map estimation via agreement on trees message passing and linear programming we develop and analyze methods for computing provably optimal maximum a posteriori probability map configurations for a subclass of markov random fields defined on graphs with cycles by decomposing the original distribution into a convex combination of tree structured distributions we obtain an upper bound on the optimal value of the original problem i e the log probability of the map assignment in terms of the combined optimal values of the tree problems we prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common an important implication is that any such shared configuration must also be a map configuration for the original distribution next we develop two approaches to attempting to obtain tight upper bounds a a tree relaxed linear program lp which is derived from the lagrangian dual of the upper bounds and b a tree reweighted max product message passing algorithm that is related to but distinct from the max product algorithm in this way we establish a connection between a certain lp relaxation of the mode finding problem and a reweighted form of the max product min sum message passing algorithm

evaluating kube and pentland s fractal imaging model the paper assesses the validity of a model proposed by kube and pentland 1988 that relates a rough surface to its image texture simulation was used to assess whether a linear approximation is appropriate and whether the optimal linear filter agrees with the predictions of kube and pentland s model the predictions of the model about the image directionality were also assessed on real images it was found that a linear model is capable of modeling the imaging process for surfaces of moderate roughness and lambertian reflectance and that subject to a small modification kube and pentland s model accurately predicts the relationship between surface and image spectra

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

closed form solution of local shape from shading at critical points in the theory of shape from shading behaviours of the local solution around a critical point of the image play an important role this paper shows that the second derivatives of the object surface can be locally determined at these image critical points closed form expressions of the surface second derivatives in terms of the second derivatives of the image brightness and of the reflectance map are shown they are derived as follows by differentiating the image irradiance equation twice at an image critical point a set of polynomial equations is obtained that contains the second derivatives of the surface of the image brightness and of the reflectance map regarding these equations as simultaneous equations for unknown surface second derivatives they are algebraically solved and their explicit expressions are derived such a derivation is possible only at image critical points and is impossible at any other image point the applicability of the derived expressions to noisy images is tested using synthetic images

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

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

on differential photometric reconstruction for unknown isotropic brdfs this paper presents a comprehensive theory of photometric surface reconstruction from image derivatives in the presence of a general unknown isotropic brdf we derive precise topological classes up to which the surface may be determined and specify exact priors for a full geometric reconstruction these results are the culmination of a series of fundamental observations first we exploit the linearity of chain rule differentiation to discover photometric invariants that relate image derivatives to the surface geometry regardless of the form of isotropic brdf for the problem of shape from shading we show that a reconstruction may be performed up to isocontours of constant magnitude of the gradient for the problem of photometric stereo we show that just two measurements of spatial and temporal image derivatives from unknown light directions on a circle suffice to recover surface information from the photometric invariant surprisingly the form of the invariant bears a striking resemblance to optical flow however it does not suffer from the aperture problem this photometric flow is shown to determine the surface up to isocontours of constant magnitude of the surface gradient as well as isocontours of constant depth further we prove that specification of the surface normal at a single point completely determines the surface depth from these isocontours in addition we propose practical algorithms that require additional initial or boundary information but recover depth from lower order derivatives our theoretical results are illustrated with several examples on synthetic and real data

a fast algorithm for the unique decipherability of multivalued encodings abstract multivalued encodings constitute an interesting generalization of ordinary encodings in that they allow each source symbol to be encoded by more than one codeword in this paper the problem of testing the property of unique decipherability of multivalued encodings is considered we provide an efficient algorithm whose time complexity is o c where c is the number of codewords and is the sum of their lengths it is remarkable that the running time equals that of the fastest algorithms for testing the much simpler property of unique decipherability of ordinary encodings

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 note on multiset decipherable codes in a recent paper a lempel ibid vol it 32 p 714 16 1986 introduced the notion of a multiset decipherable msd code to handle some special problems of information transmission he showed that no msd code contains a full prefix code as a proper subcode he further conjectured that no msd code contains a full uniquely decipherable code as a proper subcode and that every msd code satisfies the kraft inequality a proof of the first conjecture and a disproof of the second are given

multi view stereo reconstruction and scene flow estimation with a global image based matching score we present a new variational method for multi view stereovision and non rigid three dimensional motion estimation from multiple video sequences our method minimizes the prediction error of the shape and motion estimates both problems then translate into a generic image registration task the latter is entrusted to a global measure of image similarity chosen depending on imaging conditions and scene properties rather than integrating a matching measure computed independently at each surface point our approach computes a global image based matching score between the input images and the predicted images the matching process fully handles projective distortion and partial occlusions neighborhood as well as global intensity information can be exploited to improve the robustness to appearance changes due to non lambertian materials and illumination changes without any approximation of shape motion or visibility moreover our approach results in a simpler more flexible and more efficient implementation than in existing methods the computation time on large datasets does not exceed thirty minutes on a standard workstation finally our method is compliant with a hardware implementation with graphics processor units our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency we have successfully tested our motion estimation algorithm on a very challenging multi view video sequence of a non rigid scene

