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

the eikonal equation some results applicable to computer vision in this paper we investigate certain first order partial differential equations which formulate the relationship between the light reflected from a surface and its shape particular emphasis is given to eikonal equations two results are presented first we prove that a special type of eikonal equation has only one convex and positive c2 solution in some neighborhood of a singular point using this result we show that a restricted form of this equation has exactly two solutions these results have application in scanning electron microscopy

a probabilistic framework for specular shape from shading one of the problems that hinders conventional methods for shape from shading is the presence of local specularities which may be misidentified as high curvature surface features in this paper we address the problem of estimating the proportions of lambertian and specular reflection components in order to improve the quality of surface normal information recoverable using shape from shading the framework for our study is provided by the iterated conditional modes algorithm we develop a maximum a posteriori probability map estimation method for estimating the mixing proportions for lambertian and specular reflectance and also for recovering local surface normals the map estimation scheme has two model ingredients first there are separate conditional measurement densities which describe the distributions of surface normal directions for the lambertian and specular reflectance components we experimentally compare three different models for the specular component the second ingredient is a smoothness prior which models the distribution of surface normal directions over local image regions we demonstrate the utility of method on real world data ground truth data is provided by imagery obtained with crossed polaroid filters this reveals not only that the method accurately estimates the proportion of specular reflection but that it also results in good surface normal reconstruction in the proximity of specular highlights

dominance of milnor attractors in globally coupled dynamical systems with more than 7 2 degrees of freedom the prevalence of milnor attractors has recently been reported in a class of high dimensional dynamical systems we study how this prevalence depends on the number of degrees of freedom by using a globally coupled map and show that the basin fraction of milnor attractors increases drastically around 5 10 degrees of freedom saturating for higher numbers of degrees of freedom it is argued that this dominance of milnor attractors in the basin arises from a combinatorial explosion of the basin boundaries in addition the dominance is also found in a system without permutation symmetry i e a coupled dynamical system of nonidentical elements possible relevance to the magic number 7 62 in psychology is briefly discussed

numerical implementation of dynamical mean field theory for disordered systems application to the lotka volterra model of ecosystems dynamical mean field theory dmft is a tool that allows one to analyze the stochastic dynamics of n interacting degrees of freedom in terms of a self consistent 1 body problem in this work focusing on models of ecosystems we present the derivation of dmft through the dynamical cavity method and we develop a method for solving it numerically our numerical procedure can be applied to a large variety of systems for which dmft holds we implement and test it for the generalized random lotka volterra model and show that complex dynamical regimes characterized by chaos and aging can be captured and studied by this framework

surface topography using shape from shading abstract this paper demonstrates how a recently reported shape from shading scheme can be used to extract topographic information from 2d intensity imagery worthington and hancock ieee trans pattern anal mach intell 21 1999 1250 1267 the shape from shading scheme has two important features which enhance the recovered surface description firstly it uses a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning secondly we use curvature information to impose topographic constraints on the recovered needle map the topographic information is captured using the shape index of koenderink and van doorn image vision comput 10 1992 557 565 and consistency is imposed using a robust error function we show that the new shape from shading scheme leads to a meaningful topographic labelling of 3d surface structures moreover the resulting topographic information proves to be useful in a simple histogram based object recognition scheme

a multiresolution approach for shape from shading coupling deterministic and stochastic optimization shape from shading is an ill posed inverse problem for which there is no completely satisfactory solution in the existing literature in this paper we address shape from shading as an energy minimization problem we first show that the deterministic approach provides efficient algorithms in terms of cpu time but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima we derive an alternative stochastic approach using simulated annealing the obtained results strongly outperform the results of the deterministic approach the shortcoming is an extreme slowness of the optimization therefore we propose a hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

on the finite element solution of the pure neumann problem this paper considers the finite element approximation and algebraic solution of the pure neumann problem our goal is to present a concise variational framework for the finite element solution of the neumann problem that focuses on the interplay between the algebraic and variational problems while many of the results that stem from our analysis are known by some experts they are seldom derived in a rigorous fashion and remain part of numerical folklore as a result this knowledge is not accessible or appreciated by many practitioners both novices and experts in one source our paper contributes a simple yet insightful link between the continuous and algebraic variational forms that will prove useful

