application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

elastically adaptive deformable models we present a technique for the automatic adaptation of a deformable model s elastic parameters within a kalman filter framework for shape estimation applications the novelty of the technique is that the model s elastic parameters are not constant but spatio temporally varying the variation of the elastic parameters depends on the distance of the model from the data and the rate of change of this distance each pass of the algorithm uses physics based modeling techniques to iteratively adjust both the geometric and the elastic degrees of freedom of the model in response to forces that are computed from the discrepancy between the model and the data by augmenting the state equations of an extended kalman filter to incorporate these additional variables we are able to significantly improve the quality of the shape estimation therefore the model s elastic parameters are always initialized to the same value and they are subsequently modified depending on the data and the noise distribution we present results demonstrating the effectiveness of our method for both two dimensional and three dimensional data

regularized bundle adjustment to model heads from image sequences without calibration data we address the structure from motion problem in the context of head modeling from video sequences for which calibration data is not available this task is made challenging by the fact that correspondences are difficult to establish due to lack of texture and that a quasi euclidean representation is required for realism we have developed an approach based on regularized bundle adjustment it takes advantage of our rough knowledge of the head s shape in the form of a generic face model it allows us to recover relative head motion and epipolar geometry accurately and consistently enough to exploit a previously developed stereo based approach to head modeling in this way complete and realistic head models can be acquired with a cheap and entirely passive sensor such as an ordinary video camera with minimal manual intervention we chose to demonstrate and evaluate our technique mainly in the context of head modeling we do so because it is the application for which all the tools required to perform the complete reconstruction are available to us we will however argue that the approach is generic and could be applied to other tasks such as body modeling for which generic facetized models exist

multi level shape representation using global deformations andlocally adaptive finite elements we present a model based method for the multi level shape pose estimation and abstraction of an object s surface from range data the surface shape is estimated based on the parameters of a superquadric that is subjected to global deformations tapering and bending and a varying number of levels of local deformations local deformations are implemented using locally adaptive finite elements whose shape functions are piecewise cubic functions with c 1 continuity the surface pose is estimated based on the model s translational and rotational degrees of freedom the algorithm first does a coarse fit solving for a first approximation to the translation rotation and global deformation parameters and then does several passes of mesh refinement by locally subdividing triangles based on the distance between the given datapoints and the model the adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties of conformity non degeneracy and smoothness are maintained each pass of the algorithm uses physics based modeling techniques to iteratively adjust the global and local parameters of the model in response to forces that are computed from approximation errors between the model and the data we present results demonstrating the multi level shape representation for both sparse and dense range data

a note on distributional properties of the joreskog sorbom fit indices in introducing the lisrel model for systems of linear structural equations joreskog and sorbom proposed two goodness of fit indices gfi and agfi their asymptotic distributions and some statistical properties are discussed

statistical approach to shape from shading reconstruction of three dimensional face surfaces from single two dimensional images the human visual system is proficient in perceiving three dimensional shape from the shading patterns in a two dimensional image how it does this is not well understood and continues to be a question of fundamental and practical interest in this paper we present a new quantitative approach to shape from shading that may provide some answers we suggest that the brain through evolution or prior experience has discovered that objects can be classified into lower dimensional object classes as to their shape extraction of shape from shading is then equivalent to the much simpler problem of parameter estimation in a low dimensional space we carry out this proposal for an important class of three dimensional 3d objects human heads from an ensemble of several hundred laser scanned 3d heads we use principal component analysis to derive a low dimensional parameterization of head shape space an algorithm for solving shape from shading using this representation is presented it works well even on real images where it is able to recover the 3d surface for a given person maintaining facial detail and identity from a single 2d image of his face this algorithm has applications in face recognition and animation

q manifolds and mackenzie theory double lie algebroids were discovered by kirill mackenzie from the study of double lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for lie algebroids and double vector bundles in this paper we establish a simple alternative characterization of double lie algebroids in a supermanifold language namely we show that a double lie algebroid in mackenzie s sense is equivalent to a double vector bundle endowed with a pair of commuting homological vector fields of appropriate weights our approach helps to simplify and elucidate mackenzie s original definition we show how it fits into a bigger picture of equivalent structures on neighbor double vector bundles it also opens ways for extending the theory to multiple lie algebroids which we introduce here

a robust real time algorithm for facial shape recovery from a single image containing cast shadow under general unknown lighting it is difficult to find a non iterative solution for statistical shape from shading sfs for a single image containing cast shadow under unknown arbitrary light conditions this is because it is not trivial to find a mapping from a convex cone in the image space to a point in the depth space to find a non iterative solution for the statistical sfs which has not been done yet to our knowledge we show that it is possible to approximate a cone of images illumination cone to a polytope by a nonlinear function which is a transform from cartesian coordinates to hyperspherical coordinates the images of a subject form a convex cone in the image space and it can be better to use the direction of an image in hyperspherical coordinates as an input feature for the mapping rather than the image itself the maximum error occurs on one of the vertices of the polytope if we choose the objective function to be the squared error of a linear function in the hyperspherical space hence we can solve the least square problem using the cost only for the vertices in deriving the solution we use the generalized rayleigh quotient canonical correlation analysis cca and prior information on input images to reduce the solution space and improve 3 d reconstruction performance in experiments the proposed scheme performs robustly under light variations and is fast enough for real time applications

multidimensional morphable models a framework for representing and matching object classes we describe a flexible model for representing images of objects of a certain class known a priori such as faces and introduce a new algorithm for matching it to a novel image and thereby perform image analysis the flexible model known as a multidimensional morphable model is learned from example images of objects of a class in this paper we introduce an effective stochastic gradient descent algorithm that automatically matches a model to a novel image several experiments demonstrate the robustness and the broad range of applicability of morphable models our approach can provide novel solutions to several vision tasks including the computation of image correspondence object verification and image compression

