3d structure recovery and unwarping of surfaces applicable to planes the deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry lengths and areas are conserved and vanishing gaussian curvature we show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape we show that these partial differential equations can be reduced to the hopf equation that arises in non linear wave propagation and deformations of the paper can be interpreted in terms of the characteristics of this equation a new exact integration of these equations is developed that relates the 3 d structure of the applicable surface to an image the solution is tested by comparison with particular exact solutions we present results for both the forward and the inverse 3d structure recovery problem

memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized langevin equation we investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized langevin equation using laplace analysis together with tauberian theorems we derive asymptotic expressions for the mean values variances and velocity autocorrelation function in terms of the long time behavior of the memory kernel and the correlation function of the random force the internal and external noise cases are analyzed a simple criterion to determine if the diffusion process is normal or anomalous is established

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

generalizing the prediction sum of squares statistic and formula application to linear fractional image warp and surface fitting the prediction sum of squares statistic uses the principle of leave one out cross validation in linear least squares regression it is computationally attractive as it can be computed non iteratively however it has limitations it does not handle coupled measurements which should be held out simultaneously and is specific to the principle of leave one out which is known to overfit when used for selecting a model s complexity we propose multiple exclusion press mexpress which generalizes press to coupled measurements and other types of cross validation while retaining computational efficiency with the non iterative mexpress formula using mexpress various strategies to resolve overfitting can be efficiently implemented the core principle is to exclude training data too close or too similar to the validation data we show that this allows one to select the number of control points automatically in three cases i the estimation of linear fractional warps for dense image registration from point correspondences ii surface reconstruction from a dense depth map obtained by a depth sensor and iii surface reconstruction from a sparse point cloud obtained by shape from template

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

shape from regular patterns niis paper describes an aigoritlitr1 to obtaitl local surface orierltatiorr frofti the apparetlt surface pattertl distortion in an image we propose a spherical projection to model perspctiue imaging a trtappitlg is debtled based of1 the measurement of the local distortions of a repeated known rexture pattern due io the image projection 77tis mapping maps an apparent shape on the image sphere lo a locus of possible surface orienrations on the gaussian sphere an ireratiw constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation 7lis algorithm can recover local surface orientation as well as interpolate surjace orientations where no information is auailable xis algorithm is applied to a real image ro demonstrate its perfontlance

a stable analytical framework for isometric shape from template by surface integration shape from template sft reconstructs the shape of a deforming surface from a single image a 3d template and a deformation prior for isometric deformations this is a well posed problem however previous methods which require no initialization break down when the perspective effects are small which happens when the object is small or viewed from larger distances that is they do not handle all projection geometries we propose stable sft methods that accurately reconstruct the 3d shape for all projection geometries we follow the existing approach of using first order differential constraints and obtain local analytical solutions for depth and the first order quantities the depth gradient or the surface normal previous methods use the depth solution directly to obtain the 3d shape we prove that the depth solution is unstable when the projection geometry tends to affine while the solution for the first order quantities remain stable for all projection geometries we therefore propose to solve sft by first estimating the first order quantities either depth gradient or surface normal and integrating them to obtain shape we validate our approach with extensive synthetic and real world experiments and obtain significantly more accurate results compared to previous initialization free methods our approach does not require any optimization which makes it very fast

isometric non rigid shape from motion with riemannian geometry solved in linear time we study isometric non rigid shape from motion iso nrsfm given multiple intrinsically calibrated monocular images we want to reconstruct the time varying 3d shape of a thin shell object undergoing isometric deformations we show that iso nrsfm is solvable from local warps the inter image geometric transformations we propose a new theoretical framework based on the riemmanian manifold to represent the unknown 3d surfaces as embeddings of the camera s retinal plane this allows us to use the manifold s metric tensor and christoffel symbol cs fields these are expressed in terms of the first and second order derivatives of the inverse depth of the 3d surfaces which are the unknowns for iso nrsfm we prove that the metric tensor and the cs are related across images by simple rules depending only on the warps this forms a set of important theoretical results we show that current solvers cannot solve for the first and second order derivatives of the inverse depth simultaneously we thus propose an iterative solution in two steps 1 we solve for the first order derivatives assuming that the second order derivatives are known we initialise the second order derivatives to zero which is an infinitesimal planarity assumption we derive a system of two cubics in two variables for each image pair the sum of squares of these polynomials is independent of the number of images and can be solved globally forming a well posed problem for n geq 3 images 2 we solve for the second order derivatives by initialising the first order derivatives from the previous step we solve a linear system of 4n 4 equations in three variables we iterate until the first order derivatives converge the solution for the first order derivatives gives the surfaces normal fields which we integrate to recover the 3d surfaces the proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets

nonrigid structure from motion estimating shape and motion with hierarchical priors this paper describes methods for recovering time varying shape and motion of nonrigid 3d objects from uncalibrated 2d point tracks for example given a video recording of a talking person we would like to estimate the 3d shape of the face at each instant and learn a model of facial deformation time varying shape is modeled as a rigid transformation combined with a nonrigid deformation reconstruction is ill posed if arbitrary deformations are allowed and thus additional assumptions about deformations are required we first suggest restricting shapes to lie within a low dimensional subspace and describe estimation algorithms however this restriction alone is insufficient to constrain reconstruction to address these problems we propose a reconstruction method using a probabilistic principal components analysis ppca shape model and an estimation algorithm that simultaneously estimates 3d shape and motion for each instant learns the ppca model parameters and robustly fills in missing data points we then extend the model to represent temporal dynamics in object shape allowing the algorithm to robustly handle severe cases of missing data

anomalous diffusion and the first passage time problem we study the distribution of the first passage time fpt in levy type anomalous diffusion using the recently formulated fractional fokker planck equation we obtain three results 1 we derive an explicit expression for the fpt distribution in terms of fox or h functions when the diffusion has zero drift 2 for the nonzero drift case we obtain an analytical expression for the laplace transform of the fpt distribution 3 we express the fpt distribution in terms of a power series for the case of two absorbing barriers the known results for ordinary diffusion brownian motion are obtained as special cases of our more general results

wavelet descriptors for multiresolution recognition of handprinted characters we present a novel set of shape descriptors that represents a digitized pattern in a concise way and that is particularly well suited for the recognition of handprinted characters the descriptor set is derived from the wavelet transform of a pattern s contour the approach is closely related to feature extraction methods by fourier series expansion the motivation to use an orthonormal wavelet basis rather than the fourier basis is that wavelet coefficients provide localized frequency information and that wavelets allow us to decompose a function into a multiresolution hierarchy of localized frequency bands we describe a character recognition system that relies upon wavelet descriptors to simultaneously analyze character shape at multiple levels of resolution the system was trained and tested on a large database of more than 6000 samples of handprinted alphanumeric characters the results show that wavelet descriptors are an efficient representation that can provide for reliable recognition in problems with large input variability

direct estimation of nonrigid registrations with image based self occlusion reasoning the registration problem for images of a deforming surface has been well studied external occlusions are usually well handled in 2d image based registration self occlusions are more challenging consequently the surface is usually assumed to be only slightly self occluding this paper is about image based nonrigid registration with self occlusion reasoning a specific framework explicitly modeling self occlusions is proposed it is combined with an intensity based ldquodirectrdquo data term for registration self occlusions are detected as shrinkage areas in the 2d warp experimental results on several challenging data sets show that our approach successfully registers images with self occlusions while effectively detecting the self occluded regions

fractional model equation for anomalous diffusion abstract in recent years the phenomenon of anomalous diffusion has attracted more and more attention one of the main impulses was initiated by de gennes idea of the ant in the labyrinth several authors presented asymptotic probability density functions for the location of a random walker on a fractal object as this density function and the time dependence of its second moment are now well established a modified diffusion equation providing the correct result is formulated the parameters of this fractional partial differential equation are uniquely determined by the fractal hausdorff dimension of the underlying object and the anomalous diffusion exponent the presented equation reduces exactly to the ordinary isotropic diffusion equation by appropriate choice of the parameters a closed form solution is given in terms of fox s h function in the asymptotic case a halved diffusion equation can be established furthermore the differences to equations considered previously are discussed

anomalous diffusion with linear reaction dynamics from continuous time random walks to fractional reaction diffusion equations we have revisited the problem of anomalously diffusing species modeled at the mesoscopic level using continuous time random walks to include linear reaction dynamics if a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term if the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term we have also developed further extensions of the ctrw model to include more general reaction dynamics

diffusion equations for a markovian jumping process we consider a markovian jumping process which is defined in terms of the jump size distribution and the waiting time distribution with a position dependent frequency in the diffusion limit we assume the power law form for the frequency for small steps we derive the fokker planck equation and show the presence of the normal diffusion subdiffusion and superdiffusion for the l evy distribution of the step size we construct a fractional equation which possesses a variable coefficient and solve it in the diffusion limit then we calculate fractional moments and define the fractional diffusion coefficient as a natural extension to the cases with the divergent variance we also solve the master equation numerically and demonstrate that there are deviations from the l evy stable distribution for large wave numbers