object recognition using shape from shading investigates whether surface topography information extracted from intensity images using a shape from shading sfs algorithm can be used for the purposes of 3d object recognition we consider how curvature and shape index information delivered by this algorithm can be used to recognize objects based on their surface topography we explore two contrasting object recognition strategies the first of these is based on a low level attribute summary and uses histograms of curvature and orientation measurements the second approach is based on the structural arrangement of constant shape index maximal patches and their associated region attributes we show that region curvedness and a string ordering of the regions according to size provides recognition accuracy of about 96 percent by polling various recognition schemes including a graph matching method we show that a recognition rate of 98 99 percent is achievable

direct analytical methods for solving poisson equations in computer vision problems direct analytical methods are discussed for solving poisson equations of the general form delta u f on a rectangular domain some embedding techniques that may be useful when boundary conditions obtained from stereo and occluding boundary are defined on arbitrary contours are described the suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms applications to shape from shading lightness and optical flow problems are also discussed a proof for the existence and convergence of the flow estimates is given experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations

algorithm for counting large directed loops we derive a belief propagation algorithm for counting large loops in a directed network we evaluate the distribution of the number of small loops in a directed random network with given degree sequence we apply the algorithm to a few characteristic directed networks of various network sizes and loop structures and compare the algorithm with exhaustive counting results when possible the algorithm is adequate in estimating loop counts for large directed networks and can be used to compare the loop structure of directed networks and their randomized counterparts

shape from periodic texture using the eigenvectors of local affine distortion shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly without the need for iterative numerical optimization we work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks the key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces in particular the leading eigenvector points in the tilt direction although not as geometrically transparent the direction of the second eigenvector can be used to estimate the slant direction the required affine distortion matrices are computed using the correspondences between spectral peaks established on the basis of their energy ordering we apply the method to a variety of real world and synthetic imagery

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

mass extinction in a dynamical system of evolution with variable dimension introducing the effect of extinction into the so called replicator equations in mathematical biology we construct a general model where the diversity of species i e the dimension of the equation is a time dependent variable the system shows very different behavior from the original replicator equation and leads to mass extinction when the system initially has high diversity the present theory can serve as a mathematical foundation for the paleontologic theory for mass extinction this extinction dynamics is a prototype of dynamical systems where the variable dimension is inevitable

vorticity velocity pressure formulation for stokes problem we propose a three field formulation for efficiently solving a twodimensional stokes problem in the case of nonstandard boundary conditions more specifically we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary the proposed computational methodology consists in reformulating the considered boundary value problem via a mixed type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the lagrange multiplier the obtained formulation is then discretized and a convergence analysis is performed a priori error estimates are established and some numerical results are presented to highlight the perfomance of the proposed computational methodology

application of modified homotopy perturbation method for solving the augmented systems in this paper a new approach is proposed for solving the augmented systems based on the modified homotopy perturbation method we construct the new iterative methods and derive the sufficient and necessary conditions for guaranteeing its convergence some numerical experiments show that this method is more simple and effective

a model in a coupled system of simple neural oscillators with delays we consider a coupled system of simple neural oscillators using the symmetric functional differential equation theories of wu j wu symmetric functional differential equations and neural networks with memory transactions of the american mathematical society 350 12 1998 4799 4838 we demonstrate the multiple hopf bifurcations of the equilibrium at the origin the existence of multiple branches of bifurcating periodic solution is obtained then some numerical simulations support our analysis results

perturbation bounds for constrained and weighted least squares problems we derive perturbation bounds for the constrained and weighted linear least squares ls problems both the full rank and rank deficient cases are considered the analysis generalizes some results of earlier works

some remarks on the shape from shading problem in computer vision the shape from shading problem in computer vision see horn 11 deals with the reconstruction of the shape of an object from a two dimensional image we consider an object illuminated by a point source the reflected light being recorded on a photographic plate at a fixed position the intensity of the reflected light is a function of the position of the source the position of the plate and the normal to the surface of the object if the surface is given as u u x jj this leads see horn i to a first order partial differential equation of the form

a framework for equilibrium equations the equations of equilibrium in a wide class of applications share a common structure the discrete case leads to a positive definite symmetric matrix a t ca in which a is rectangular and c is often diagonal the continuous case linear or nonlinear repeats that pattern there is a minimum principle for the potentials and a dual principle for the flow variables we try to clarify these different expressions of the same law