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

a skeleton family generator via physics based deformable models this paper presents a novel approach for object skeleton family extraction the introduced technique utilizes a 2 d physics based deformable model that parameterizes the objects shape deformation equations are solved exploiting modal analysis and proportional to model physical characteristics a different skeleton is produced every time generating in this way a family of skeletons the theoretical properties and the experiments presented demonstrate that obtained skeletons match to hand labeled skeletons provided by human subjects even in the presence of significant noise and shape variations cuts and tears and have the same topology as the original skeletons in particular the proposed approach produces no spurious branches without the need of any known skeleton pruning method

a coupled statistical model for face shape recovery from brightness images we focus on the problem of developing a coupled statistical model that can be used to recover facial shape from brightness images of faces we study three alternative representations for facial shape these are the surface height function the surface gradient and a fourier basis representation we jointly capture variations in intensity and the surface shape representations using a coupled statistical model the model is constructed by performing principal components analysis on sets of parameters describing the contents of the intensity images and the facial shape representations by fitting the coupled model to intensity data facial shape is implicitly recovered from the shape parameters experiments show that the coupled model is able to generate accurate shape from out of training sample intensity images

boundary finding with prior shape and smoothness models we propose a unified framework for boundary finding where a bayesian formulation based on prior knowledge and the edge information of the input image likelihood is employed the prior knowledge in our framework is based on principal component analysis of four different covariance matrices corresponding to independence smoothness statistical shape and combined models respectively indeed snakes modal analysis fourier descriptors and point distribution models can be derived from or linked to our approaches of different prior models when the true training set does not contain enough variability to express the full range of deformations a mixed covariance matrix uses a combined prior of the smoothness and statistical variation modes it adapts gradually to use more statistical modes of variation as larger data sets are available

physically based active shape models initialization and optimization in this paper we describe a new approach for 2 d object segmentation using an automatic method applied on images with problems as partial information overlapping objects many objects in a single scene severe noise conditions and locating objects with a very high degree of deformation we use a physically based shape model to obtain a deformable template which is defined on a canonical orthogonal coordinate system the proposed methodology works starting from the output of an edge detector which is processed to automatically obtain an approximation of the shape the final estimation of the shapes is obtained fitting a deformable template model which is defined on a learned surface of deformation results from biological images are presented

manin triples for lie bialgebroids in his study of dirac structures a notion which includes both poisson structures and closed 2 forms t courant introduced a bracket on the direct sum of vector fields and 1 forms this bracket does not satisfy the jacobi identity except on certain subspaces in this paper we systematize the properties of this bracket in the definition of a courant algebroid this structure on a vector bundle e rightarrow m consists of an antisymmetric bracket on the sections of e whose jacobi anomaly has an explicit expression in terms of a bundle map e rightarrow tm and a field of symmetric bilinear forms on e when m is a point the definition reduces to that of a lie algebra carrying an invariant nondegenerate symmetric bilinear form for any lie bialgebroid a a over m a notion defined by mackenzie and xu there is a natural courant algebroid structure on a oplus a which is the drinfel d double of a lie bialgebra when m is a point conversely if a and a are complementary isotropic subbundles of a courant algebroid e closed under the bracket such a bundle with dimension half that of e is called a dirac structure there is a natural lie bialgebroid structure on a a whose double is isomorphic to e the theory of manin triples is thereby extended from lie algebras to lie algebroids our work gives a new approach to bihamiltonian structures and a new way of combining two poisson structures to obtain a third one we also take some tentative steps toward generalizing drinfel d s theory of poisson homogeneous spaces from groups to groupoids

3 d shape recovery using distributed aspect matching an approach to the recovery of 3 d volumetric primitives from a single 2 d image is presented the approach first takes a set of 3 d volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives conditional probabilities capture the ambiguity of mappings between levels of the hierarchy from a region segmentation of the input image the authors present a formulation of the recovery problem based on the grouping of the regions into aspects no domain independent heuristics are used only the probabilities inherent in the aspect hierarchy are exploited once the aspects are recovered the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity as a front end to an object recognition system the approach provides the indexing power of complex 3 d object centered primitives while exploiting the convenience of 2 d viewer centered aspect matching aspects are used to represent a finite vocabulary of 3 d parts from which objects can be constructed

superquadric segmentation in range images via fusion of region and boundary information the high potential of superquadrics as modeling elements for image segmentation tasks has been pointed out for years in the computer vision community in this work we employ superquadrics as modeling elements for multiple object segmentation in range images segmentation is executed in two stages first a hypothesis about the values of the segmentation parameters is generated second the hypothesis is refined locally in both stages object boundary and region information are considered boundary information is derived via model based edge detection in the input range image hypothesis generation uses boundary information to isolate image regions that can be accurately described by superquadrics within hypothesis refinement a game theoretic framework is used to fuse the two information sources by associating an objective function to each information source iterative optimization of the two objective functions in succession outputs a precise description of all image objects we demonstrate experimentally that this approach substantially improves the most established method in superquadric segmentation in terms of accuracy and computational efficiency we demonstrate the applicability of our segmentation framework in real world applications by constructing a novel robotic system for automatic unloading of jumbled box like objects from platforms

stochastic approximation and rate distortion analysis for robust structure and motion estimation recent research on structure and motion recovery has focused on issues related to sensitivity and robustness of existing techniques one possible reason is that in practical applications the underlying assumptions made by existing algorithms are often violated in this paper we propose a framework for 3d reconstruction from short monocular video sequences taking into account the statistical errors in reconstruction algorithms detailed error analysis is especially important for this problem because the motion between pairs of frames is small and slight perturbations in its estimates can lead to large errors in 3d reconstruction we focus on the following issues physical sources of errors their experimental and theoretical analysis robust estimation techniques and measures for characterizing the quality of the final reconstruction we derive a precise relationship between the error in the reconstruction and the error in the image correspondences the error analysis is used to design a robust recursive multi frame fusion algorithm using stochastic approximation as the framework since it is capable of dealing with incomplete information about errors in observations rate distortion analysis is proposed for evaluating the quality of the final reconstruction as a function of the number of frames and the error in the image correspondences finally to demonstrate the effectiveness of the algorithm examples of depth reconstruction are shown for different video sequences

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

representation of similarity in three dimensional object discrimination how does the brain represent visual objects in simple perceptual generalization tasks the human visual system performs as if it represents the stimuli in a low dimensional metric psychological space shepard 1987 in theories of three dimensional 3d shape recognition the role of feature space representations as opposed to structural biederman 1987 or pictorial ullman 1989 descriptions has long been a major point of contention if shapes are indeed represented as points in a feature space patterns of perceived similarity among different objects must reflect the structure of this space the feature space hypothesis can then be tested by presenting subjects with complex parameterized 3d shapes and by relating the similarities among subjective representations as revealed in the response data by multidimensional scaling shepard 1980 to the objective parameterization of the stimuli the results of four such tests accompanied by computational simulations support the notion that discrimination among 3d objects may rely on a low dimensional feature space representation and suggest that this space may be spanned by explicitly encoded class prototypes

self calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters in this paper the theoretical and practical feasibility of self calibration in the presence of varying intrinsic camera parameters is under investigation the paper s main contribution is to propose a self calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming focusing cameras the feasibility of the approach is illustrated on real and synthetic examples besides this a theoretical proof is given which shows that the absence of skew in the image plane is sufficient to allow for self calibration a counting argument is developed which depending on the set of constraints gives the minimum sequence length for self calibration and a method to detect critical motion sequences is proposed

