a polynomial piecewise constant approximation method based on dual constraint relaxation for segmenting images with intensity inhomogeneity abstract in the past decade several local region based level set models have been proposed to segment images with intensity inhomogeneity in general these models are designed based on one assumption i e intensity inhomogeneity is slowly varying in image domain however this assumption is not valid for those images with serious intensity inhomogeneity which inevitably leads to poor segmentation performance of existing models in this paper we propose a novel level set method named as polynomial piecewise constant approximation ppca to well segment images with serious intensity inhomogeneity the basic idea of the ppca method is to transform the original image to piecewise constant image so as to make piecewise constant segmentation criterion become applicable specially we firstly define an initial objective function with some constraint conditions to transform the original image then in order to obtain desirable piecewise constant image and highlight the anti noise performance the ppca method is used to realize the dual constraint relaxation for objective function the dual constraint relaxation reflects in two parts on one hand the objective function based on local region is exploited to replace the pointwise approximation method on the other hand considering the variance of local intensity distribution and the reliability of polynomial approximation we utilize a gaussian pyramid convolution strategy to devise polynomial fitting the ppca method relaxes the constraint condition of objective function so that the piecewise constant image is easily approximated according to piecewise constant segmentation criterion we obtain the partial differential equation based on polynomial piecewise constant approximation finally we utilize level set method to construct the energy functional the visual and quantitative experimental results demonstrate that the proposed ppca method can yield better results than existing classical local models for segmenting images with serious intensity inhomogeneity

segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

robust noise region based active contour model via local similarity factor for image segmentation abstract image segmentation using a region based active contour model could present difficulties when its noise distribution is unknown to overcome this problem this paper proposes a novel region based model for the segmentation of objects or structures in images by introducing a local similarity factor which relies on the local spatial distance within a local window and local intensity difference to improve the segmentation results by using this local similarity factor the proposed method can accurately extract the object boundary while guaranteeing certain noise robustness furthermore the proposed algorithm completely avoids the pre processing steps typical of region based contour model segmentation resulting in a higher preservation of image details experiments performed on synthetic images and real word images demonstrate that the proposed algorithm as compared with the state of art algorithms is more efficient and robust to higher noise level manifestations in the images

sobolev active contours all previous geometric active contour models that have been formulated as gradient flows of various energies use the same l 2 type inner product to define the notion of gradient recent work has shown that this inner product induces a pathological riemannian metric on the space of smooth curves however there are also undesirable features associated with the gradient flows that this inner product induces in this paper we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with sobolev type inner products we call the resulting flows sobolev active contours sobolev metrics induce favorable regularity properties in their gradient flows in addition sobolev active contours favor global translations but are not restricted to such motions they are also less susceptible to certain types of local minima in contrast to traditional active contours these properties are particularly useful in tracking applications we demonstrate the general methodology by reformulating some standard edge based and region based active contour models as sobolev active contours and show the substantial improvements gained in segmentation

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

a fast multiphase image segmentation model for gray images abstract in this paper we propose a fast multiphase image segmentation model for gray images our proposed model is based on the piecewise constant multiphase vese chan model the globally convex segmentation method and the split bregman method our proposed model has the advantages of the vese chan model and can deal with piecewise constant multiphase images well besides our proposed model is much more efficient than the vese chan model by applying the globally convex segmentation method and the split bregman method we have tested our proposed model with many synthetic and real images experimental results have demonstrated the efficiency and robustness of our proposed model