deciding multiset decipherability an o n sup 2 l time and o n k l space algorithm is provided for deciding whether or not a finite set c consisting of n words having total length l where all words are taken over a k element alphabet is a multiset decipherable code the algorithm is based on a technique related to dominoes at an easily stage it decides in o nl time and o n k l space whether or not the set c is uniquely decipherable

on unique multiset and set decipherability of three word codes the concepts of unique decipherability ud multiset decipherability msd and set decipherability sd of codes were developed to handle some special problems in the transmission of information in unique decipherability different sequences of codewords carry different information in multiset decipherability the information of interest is the multiset of codewords used in the encoding process so that order in which transmitted words are received is immaterial in set decipherability it is the set of codewords that is relevant information so the order and the multiplicity of words are immaterial lempel 1986 showed that the ud and msd properties coincide for two word codes and conjectured that every three word msd code is a ud code guzman 1995 showed that the ud msd and sd properties coincide for two word codes and conjectured that these properties coincide for three word codes in this paper we answer both conjectures positively for all three word codes c sub 1 c sub 2 c sub 3 satisfying c sub 1 c sub 2 spl les c sub 3 our procedures are based on techniques related to dominoes

indoor scene reconstruction using near light photometric stereo we propose a novel framework for photometric stereo ps under low light conditions using uncalibrated near light illumination it operates on free form video sequences captured with a minimalistic and affordable setup we address issues such as albedo variations shadowing perspective projections and camera noise our method uses specular spheres detected with a perspective correcting hough transform to robustly triangulate light positions in the presence of outliers via a least squares approach furthermore we propose an iterative reweighting scheme in combination with an ell p norm minimizer to robustly solve the calibrated near light ps problem in contrast to other approaches our framework reconstructs depth albedo relative to light source intensity and normals simultaneously and is demonstrated on synthetic and real world scenes

recovery of surfaces with discontinuities by fusing shading and range data within a variational framework this work provides a variational framework for fusing range and intensity data for recovering regularized surfaces it is shown that this framework provides natural boundary conditions for the shape from shading problem results in a new shape from shading formulation in the absence of range data and provides a new fusion paradigm when range data is incorporated the approach is demonstrated on simulated range and intensity images error analysis with respect to the ground truth surface is presented it is shown that the formulation performs well even in very noisy images

on multiset decipherable codes corresp in certain applications it is necessary to communicate a description of a sequence of events where the information of interest is which one of a set of possible events has occurred including multiplicity but where the order of occurrence is irrelevant typical examples are online compilations of inventories construction of histograms or updating of relative frequencies suitable codes for this purpose need not be uniquely decipherable ud in fact all that is required of such a code is that given a finite message over the code every possible parsing of the message into codewords must yield the same multiset of codewords a code with this property is referred to as a multiset decipherable msd code an msd code is said to be proper if it is not a ud code it is shown that for every n 3 there exist proper msd codes with n words for n 2 every msd code is necessarily a ud code and all evidence points to the same conclusion for n 3 it is further shown that no msd code contains a full prefix code or a full suffix code as a proper subcode and it is conjectured that despite the weaker decipherability condition every msd code satisfies the kraft inequality

quantal symmetry for a system with a singular higher order lagrangian based on the phase space generating functional of the green function for a constrained hamiltonian system with a singular higher order lagrangian the canonical ward identities for such a system under the local and global transformation have been derived respectively the quantal conserved charge qcc under the global symmetry transformation is also deduced in general these qccs are different from the noether charge in classical theory a comparison of these quantal conservation laws with those deriving from the configuration space path integral for gauge invariant theories is discussed we give a preliminary application of our results to yang mills ym theory and chern simons cs theory with higher order derivatives a new form of gauge ghost proper vertices and new conserved charges at the quantum level are obtained for the ym theory the quantal becchi rouet stora brs conserved charges and conserved angular momentum are also derived for cs theory the advantage of our canonical formalism is that we do not carry out the integration over the canonical momenta in the phase space path integral as usually performed