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

appearance based structure from motion using linear classes of 3 d models in this paper we address the problem of recovering 3 d models from sequences of partly calibrated images with unknown correspondence to that end we integrate tracking structure from motion with geometric constraints specifically in the form of linear class models in a single framework the key to making the proposed approach work is the use of appearance based model matching and refinement which updates the estimated correspondences on each iteration of the algorithm another key feature is the matching of a 3 d model directly with the input images without the conventional 2 step approach of stereo data recovery and 3 d model fitting initialization of the linear class model to one of the input images the reference image is currently partly manual this synthesis and refine approach or appearance based constrained structure from motion abcsfm is especially useful in recovering shapes of objects whose general structure is known but which may have little discernable texture in significant parts of their surfaces we applied the proposed approach to 3 d face modeling from multiple images to create new 3 d faces for decface a synthetic talking head developed at cambridge research laboratory digital equipment corporation the decface model comprises a collection of 3 d triangular and rectangular facets with nodes as vertices in recovering the decface model we assume that the sequence of images is taken with a camera with unknown focal length and pose the geometric constraints used are of the form of linear combination of prototypes of 3 d faces of real people results of this approach show its good convergence properties and its robustness against cluttered backgrounds

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

acquiring 3 d models from sequences of contours this paper explores shape from contour for acquiring 3 d graphics models in this method a continuous sequence of images is taken as an object rotates a smooth convex shape can be estimated instantaneously from its contour and by the first derivative of contour movement trace of contour or contour distribution with time we also analyze shapes that do not satisfy the conditions of smoothness and visibility which are indispensable for modeling an object a region that does not expose as contour yields a nonsmoothness in the tracked contour movement we can thus detect such a region by contour distribution filtering and extract its accurate location by computing the left and right derivatives of the distribution this has not been studied previously these unknown regions are obtained for further investigation using other visual cues a general approach for building a geometrical object model using contours is then described the entire process from silhouettes to a 3 d model is based local computation this is promising for producing shapes in real time our direct goal is to establish 3 d graphics models of human faces for the growing needs of visual communications we have obtained some good results

hierarchical active shape models using the wavelet transform active shape models asms are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability this paper presents a method that overcomes this limitation by using a hierarchical formulation of active shape models using the wavelet transform the statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis and used as priors in the contour s deformation some of these priors reflect relatively global shape characteristics of the object boundaries whereas some of them capture local and high frequency shape characteristics and thus serve as local smoothness constraints this formulation achieves two objectives first it is robust when only a limited number of training samples is available second by using local statistics as smoothness constraints it eliminates the need for adopting ad hoc physical models such as elasticity or other smoothness models which do not necessarily reflect true biological variability examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved even with as few as five training samples

smooth functional and structural maps on the neocortex via orthonormal bases of the laplace beltrami operator functional and structural maps such as a curvature cortical thickness and functional magnetic resonance imaging mri maps indexed over the local coordinates of the cortical manifold play an important role in neuropsychiatric studies due to the highly convoluted nature of the cerebral cortex and image quality these functions are generally uninterpretable without proper methods of association and smoothness onto the local coordinate system in this paper we generalized the spline smoothing problem wahba 1990 from a sphere to any arbitrary two dimensional 2 d manifold with boundaries we first seek a numerical solution to orthonormal basis functions of the laplace beltrami lb operator with neumann boundary conditions for a 2 d manifold m then solve the spline smoothing problem in a reproducing kernel hilbert space r k h s of real valued functions on manifold m with kernel constructed from the basis functions the explicit discrete lb representation is derived using the finite element method calculated directly on the manifold coordinates so that finding discrete lb orthonormal basis functions is equivalent to solving an algebraic eigenvalue problem and then smoothed functions in r k h s can be represented as a linear combination of the basis functions we demonstrate numerical solutions of spherical harmonics on a unit sphere and brain orthonormal basis functions on a planum temporale manifold then synthetic data is used to quantify the goodness of the smoothness compared with the ground truth and discuss how many basis functions should be incorporated in the smoothing we present applications of our approach to smoothing sulcal mean curvature cortical thickness and functional statistical maps on submanifolds of the neocortex

on the sequential accumulation of evidence in this paper we introduce a method for sequentially accumulating evidence as it pertains to an active observer seeking to identify an object in a known environment we develop a probabilistic framework based on a generalized inverse theory where assertions are represented by conditional probability density functions this leads to a sequential recognition strategy in which evidence is accumulated over successive viewpoints using bayesian chaining until a definitive assertion can be made to illustrate the theory we show how the characteristics of belief distributions can be exploited in a model based recognition problem where the task is to identify an unknown model from a database of known objects on the basis of parameter estimates we illustrate the robustness of the algorithm through recognition experiments in two very different contexts 1 a highly structured recognition context where 3 d parametric models can be estimated directly from range data 2 a complex environment where the relationship between the data and the model is learned through an appearance based strategy specifically the flow fields computed through the object s motion are used as structural signatures for recognition

lie bialgebroids and poisson groupoids lie bialgebras arise as infinitesimal invariants of poisson lie groups a lie bialgebra is a lie algebra g with a lie algebra structure on the dual g which is compatible with the lie algebra g in a certain sense for a poisson group g the multiplicative poisson structure induces a lie algebra structure on the lie algebra dual g which makes g g into a lie bialgebra in fact there is a one one correspondence between poisson lie groups and lie bialgebras if the lie groups are assumed to be simply connected 7 16 19 the importance of poisson lie groups themselves arises in part from their role as classical limits of quantum groups 8 and in part because they provide a class of poisson structures for which the realization problem is tractable 15 poisson groupoids were introduced by weinstein 24 as a generalization of both poisson lie groups and the symplectic groupoids which arise in the integration of arbitrary poisson manifolds 4 11 he noted that the lie algebroid dual a g of a poisson groupoid g itself has a lie algebroid structure but did not develop the infinitesimal structure further in this paper we introduce and study a natural infinitesimal invariant for poisson groupoids the lie bialgebroids of the title our ultimate purpose is to develop a lie theory for poisson groupoids parallel to that for poisson groups in this paper we are primarily concerned with the first half of this process that is with the construction of the lie bialgebroid of a poisson groupoid after the preliminary 2 in which we describe the generalization to arbitrary lie algebroids of the exterior calculus and schouten calculus in 3 we define a lie bialgebroid to be a lie algebroid a whose dual a is also equipped with a lie algebroid structure such that the coboundary operator d a a associated to a satisfies a cocycle equation with respect to a the lie algebra of sections of a this is clearly a straightforward extension of the concept of a lie bialgebra 16 but cannot be formalized in lie algebroid cohomological terms since there is no satisfactory adjoint representation for a general lie algebroid most of 3 is devoted to proving that this definition is self dual if a a is a lie bialgebroid then a a is also in 4 we briefly consider the special case of lie bialgebroids satisfying a triangularity condition which include some important examples such as the usual triangular lie bialgebras and lie bialgebroids associated to poisson manifolds the techniques used in 2 4 are similar to those known for lie bialgebras it would be possible by suitably generalizing the proof for poisson groups to prove