anomalous subdiffusion with multispecies linear reaction dynamics we have introduced a set of coupled fractional reaction diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics the model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics the effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms one consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species the general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail we have carried out monte carlo simulations corresponding to these special cases and we find excellent agreement with theory

monocular template based reconstruction of inextensible surfaces we present a monocular 3d reconstruction algorithm for inextensible deformable surfaces it uses point correspondences between a single image of the deformed surface taken by a camera with known intrinsic parameters and a template the main assumption we make is that the surface shape as seen in the template is known since the surface is inextensible its deformations are isometric to the template we exploit the distance preservation constraints to recover the 3d surface shape as seen in the image though the distance preservation constraints have already been investigated in the literature we propose a new way to handle them spatial smoothness priors are easily incorporated as well as temporal smoothness priors in the case of reconstruction from a video the reconstruction can be used for 3d augmented reality purposes thanks to a fast implementation we report results on synthetic and real data some of them are compared to stereo based 3d reconstructions to demonstrate the efficiency of our method

n dimensional fractional diffusion equation and green function approach spatially dependent diffusion coefficient and external force we investigate an n dimensional fractional diffusion equation with radial symmetry by using the green function approach we consider in our analysis the spatial dependence on the diffusion coefficient and the presence of an external force in particular we employ boundary conditions in a finite interval and after we extend it to a semi infinite interval we also show that a rich class of diffusive processes including normal and anomalous ones can be obtained from the solutions found here

generalized ornstein uhlenbeck processes we solve a physically significant extension of a classic problem in the theory of diffusion namely the ornstein uhlenbeck process ornstein and uhlenbeck phys rev 36 823 1930 our generalized ornstein uhlenbeck systems include a force which depends upon the position of the particle as well as upon time they exhibit anomalous diffusion at short times and non maxwellian velocity distributions in equilibrium two approaches are used some statistics are obtained from a closed form expression for the propagator of the fokker planck equation for the case where the particle is initially at rest in the general case we use spectral decomposition of a fokker planck equation employing nonlinear creation and annihilation operators to generate the spectrum which consists of two staggered ladders

exact propagator for generalized ornstein uhlenbeck processes a closed form expression for the propagator is derived in terms of modified bessel functions for the fokker planck equation for a physically important generalization of the ornstein uhlenbeck process where the diffusion constant d p is a function of the momentum the closed form is found for the general case d p approximately p alpha where alpha or 0 and leads to the standard gaussian form for alpha 0 the propagator for the specific case d p approximately p 1 is used to derive analytic expressions for probability distributions and correlation coefficients an exact expression is found for the constant of proportionality for the anomalous diffusion of the mean square displacement of a particle at short times

description of diffusive and propagative behavior on fractals the known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes after that we propose a description developed in the context of the intrinsic metric of fractals which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime we show that our approach has a stronger physical justification than previous works on this field the most important result we present is the introduction of a dependence on time and space for the conductivity in fractals which is deduced by scaling arguments and supported by computer simulations finally the diffusion equation is used to introduce the possibility of reaction diffusion processes on fractals and analyze their properties specifically an analytic expression for the speed of the corresponding travelling fronts which can be of great interest for application purposes is derived

shape from template we study a problem that we call shape from template which is the problem of reconstructing the shape of a deformable surface from a single image and a 3d template current methods in the literature address the case of isometric deformations and relax the isometry constraint to the convex inextensibility constraint solved using the so called maximum depth heuristic we call these methods zeroth order since they use image point locations the zeroth order differential structure to solve the shape inference problem from a perspective image we propose a novel class of methods that we call first order the key idea is to use both image point locations and their first order differential structure the latter can be easily extracted from a warp between the template and the input image we give a unified problem formulation as a system of pdes for isometric and conformal surfaces that we solve analytically this has important consequences first it gives the first analytical algorithms to solve this type of reconstruction problems second it gives the first algorithms to solve for the exact constraints third it allows us to study the well posedness of this type of reconstruction we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale in the latter case the candidate solution surfaces are obtained analytically experimental results on simulated and real data show that our isometric methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy while our conformal methods largely outperform all isometric methods for extensible deformations

superdiffusion of a random walk driven by an ergodic markov process with switching we propose a markov model with an ergodic two component switching mechanism that dynamically generates anomalous diffusion the first component plays the role of a hidden parameter the second one is the switching component generating the superdiffusion of a random walker and is itself non markovian the model is studied numerically using the monte carlo technique