model ecosystems with random nonlinear interspecies interactions the principle of competitive exclusion in ecology establishes that two species living together cannot occupy the same ecological niche here we present a model ecosystem in which the species are described by a series of phenotypic characters and the strength of the competition between two species is given by a nondecreasing modulating function of the number of common characters using analytical tools of statistical mechanics we find that the ecosystem diversity defined as the fraction of species that coexist at equilibrium decreases as the complexity i e number of characters of the species increases regardless of the modulating function by considering both selective and random elimination of the links in the community web we show that ecosystems composed of simple species are more robust than those composed of complex species in addition we show that the puzzling result that there exists either rich or poor ecosystems for a linear modulating function is not typical of communities in which the interspecies interactions are determined by a complementarity rule

maximum likelihood estimation of depth maps using photometric stereo photometric stereo and depth map estimation provide a way to construct a depth map from images of an object under one viewpoint but with varying illumination directions while estimating surface normals using the lambertian model of reflectance is well established depth map estimation is an ongoing field of research and dealing with image noise is an active topic using the zero mean gaussian model of image noise this paper introduces a method for maximum likelihood depth map estimation that accounts for the propagation of noise through all steps of the estimation process solving for maximum likelihood depth map estimates involves an independent sequence of nonlinear regression estimates one for each pixel followed by a single large and sparse linear regression estimate the linear system employs anisotropic weights which arise naturally and differ in value to related work the new depth map estimation method remains efficient and fast making it practical for realistic image sizes experiments using synthetic images demonstrate the method s ability to robustly estimate depth maps under the noise model practical benefits of the method on challenging imaging scenarios are illustrated by experiments using the extended yale face database b and an extensive data set of 500 reflected light microscopy image sequences

shape from shading using probability functions and belief propagation shape from shading sfs aims to reconstruct the three dimensional shape of an object from a single shaded image this article proposes an improved framework based on belief propagation for computing sfs the implementation of the well known brightness integrability and smoothness constraints inside this framework is shown we implement the constraints as probability density functions for example the brightness constraint is a two dimensional probability density function that relates all possible surface gradients at a pixel to their probability given the pixel intensity a straightforward extension of the framework to photometric stereo is presented where multiple images of the same scene taken under different lighting conditions are available the results are promising especially since the solution is obtained by iteratively applying simple operations on a regular grid of points the presented framework therefore can be implemented in parallel and is a reasonably likely biological scheme

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

new constraints on data closeness and needle map consistency for shape from shading this paper makes two contributions to the problem of needle map recovery using shape from shading first we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning second we exploit the improved ease of control of the new shape from shading process to investigate various types of needle map consistency constraint the first set of constraints are based on needle map smoothness the second avenue of investigation is to use curvature information to impose topographic constraints third we explore ways in which the needle map is recovered so as to be consistent with the image gradient field in each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle map we provide an experimental assessment of the new shape from shading framework on both real world images and synthetic images with known ground truth surface normals the main conclusion drawn from our analysis is that the data closeness constraint improves the efficiency of shape from shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle map

a solution of the dichromatic model for multispectral photometric invariance in this paper we address the problem of photometric invariance in multispectral imaging making use of an optimisation approach based upon the dichromatic model in this manner we cast the problem of recovering the spectra of the illuminant the surface reflectance and the shading and specular factors in a structural optimisation setting making use of the additional information provided by multispectral imaging and the structure of image patches we recover the dichromatic parameters of the scene to do this we formulate a target cost function combining the dichromatic error and the smoothness priors for the surfaces under study the dichromatic parameters are recovered through minimising this cost function in a coordinate descent manner the algorithm is quite general in nature admitting the enforcement of smoothness constraints and extending in a straightforward manner to trichromatic settings moreover the objective function is convex with respect to the subset of variables to be optimised in each alternating step of the minimisation strategy this gives rise to an optimal closed form solution for each of the iterations in our algorithm we illustrate the effectiveness of our method for purposes of illuminant spectrum recovery skin recognition material clustering and specularity removal we also compare our results to a number of alternatives

new riemannian techniques for directional and tensorial image data this paper develops new geometrical filtering and edge detection algorithms for processing non euclidean image data we view image data as residing on a riemannian manifold and we work with a representation based on the exponential map for this manifold together with the riemannian weighted mean of image data we show how the weighted mean can be efficiently computed using newton s method which converges faster than the gradient descent method described elsewhere in the literature based on geodesic distances and the exponential map we extend the classical median filter and the perona malik anisotropic diffusion technique to smooth non euclidean image data we then propose an anisotropic gaussian kernel for image filtering and we also show how both the median filter and the anisotropic gaussian filter can be combined to develop a new edge preserving filter which is effective at removing both gaussian noise and impulse noise by using the intrinsic metric of the feature manifold we also generalise di zenzo s structure tensor to non euclidean images for edge detection we demonstrate the applications of our riemannian filtering and edge detection algorithms both on directional and tensor valued images