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

stochastic motion and the level set method in computer vision stochastic active contours based on recent work on stochastic partial differential equations spdes this paper presents a simple and well founded method to implement the stochastic evolution of a curve first we explain why great care should be taken when considering such an evolution in a level set framework to guarantee the well posedness of the evolution and to make it independent of the implicit representation of the initial curve a stratonovich differential has to be introduced to implement this differential a standard ito plus drift approximation is proposed to turn an implicit scheme into an explicit one subsequently we consider shape optimization techniques which are a common framework to address various applications in computer vision like segmentation tracking stereo vision etc the objective of our approach is to improve these methods through the introduction of stochastic motion principles the extension we propose can deal with local minima and with complex cases where the gradient of the objective function with respect to the shape is impossible to derive exactly finally as an application we focus on image segmentation methods leading to what we call stochastic active contours

localizing region based active contours in this paper we propose a natural framework that allows any region based segmentation energy to be re formulated in a local way we consider local rather than global image statistics and evolve a contour based on local information localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method the presented technique is versatile enough to be used with any global region based active contour energy and instill in it the benefits of localization we describe this framework and demonstrate the localization of three well known energies in order to illustrate how our framework can be applied to any energy we then compare each localized energy to its global counterpart to show the improvements that can be achieved next an in depth study of the behaviors of these energies in response to the degree of localization is given finally we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models

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

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

optimal gabor filters for texture segmentation texture segmentation involves subdividing an image into differently textured regions many texture segmentation schemes are based on a filter bank model where the filters called gabor filters are derived from gabor elementary functions the goal is to transform texture differences into detectable filter output discontinuities at texture boundaries by locating these discontinuities one can segment the image into differently textured regions distinct discontinuities occur however only if the gabor filter parameters are suitably chosen some previous analysis has shown how to design filters for discriminating simple textures designing filters for more general natural textures though has largely been done ad hoc we have devised a more rigorously based method for designing gabor filters it assumes that an image contains two different textures and that prototype samples of the textures are given a priori we argue that gabor filter outputs can be modeled as rician random variables often approximated well as gaussian rv s and develop a decision theoretic algorithm for selecting optimal filter parameters to improve segmentations for difficult texture pairs we also propose a multiple filter segmentation scheme motivated by the rician model experimental results indicate that our method is superior to previous methods in providing useful gabor filters for a wide range of texture pairs

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

segmentation of gabor filtered textures using deterministic relaxation a supervised texture segmentation scheme is proposed in this article the texture features are extracted by filtering the given image using a filter bank consisting of a number of gabor filters with different frequencies resolutions and orientations the segmentation model consists of feature formation partition and competition processes in the feature formation process the texture features from the gabor filter bank are modeled as a gaussian distribution the image partition is represented as a noncausal markov random field mrf by means of the partition process the competition process constrains the overall system to have a single label for each pixel using these three random processes the a posteriori probability of each pixel label is expressed as a gibbs distribution the corresponding gibbs energy function is implemented as a set of constraints on each pixel by using a neural network model based on hopfield network a deterministic relaxation strategy is used to evolve the minimum energy state of the network corresponding to a maximum a posteriori map probability this results in an optimal segmentation of the textured image the performance of the scheme is demonstrated on a variety of images including images from remote sensing

an improved region based model with local statistical features for image segmentation in this paper we propose a new region based active contour model acm for image segmentation in particular this model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighborhood of a contour by this improved region fitting term images with noise intensity non uniformity and low contrast boundaries can be well segmented integrated with the duality theory and the anisotropic diffusion process based on structure tensor a new regularization term is defined through the duality formulation to penalize the length of active contour by this new regularization term the structural information of images is utilized to improve the ability of capturing the geometric features such as corners and cusps from a numerical point of view we minimize the energy function of our model by an efficient dual algorithm which avoids the instability and the non differentiability of traditional numerical solutions e g the gradient descent method experiments on medical and natural images demonstrate the advantages of the proposed model over other segmentation models in terms of both efficiency and accuracy

an error free levison algorithm to solve integer toeplitz system abstract this paper presents an error free form of levison algorithm to solve integer nonsymmetrical toeplitz system it removes roundoff errors their accumulation can when using classic algorithms deteriorate or destroy the solution it retains the speed of original levison algorithms its modular form can be easily implemented for parallel computer

