correspondence with cumulative similarity transforms a local image transform based on cumulative similarity measures is defined and is shown to enable efficient correspondence and tracking near occluding boundaries unlike traditional methods this transform allows correspondences to be found when the only contrast present is the occluding boundary itself and when the sign of contrast along the boundary is possibly reversed the transform is based on the idea of a cumulative similarity measure which characterizes the shape of local image homogeneity both the value of an image at a particular point and the shape of the region with locally similar and connected values is captured this representation is insensitive to structure beyond an occluding boundary but is sensitive to the shape of the boundary itself which is often an important cue we show results comparing this method to traditional least squares and robust correspondence matching

a multistage optimal active contour model energy minimizing active contour models or snakes can be used in many applications such as edge detection motion tracking image matching computer vision and three dimensional 3 d reconstruction we present a novel snake that is superior both in accuracy and convergence speed over previous snake algorithms high performance is achieved by using spline representation and dividing the energy minimization process into multiple stages the first stage is designed to optimize the convergence speed in order to allow the snake to quickly approach the minimum energy state the second stage is devoted to snake refinement and to local minimization of energy thereby driving the snake to a quasiminimum energy state the third stage uses the bellman 1957 optimality principle to fine tune the snake to the global minimum energy state this three stage scheme is optimized for both accuracy and speed

deformable contours modeling and extraction this paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images we propose a global contour model based on a stable and regenerative shape matrix which is invariant and unique under rigid motions combined with markov random field to model local deformations this yields prior distribution that exerts influence over a global model while allowing for deformations we then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model we discuss pertinent issues in shape training energy minimization line search strategies minimax regularization and initialization by generalized hough transform finally we present experimental results and compare its performance to rigid template matching

tracking deformable objects in the plane using an active contour model the problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed in evaluating these problems a technique based on an active contour model commonly called a snake is examined the technique is applied to cell locomotion and tracking studies the snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases a detailed analysis of the snake model emphasizing its limitations and shortcomings is presented and improvements to the original description of the model are proposed problems of convergence of the optimization scheme are considered in particular an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed hierarchical filtering methods as well as a continuation method based on a discrete sale space representation are discussed results for both segmentation and tracking are presented possible failures of the method are discussed

shortest paths with higher order regularization this paper describes a new method of finding thin elongated structures in images and volumes we use shortest paths to minimize very general functionals of higher order curve properties such as curvature and torsion our method uses line graphs to find the optimal path on a given discretization often in the order of seconds on a single computer the curves are then refined using local optimization making it possible to recover very smooth curves we are able to place constraints on our curves such as maximum integrated curvature or a maximum curvature at any point of the curve to our knowledge we are the first to perform experiments in three dimensions with curvature and torsion regularization the largest graphs we process have over a hundred billion arcs experiments on medical images and in multi view reconstruction show the significance and practical usefulness of higher order regularization

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

weighted means in stochastic approximation of minima weighted averages of kiefer wolfowitz type procedures which are driven by larger step lengths than usual can achieve the optimal rate of convergence a priori knowledge of a lower bound on the smallest eigenvalue of the hessian matrix is avoided the asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a newton type adaptive algorithm several different gradient estimates are considered one of them leads to a vanishing asymptotic bias this gradient estimate applied with the weighted averaging algorithm usually yields a better asymptotic mean squared error than applied with the standard algorithm

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

weak continuity with structural constraints nonlinear regression and nonlinear regularization are two powerful approaches to segmentation and nonlinear filtering in this correspondence we propose a hybrid approach that effectively combines the best of both worlds and can be efficiently implemented via the viterbi algorithm

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

self affine mapping system and its application to object contour extraction a self affine mapping system which has conventionally been used to produce fractal images is used to fit rough lines to contours the self affine map s parameters are detected by analyzing the blockwise self similarity of a grayscale image using a simplified algorithm in fractal encoding the phenomenon that edges attract mapping points in self affine mapping is utilized in the proposed method the boundary of the foreground region of an alpha mask is fitted by mapping iterations of the region it is shown that the proposed method accurately produces not only smooth curves but also sharp corners and has the ability to extract both distinct edges and blurred edges using the same parameter it is also shown that even large gaps between the hand drawn line and the contour can be fitted well by the recursive procedure of the proposed algorithm in which the block size is progressively decreased these features reduce the time required for drawing contours by hand

attractable snakes based on the greedy algorithm for contour extraction abstract while most improved snakes were built under the original variational scheme this paper presents an attractable snake based on the greedy snake williams and shah cvgip image understanding 55 1 1992 14 26 by use of a direct feedback mechanism that is seamlessly consistent with the search strategy of the greedy algorithm the proposed approach is capable of inheriting the simplicity and efficiency of that algorithm and performing competitively with related snakes to avoid undesirable local minima an overall optimal edge detector is designed a suitable synthetic convergent criterion is proposed which enables snakes to converge normally or oscillatingly on target objects an adaptive interpolation scheme that encourages snakes to accurately sense the details of object shapes is also described this model is applied to extract contours from various images with encouraging results

encoding of a priori information in active contour models the theory of active contours models the problem of contour recovery as an energy minimization process the computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions in this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models the grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images the variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework we propose an algorithmic solution that combines a nondeterministic version of the knuth morris pratt algorithm for string matching with a time delayed discrete dynamic programming algorithm for energy minimization the numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion

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

guiding ziplock snakes with a priori information in this paper we present a method to combine a grammatical model that encodes a priori shape information with the ziplock snakes presented by neuenschwander et al 1997 a competing mechanism is adopted to take advantage of the shape models without inducing excessive computation the resulting model based ziplock snakes have many advantages over the original model they can accurately locate contour features produce more refined results and deal with multiple contours missing image cues and noise

optimization of the transient and steady state behavior of discrete event systems we present a general framework for applying simulation to optimize the behavior of discrete event systems our approach involves modeling the discrete event system under study as a general state space markov chain whose distribution depends on the decision parameters we then show how simulation and the likelihood ratio method can be used to evaluate the performance measure of interest and its gradient and we present conditions that guarantee that the robbins monro stochastic approximation algorithm will converge almost surely to the optimal values of the decision parameters both transient and steady state performance measures are considered for steady state performance measures we consider both the case when the markov chain of interest is regenerative in the standard sense as well as the case when this markov chain is harris recurrent and thereby regenerative in a wider sense

non universal critical dynamics of the one dimensional potts models the one dimensional kinetic potts models are studied for both glauber and kawasaki dynamics with different transition rates rigorous lower bounds for the dynamical exponent z are obtained from the initial response rate and the scaling hypothesis for the relaxation time it is shown that the z exponent is non universal for several periodic models with a basic unit cell j1 j2 jm containing different coupling constants the critical dynamics of the alternating bond model is also studied by a simple argument about the movement of domain walls

a theory of kinematics for the potts model a master equation formulation of the kinetic q state potts model is presented it is shown that this formulation reduces to glauber s dynamics in the ising limit the single spin problem is considered and the properties of its q 1 temperature dependent relaxation times are studied the linear chain problem is much harder than in the glauber case a variational method is used to obtain a lower bound for the dynamical critical exponent z or 3 for q 2 a discussion of these and related problems is presented

on the generalised glauber kinetics for a one dimensional potts chain the one dimensional potts chain dynamics is analysed by means of the direct space renormalisation technique in contrast to previous work one needs no restriction on the value of the potts dimensionality q they use the generalised glauber kinetics for the chain and find that the value of the dynamical critical exponent z is not universal i e it depends on both potts dimensionality and the transition rates asymmetry coefficient lambda

critical dynamics of the kinetic potts model on some fractals the critical dynamics of the kinetic potts model on koch curves and regular fractals is studied by means of the exact time dependent renormalization group method different critical dynamics are found on these two families of fractals it is shown that the value of the dynamic critical exponent z depends on both the potts dimensionality q and the transition rates asymmetry coefficient alpha for koch curves the scaling law of the dynamics exponent z df f q alpha v while for regular fractals z df 2f q alpha v where f q alpha characterizes the dependence of the dynamics exponent z on potts dimensionality q and the transition rates asymmetry coefficient alpha and v is the static exponent of the correlation length

game theoretic integration for image segmentation robust segmentation of structures from an image is essential for a variety of image analysis problems however the conventional methods of region based segmentation and gradient based boundary finding are often frustrated by poor image quality here we propose a method to integrate the two approaches using game theory in an effort to form a unified approach that is robust to noise and poor initialization this combines the perceptual notions of complete boundary information using edge data and shape priors with gray level homogeneity using two computational modules the novelty of the method is that this is a bidirectional framework whereby both computational modules improve their results through mutual information sharing a number of experiments were performed both on synthetic datasets and datasets of real images to evaluate the new approach and it is shown that the integrated method typically performs better than conventional gradient based boundary finding

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

non universality in the dynamics of the one dimensional potts model the authors discuss two recent papers on the dynamics of the one dimensional potts model which yield different values of the dynamical critical exponent they show that in fact there are choices of the transition rates which yield arbitrarily large non universal exponents

robust automatic selection of optimal views in multi view free form object recognition this paper addresses the issue of automatic selection of the best and the optimum number of representative views for each object in a database that can enable the accurate recognition of that object from any single arbitrary view of the object the object boundary in each view is represented by its curvature scale space css image the css representation has been selected for mpeg 7 standardisation as a contour shape descriptor the paper also presents a novel method for fusion of results from combined shape descriptors the utilisation of this method for multi view three dimensional 3 d object recognition has been explored the object boundary of each view is represented effectively using the css technique moment invariants and fourier descriptors it has been shown that the results obtained from the fusion method are superior to the results obtained from any single technique the method has been tested on a collection of free form 3 d objects each object has been modelled using an optimal number of silhouette contours obtained from different viewpoints this number varies depending on the complexity of the object and the measure of expected accuracy a comprehensive analysis of the performance of the system has been given