vector transport for shape from shading in this paper we describe a new shape from shading method we show how the parallel transport of surface normals can be used to impose curvature consistency and also to iteratively update surface normal directions so as to improve the brightness error we commence by showing how to make local estimates of the hessian matrix from surface normal information with the local hessian matrix to hand we develop an em like algorithm for updating the surface normal directions at each image location parallel transport is applied to the neighbouring surface normals to generate a sample of local surface orientation predictions from this sample a local weighted estimate of the image brightness is made the transported surface normal which gives the brightness prediction which is closest to this value is selected as the revised estimate of surface orientation the revised surface normals obtained in this way may in turn be used to re estimate the hessian matrix and the process iterated until stability is reached we experiment with the method on a variety of real world and synthetic data here we explore the properties of the fields of surface normals and the height data delivered by the method

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

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

a graph spectral approach to shape from shading in this paper we explore how graph spectral methods can be used to develop a new shape from shading algorithm we characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction modeling the blocks of the weight matrix as distinct surface patches we use a graph seriation method to find a surface integration path that maximizes the sum of curvature dependent weights and that can be used for the purposes of height reconstruction to smooth the reconstructed surface we fit quadrics to the height data for each patch the smoothed surface normal directions are updated ensuring compliance with lambert s law the processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained we provide results on synthetic and real world imagery

practical matrix completion and corruption recovery using proximal alternating robust subspace minimization low rank matrix completion is a problem of immense practical importance recent works on the subject often use nuclear norm as a convex surrogate of the rank function despite its solid theoretical foundation the convex version of the problem often fails to work satisfactorily in real life applications real data often suffer from very few observations with support not meeting the randomness requirements ubiquitous presence of noise and potentially gross corruptions sometimes with these simultaneously occurring this paper proposes a proximal alternating robust subspace minimization method to tackle the three problems the proximal alternating scheme explicitly exploits the rank constraint on the completed matrix and uses the ell 0 l 0 pseudo norm directly in the corruption recovery step we show that the proposed method for the non convex and non smooth model converges to a stationary point although it is not guaranteed to find the global optimal solution in practice we find that our algorithm can typically arrive at a good local minimizer when it is supplied with a reasonably good starting point based on convex optimization extensive experiments with challenging synthetic and real data demonstrate that our algorithm succeeds in a much larger range of practical problems where convex optimization fails and it also outperforms various state of the art algorithms

random replicators with high order interactions we use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of n species interacting via random mutual interactions as well as via deterministic self interactions of order p 2 we show that the main effect of increasing the order of the interactions among the species is to make the system less competitive in the sense that the fraction of extinct species is greatly reduced in addition we find that for p 2 there is a threshold value which gives a lower bound to the concentration of the surviving species preventing then the existence of rare species and consequently increasing the robustness of the ecosystem to external perturbations

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

rank abundance relations in evolutionary dynamics of random replicators we present a nonequilibrium statistical mechanics description of rank abundance relations rar in random community models of ecology specifically we study a multispecies replicator system with quenched random interaction matrices we here consider symmetric interactions as well as asymmetric and antisymmetric cases rars are obtained analytically via a generating functional analysis describing fixed point states of the system in terms of a small set of order parameters and in dependence on the symmetry or otherwise of interactions and on the productivity of the community our work is an extension of tokita phys rev lett 93 178102 2004 where the case of symmetric interactions was considered within an equilibrium setup the species abundance distribution in our model come out as truncated normal distributions or transformations thereof and in some case are similar to left skewed distributions observed in ecology we also discuss the interaction structure of the resulting food web of stable species at stationarity cases of heterogeneous cooperation pressures as well as effects of finite system size and of higher order interactions