higher order approximations to the distributions of fit indexes under fixed alternatives in structural equation models higher order approximations to the distributions of fit indexes for structural equation models under fixed alternative hypotheses are obtained in nonnormal samples as well as normal ones the fit indexes include the normal theory likelihood ratio chi square statistic for a posited model the corresponding statistic for the baseline model of uncorrelated observed variables and various fit indexes as functions of these two statistics the approximations are given by the edgeworth expansions for the distributions of the fit indexes under arbitrary distributions numerical examples in normal and nonnormal samples with the asymptotic and simulated distributions of the fit indexes show the relative inappropriateness of the normal theory approximation using noncentral chi square distributions a simulation for the confidence intervals of the fit indexes based on the normal theory studentized estimators under normality with a small sample size indicates an advantage for the approximation by the cornish fisher expansion over those by the noncentral chi square distribution and the asymptotic normality

deformable shape finding with models based on kernel methods in this paper a new kernel based deformable model is proposed for detecting deformable shapes to incorporate valuable information for shape detection such as edge orientations into the shape representation a novel scheme based on kernel methods has been utilized the variation model of a deformable shape is established by a set of training samples of the shape represented in a kernel feature space the proposed deformable model consists of two parts a set of basis vectors describing the sample subspace including the shape representations of the training samples and a feasibility constraint generated by the one class support vector machine to describe the feasible region of the training samples in the sample subspace the aim of the proposed feasibility constraint is to avoid finding some invalid shapes by using the proposed deformable model an efficient algorithm without initial solutions is developed for shape detection the proposed approach was tested against real images experimental results show the effectiveness of the proposed deformable model and prove the feasibility of the proposed approach

independent component analysis a flexible nonlinearity and decorrelating manifold approach independent component analysis ica finds a linear transformation to variables that are maximally statistically independent we examine ica and algorithms for finding the best transformation from the point of view of maximizing the likelihood of the data in particular we discuss the way in which scaling of the unmixing matrix permits a static nonlinearity to adapt to various marginal densities we demonstrate a new algorithm that uses generalized exponential functions to model the marginal densities and is able to separate densities with light tails we characterize the manifold of decorrelating matrices and show that it lies along the ridges of high likelihood unmixing matrices in the space of all unmixing matrices we show how to find the optimum ica matrix on the manifold of decorrelating matrices and as an example we use the algorithm to find independent component basis vectors for an ensemble of portraits

fast facial shape recovery from a single image with general unknown lighting by using tensor representation in this paper we propose a fast 3 d facial shape recovery algorithm from a single image with general unknown lighting in order to derive the algorithm we formulate a nonlinear least square problem with two parameter vectors which are related to personal identity and light conditions we then combine the spherical harmonics for the surface normals of a human face with tensor algebra and show that in a certain condition the dimensionality of the least square problem can be further reduced to one tenth of the regular subspace based model by using tensor decomposition n mode svd which greatly speeds up the computations in order to enhance the shape recovery performance we have incorporated prior information in updating the parameters in the experiment the proposed algorithm takes less than 0 4s to reconstruct a face and shows a significant performance improvement over other reported schemes

simplex mesh diffusion snakes integrating 2d and 3d deformable models and statistical shape knowledge in a variational framework in volumetric medical imaging the boundaries of structures are frequently blurred due to insufficient resolution this artefact is particularly serious in structures such as articular joints where different cartilage surfaces appear to be linked at the contact regions traditional image segmentation techniques fail to separate such erroneously linked structures and a sensible approach has been the introduction of prior knowledge to the segmentation process although several 3d prior knowledge based techniques that could successfully segment these structures have been published most of them are pixel labelling schemes that generate pixellated images with serious geometric distortions the simplex mesh diffusion snakes segmentation technique presented here is an extension of the two dimensional diffusion snakes but without any restriction on the number of dimensions of the data set this technique integrates a simplex mesh a region based deformable model and statistical shape knowledge into a single energy functional so that it takes into account both the image information available directly from the data set and the shape statistics obtained from a training process the resulting segmentations converge correctly to well defined boundaries and provide a feasible location for those removed boundaries the algorithm has been evaluated using 2d and 3d data sets obtained with magnetic resonance imaging mri and has proved to be robust to most of the mri artefacts providing continuous and smooth curves or surfaces with sub pixel resolution additionally this novel technique opens a wide range of opportunities for segmentation and tracking time dependent 3d structures or data sets with more than three dimensions due to its non restrictive mathematical formulation

symmetric shape from shading using self ratio image in this paper we present a symmetric shape from shading sfs approach to recover both shape and albedo for symmetric objects lambertian surfaces with unknown varying albedo and orthographic projections are assumed in our formulation of symmetric sfs we have two image irradiance equations one is the standard equation used in sfs and the other is a self ratio image irradiance equation this new image irradiance equation relates the self ratio image which is defined as the ratio of two halves of the input image to light source and surface shape the introduction of the self ratio image facilitates the direct use of symmetry cue based on the self ratio image a new model based symmetric source from shading algorithm is also presented we then propose symmetric sfs algorithms to recover both shape and albedo from a single image and present experimental results the new symmetric sfs scheme has one important property the existence of a unique global solution which consists of unique local solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a cal c 2 surface proofs for the existence of a unique solution in the cases of unknown constant and non constant albedos are provided

model based deformable surface finding for medical images describes a new global shape parameterization for smoothly deformable three dimensional 3 d objects such as those found in biomedical images whose diversity and irregularity make them difficult to represent in terms of fixed features or parts this representation is used for geometric surface matching to 3 d medical image data such as from magnetic resonance imaging mri the parameterization decomposes the surface into sinusoidal basis functions four types of surfaces are modeled tori open surfaces closed surfaces and tubes this parameterization allows a wide variety of smooth surfaces to be described with a small number of parameters extrinsic model based information is incorporated by introducing prior probabilities on the parameters surface finding is formulated as an optimization problem results of the method applied to synthetic images and 3 d medical images of the heart and brain are presented

from multiple stereo views to multiple 3 d surfaces we present a framework for 3 dimensional surface reconstruction that can be used to model fully 3 d scenes from an arbitrary number of stereo views taken from vastly different viewpoints this is a key step toward producing 3 d world descriptions of complex scenes using stereo and is a very challenging problem real world scenes tend to contain many 3 d objects they do not usually conform to the 2 1 2 d assumption made by traditional algorithms and one cannot take it for granted that the computed 3 d points can easily be clustered into separate groups furthermore stereo data is often incomplete and sometimes erroneous which makes the problem even more difficult by combining a particle based representation robust fitting and optimization of an image based objective function we have been able to reconstruct surfaces without any a priori knowledge of their topology and in spite of the noisiness of the stereo data our current implementation goes through three steps initializing a set of particles from the input 3 d data optimizing their location and finally grouping them into global surfaces using several complex scenes containing multiple objects we demonstrate the competence of this method and its ability to merge information and thus to go beyond what can be done with conventional stereo alone

recovery of nonrigid motion and structure the authors introduce a physically correct model of elastic nonrigid motion this model is based on the finite element method but decouples the degrees of freedom by breaking down object motion into rigid and nonrigid vibration or deformation modes the result is an accurate representation for both rigid and nonrigid motion that has greatly reduced dimensionality capturing the intuition that nonrigid motion is normally coherent and not chaotic because of the small number of parameters involved this representation is used to obtain accurate overstrained estimates of both rigid and nonrigid global motion it is also shown that these estimates can be integrated over time by use of an extended kalman filter resulting in stable and accurate estimates of both three dimensional shape and three dimensional velocity the formulation is then extended to include constrained nonrigid motion examples of tracking single nonrigid objects and multiple constrained objects are presented