genetic algorithms in truss topological optimization the present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms in developing near optimal topologies of load bearing truss structures the problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space the development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness the approach is an adaptation of the ground structure method of topology optimization and is implemented in a two level genetic algorithm based search in this process the kinematic stability constraints are imposed at one level followed by the treatment of response constraints at a second level of optimization singular value decomposition is used to assess the kinematic stability constraints at the first level of design and results in the creation of a finite number of increasing weight stable topologies member sizing is then introduced at a second level of design where minimal weight and response constraints on stresses displacements and buckling are simultaneously considered at this level the only admissible topologies are those identified during the first stage and any stable combination thereof the design variable representation scheme allows for both the removal and addition of structural members during optimization

multiple resolution segmentation of textured images a multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior in addition an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions both algorithms use a causal gaussian autoregressive model to describe the mean variance and spatial correlation of the image textures together the algorithms can be used to perform unsupervised texture segmentation the multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified this method results in accurate segmentations and requires significantly less computation than some previously known methods the field containing the classification of each pixel in the image is modeled as a markov random field segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint at each resolution the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks the unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the aic information criterion clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters concurrently the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached

classification using geometric level sets a variational level set method is developed for the supervised classification problem nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin based loss and a geometric regularization term new to machine learning the surface area of the decision boundary this geometric level set classifier is analyzed in terms of consistency and complexity through the calculation of its e entropy for multicategory classification an efficient scheme is developed using a logarithmic number of decision functions in the number of classes rather than the typical linear number of decision functions geometric level set classification yields performance results on benchmark data sets that are competitive with well established methods

relaxed notions of curvature and a lumped strain method for elastic plates the paper proposes an approximation method lumped strain method lsm for elastic plates based on generalized notions of the gaussian and mean curvatures and on a relaxation of the energy functional to the space of continuous piecewise linear functions the method adapts ideas from the theory of gamma convergence we restrict our attention to the case of the simply supported plate and state the proof of convergence of the method we give an application to the rhombic plate and compare the results with those obtained by standard finite element approximations

segmentation by texture using correlation the correlation coefficients are used for segmentation according to texture they are first evaluated on a set of square regions forming two levels of the quadratic picture tree or pyramid if the coefficients of a square and its four children in the tree are similar then that region is considered to be of uniform texture if not it is replaced by its children in this way the split and merge algorithm is used to achieve a preliminary segmentation it is followed by a grouping algorithm using the correlation coefficients and the region adjacency graph plus a small region elimination step the latter regions are grouped according to their gray level because texture cannot be defined reliably on very small regions examples of implementation on four pictures are included

active contours driven by local image fitting energy a new region based active contour model that embeds the image local information is proposed in this paper by introducing the local image fitting lif energy to extract the local image information our model is able to segment images with intensity inhomogeneities moreover a novel method based on gaussian filtering for variational level set is proposed to regularize the level set function it can not only ensure the smoothness of the level set function but also eliminate the requirement of re initialization which is very computationally expensive experiments show that the proposed method achieves similar results to the lbf local binary fitting energy model but it is much more computationally efficient in addition our approach maintains the sub pixel accuracy and boundary regularization properties

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

γ convergence of external approximations in boundary value problems involving the bi laplacian in addition to the various uses it was introduced for the theory of convergence offers a rather natural setting for discussing and developing nonorthodox approximation methods for variational problems for certain boundary value problems involving the bi laplacian sequences of discrete functionals are here defined and are shown to converge to the corresponding functionals of the continuous problems the minimizers of the discrete functionals provide converging approximations to the solution of the limit problem in question thus we obtain approximation schemes that are nonconforming but direct and that can be treated by current algorithms for symmetric and positive definite functionals the class of problems considered in this paper includes the stokes problem in fluid dynamics the loading problem of 2 d isotropic elastostatics and some boundary value problems of the kirchhoff love theory of plates also discussed is an extension of the discretization method that seems suitable for treating more general boundary value problems of elastic plates but whose convergence is conditional to a conjecture that remains to be proved a relevant application to the so called babuska paradox is presented