a class of constrained clustering algorithms for object boundary extraction boundary extraction is a key task in many image analysis operations this paper describes a class of constrained clustering algorithms for object boundary extraction that includes several well known algorithms proposed in different fields deformable models constrained clustering data ordering and traveling salesman problems the algorithms belonging to this class are obtained by the minimization of a cost function with two terms a quadratic regularization term and an image dependent term defined by a set of weighting functions the minimization of the cost function is achieved by lowpass filtering the previous model shape and by attracting the model units toward the centroids of their attraction regions to define a new algorithm belonging to this class the user has to specify a regularization matrix and a set of weighting functions that control the attraction of the model units toward the data the usefulness of this approach is twofold it provides a unified framework for many existing algorithms in pattern recognition and deformable models and allows the design of new recursive schemes

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

a linear framework for region based image segmentation and inpainting involving curvature penalization we present the first method to handle curvature regularity in region based image segmentation and inpainting that is independent of initialization to this end we start from a new formulation of length based optimization schemes based on surface continuation constraints and discuss the connections to existing schemes the formulation is based on a cell complex and considers basic regions and boundary elements the corresponding optimization problem is cast as an integer linear program we then show how the method can be extended to include curvature regularity again cast as an integer linear program here we are considering pairs of boundary elements to reflect curvature moreover a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables we show that by solving the linear programming relaxation one gets reasonably close to the global optimum and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity

edge detection in noisy data using finite mixture distribution analysis abstract an algorithm which identifies discontinuities in noisy data is presented the signal is modelled as step edges with additive normally distributed noise present using finite mixture analysis and information criteria a variable number of mixtures are identified together with the location of the respective edges separating them the problem is solved using a dynamic programming approach which ensures globally optimal edge positions according to the signal model of a finite mixture of normal distributions the computational complexity is of order mn 2 where m is the number of discontinuities in the mixture and n is the number of data points in the signal the algorithm is tested on a range of real and synthetic signals and yields as accurate edge positions as a corresponding minimum square error method among applications for this algorithm is edge detection in medical images and examples from ultrasound imaging are included

boundary vector field for parametric active contours snakes are widely used in the fields of computer vision and image processing there are a number of shortcomings of the traditional snakes including the capture range problem and the concave object extraction problem gradient vector flow snake enhances the concave object extraction capability however it suffers from high computational requirement in this paper we present a new external force which is generated by a novel interpolation scheme which reduces the computational requirement significantly and at the same time improves the capture range and concave object extraction capability

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

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

deformable shape detection and description via model based region grouping a method for deformable shape detection and recognition is described deformable shape templates are used to partition the image into a globally consistent interpretation determined in part by the minimum description length principle statistical shape models enforce the prior probabilities on global parametric deformations for each object class once trained the system autonomously segments deformed shapes from the background while not merging them with adjacent objects or shadows the formulation can be used to group image regions obtained via any region segmentation algorithm e g texture color or motion the recovered shape models can be used directly in object recognition experiments with color imagery are reported

generating discriminating cartoon faces using interacting snakes as a computational bridge between the high level a priori knowledge of object shape and the low level image data active contours or snakes are useful models for the extraction of deformable objects we propose an approach for manipulating multiple snakes iteratively called interacting snakes that minimizes the attraction energy functionals on both contours and enclosed regions of individual snakes and the repulsion energy functionals among multiple snakes that interact with each other we implement the interacting snakes through explicit curve parametric active contours representation in the domain of face recognition we represent human faces semantically via facial components such as eyes mouth face outline and the hair outline each facial component is encoded by a closed or open snake that is drawn from a 3d generic face model a collection of semantic facial components form a hypergraph called semantic face graph which employs interacting snakes to align the general facial topology onto the sensed face images experimental results show that a successful interaction among multiple snakes associated with facial components makes the semantic face graph a useful model for face representation including cartoon faces and caricatures and recognition

tracking of tubular molecules for scientific applications in this paper we present a system for detection and tracking of tubular molecules in images the automatic detection and characterization of the shape location and motion of these molecules can enable new laboratory protocols in several scientific disciplines the uniqueness of the proposed system is twofold at the macro level the novelty of the system lies in the integration of object localization and tracking using geometric properties at the micro level in the use of high and low level constraints to model the detection and tracking subsystem the underlying philosophy for object detection is to extract perceptually significant features from the pixel level image and then use these high level cues to refine the precise boundaries in the case of tubular molecules the perceptually significant features are antiparallel line segments or equivalently their axis of symmetries the axis of symmetry infers a coarse description of the object in terms of a bounding polygon the polygon then provides the necessary boundary condition for the refinement process which is based on dynamic programming for tracking the object in a time sequence of images the refined contour is then projected onto each consecutive frame

