike moments and a selected subset of zernike moments which are not in successive sequence both hybrid algorithms have been applied in real world application in the classification of rice grains using full set and subset of zernike moments the classification performance using optimal subset of zernike moments is better than using full set of zernike moments

optimal dynamic treatment regimes summary a dynamic treatment regime is a list of decision rules one per time interval for how the level of treatment will be tailored through time to an individual s changing status the goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response to explicate our objective and to state the assumptions we use the potential outcomes model the method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules we illustrate the methodology proposed via a small simulation

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a unified methodology for the efficient computation of discrete orthogonal image moments a novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments the computation scheme is mainly based on a new image representation method the image slice representation isr method according to which an image can be expressed as the outcome of an appropriate combination of several non overlapped intensity slices this image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities black or any other gray level value therefore the image block representation can be effectively applied to describe the image in a more compact way once the image is partitioned into intensity blocks the computation of the image moments can be accelerated as the moments can be computed by using decoupled computation forms the proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results as has been concluded through a detailed experimental investigation

numerical verification of solutions for signorini problems using newton like method we proposed a numerical method to verify the existence of solutions for a simplified signorini problem comput math appl 2000 40 1003 1013 using sequential iteration method we numerically constructed a set containing solutions that satisfies the hypothesis of schauder s fixed point theorem in a certain sobolev space it is difficult to apply this method to the problem of which associated operator is not retractive in a neighborhood of the solution in this paper in order to overcome such a difficulty we describe an alternative approach to this problem numerical examples are presented copyright 2007 john wiley sons ltd

multiple subclass pattern recognition a maximin correlation approach this paper addresses a correlation based nearest neighbor pattern recognition problem where each class is given as a collection of subclass templates the recognition is performed in two stages in the first stage the class is determined templates for this stage are created using the subclass templates assignment into subclasses occurs in the second stage this two stage approach may be used to accelerate template matching in particular the second stage may be omitted when only the class needs to be determined the authors present a method for optimal aggregation of subclass templates into class templates for each class the new template is optimal in that it maximizes the worst case i e minimum correlation with its subclass templates an algorithm which solves this maximin optimization problem is presented and its correctness is proved in addition test results are provided indicating that the algorithm s execution time is polynomial in the number of subclass templates the authors show tight bounds on the maximin correlation the bounds are functions only of the number of original subclass templates and the minimum element in their correlation matrix the algorithm is demonstrated on a multifont optical character recognition problem

a new class of zernike moments for computer vision applications a modified direct method for the computation of the zernike moments is presented in this paper the presence of many factorial terms in the direct method for computing the zernike moments makes their computation process a very time consuming task although the computational power of the modern computers is impressively increasing the calculation of the factorial of a big number is still an inaccurate numerical procedure the main concept of the present paper is that by using stirling s approximation formula for the factorial and by applying some suitable mathematical properties a novel factorial free direct method can be developed the resulted moments are not equal to those computed by the original direct method but they are a sufficiently accurate approximation of them besides their variability does not affect their ability to describe uniquely and distinguish the objects they represent this is verified by pattern recognition simulation examples

a numerical verification method for the existence of weak solutions for nonlinear boundary value problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for nonlinear two point boundary value problems bvp we formulate the problem as a fixed point of a newton like operator and present a verification algorithm by computer based on sadovskii s fixed point theorem in order to compute the newton type iterative sequences in infinite dimensional space two concepts the rounding and the rounding error are introduced also some numerical examples are illustrated we emphasize that since the present method uses the weak formulation of bvp and the finite element approximations instead of the existing validation techniques it is aslo applicable in principle to the bvp for partial differential equations as it stands

a hybrid genetic algorithm with the baldwin effect here we present a new hybrid genetic algorithm hga with the baldwin effect in the hga a local search is employed to change the fitness of individuals but the acquired improvements do not change the individual itself this local search step exploits the baldwin effect some numerical applications show that this algorithm can yield the global optimum more efficiently than commonly used hgas a theorem is presented that guarantees the convergence in probability of the new hga

maximin effects in inhomogeneous large scale data large scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources we look at regression models and the effect of randomly changing coefficients where the change is either smoothly in time or some other dimension or even without any such structure fitting varying coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary if we just ask for a model estimator that shows good predictive properties for all regimes of the data then we are aiming for a simple linear model that is reliable for all possible subsets of the data we propose the concept of maximin effects and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators making computations on large scale data feasible empirical examples complement the novel methodology and theory

projection and self adaptive projection methods for the signorini problem with the bem abstract we propose two new projection methods for solving the signorini problem and study the relationship between them since the signorini boundary condition is equivalent to a projection fixed point problem the methods formulate the signorini boundary condition into a sequence of robin boundary conditions and only require solving a variational problem with simple boundary conditions at each iterative step the convergence speed of the first method depends on the parameter heavily and it is difficult to choose a proper for individual problems to improve the efficiency of the method we propose an adaptive projection method which adjusts the parameter automatically per iteration we establish the convergence analysis of the methods because the signorini boundary condition is given in an iterative form by the potential and its derivative on the boundary of the domain we can easily provide the boundary element approximation of the problem finally we present some numerical simulations which illustrate the performance of the methods