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

three dimensional reconstruction of points and lines with unknown correspondence across images three dimensional reconstruction from a set of images is an important and difficult problem in computer vision in this paper we address the problem of determining image feature correspondences while simultaneously reconstructing the corresponding 3d features given the camera poses of disparate monocular views first two new affinity measures are presented that capture the degree to which candidate features from different images consistently represent the projection of the same 3d point or 3d line an affinity measure for point features in two different views is defined with respect to their distance from a hypothetical projected 3d pseudo intersection point similarly an affinity measure for 2d image line segments across three views is defined with respect to a 3d pseudo intersection line these affinity measures provide a foundation for determining unknown correspondences using weighted bipartite graphs representing candidate point and line matches across different images as a result of this graph representation a standard graph theoretic algorithm can provide an optimal simultaneous matching and triangulation of points across two views and lines across three views experimental results on synthetic and real data demonstrate the effectiveness of the approach

robust shape recovery from occluding contours using a linear smoother recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent for three or more views shape recovery is possible and several algorithms have recently been developed for this purpose we present a new approach to the multiframe stereo problem that does not depend on differential measurements in the image which may be noise sensitive instead we use a linear smoother to optimally combine all of the measurements available at the contours and other edges in all of the images this allows us to extract a robust and reasonably dense estimate of surface shape and to integrate shape information from both surface markings and occluding contours results are presented which empirically show that in the presence of noise smoothing over more than three views reduces the error even when the epipolar curve is nonplanar

recovery of parametric models from range images the case for superquadrics with global deformations a method for recovery of compact volumetric models for shape representation of single part objects in computer vision is introduced the models are superquadrics with parametric deformations bending tapering and cavity deformation the input for the model recovery is three dimensional range points model recovery is formulated as a least squares minimization of a cost function for all range points belonging to a single part during an iterative gradient descent minimization process all model parameters are adjusted simultaneously recovery position orientation size and shape of the model such that most of the given range points lie close to the model s surface a specific solution among several acceptable solutions where are all minima in the parameter space can be reached by constraining the search to a part of the parameter space the many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization results using real range data show that the recovered models are stable and that the recovery procedure is fast

an improved time adaptive self organizing map for high speed shape modeling in this paper an improved active contour model based on the time adaptive self organizing map with a high convergence speed and low computational complexity is proposed for this purpose the active contour model based on the original time adaptive self organizing map is modified in two ways adaptation of the speed parameter and reduction of the number of neurons by adapting the speed parameter the neuron motion speed is determined based on the distance of each neuron from the shape boundary which results in an increase in the speed of convergence of the contour using a smaller number of neurons the computational complexity is reduced to achieve this the number of neurons used in the contour is determined based on the boundary curvature the proposed model is studied and compared with the original time adaptive self organizing map both models are used in several experiments including a tracking application results reveal the higher speed and very good performance of the proposed model for real time applications

recovering facial shape using a statistical model of surface normal direction in this paper we show how a statistical model of facial shape can be embedded within a shape from shading algorithm we describe how facial shape can be captured using a statistical model of variations in surface normal direction to construct this model we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to cartesian points on a local tangent plane the distribution of surface normal directions is captured using the covariance matrix for the projected point positions the eigenvectors of the covariance matrix define the modes of shape variation in the fields of transformed surface normals we show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by lambert s law we demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details we assess the accuracy of the technique on a variety of images with ground truth and real world images

elastic model based segmentation of 3 d neuroradiological data sets this paper presents a new technique for the automatic model based segmentation of three dimensional 3 d objects from volumetric image data the development closely follows the seminal work of taylor and cootes on active shape models but is based on a hierarchical parametric object description rather than a point distribution model the segmentation system includes both the building of statistical models and the automatic segmentation of new image data sets via a restricted elastic deformation of shape models geometric models are derived from a sample set of image data which have been segmented by experts the surfaces of these binary objects are converted into parametric surface representations which are normalized to get an invariant object centered coordinate system surface representations are expanded into series of spherical harmonics which provide parametric descriptions of object shapes it is shown that invariant object surface parametrization provides a good approximation to automatically determine object homology in terms of sets of corresponding sets of surface points gray level information near object boundaries is represented by 1 d intensity profiles normal to the surface considering automatic segmentation of brain structures as their driving application the authors choice of coordinates for object alignment was the well accepted stereotactic coordinate system major variation of object shapes around the mean shape also referred to as shape eigenmodes are calculated in shape parameter space rather than the feature space of point coordinates segmentation makes use of the object shape statistics by restricting possible elastic deformations into the range of the training shapes the mean shapes are initialized in a new data set by specifying the landmarks of the stereotactic coordinate system the model elastically deforms driven by the displacement forces across the object s surface which are generated by matching local intensity profiles elastical deformations are limited by setting bounds for the maximum variations in eigenmode space the technique has been applied to automatically segment left and right hippocampus thalamus putamen and globus pallidus from volumetric magnetic resonance scans taken from schizophrenia studies the results have been validated by comparison of automatic segmentation with the results obtained by interactive expert segmentation

analysing images of curved surfaces a reflectance map makes the relationship between image intensity and surface orientation explicit trade offs between image intensity and surface orientation emerge which cannot be resolved locally in a single view existing methods for determining surface orientation from a single view embody assumptions about surface curvature the hessian matrix is introduced to represent surface curvature properties of surface curvature are expressed as properties of the hessian matrix for several classes of surface image analysis simplifies this result has already been established for planar surfaces forming trihedral corners similar simplification is demonstrated for developable surfaces and for the subclass of surfaces known as generalized cones these studies help to delineate shape information that can be determined from geometric measurements at object boundaries and shape information that can be determined from intensity measurements over sections of smoothly curved surface a novel technique called photometric stereo is discussed the idea of stereo is to obtain multiple images in order to determine the underlying scene precisely in photometric stereo the viewing direction is constant multiple images are obtained by varying the incident illumination it is shown that this provides sufficient information to determine surface orientation at each image point