critical dynamics of the spin exchange model in quasilinear fractal geometries comments on the dynamic critical exponents recently reported by leyvraz and jan ibid vol 19 p 603 1986 in particular that for the spin exchange kinetic ising model in one dimension z 3 this result is at variance with rigorous inequalities that z cannot be less than five for this model i e z or 5 the source of the discrepancy appears to lie in the monte carlo algorithm which subsumes a critically slow dynamical process leading to an apparently faster dynamics in the critical region in addition the author extends the finding for one dimension to the quasilinear non branching fractal koch curve concluding z 3df where df is the fractal dimension he discusses the physical factors comprising the lower bound to the dynamic exponent in one dimension z 5 he then obtains the generalised lower bound for spin exchange dynamics of the non branching koch curve z 3df dw 5df where dw is the random walk dimension

fuzzy shape memory snakes for the automatic off line signature verification problem this paper introduces an adapted fuzzy snake approach for efficiently solving some of the practical constraints in the off line signature verification problem our method is called fuzzy shape memory snakes due to its resemblance to shape memory alloys which are metals that in high temperature conditions can remember their original shape in our approach the snake also remembers its geometry during its iterative adjustment to a test signature off line signature verification aims to establish the degree of genuineness of a given test signature when compared to a reference signature due to the shape and size variability in signatures of the same subject a system with tolerance to imprecision and also with some memory of its initial configured shape would be very useful for this complex verification problem to our knowledge snakes and other active contour models have not been previosly applied to the offline signature verification problem we consider that they could be properly adapted to be useful for this task consequently we have developed a fuzzy snake framework for signature verification which takes into account some practical constraints of this problem when applied to bank checks over other signature verification systems our approach has the advantage of using only one training signature per person we introduce the fuzziness for the considered signature verification problem in a double direction first when iteratively adjusting a shape memory snake which is obtained from the training signature to a considered test signature second when measuring the similarity degree between the snake and the test signature after the adjustment or verification task using a takagi sugeno fuzzy inference system which is trained with three signature features coincidence distance and energy provided by the adjustment some advantages of our approach are that some involved parameters in the internal shape snake energy are now eliminated and a more efficient and natural snake adjustment to the test signature is achieved this paper also provides a study of the biometric classification errors when comparing our off line signature verification approach to other non fuzzy ones using the same signature database

automatic image segmentation by dynamic region merging this paper addresses the automatic image segmentation problem in a region merging style with an initially oversegmented image in which many regions or superpixels with homogeneous color are detected an image segmentation is performed by iteratively merging the regions according to a statistical test there are two essential issues in a region merging algorithm order of merging and the stopping criterion in the proposed algorithm these two issues are solved by a novel predicate which is defined by the sequential probability ratio test and the minimal cost criterion starting from an oversegmented image neighboring regions are progressively merged if there is an evidence for merging according to this predicate we show that the merging order follows the principle of dynamic programming this formulates the image segmentation as an inference problem where the final segmentation is established based on the observed image we also prove that the produced segmentation satisfies certain global properties in addition a faster algorithm is developed to accelerate the region merging process which maintains a nearest neighbor graph in each iteration experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm

energy minimization of contours using boundary conditions reconstruction of objects from a scene may be viewed as a data fitting problem using energy minimizing splines as the basic shape the process of obtaining the minimum to construct the best shape can sometimes be important some of the potential problems in the euler lagrangian variational solution proposed by kass et al 1988 were brought to light by amini et al 1990 and a dynamic programming dp method was also suggested in this paper we further develop the dp solution we show that in certain cases the discrete form of the solution presented by amini et al and adopted subsequently by others may also produce local minima and develop a strategy to avoid this we provide a stronger form of the conditions necessary to derive a solution when the energy depends on the second derivative as in the case of active contours

on deformable models for visual pattern recognition this paper reviews model based methods for non rigid shape recognition these methods model match and classify non rigid shapes which are generally problematic for conventational algorithms using rigid models issues including model representation optimization criteria formulation model matching and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field this paper emphasizes on 2d deformable models their potential applications and future research directions particularly on deformable pattern classification are discussed

adaptive stochastic approximation by the simultaneous perturbation method stochastic approximation sa has long been applied for problems of minimizing loss functions or root finding with noisy input information as with all stochastic search algorithms there are adjustable algorithm coefficients that must be specified and that can have a profound effect on algorithm performance it is known that choosing these coefficients according to an sa analog of the deterministic newton raphson algorithm provides an optimal or near optimal form of the algorithm however directly determining the required hessian matrix or jacobian matrix for root finding to achieve this algorithm form has often been difficult or impossible in practice the paper presents a general adaptive sa algorithm that is based on a simple method for estimating the hessian matrix while concurrently estimating the primary parameters of interest the approach applies in both the gradient free optimization kiefer wolfowitz and root finding stochastic gradient based robbins monro settings and is based on the simultaneous perturbation sp idea introduced previously the algorithm requires only a small number of loss function or gradient measurements per iteration independent of the problem dimension to adaptively estimate the hessian and parameters of primary interest aside from introducing the adaptive sp approach the paper presents practical implementation guidance asymptotic theory and a nontrivial numerical evaluation also included is a discussion and numerical analysis comparing the adaptive sp approach with the iterate averaging approach to accelerated sa