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

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

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

an iterative error free algorithm to solve vandermonde systems the paper describes an algorithm to solve vandermonde system of linear equations the algorithm is error free i e it does not introduce either rounding off errors or errors caused by finite length of computer word into the solution cost analysis and its comparison to alternative error free method are included

dream 2 s deformable regions driven by an eulerian accurate minimization method for image and video segmentation this paper deals with image and video segmentation using active contours we propose a general form for the energy functional related to region based active contours we compute the associated evolution equation using shape derivation tools and accounting for the evolving region based terms then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions as an example it has been successfully applied to face segmentation in real video sequences

texture classification by wavelet packet signatures this correspondence introduces a new approach to characterize textures at multiple scales the performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty five natural textures both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations where each wavelet packet channel reflected a specific scale and orientation sensitivity wavelet packet representations for twenty five natural textures were classified without error by a simple two layer network classifier an analyzing function of large regularity d sub 20 was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments d sub 6 in addition energy representations computed from the standard wavelet decomposition alone 17 features provided classification without error for the twenty five textures included in our study the reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation classification and subtle discrimination of texture

image segmentation by unifying region and boundary information a two stage method of image segmentation based on gray level cooccurrence matrices is described an analysis of the distributions within a cooccurrence matrix defines an initial pixel classification into both region and interior or boundary designations local consistency of pixel classification is then implemented by minimizing the entropy of local information where region information is expressed via conditional probabilities estimated from the cooccurrence matrices and boundary information via conditional probabilities which are determined a priori the method robustly segments an image into homogeneous areas and generates an edge map the technique extends easily to general edge operators an example is given for the canny operator applications to synthetic and forward looking infrared flir images are given

rapid and brief communication gacv geodesic aided c v method a novel algorithm for image segmentation is proposed the proposed method incorporates geodesic curves and c v method to raise active contours performance on image segmentation moreover we extend our method to color images by practical experiments it is verified that our model obtains better results than original methods especially with respect to images within holes complex background weak edges and noise

flux maximizing geometric flows several geometric active contour models have been proposed for segmentation in computer vision and image analysis the essential idea is to evolve a curve in 2d or a surface in 3d under constraints from image forces so that it clings to features of interest in an intensity image recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented however it is still unclear how to apply these techniques to images of narrow elongated structures such as blood vessels where intensity contrast may be low and reliable region statistics cannot be computed to address this problem we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve in 2d or a surface in 3d the key idea is to exploit the direction of the vector field along with its magnitude the calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions we illustrate its advantages with several level set based segmentations of 2d and 3d angiography images of blood vessels

global regularizing flows with topology preservation for active contours and polygons active contour and active polygon models have been used widely for image segmentation in some applications the topology of the object s to be detected from an image is known a priori despite a complex unknown geometry and it is important that the active contour or polygon maintain the desired topology in this work we construct a novel geometric flow that can be added to image based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon we emphasize that unlike other methods for topology preservation the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change the flow also serves as a global regularity term for the evolving contour and has smoothness properties similar to curvature flow these properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes the proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles the evolution of a single point on the contour depends on all other points of the contour which is different from traditional curve evolutions in the computer vision literature

gibbs random fields cooccurrences and texture modeling gibbs random field grf models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination the authors show an explicit relationship between cooccurrences and a large class of grf s this result comes from a new framework based on a set theoretic concept called the aura set and on measures of this set aura measures this framework is also shown to be useful for relating different texture analysis tools the authors show how the aura set can be constructed with morphological dilation how its measure yields cooccurrences and how it can be applied to characterizing the behavior of the gibbs model for texture in particular they show how the aura measure generalizes to any number of gray levels and neighborhood order some properties previously known for just the binary nearest neighbor grf finally the authors illustrate how these properties can guide one s intuition about the types of grf patterns which are most likely to form