shape from recognition a novel approach for 3 d face shape recovery in this paper we develop a novel framework for robust recovery of three dimensional 3 d surfaces of faces from single images the underlying principle is shape from recognition i e the idea that pre recognizing face parts can constrain the space of possible solutions to the image irradiance equation thus allowing robust recovery of the 3 d structure of a specific part parts of faces like nose lips and eyes are recognized and localized using robust expansion matching filter templates under varying pose and illumination specialized backpropagation based neural networks are then employed to recover the 3 d shape of particular face parts representation using principal components allows to efficiently encode classes of objects such as nose lips etc the specialized networks are designed and trained to map the principal component coefficients of the part images to another set of principal component coefficients that represent the corresponding 3 d surface shapes to achieve robustness to viewing conditions the network is trained with a wide range of illumination and viewing directions a method for merging recovered 3 d surface regions by minimizing the sum squared error in overlapping areas is also derived quantitative analysis of the reconstruction of the surface parts in varying illumination and pose show relatively small errors indicating that the method is robust and accurate several examples showing recovery of the complete face also illustrate the efficacy of the approach

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

cooperative robust estimation using layers of support we present an approach to the problem of representing images that contain multiple objects or surfaces rather than using an edge based approach to represent the segmentation of a scene we propose a multilayer estimation framework which uses support maps to represent the segmentation of the image into homogeneous chunks this support based approach can represent objects that are split into disjoint regions or have surfaces that are transparently interleaved our framework is based on an extension of robust estimation methods that provide a theoretical basis for support based estimation we use a selection criteria derived from the minimum description length principle to decide how many support maps to use in describing an image our method has been applied to a number of different domains including the decomposition of range images into constituent objects the segmentation of image sequences into homogeneous higher order motion fields and the separation of tracked motion features into distinct rigid body motions

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

the category of z2n supermanifolds in physics and in mathematics z2n gradings n 2 appear in various fields the corresponding sign rule is determined by the scalar product of the involved z2n degrees the z2n supergeometry exhibits challenging differences with the classical one nonzero degree even coordinates are not nilpotent and even respectively odd coordinates do not necessarily commute respectively anticommute pairwise in this article we develop the foundations of the theory we define z2n supermanifolds and provide examples in the ringed space and coordinate settings we thus show that formal series are the appropriate substitute for nilpotency moreover the class of z2 supermanifolds is closed with respect to the tangent and cotangent functors we explain that any n fold vector bundle has a canonical superization to a z2n supermanifold and prove that the fundamental theorem describing supermorphisms in terms of coordinates can be extended to the z2n context

a multiple baseline stereo a stereo matching method that uses multiple stereo pairs with various baselines generated by a lateral displacement of a camera to obtain precise distance estimates without suffering from ambiguity is presented matching is performed simply by computing the sum of squared difference ssd values the ssd functions for individual stereo pairs are represented with respect to the inverse distance and are then added to produce the sum of ssds this resulting function is called the sssd in inverse distance it is shown that the sssd in inverse distance function exhibits a unique and clear minimum at the correct matching position even when the underlying intensity patterns of the scene include ambiguities or repetitive patterns the authors first define a stereo algorithm based on the sssd in inverse distance and present a mathematical analysis to show how the algorithm can remove ambiguity and increase precision experimental results with real stereo images are presented to demonstrate the effectiveness of the algorithm

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

facial shape from shading and recognition using principal geodesic analysis and robust statistics the aim in this paper is to use principal geodesic analysis to model the statistical variations for sets of facial needle maps we commence by showing how to represent the distribution of surface normals using the exponential map shape deformations are described using principal geodesic analysis on the exponential map using ideas from robust statistics we show how this deformable model may be fitted to facial images in which there is significant self shadowing moreover we demonstrate that the resulting shape from shading algorithm can be used to recover accurate facial shape and albedo from real world images in particular the algorithm can effectively fill in the facial surface when more than 30 of its area is subject to self shadowing to investigate the utility of the shape parameters delivered by the method we conduct experiments with illumination insensitive face recognition we present a novel recognition strategy in which similarity is measured in the space of the principal geodesic parameters we also use the recovered shape information to generate illumination normalized prototype images on which recognition can be performed finally we show that from a single input image we are able to generate the basis images employed by a number of well known illumination insensitive recognition algorithms we also demonstrate that the principal geodesics provide an efficient parameterization of the space of harmonic basis images

adjusting shape parameters using model based optical flow residuals we present a method for estimating the shape of a deformable model using the least squares residuals from a model based optical flow computation this method is built on top of an estimation framework using optical flow and image features where optical flow affects only the motion parameters of the model using the results of this computation our new method adjusts all of the parameters so that the residuals from the flow computation are minimized we present face tracking experiments that demonstrate that this method obtains a better estimate of shape compared to related frameworks

rigid affine and locally affine registration of free form surfaces in this paper we propose a new framework to perform nonrigid surface registration it is based on various extensions of an iterative algorithm recently presented by several researchers besl and mckay 1992 champleboux et al 1992 chen and medioni 1992 menq and lai 1992 zhang 1994 to rigidly register surfaces represented by a set of 3d points when a prior estimate of the displacement is available our framework consists of three stages first we search for the best rigid displacement to superpose the two surfaces we show how to efficiently use curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm second we search for the best affine transformation we introduce differential information in points coordinates this allows us to match locally similar points then we show how principal frames and curvatures are transformed by an affine transformation finally we introduce this differential information in a global criterion minimized by extended kalman filtering in order to ensure the convergence of the algorithm third we locally deform the surface instead of computing a global affine transformation we attach to each point a local affine transformation varying smoothly along the surface we call this deformation a locally affine deformation all these stages are illustrated with experiments on various real biomedical surfaces teeth faces skulls brains and hearts which demonstrate the validity of the approach

three dimensional face shape by local fitting to a single reference model the authors present a simple method to estimate the three dimensional shape of a face from an input image using a single reference model based on least squares between the output of the linear nonlinear ln neuronal model applied to blocks from an intensity image and blocks from a depth reference model the authors present the results obtained by varying the ln model parameters and estimate their best values which provide an acceptable reconstruction of each subject s depth the authors show that increasing the light source angle over the horizontal plane in the input image produces slight increases in reconstruction error but increasing the ambient light proportion produces greater increases in reconstruction error the authors applied the method to predict each subject s unknown depth using different individual reference models and an average reference model which provides the best results as a noise reduction technique the authors perform a point by point weighted averaging with the average reference model with weights equal to the fractions of the squares of the laplacian of a gaussian applied to the prediction and to the reference depth over the sum of both finally the authors present acceptable visual results obtained from external images of faces under arbitrary illumination having performed an illumination estimation previously