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 framework for multiple snakes and its applications we present a framework for segmentation of multiple objects whose shapes are similar but image qualities are different our framework is based on the snake or active contour method in which a new kind of energy called group energy is introduced the group energy is used to handle the sharing of properties across multiple objects and also to allow contours of objects with good image qualities to be used as reference contours for remaining objects during optimization in this framework we also deal with rotations among similar objects by applying group energy after removing the rotation offset comprehensive testing has been performed on synthetic and real images demonstrating that our framework has significantly better performance of segmentation compared to the original individual snake

on stochastic gradient and subgradient methods with adaptive steplength sequences traditionally stochastic approximation sa schemes have been popular choices for solving stochastic optimization problems however the performance of standard sa implementations can vary significantly based on the choice of the steplength sequence and in general little guidance is provided about good choices motivated by this gap we present two adaptive steplength schemes for strongly convex differentiable stochastic optimization problems equipped with convergence theory that aim to overcome some of the reliance on user specific parameters the first scheme referred to as a recursive steplength stochastic approximation rsa scheme optimizes the error bounds to derive a rule that expresses the steplength at a given iteration as a simple function of the steplength at the previous iteration and certain problem parameters the second scheme termed as a cascading steplength stochastic approximation csa scheme maintains the steplength sequence as a piecewise constant decreasing function with the reduction in the steplength occurring when a suitable error threshold is met then we allow for nondifferentiable objectives but with bounded subgradients over a certain domain in such a regime we propose a local smoothing technique based on random local perturbations of the objective function that leads to a differentiable approximation of the function assuming a uniform distribution on the local randomness we establish a lipschitzian property for the gradient of the approximation and prove that the obtained lipschitz bound grows at a modest rate with problem size this facilitates the development of an adaptive steplength stochastic approximation framework which now requires sampling in the product space of the original measure and the artificially introduced distribution

a wavelet frame based image force model for active contouring algorithms this paper proposes a directional image force dif for active contouring dif is the inner product of the zero crossing strength zcs of wavelet frame coefficients and the normal of a snake by representing strength and orientation of edges at multiple resolution levels dif markedly improves the immunity of snakes to noise and convexity

adaptive reproducing kernel particle method for extraction of the cortical surface we propose a novel adaptive approach based on the reproducing kernel particle method rkpm to extract the cortical surfaces of the brain from three dimensional 3 d magnetic resonance images mris to formulate the discrete equations of the deformable model a flexible particle shape function is employed in the galerkin approximation of the weak form of the equilibrium equations the proposed support generation method ensures that support of all particles cover the entire computational domains the deformable model is adaptively adjusted by dilating the shape function and by inserting or merging particles in the high curvature regions or regions stopped by the target boundary the shape function of the particle with a dilation parameter is adaptively constructed in response to particle insertion or merging the proposed method offers flexibility in representing highly convolved structures and in refining the deformable models self intersection of the surface during evolution is prevented by tracing backward along gradient descent direction from the crest interface of the distance field which is computed by fast marching these operations involve a significant computational cost the initial model for the deformable surface is simple and requires no prior knowledge of the segmented structure no specific template is required e g an average cortical surface obtained from many subjects the extracted cortical surface efficiently localizes the depths of the cerebral sulci unlike some other active surface approaches that penalize regions of high curvature comparisons with manually segmented landmark data are provided to demonstrate the high accuracy of the proposed method we also compare the proposed method to the finite element method and to a commonly used cortical surface extraction approach the cruise method we also show that the independence of the shape functions of the rkpm from the underlying mesh enhances the convergence speed of the deformable model

adaptive nonlinear shape matching for unconstrained handwritten character recognition in this paper we propose an adaptive nonlinear shape matching method which can compensate for the various distortions in unconstrained handwritten characters in the proposed method structural information is incorporated to improve the accuracy of matching and only neighboring pixels of each black pixel are considered to reduce the computational complexity of single matching procedure also iterative nonlinear shape matching procedures in each subregion are adaptively accomplished according to the results of that subregion in order to accelerate the convergence speed of the matching procedure in order to verify the performance of the proposed method experiments with large set unconstrained handwritten hangul character database pe92 have been performed experimental results reveal that the proposed method is superior to the previous nonlinear shape matching method in processing speed and accuracy of matching