ecological communities from random generalized lotka volterra dynamics with nonlinear feedback we investigate the outcome of generalized lotka volterra dynamics of ecological communities with random interaction coefficients and nonlinear feedback we show in simulations that the saturation of nonlinear feedback stabilizes the dynamics this is confirmed in an analytical generating functional approach to generalized lotka volterra equations with piecewise linear saturating response for such systems we are able to derive self consistent relations governing the stable fixed point phase and to carry out a linear stability analysis to predict the onset of unstable behavior we investigate in detail the combined effects of the mean variance and covariance of the random interaction coefficients and the saturation value of the nonlinear response we find that stability and diversity increases with the introduction of nonlinear feedback where decreasing the saturation value has a similar effect to decreasing the covariance we also find cooperation to no longer have a detrimental effect on stability with nonlinear feedback and the order parameters mean abundance and diversity to be less dependent on the symmetry of interactions with stronger saturation

complementarity and diversity in a soluble model ecosystem complementarity among species with different traits is one of the basic processes affecting biodiversity defined as the number of species in the ecosystem we present here a soluble model of microbial based ecosystems in which the species are characterized by binary traits and their pairwise interactions follow a complementarity principle manipulation of the species composition and so the study of its effects on the species diversity is achieved through the introduction of a bias parameter favoring one of the traits using statistical mechanics tools we find explicit expressions for the allowed values of the equilibrium species concentrations in terms of the control parameters of the model

a non local low rank approach to enforce integrability we propose a new approach to enforce integrability using recent advances in non local methods our formulation consists in a sparse gradient data fitting term to handle outliers together with a gradient domain non local low rank prior this regularization has two main advantages 1 the low rank prior ensures similarity between non local gradient patches which helps recovering high quality clean patches from severe outliers corruption and 2 the low rank prior efficiently reduces dense noise as it has been shown in recent image restoration works we propose an efficient solver for the resulting optimization formulation using alternate minimization experiments show that the new method leads to an important improvement compared with previous optimization methods and is able to efficiently handle both outliers and dense noise mixed together

structured backward errors for kkt systems karush kuhn tucker kkt systems are linear systems with coefficient matrices of the form graphics where h is symmetric a normwise structured backward error for kkt systems is defined and a com

a graph spectral method for surface height recovery this paper describes a graph spectral method for 3d surface integration the algorithm takes as its input a 2d field of surface normal estimates delivered for instance by a shape from shading or shape from texture procedure we commence by using the surface normals to obtain an affinity weight matrix whose elements are related to the surface curvature the weight matrix is used to compute a row normalized transition probability matrix and we pose the recovery of the integration path as that of finding the steady state random walk for the markov chain defined by this matrix the steady state random walk is given by the leading eigenvector of the original affinity weight matrix by threading the surface normals together along the path specified by the magnitude order of the components of the leading eigenvector we perform surface integration the height increments along the path are simply related to the traversed path length and the slope of the local tangent plane the method is evaluated on needle maps delivered by a shape from shading algorithm applied to real world data and also on synthetic data the method is compared with the local geometric height reconstruction method of bors hancock and wilson and the global methods of horn and brooks and frankot and chellappa

graph edit distance from spectral seriation this paper is concerned with computing graph edit distance one of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance hence our aim is to convert graphs to string sequences so that string matching techniques can be used to do this we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order we show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix we pose the problem of graph matching as a maximum a posteriori probability map alignment of the seriation sequences for pairs of graphs this treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability we compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice the edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched we demonstrate the utility of the edit distance on a number of graph clustering problems

shape from shading using the heat equation this paper offers two new directions to shape from shading namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low dimensional embedding turning our attention to the first of these contributions we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that lambert s law is satisfied we perform our analysis on a plane perpendicular to the light source direction where the z component of the surface normal is equal to the normalized image brightness the x y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation we solve the heat equation for the scalar potential and hence recover the azimuthal component of the surface normal from the average image brightness making use of a simple finite difference method the second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals we experiment with the resulting method on a variety of real world image data where it produces qualitatively good reconstructed surfaces

random replicators with asymmetric couplings systems of interacting random replicators are studied using generating functional techniques while replica analyses of such models are limited to systems with symmetric couplings dynamical approaches as presented here allow us specifically to address cases with asymmetric interactions where there is no lyapunov function governing the dynamics we focus on replicator models with gaussian couplings of general symmetry between p 2 species and discuss how an effective description of the dynamics can be derived in terms of a single species process upon making a fixed point ansatz persistent order parameters in the ergodic stationary states can be extracted from this process and different types of phase transitions can be identified and related to each other we discuss the effects of asymmetry in the couplings on the order parameters and the phase behaviour for p 2 and p 3 numerical simulations verify our theory for the case of cubic interactions numerical experiments indicate regimes in which only a finite number of species survives even when the thermodynamic limit is considered