particle sft a provably convergent fast shape from template algorithm the shape from template sft problem is to recover the 3d shape of a deformable object from a single image given a 3d template and a deformation constraint we propose particle sft a new sft algorithm which handles isometric and non isometric deformations we build particle sft upon a particle system guided by deformation and reprojection constraint projections reconstruction is achieved by evolving particles to a globally attractive equilibrium while taking observable external forces such as gravity into account if any particle sft may be used to refine an existing initial shape however in practice we simply use the template as initial guess this is because as opposed to the existing refining methods particle sft has an extremely wide convergence basin particle sft is also faster than the existing refining methods this is because it moves pieces of the shape s mesh independently to achieve larger step size by optimal constraint projection we proved its convergence to a fixed point we experimented it with synthetic and real data it has the same accuracy as the best performing isometric method and consistently outperforms all existing elastic methods in almost all cases while being much faster

superaging correlation function and ergodicity breaking for brownian motion in logarithmic potentials we consider an overdamped brownian particle moving in a confining asymptotically logarithmic potential which supports a normalized boltzmann equilibrium density we derive analytical expressions for the two time correlation function and the fluctuations of the time averaged position of the particle for large but finite times we characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential and we support our predictions with extensive langevin simulations while the boltzmann measure is used to obtain stationary correlation functions we show how the non normalizable infinite covariant density is related to the superaging behavior

surface deformation models for nonrigid 3d shape recovery three dimensional detection and shape recovery of a nonrigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data here we introduce an approach to creating such models for deformable 3d surfaces we exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets we use this set of angles to create a representative set of potential shapes which we feed to a simple dimensionality reduction technique to produce low dimensional 3d deformation models we show that these models can be used to accurately model a wide range of deforming 3d surfaces from video sequences acquired under realistic conditions

exact propagator for a fokker planck equation first passage time distribution and anomalous diffusion we obtain an exact form for the propagator of the fokker planck equation t xd x x x f x t with d x d x in presence of the external force f x t k t x k x x using the results found here we also investigate the mean square displacement survival probability and first passage time distribution in addition we discuss the connection of these results with anomalous diffusion phenomena

feature based deformable surface detection with self occlusion reasoning this paper presents a method for detecting a textured deformed surface in an image it uses wide baseline point matches between a template and the input image the main contribution of the paper is twofold first we propose a robust method based on local surface smoothness capable of discarding outliers from the set of point matches our method handles large proportions of outliers beyond 70 with less than 15 of false positives even when the surface self occludes second we propose a method to estimate a self occlusion resistant warp from point matches our method allows us to realistically retexture the input image a pixel based direct registration approach is also proposed bootstrapped by our robust point based method it finely tunes the warp parameters using the value intensity or color of all the visible surface pixels the proposed framework was tested with simulated and real data convincing results are shown for the detection and retexturing of deformed surfaces in challenging images

analytical solutions for diffusion on fractal objects a generalization of the euclidean diffusion equation is proposed for diffusion on fractals on the basis of a scaling argument a renormalization group theory for the green s function and numerical tests conjectures on the applicability to natural fractals such as porous media are presented

shape from template with curves shape from template sft is the problem of using a shape template to infer the shape of a deformable object observed in an image the usual case of sft is surface sft where the shape is a 2d surface embedded in 3d and the image is a 2d perspective projection we introduce curve sft comprising two new cases of sft where the shape is a 1d curve the first new case is when the curve is embedded in 2d and the image a 1d perspective projection the second new case is when the curve is embedded in 3d and the image a 2d perspective projection we present a thorough theoretical study of these new cases for isometric deformations which are a good approximation of ropes cables and wires unlike surface sft we show that curve sft is only ever solvable up to discrete ambiguities we present the necessary and sufficient conditions for solvability with critical point analysis we further show that unlike surface sft curve sft cannot be solved locally using exact non holonomic partial differential equations our main technical contributions are two fold first we give a stable global reconstruction method that models the problem as a discrete hidden markov model this can generate all candidate solutions second we give a non convex refinement method using a novel angle based deformation parameterization we present quantitative and qualitative results showing that real curve shaped objects such as a necklace can be successfully reconstructed with curve sft

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

cramer rao bounds for parametric shape estimation in inverse problems we address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems when the boundaries are parameterized by a finite number of unknown variables our model applies to multiple unknown objects each with its own unknown gray level or color and boundary parameterization on an arbitrary known background while such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the cramer rao lower bounds very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation we provide a general formula for computing cramer rao lower bounds in inverse problems where the observations are related to the object by a general linear transform followed by a possibly nonlinear and noisy measurement system as an illustration we derive explicit formulas for computed tomography fourier imaging and deconvolution problems the bounds reveal that highly accurate parametric reconstructions are possible in these examples using severely limited and noisy data