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

a scaled stochastic approximation algorithm consider a stochastic system of such complexity that its performance can only be evaluated by using simulation or direct experimentation to optimize the expected performance of such systems as a function of several continuous input parameters decision variables we present a scaled stochastic approximation algorithm for finding the zero root of the gradient of the response function in each iteration of the scaled algorithm two independent gradient estimates are sampled at the current estimate of the optimal input parameter vector to compute a scale free estimate of the next search direction we establish sufficient conditions to ensure strong consistency and asymptotic normality of the resulting estimator of the optimal input parameter vector strong consistency is also established for a variant of the scaled algorithm with kesten s acceleration an experimental performance comparison of the scaled algorithm and the classical robbins monro algorithm in two simple queueing systems reveals some of the practical advantages of the scaled algorithm

a coarse to fine deformable contour optimization framework this paper introduces a novel coarse to fine deformable contour optimization framework which is composed of two main components the first component uses scale space and information theories to produce a coarser representation of the input image to be used in a coarse to fine optimization scheme the employment of information theory ensures that maximal image information is propagated to the coarse images and employment of scale spaces provides a mechanism to change the image coarseness locally based on the deformable contour model definition the second component of this framework uses a novel combination of dynamic programming and gradient descent methods to optimize the contour energy on coarser representations and then use the obtained coarse contour positions in finer optimizations the motivation in using a combination of dynamic programming and gradient descent method is to take advantage of each method s efficiency and avoid their drawbacks in order to verify the performance of this framework we constructed a deformable contour model for the spatiotemporal tracking of closed contours and optimized the model energy under this framework experiments on this system performed using synthetic images and real world echocardiographic sequences demonstrated the effectiveness and practicality of this framework

the contracting curve density algorithm fitting parametric curve models to images using local self adapting separation criteria the task of fitting parametric curve models to the boundaries of perceptually meaningful image regions is a key problem in computer vision with numerous applications such as image segmentation pose estimation object tracking and 3 d reconstruction in this article we propose the contracting curve density ccd algorithm as a solution to the curve fitting problem the ccd algorithm extends the state of the art in two important ways first it applies a novel likelihood function for the assessment of a fit between the curve model and the image data this likelihood function can cope with highly inhomogeneous image regions because it is formulated in terms of local image statistics the local image statistics are learned on the fly from the vicinity of the expected curve they provide therefore locally adapted criteria for separating the adjacent image regions these local criteria replace often used predefined fixed criteria that rely on homogeneous image regions or specific edge properties the second contribution is the use of blurred curve models as efficient means for iteratively optimizing the posterior density over possible model parameters these blurred curve models enable the algorithm to trade off two conflicting objectives namely heaving a large area of convergence and achieving high accuracy we apply the ccd algorithm to several challenging image segmentation and 3 d pose estimation problems our experiments with rgb images show that the ccd algorithm achieves a high level of robustness and sub pixel accuracy even in the presence of severe texture shading clutter partial occlusion and strong changes of illumination

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

martingale transforms with non atomic limits and stochastic approximation a sufficient condition for the limit of a martingale transform to posses a continuous distribution is given the result is used to show that for a stochastic approximation procedure if the adjustment rate is too small then it would not converge to the target value a s furthermore if the adjustment rate is taken to be 1 n as usual but the derivative of the regression function at the target value is 0 then the convergence rate is shown to be logn instead of sqrt n the rate obtained when the derivative is non zero

multichannel deconvolution of seismic signals using statistical mcmc methods in this paper we propose two multichannel blind deconvolution algorithms for the restoration of two dimensional 2d seismic data both algorithms are based on a 2d reflectivity prior model and use iterative multichannel deconvolution procedures which deconvolve the seismic data while taking into account the spatial dependency between neighboring traces the first algorithm employs in each step a modified maximum posterior mode mpm algorithm which estimates a reflectivity column from the corresponding observed trace using the estimate of the preceding reflectivity column the second algorithm takes into account estimates of both the preceding and subsequent columns in the estimation process both algorithms are applied to synthetic and real data and demonstrate better results compared to those obtained by a single channel deconvolution method expectedly the second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm

precise segmentation of multimodal images we propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region of interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels we follow the most conventional approaches in that initial images and desired maps of regions are described by a joint markov gibbs random field mgrf model of independent image signals and interdependent region labels however our focus is on more accurate model identification to better specify region borders each empirical distribution of image signals is precisely approximated by a linear combination of gaussians lcg with positive and negative components we modify an expectation maximization em algorithm to deal with the lcgs and also propose a novel em based sequential technique to get a close initial lcg approximation with which the modified em algorithm should start the proposed technique identifies individual lcg models in a mixed empirical distribution including the number of positive and negative gaussians initial segmentation based on the lcg models is then iteratively refined by using the mgrf with analytically estimated potentials the convergence of the overall segmentation algorithm at each stage is discussed experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms

affine similar shape retrieval application to multiview 3 d object recognition the feasibility of representing a three dimensional 3 d object with a small number of standard views is studied the object boundary of each view is considered as a two dimensional 2 d shape and is represented by the locations of the maxima of its curvature scale space css image contours the idea is to identify an unknown object from an image taken from a random view by using the stored descriptions of the standard views the css image has been selected for mpeg 7 standardization the maxima of css image have already been used to represent 2 d shapes in different applications under similarity transforms since the new application involves affine transforms we first examine the effects of general affine transforms on the representation and show that the locations of the maxima of the css image do not move dramatically even under large affine transformations our system for shape based retrieval from large image databases is then applied to multiview 3 d object representation and recognition our collection of 3 d objects consists of 18 aircraft of different shapes three silhouette contours corresponding to random views are separately used as input for each object results indicate that robust and efficient 3 d free form object recognition through multiview representation can be achieved using the css representation

optimal estimation of contour properties by cross validated regularization the problem of estimating the properties of smooth continuous contours from discrete noisy samples is used as vehicle to demonstrate the robustness of cross validated regularization applied to a vision problem a method for estimation of contour properties based on smoothing spline approximations is presented generalized cross validation is to devise an automatic algorithm for finding the optimal value of the smoothing regularization parameter from the data the cross validated smoothing splines are then used to obtain optimal estimates of the derivatives of quantized contours experimental results are presented which demonstrate the robustness of the method applied to the estimation of curvature of quantized contours under variable scale rotation and partial occlusion these results suggest the application of generalized cross validation to other computer vision algorithms involving regularization

dynamics of the infinite ranged potts model we formulate a theory of single spin flip dynamics for the infinite rangeq state potts model we derive a fokker planck equation without diffusive term from a phenomenological master equation it describes the approach to equilibrium of the time dependent probability density and thus generalizes griffiths 1966 result for the ising model we particularly compare the dynamic evolutions ofq 2 andq 3 systems when sinusoidal external fields are applied in the caseq 2 we find evidence of a nonequilibrium phase transition and forq 3 period doubling bifurcations are observed yielding a good estimate of feigenbaum s universal exponent

dynamic programming for detecting tracking and matching deformable contours the problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision terzopoulos et al 1987 proposed an approach to detect the contour regions of complex shapes assuming a user selected initial contour not very far from the desired solution we propose to further explore the information provided by the user s selected points and apply an optimal method to detect contours which allows a segmentation of the image the method is based on dynamic programming dp and applies to a wide variety of shapes it is exact and not iterative we also consider a multiscale approach capable of speeding up the algorithm by a factor of 20 although at the expense of losing the guaranteed optimality characteristic the problem of tracking and matching these contours is addressed for tracking the final contour obtained at one frame is sampled and used as initial points for the next frame then the same dp process is applied for matching a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not the algorithm is again based on dp and the optimal solution is guaranteed we have demonstrated the algorithms on natural objects in a large spectrum of applications including interactive segmentation and automatic tracking of the regions of interest in medical images

3 d model localization using high resolution reconstruction of monocular image sequences in this paper we present a complete system for the recognition and localization of a three dimensional 3 d model from a sequence of monocular images with known motion the originality of this system is twofold first it uses a purely 3 d approach starting from the 3 d reconstruction of the scene and ending by the 3 d matching of the model second unlike most monocular systems we do not use token tracking to match successive images rather subpixel contour matching is used to recover more precisely complete 3 d contours in contrast with the token tracking approaches which yield a representation of the 3 d scene based on disconnected segments or points this approach provides us with a denser and higher level representation of the scene the reconstructed contours are fused along successive images using a simple result derived from the kalman filter theory the fusion process increases the localization precision and the robustness of the 3 d reconstruction finally corners are extracted from the 3 d contours they are used to generate hypotheses of the model position using a hypothesize and verify algorithm that is described in detail this algorithm yields a robust recognition and precise localization of the model in the scene results are presented on infrared image sequences with different resolutions demonstrating the precision of the localization as well as the robustness and the low computational complexity of the algorithms

feedback and weighting mechanisms for improving jacobian estimates in the adaptive simultaneous perturbation algorithm it is known that a stochastic approximation sa analogue of the deterministic newton raphson algorithm provides an asymptotically optimal or near optimal form of stochastic search however directly determining the required jacobian matrix or hessian matrix for optimization has often been difficult or impossible in practice this paper presents a general adaptive sa algorithm that is based on a simple method for estimating the jacobian matrix while concurrently estimating the primary parameters of interest relative to prior methods for adaptively estimating the jacobian matrix the paper introduces two enhancements that generally improve the quality of the estimates for underlying jacobian hessian matrices thereby improving the quality of the estimates for the primary parameters of interest the first enhancement rests on a feedback process that uses previous jacobian estimates to reduce the error in the current estimate the second enhancement is based on an optimal weighting of per iteration jacobian estimates from the use of simultaneous perturbations the algorithm requires only a small number of loss function or gradient measurements per iteration independent of the problem dimension to adaptively estimate the jacobian matrix and parameters of primary interest