perturbation analysis of generalized saddle point systems we discuss the perturbation analysis of generalized saddle point systems in this paper we give the nonlinear perturbation bounds then derive the condition numbers and analyze the sensitivity of the computed solutions

incorporating illumination constraints in deformable models for shape from shading and light direction estimation we present a method for the integration of nonlinear holonomic constraints in deformable models and its application to the problems of shape and illuminant direction estimation from shading experimental results demonstrate that our method performs better than previous shape from shading algorithms applied to images of lambertian objects under known illumination it is also more general as it can be applied to non lambertian surfaces and it does not require knowledge of the illuminant direction in this paper 1 we first develop a theory for the numerically robust integration of nonlinear holonomic constraints within a deformable model framework in this formulation we use lagrange multipliers and a baumgarte stabilization approach 1972 2 we also describe a fast new method for the computation of constraint based forces in the case of high numbers of local parameters 3 we demonstrate how any type of illumination constraint from the simple lambertian model to more complex highly nonlinear models can be incorporated in a deformable model framework 4 we extend our method to work when the direction of the light source is not known we couple our shape estimation method with a method for light estimation in an iterative process where improved shape estimation results in improved light estimation and vice versa 5 we perform a series of experiments

shape from shading using graph cuts in this paper we investigate the applicability of graph cuts to the sfs shape from shading problem we propose a new semi global method for sfs using graph cuts the new algorithm combines the local method proposed by lee and rosenfeld c h lee a rosenfeld improved methods of estimating shape from shading using the light source coordinate system artif intell 26 1985 125 143 and a global method using an energy minimization technique by employing a new global energy minimization formulation the convex concave ambiguity problem of lee and rosenfeld s method can be resolved efficiently a new combinatorial optimization technique the graph cuts method is used for the minimization of the proposed energy functional experimental results on a variety of synthetic and real world images show that the proposed algorithm reconstructs the 3 d shape of objects very efficiently

comparison of performance of iterative methods for singular and nonsingular saddle point linear systems arising from navier stokes equations abstract we compare the convergence performance of iterative methods for solving singular and nonsingular linear systems arising from discretization and linearization of the steady state navier stokes equations with a combination of analytic and empirical results we study the effects of singularity and nonsingularity on convergence we will show that the convergence performance for solving a singular linear system is better than that for solving a nonsingular linear system

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

gender discriminating models from facial surface normals in this paper we show how to use facial shape information to construct discriminating models for gender classification we represent facial shapes using 2 5d fields of facial surface normals and investigate three different methods to improve the gender discriminating capacity of the model constructed using the standard eigenspace method the three methods are novel variants of principal geodesic analysis pga namely a weighted pga b supervised weighted pga and c supervised pga our starting point is to define a weight map over the facial surface that indicates the importance of different locations in discriminating gender we show how to compute the relevant weights and how to incorporate the weights into the 2 5d model construction we evaluate the performance of the alternative methods using facial surface normals extracted from 3d range images or recovered from brightness images experimental results demonstrate the effectiveness of our methods moreover the classification accuracy which is as high as 97 demonstrates the effectiveness of using facial shape information for gender classification

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

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

coarse view synthesis using shape from shading this paper investigates the use of shape from shading for coarse view synthesis the aim of our study is to determine whether needle maps delivered by a new shape from shading sfs algorithm can be used as a compact object representation for the purposes of efficiently generating appearance manifolds specifically we aim to show that the needle maps can be used to generate novel object views under changing light source and viewer directions to this end we conduct two sets of experiments firstly we use the recovered needle maps to re illuminate objects under varying lighting directions here we show that a single input image can be used to construct relatively faithful re illuminations under radical illumination changes secondly we investigate how the needle map can be used to generate new object poses here we show that needle maps can be used for both view interpolation and view extrapolation

a note on solving ep inconsistent linear systems in this note we reconsider the problem posed in s l zhang y oyanagi m su gihara necessary and sufficient conditions for the convergence of orthomin k on singular and inconsistent linear systems numer math 87 2000 391 405 we give a stopping criterion for the iterative methods to ep inconsistent linear systems