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

high dimensional statistical measure for region of interest tracking this paper deals with region of interest roi tracking in video sequences the goal is to determine in successive frames the region which best matches in terms of a similarity measure a roi defined in a reference frame some tracking methods define similarity measures which efficiently combine several visual features into a probability density function pdf representation thus building a discriminative model of the roi this approach implies dealing with pdfs with domains of definition of high dimension to overcome this obstacle a standard solution is to assume independence between the different features in order to bring out low dimension marginal laws and or to make some parametric assumptions on the pdfs at the cost of generality we discard these assumptions by proposing to compute the kullback leibler divergence between high dimensional pdfs using the k th nearest neighbor framework in consequence the divergence is expressed directly from the samples i e without explicit estimation of the underlying pdfs as an application we defined 5 7 and 13 dimensional feature vectors containing color information including pixel based gradient based and patch based and spatial layout the proposed procedure performs tracking allowing for translation and scaling of the roi experiments show its efficiency on a movie excerpt and standard test sequences selected for the specific conditions they exhibit partial occlusions variations of luminance noise and complex motion

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

an unconstrained mixed method for the biharmonic problem in this work we present a finite element method for the biharmonic problem based on the primal mixed formulation of ciarlet and raviart a mixed finite element method for the biharmonic equation in symposium on mathematical aspects of finite elements in partial differential equations c de boor ed academic press new york 1974 pp 125 143 we introduce a dual mesh and a suitable approximation of the constraint that enables us to eliminate the auxiliary variable with no computational effort thus the discrete problem turns to be governed by a system of linear equations with symmetric and positive definite coefficients and can be solved by classical algorithms the construction of the stiffness matrix is obtained by using courant triangles and can be done with great efficiency

active contours driven by global and local weighted signed pressure force for image segmentation abstract this paper proposes a new global and local weighted signed pressure force spf based active contour model acm to segment various types of images first by introducing the normalized global minimum absolute differences as the coefficients of global inner and outer region fitting centers a new global weighted spf gwspf is defined which makes the best of the difference information of inner and outer regions and improves segmentation performance second by introducing the normalized local minimum absolute differences as the coefficients of local inner and outer region fitting centers similarly a new local weighted spf lwspf is defined and added to the above global weighted spf third the global and local within class variances of the image are used to weight the gwspf and the lwspf which can automatically adjust the effect degrees of the gwspf and the lwspf experiments on many kinds of real world images have validated that the proposed model is superior to popular acms in segmentation accuracy in addition it is robust to the initial curve

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

a variational framework for multiregion pairwise similarity based image segmentation variational cost functions that are based on pairwise similarity between pixels can be minimized within level set framework resulting in a binary image segmentation in this paper we extend such cost functions and address multi region image segmentation problem by employing a multi phase level set framework for multi modal images cost functions become more complicated and relatively difficult to minimize we extend our previous work proposed for background foreground separation to the segmentation of images in more than two regions we also demonstrate an efficient implementation of the curve evolution which reduces the computational time significantly finally we validate the proposed method on the berkeley segmentation data set by comparing its performance with other segmentation techniques

robust level set image segmentation via a local correntropy based k means clustering it is still a challenging task to segment real world images since they are often distorted by unknown noise and intensity inhomogeneity to address these problems we propose a novel segmentation algorithm via a local correntropy based k means lck clustering due to the correntropy criterion the clustering algorithm can decrease the weights of the samples that are away from their clusters as a result lck based clustering algorithm can be robust to the outliers the proposed lck clustering algorithm is incorporated into the region based level set segmentation framework the iteratively re weighted algorithm is used to solve the lck based level set segmentation method extensive experiments on synthetic and real images are provided to evaluate our method showing significant improvements on both noise sensitivity and segmentation accuracy as compared with the state of the art approaches

geodesic active contours and level sets for the detection and tracking of moving objects this paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model this model is composed of two components namely the static background and the mobile moving objects one both components are zero mean and obey laplacian or gaussian law this statistical framework is used to provide the motion detection boundaries additionally the original frame is used to provide the moving object boundaries then the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function this function is minimized using a gradient descent method a new approach named hermes is proposed which exploits aspects from the well known front propagation algorithms and compares favorably to them very promising experimental results are provided using real video sequences