unsupervised contour representation and estimation using b splines and a minimum description length criterion this paper describes a new approach to adaptive estimation of parametric deformable contours based on b spline representations the problem is formulated in a statistical framework with the likelihood function being derived from a region based image model the parameters of the image model the contour parameters and the b spline parameterization order i e the number of control points are all considered unknown the parameterization order is estimated via a minimum description length mdl type criterion a deterministic iterative algorithm is developed to implement the derived contour estimation criterion the result is an unsupervised parametric deformable contour it adapts its degree of smoothness complexity number of control points and it also estimates the observation image model parameters the experiments reported in the paper performed on synthetic and real medical images confirm the adequate and good performance of the approach

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

salient closed boundary extraction with ratio contour we present ratio contour a novel graph based method for extracting salient closed boundaries from noisy images this method operates on a set of boundary fragments that are produced by edge detection boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency we encode the gestalt laws of proximity and continuity in a novel boundary saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary this new measure attempts to remove a possible bias toward short boundaries we present a polynomial time algorithm for finding the most salient closed boundary we also present supplementary preprocessing steps that facilitate the application of ratio contour to real images we compare ratio contour to two closely related methods for extracting closed boundaries elder and zucker s method based on the shortest path algorithm and williams and thornber s method based on spectral analysis and a strongly connected components algorithm this comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images

shape matching using lat and its application to handwritten numeral recognition this paper describes an iterative technique for gradually deforming a mask binary image with successive local affine transformation lat operations so as to yield the best match to an input binary image as one new and promising approach toward robust handwritten character recognition the method uses local shapes in the sense that the lat of each point at one location is optimized using locations of other points by means of least squares data fitting using gaussian window functions it also uses a multiscale refinement technique that decreases the spread of window functions with each iteration especially in handwritten character recognition structural information is indispensable for robust shape matching or discrimination the method is enhanced to explicitly incorporate structures by weighting the above least squares criterion with similarity measures of both topological and geometric features of the mask and input images moreover deformation constraints are imposed on each iteration not only to promote and stabilize matching convergence but also to suppress an excessive matching process shape matching experiments have been successfully carried out using skeletons of totally unconstrained handwritten numerals

constrained active appearance models for segmentation of triplane echocardiograms this paper presents multiview and multiframe active appearance models aams for left ventricular segmentation in triplane echocardiograms we describe a general way of integrating local edge detector based segmentation algorithms into the aam framework the feasibility of this approach is evaluated by comparing an aam constrained by a dynamic programming dp based snake with an unconstrained aam and an aam constrained by manually defined landmarks a leave one out validation scheme was used for training and testing of the methods evaluation was done in 36 patients suffering from various heart diseases using manually determined volumes and ejection fractions ef as reference the segmentation was initialized by manual selection of the mitral annulus and apex in three imaging planes the differences in volume between manual segmentation and the best automatic method dp constrained aam were 3 1 plusmn 20 ml meanplusmnsd at end diastole and 0 61 plusmn 13 ml at end systole the difference in ef was 1 3 plusmn 6 3 comparable to the interobserver variability we show that 1 constraining the model to manually defined landmarks improves volume and ef estimates compared to unconstrained aams 2 further improvement is achieved using a dp constrained aam and 3 segmentation in triplane echocardiograms gives higher accuracy than single plane data

wall position and thickness estimation from sequences of echocardiographic images presents a new method for endocardial inner and epicardial outer contour estimation from sequences of echocardiographic images the framework herein introduced is fine tuned for parasternal short axis views at the papillary muscle level the underlying model is probabilistic it captures the relevant features of the image generation physical mechanisms and of the heart morphology contour sequences are assumed to be two dimensional noncausal first order markov random processes each variable has a spatial index and a temporal index the image pixels are modeled as rayleigh distributed random variables with means depending on their positions inside endocardium between endocardium and pericardium or outside pericardium the complete probabilistic model is built under the bayesian framework as estimation criterion the maximum a posteriori map is adopted to solve the optimization problem one is led to joint estimation of contours and distributions parameters the authors introduce an algorithm herein named iterative multigrid dynamic programming imdp it is a fully data driven scheme with no ad hoc parameters the method is implemented on an ordinary workstation leading to computation times compatible with operational use experiments with simulated and real images are presented

multivariate adaptive stochastic approximation on considere une version multivariable de l approximation stochastique adaptative developpee recemment par lai et robbins 1978 1979