specific locking in populations dynamics symmetry analysis for coupled heteroclinic cycles population dynamics on two sites of ecological fields are studied each site shows oscillatory dynamics with a heteroclinic cycle or a limit cycle attractor and populations migrate between two sites diffusively in this system frequency locking states with specific ratios between the oscillations of two sites are observed the selection of the ratios are explained with the symmetry of the phase space other properties of the locking states as behaviors intrinsic to heteroclinic cycles are also discussed

estimation of illuminant direction albedo and shape from shading a robust approach to the recovery of shape from shading information is presented assuming uniform albedo and lambertian surface for the imaging model two methods for estimating the azimuth of the illuminant are presented one is based on local estimates on smooth patches and the other method uses shading information along image contours the elevation of the illuminant and surface albedo are estimated from image statistics taking into consideration the effect of self shadowing with the estimated reflectance map parameters the authors then compute the surface shape using a procedure that implements the smoothness constraint by requiring the gradients of reconstructed density to be close to the gradients of the input image the algorithm is data driven stable updates the surface slope and height maps simultaneously and significantly reduces the residual errors in irradiance and integrability terms a hierarchical implementation of the algorithm is presented typical results on synthetic and images are given to illustrate the usefulness of the approach

shape from shading with a linear triangular element surface model the authors propose to combine a triangular element surface model with a linearized reflectance map to formulate the shape from shading problem the main idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements and express the approximating surface as a linear combination of a set of nodal basis functions since the surface normal of a triangular element is uniquely determined by the heights of its three vertices or nodes image brightness can be directly related to nodal heights using the linearized reflectance map the surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique the proposed method does not require any integrability constraint or artificial assumptions on boundary conditions simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method

shape estimation of transparent objects by using inverse polarization ray tracing few methods have been proposed to measure three dimensional shapes of transparent objects such as those made of glass and acrylic in this paper we propose a novel method for estimating the surface shapes of transparent objects by analyzing the polarization state of the light existing methods do not fully consider the reflection refraction and transmission of the light occurring inside a transparent object we employ a polarization raytracing method to compute both the path of the light and its polarization state polarization raytracing is a combination of conventional raytracing which calculates the trajectory of light rays and mueller calculus which calculates the polarization state of the light first we set an initial value of the shape of the transparent object then by changing the shape the method minimizes the difference between the input polarization data and the rendered polarization data calculated by polarization raytracing finally after the iterative computation is converged the shape of the object is obtained we also evaluate the method by measuring some real transparent objects

learning shape from shading by a multilayer network the multilayer feedforward network has often been used for learning a nonlinear mapping based on a set of examples of the input output data in this paper we present a novel use of the network in which the example data are not explicitly given we consider the problem of shape from shading in computer vision where the input image coordinates and the output surface depth satisfy only a known differential equation we use the feedforward network as a parametric representation of the object surface and reformulate the shape from shading problem as the minimization of an error function over the network weights the stochastic gradient and conjugate gradient methods are used for the minimization boundary conditions for either surface depth or surface normal or both can be imposed by adjusting the same network at different levels it is further shown that the light source direction can be estimated based on an initial guess by integrating the source estimation with the surface estimation extensions of the method to a wider class of problems are discussed the efficiency of the method is verified by examples of both synthetic and real images

broken ergodicity and memory in the minority game we study the dynamics of the batch minority game with market impact correction using generating functional techniques to carry out the quenched disorder average we find that the assumption of weak long term memory which one usually makes in order to calculate ergodic stationary states breaks down when the persistent autocorrelation becomes larger than cc0 772 we show that this condition remarkably coincides with the at line found in an earlier static calculation this result suggests a new scenario for ergodicity breaking in disordered systems

statistical condition estimation for linear systems the standard approach to measuring the condition of a linear system compresses all sensitivity information into one number thus a loss of information can occur in situations in which the standard condition number with respect to inversion does not accurately reflect the actual sensitivity of a solution or particular entries of a solution it is shown that a new method for estimating the sensitivity of linear systems addresses these difficulties the new procedure measures the effects on the solution of small random changes in the input data and by properly scaling the results obtains reliable condition estimates for each entry of the computed solution moreover this approach which is referred to as small sample statistical condition estimation is no more costly than the standard 1 norm or power method 2 norm condition estimates and it has the advantage of considerable flexibility for example it easily accommodates restrictions on or structure associated with allowable perturbations the method also has a rigorous statistical theory available for the probability of accuracy of the condition estimates however it gives no estimate of an approximate null vector for nearly singular systems the theory of this approach is discussed along with several illustrative examples