active contours driven by local likelihood image fitting energy for image segmentation accurate image segmentation is an essential step in image analysis and understanding where active contour models play an important part due to the noise low contrast and intensity inhomogeneity in images many segmentation algorithms suffer from limited accuracy this paper presents a novel region based active contour model for image segmentation by using the variational level set formulation in this model we construct the local likelihood image fitting llif energy functional by describing the neighboring intensities with local gaussian distributions the means and variances of local intensities in the llif energy functional are spatially varying functions which can be iteratively estimated during an energy minimization process to guide the contour evolving toward object boundaries to address diverse image segmentation needs we also expand this model to the multiphase level set multi scale gaussian kernels and narrowband formulations the proposed model has been compared with several state of the art active contour models on images with different modalities our results indicate that the proposed llif model achieves superior performance in image segmentation

geometrically induced force interaction for three dimensional deformable models in this paper we propose a novel 3 d deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions this external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient the evolution of the deformable model is solved using the level set method so that topological changes are handled automatically the relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves the geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries and it gives the deformable model a high invariancy in initialization configurations the voxel interactions across the whole image domain provide a global view of the object boundary representation giving the external force a long attraction range the bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross boundary initializations and facilitates the handling of weak edges and broken boundaries in addition we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm the new deformable model can effectively overcome image noise we provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images and show that the proposed method achieves significant improvements against existing image gradient techniques

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

level set evolution with locally linear classification for image segmentation this paper presents a novel local region based level set model for image segmentation in each local region we define a locally weighted least squares energy to fit a linear classifier with level set representation these local energy functions are then integrated over the whole image domain to develop a global segmentation model the objective function in this model is thereafter minimized via level set evolution in this process the parameters related to the locally linear classifier are iteratively estimated by introducing the locally linear functions to separate background and foreground in local regions our model not only achieves accurate segmentation results but also is robust to initialization extensive experiments are reported to demonstrate that our method holds higher segmentation accuracy and more initialization robustness compared with the classical region based and local region based methods

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

exact algorithm of multidimensional circulant deconvolution the paper presents an efficient algorithm to solve a one dimensional as well as n dimensional circulant convolution system the proposed algorithm does not introduce computational errors into the solution its derivation is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

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

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

a new fast multiphase image segmentation algorithm based on nonconvex regularizer we present a new variational model for the soft multiphase image segmentation in the model we introduce a nonconvex regularizer on the membership functions which are used as indicators of different homogeneous regions the nonconvex regularizer performs better than the usual convex ones in that i it well preserves geometric shapes of the homogeneous regions and ii it protects edges from oversmoothing which is a common drawback of the convex regularizer to solve the nonconvex minimization problem we design a new fast alternative iteration algorithm which is robust to the setting of the parameters in the model we conduct comprehensive experiments to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for image segmentation the algorithm achieves more accurate results compared to other well known convex variational methods for image segmentation

level set segmentation with multiple regions the popularity of level sets for segmentation is mainly based on the sound and convenient treatment of regions and their boundaries unfortunately this convenience is so far not known from level set methods when applied to images with more than two regions this communication introduces a comparatively simple way how to extend active contours to multiple regions keeping the familiar quality of the two phase case we further suggest a strategy to determine the optimum number of regions as well as initializations for the contours

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

error free algorithms to solve special and general discrete systems of linear equations this paper presents a survey of error free algorithms to solve various systems of linear equations the presented algorithms do not introduce computational errors into the solution and thus they are well suited to solve ill conditioned linear systems the error free algorithms are based on modulo arithmetic two basic approaches have been investigated in the paper the first one is based on iterative scheme using one modulus only the other one is parallel and uses several moduli and the chinese theorem it is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals

the set of forces that ideal trusses or wire webs under tension can support abstract the problem of determining those multiplets of forces or sets of force multiplets acting at a set of points such that there exists a truss structure or wire web that can support these force multiplets with all the elements of the truss or wire web being under tension is considered the two dimensional problem where the points are at the vertices of a convex polygon is essentially solved each multiplet of forces must be such that the net anticlockwise torque around any vertex of the forces summed over any number of consecutive points clockwise past the vertex must be non negative and one can find a truss structure that supports under tension and only supports those force multiplets in a convex polyhedron of force multiplets that is generated by a finite number of force multiplets each satisfying the torque condition progress is also made on the problem where only a subset of the points are at the vertices of a convex polygon and the other points are inside in particular in the case where only one point is inside an explicit procedure is described for constructing a suitable truss if one exists an alternative recipe to that provided by guevara vasquez et al 2011 based on earlier work of camar eddine and seppecher 2003 is given for constructing a truss structure with elements under either compression or tension that supports an arbitrary collection of balanced forces at the vertices of a convex polygon finally some constraints are given on the forces that a three dimension truss or wire web under tension must satisfy

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

active curve recovery of region boundary patterns this study investigates the recovery of region boundary patterns in an image by a variational level set method which drives an active curve to coincide with boundaries on which a feature distribution matches a reference distribution we formulate the scheme for both the kullback leibler and the bhattacharyya similarities and apply it in two conditions the simultaneous recovery of all region boundaries consistent with a given outline pattern and segmentation in the presence of faded boundary segments the first task uses an image based geometric feature and the second a photometric feature in each case the corresponding curve evolution equation can be viewed as a geodesic active contour gac flow having a variable stopping function which depends on the feature distribution on the active curve this affords a potent global representation of the target boundaries which can effectively drive active curve segmentation in a variety of otherwise adverse conditions detailed experimentation shows that the scheme can significantly improve on current region and edge based formulations

a lumped stress method for plane elastic problems and the discrete continuum approximation this paper proposes a rational method to approximate a plane elastic body through a latticed structure composed of truss elements the method is based on the introduction of a relaxed stress energy that allows an extension of the original problem to a larger space of admissible stress fields including stresses concentrated along lines use is made of polyhedral approximations of the airy stress function the truss analogy is employed to obtain a displacement formulation the paper includes several numerical applications of the method to sample problems a numerical convergence study and comparisons with exact solutions and standard finite element approximations

an algorithm to solve hilbert systems of linear equations precisely abstract this paper presents an error free form of levison s algorithm to solve a rational general hilbert system of linear equations it removes roundoff errors their accumulation if using classic algorithms can destroy the result the algorithm employs modular arithmetic the number of necessary operations in one modulo class is proportional to n 2 the method is well suited for implementation in parallel computers

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

minimization of region scalable fitting energy for image segmentation intensity inhomogeneities often occur in real world images and may cause considerable difficulties in image segmentation in order to overcome the difficulties caused by intensity inhomogeneities we propose a region based active contour model that draws upon intensity information in local regions at a controllable scale a data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour this energy is then incorporated into a variational level set formulation with a level set regularization term from which a curve evolution equation is derived for energy minimization due to a kernel function in the data fitting term intensity information in local regions is extracted to guide the motion of the contour which thereby enables our model to cope with intensity inhomogeneity in addition the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function experimental results for synthetic and real images show desirable performances of our method

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes

unsupervised texture segmentation using markov random field models the problem of unsupervised segmentation of textured images is considered the only explicit assumption made is that the intensity data can be modeled by a gauss markov random field gmrf the image is divided into a number of nonoverlapping regions and the gmrf parameters are computed from each of these regions a simple clustering method is used to merge these regions the parameters of the model estimated from the clustered segments are then used in two different schemes one being all approximation to the maximum a posterior estimate of the labels and the other minimizing the percentage misclassification error the proposed approach is contrasted with the algorithm of s lakshamanan and h derin 1989 which uses a simultaneous parameter estimation and segmentation scheme the results of the adaptive segmentation algorithm of lakshamanan and derin are compared with a simple nearest neighbor classification scheme to show that if enough information is available simple techniques could be used as alternatives to computationally expensive schemes