gabor based kernel pca with fractional power polynomial models for face recognition this paper presents a novel gabor based kernel principal component analysis pca method by integrating the gabor wavelet representation of face images and the kernel pca method for face recognition gabor wavelets first derive desirable facial features characterized by spatial frequency spatial locality and orientation selectivity to cope with the variations due to illumination and facial expression changes the kernel pca method is then extended to include fractional power polynomial models for enhanced face recognition performance a fractional power polynomial however does not necessarily define a kernel function as it might not define a positive semidefinite gram matrix note that the sigmoid kernels one of the three classes of widely used kernel functions polynomial kernels gaussian kernels and sigmoid kernels do not actually define a positive semidefinite gram matrix either nevertheless the sigmoid kernels have been successfully used in practice such as in building support vector machines in order to derive real kernel pca features we apply only those kernel pca eigenvectors that are associated with positive eigenvalues the feasibility of the gabor based kernel pca method with fractional power polynomial models has been successfully tested on both frontal and pose angled face recognition using two data sets from the feret database and the cmu pie database respectively the feret data set contains 600 frontal face images of 200 subjects while the pie data set consists of 680 images across five poses left and right profiles left and right half profiles and frontal view with two different facial expressions neutral and smiling of 68 subjects the effectiveness of the gabor based kernel pca method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the pca method the kernel pca method with polynomial kernels the kernel pca method with fractional power polynomial models the gabor wavelet based pca method and the gabor wavelet based kernel pca method with polynomial kernels

probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

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

constructing facial identity surfaces for recognition we present a novel approach to face recognition by constructing facial identity structures across views and over time referred to as identity surfaces in a kernel discriminant analysis kda feature space this approach is aimed at addressing three challenging problems in face recognition modelling faces across multiple views extracting non linear discriminatory features and recognising faces over time first a multi view face model is designed which can be automatically fitted to face images and sequences to extract the normalised facial texture patterns this model is capable of dealing with faces with large pose variation second kda is developed to compute the most significant non linear basis vectors with the intention of maximising the between class variance and minimising the within class variance we applied kda to the problem of multi view face recognition and a significant improvement has been achieved in reliability and accuracy third identity surfaces are constructed in a pose parameterised discriminatory feature space dynamic face recognition is then performed by matching the object trajectory computed from a video input and model trajectories constructed on the identity surfaces these two types of trajectories encode the spatio temporal dynamics of moving faces

the effect of sampling error on convergence improper solutions and goodness of fit indices for maximum likelihood confirmatory factor analysis a monte carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions improper solutions and the distribution of goodness of fit indices in maximum likelihood confirmatory factor analysis nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor effects of practical significance due to sample size the number of indicators per factor and the number of factors were found for gfi agfi and rmr whereas no practical effects were found for the probability values associated with the chi square likelihood ratio test

estimating optical flow in segmented images using variable order parametric models with local deformations this paper presents a new model for estimating optical flow based on the motion of planar regions plus local deformations the approach exploits brightness information to organize and constrain the interpretation of the motion by using segmented regions of piecewise smooth brightness to hypothesize planar regions in the scene parametric flow models are estimated in these regions in a two step process which first computes a coarse fit and then estimates the appropriate parametrization of the motion of the region the initial fit is refined using a generalization of the standard area based regression approaches since the assumption of planarity is likely to be violated we allow local deformations from the planar assumption in the same spirit as physically based approaches which model shape using coarse parametric models plus local deformations this parametric plus deformation model exploits the strong constraints of parametric approaches while retaining the adaptive nature of regularization approaches experimental results on a variety of images model produces accurate flow estimates while the incorporation of brightness segmentation boundaries

optical flow constraints on deformable models with applications to face tracking optical flow provides a constraint on the motion of a deformable model we derive and solve a dynamic system incorporating flow as a hard constraint producing a model based least squares optical flow solution our solution also ensures the constraint remains satisfied when combined with edge information which helps combat tracking error accumulation constraint enforcement can be relaxed using a kalman filter which permits controlled constraint violations based on the noise present in the optical flow information and enables optical flow and edge information to be combined more robustly and efficiently we apply this framework to the estimation of face shape and motion using a 3d deformable face model this model uses a small number of parameters to describe a rich variety of face shapes and facial expressions we present experiments in extracting the shape and motion of a face from image sequences which validate the accuracy of the method they also demonstrate that our treatment of optical flow as a hard constraint as well as our use of a kalman filter to reconcile these constraints with the uncertainty in the optical flow are vital for improving the performance of our system

implicit meshes for effective silhouette handling using silhouettes in uncontrolled environments typically requires handling occlusions as well as changing or cluttered backgrounds which limits the applicability of most silhouette based methods for the purpose of 3 d shape modeling we show that representing generic 3 d surfaces as implicit surfaces lets us effectively address these issues this desirable behavior is completely independent from the way the surface deformations are parame trized to show this we demonstrate our technique in three very different cases modeling the deformations of a piece of paper represented by an ordinary triangulated mesh reconstruction and tracking a person s shoulders whose deformations are expressed in terms of dirichlet free form deformations reconstructing the shape of a human face parametrized in terms of a principal component analysis model

standard errors of fit indices using residuals in structural equation modeling the asymptotic standard errors of the correlation residuals and bentler s standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals using these results approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method further in mean structures approximations of the asymptotic standard errors of residuals standardized residuals and their summary statistics are derived in a similar manner simulations are carried out which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance correlation and mean structures are close to actual ones

representation and self similarity of shapes representing shapes in a compact and informative form is a significant problem for vision systems that must recognize or classify objects we describe a compact representation model for two dimensional 2d shapes by investigating their self similarities and constructing their shape axis trees sa trees our approach can be formulated as a variational one or equivalently as map estimation of a markov random field we start with a 2d shape its boundary contour and two different parameterizations for the contour one parameterization is oriented counterclockwise and the other clockwise to measure its self similarity the two parameterizations are matched to derive the best set of one to one point to point correspondences along the contour the cost functional used in the matching may vary and is determined by the adopted self similarity criteria e g cocircularity distance variation parallelism and region homogeneity the loci of middle points of the pairing contour points yield the shape axis and they can be grouped into a unique free tree structure the sa tree by implicitly encoding the local and global shape information into an sa tree a variety of vision tasks e g shape recognition comparison and retrieval can be performed in a more robust and efficient way via various tree based algorithms a dynamic programming algorithm gives the optimal solution in o n sup 1 where n is the size of the contour

appearance characterization of linear lambertian objects generalized photometric stereo and illumination invariant face recognition traditional photometric stereo algorithms employ a lambertian reflectance model with a varying albedo field and involve the appearance of only one object in this paper we generalize photometric stereo algorithms to handle all appearances of all objects in a class in particular the human face class by making use of the linear lambertian property a linear lambertian object is one which is linearly spanned by a set of basis objects and has a lambertian surface the linear property leads to a rank constraint and consequently a factorization of an observation matrix that consists of exemplar images of different objects e g faces of different subjects under different unknown illuminations integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account the effectiveness of the linear lambertian property is further investigated by using it for the problem of illumination invariant face recognition using just one image attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in lambert s law this enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources experimental results using standard data sets are presented

hierarchical vibrations for part based recognition of complex objects we propose a technique for the recognition and segmentation of complex shapes in 2d images using a hierarchy of finite element vibration modes in an evolutionary shape search the different levels of the shape hierarchy can influence each other which can be exploited in top down part based image analysis our method overcomes drawbacks of existing structural approaches which cannot uniformly encode shape variation and co variation or rely on training we present results demonstrating that by utilizing a quality of fit function the model explicitly recognizes missing parts of a complex shape thus allowing for categorization between shape classes

tangent lie algebroids this paper shows that a lie algebroid structure on a smooth vector bundle a to pi over q gives rise to a lie algebroid structure on the bundle ta to t pi over tq called the tangent lie algebroid the analysis uses global arguments a lie algebroid a is equivalent to a certain poisson structure on a and the tangent bundle of any poisson manifold has a tangent poisson structure the tangent poisson structure on ta is then dualized to produce the tangent lie algebroid structure on ta local calculations are used and formulae for local brackets are given

a two level generative model for cloth representation and shape from shading in this paper we present a two level generative model for representing the images and surface depth maps of drapery and clothes the upper level consists of a number of folds which will generate the high contrast ridge areas with a dictionary of shading primitives for 2d images and fold primitives for 3d depth maps these primitives are represented in parametric forms and are learned in a supervised learning phase using 3d surfaces of clothes acquired through photometric stereo the lower level consists of the remaining flat areas which fill between the folds with a smoothness prior markov random field we show that the classical ill posed problem shape from shading sfs can be much improved by this two level model for its reduced dimensionality and incorporation of middle level visual knowledge i e the dictionary of primitives given an input image we first infer the folds and compute a sketch graph using a sketch pursuit algorithm as in the primal sketch guo et al 2003 the 3d folds are estimated by parameter fitting using the fold dictionary and they form the skeleton of the drapery cloth surfaces then the lower level is computed by conventional sfs method using the fold areas as boundary conditions the two levels interact at the final stage by optimizing a joint bayesian posterior probability on the depth map we show a number of experiments which demonstrate more robust results in comparison with state of the art work in a broader scope our representation can be viewed as a two level inhomogeneous mrf model which is applicable to general shape from x problems our study is an attempt to revisit marr s idea marr and freeman 1982 of computing the 2frac12d sketch from primal sketch in a companion paper barbu and zhu 2005 we study shape from stereo based on a similar two level generative sketch representation

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

recovery of the 3 d shape of the left ventricle from echocardiographic images a computational method is reported which allows the fully automated recovery of the three dimensional shape of the cardiac left ventricle from a reduced set of apical echo views two typically ill posed problems have been faced 1 the detection of the left ventricle contours in each view and 2 the integration of the detected contour points which form a sparse and partially inconsistent data set into a single surface representation the authors solution to these problems is based on a careful integration of standard computer vision algorithms with neural networks boundary detection comprises three steps edge detection edge grouping and edge classification the first and second steps which are typical early vision tasks not involving specific domain knowledge have been performed through fast well established algorithms of computer vision the higher level task of left ventricle edge discrimination which involves the exploitation of specific knowledge about the left ventricle silhouette has been performed by feedforward neural networks following the most recent results in the field of computer vision the first step in solving the problem of recovering the ventricle surface has been the adoption of a physically inspired model of it basically the authors have modeled the left ventricle surface as a closed thin elastic surface and the data as a set of radial springs acting on it the recovery process is equivalent to the settling of the surface plus springs system into a stable configuration of minimum potential energy the finite element discretization of this model leads directly to an analog neural network implementation the efficiency of such an implementation has been remarkably enhanced through a learning algorithm which embeds specific knowledge about the shape of the left ventricle in the network experiments using clinical echographic sequences are described four apical views each with a different rotation of the probe have been acquired during a heartbeat from a set of seven normal subjects these images have been utilized to set the various processing modules and test their capabilities

determining generative models of objects under varying illumination shape and albedo from multiple images using svdand integrability we describe a method of learning generative models of objects from a set of images of the object under different and unknown illumination such a model allows us to approximate the objects appearance under a range of lighting conditions this work is closely related to photometric stereo with unknown light sources and in particular to the use of singular value decomposition svd to estimate shape and albedo from multiple images up to a linear transformation hayakawa 1994 firstly we analyze and extend the svd approach to this problem we demonstrate that it applies to objects for which the dominant imaging effects are lambertian reflectance with a distant light source and a background ambient term to determine that this is a reasonable approximation we calculate the eigenvectors of the svd on a set of real objects under varying lighting conditions and demonstrate that the first few eigenvectors account for most of the data in agreement with our predictions we then analyze the linear ambiguities in the svd approach and demonstrate that previous methods proposed to resolve them hayakawa 1994 are only valid under certain conditions we discuss alternative possibilities and in particular demonstrate that knowledge of the object class is sufficient to resolve this problem secondly we describe the use of surface consistency for putting constraints on the possible solutions we prove that this constraint reduces the ambiguities to a subspace called the generalized bas relief ambiguity gbr which is inherent in the lambertian reflectance function and which can be shown to exist even if attached and cast shadows are present belhumeur et al 1997 we demonstrate the use of surface consistency to solve for the shape and albedo up to a gbr and describe and implement a variety of additional assumptions to resolve the gbr thirdly we demonstrate an iterative algorithm that can detect and remove some attached shadows from the objects thereby increasing the accuracy of the reconstructed shape and albedo

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

even symplectic supermanifolds and double field theory over many decades the word double has appeared in various contexts which at times seem to be unrelated 1 several have some relation to mathematical physics recently this has become particularly striking in double field theory dft two doubles that are particularly relevant are double vector bundles and drinfel d doubles

linear local models for monocular reconstruction of deformable surfaces recovering the 3d shape of a nonrigid surface from a single viewpoint is known to be both ambiguous and challenging resolving the ambiguities typically requires prior knowledge about the most likely deformations that the surface may undergo it often takes the form of a global deformation model that can be learned from training data while effective this approach suffers from the fact that a new model must be learned for each new surface which means acquiring new training data and may be impractical in this paper we replace the global models by linear local models for surface patches which can be assembled to represent arbitrary surface shapes as long as they are made of the same material not only do they eliminate the need to retrain the model for different surface shapes they also let us formulate 3d shape reconstruction from correspondences as either an algebraic problem that can be solved in closed form or a convex optimization problem whose solution can be found using standard numerical packages we present quantitative results on synthetic data as well as qualitative results on real images