shading based surface detail recovery under general unknown illumination reconstructing the shape of a 3d object from multi view images under unknown general illumination is a fundamental problem in computer vision high quality reconstruction is usually challenging especially when fine detail is needed and the albedo of the object is non uniform this paper introduces vertex overall illumination vectors to model the illumination effect and presents a total variation tv based approach for recovering surface details using shading and multi view stereo mvs behind the approach are the two important observations 1 the illumination over the surface of an object often appears to be piecewise smooth and 2 the recovery of surface orientation is not sufficient for reconstructing the surface which was often overlooked previously thus we propose to use tv to regularize the overall illumination vectors and use visual hull to constrain partial vertices the reconstruction is formulated as a constrained tv minimization problem that simultaneously treats the shape and illumination vectors as unknowns an augmented lagrangian method is proposed to quickly solve the tv minimization problem as a result our approach is robust stable and is able to efficiently recover high quality surface details even when starting with a coarse model obtained using mvs these advantages are demonstrated by extensive experiments on the state of the art mvs database which includes challenging objects with varying albedo

gradient flows for optimizing triangular mesh based surfaces applications to 3d reconstruction problems dealing with visibility this article tackles the problem of using variational methods for evolving 3d deformable surfaces we give an overview of gradient descent flows when the shape is represented by a triangular mesh based surface and we detail the gradients of two generic energy functionals which embody a number of energies used in mesh processing and computer vision in particular we show how to rigorously account for visibility in the surface optimization process we present different applications including 3d reconstruction from multiple views for which the visibility is fundamental the gradient correctly takes into account the visibility changes that occur when a surface moves this forces the contours generated by the reconstructed surface to match with the apparent contours in the input images

the finest homophonic partition and related code concepts let c be a finite set of n words having total length l where all words are taken over a r element alphabet the set c is called numerically decipherable if any two factorizations of the same word over the given alphabet into words in c have the same length an o nl sup 2 time and o n k l space algorithm is presented for computing the finest homophonic partition of c provided that this set is numerically decipherable the latter property can be decided by another algorithm requiring o nl time and o n k l space the two algorithms are based on a technique related to dominoes

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

subpixel photometric stereo conventional photometric stereo recovers one normal direction per pixel of the input image this fundamentally limits the scale of recovered geometry to the resolution of the input image and cannot model surfaces with subpixel geometric structures in this paper we propose a method to recover subpixel surface geometry by studying the relationship between the subpixel geometry and the reflectance properties of a surface we first describe a generalized physically based reflectance model that relates the distribution of surface normals inside each pixel area to its reflectance function the distribution of surface normals can be computed from the reflectance functions recorded in photometric stereo images a convexity measure of subpixel geometry structure is also recovered at each pixel through an analysis of the shadowing attenuation then we use the recovered distribution of surface normals and the surface convexity to infer subpixel geometric structures on a surface of homogeneous material by spatially arranging the normals among pixels at a higher resolution than that of the input image finally we optimize the arrangement of normals using a combination of belief propagation and mcmc based on a minimum description length criterion on 3d textons over the surface the experiments demonstrate the validity of our approach and show superior geometric resolution for the recovered surfaces

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

differential geometric inference in surface stereo many traditional two view stereo algorithms explicitly or implicitly use the frontal parallel plane assumption when exploiting contextual information since e g the smoothness prior biases toward constant disparity depth over a neighborhood this introduces systematic errors to the matching process for slanted or curved surfaces these errors are nonnegligible for detailed geometric modeling of natural objects such as a human face we show how to use contextual information geometrically to avoid such errors a differential geometric study of smooth surfaces allows contextual information to be encoded in cartan s moving frame model over local quadratic approximations providing a framework of geometric consistency for both depth and surface normals the accuracy of our reconstructions argues for the sufficiency of the approximation in effect cartan s model provides the additional constraint necessary to move beyond the frontal parallel plane assumption in stereo reconstruction it also suggests how geometry can extend surfaces to account for unmatched points due to partial occlusion

bayesian helmholtz stereopsis with integrability prior helmholtz stereopsis is a 3d reconstruction method uniquely independent of surface reflectance yet its sub optimal maximum likelihood formulation with drift prone normal integration limits performance via three contributions this paper presents a complete novel pipeline for helmholtz stereopsis first we propose a bayesian formulation replacing the maximum likelihood problem by a maximum a posteriori one second a tailored prior enforcing consistency between depth and normal estimates via a novel metric related to optimal surface integrability is proposed third explicit surface integration is eliminated by taking advantage of the accuracy of prior and high resolution of the coarse to fine approach the pipeline is validated quantitatively and qualitatively against alternative formulations reaching sub millimetre accuracy and coping with complex geometry and reflectance

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

shape from shading level set propagation and viscosity solutions we present a new implementation of an algorithm aimed at recovering a 3d shape from its 2d gray level picture in order to reconstruct the shape of the object an almost arbitrarily initialized 3d function is propagated on a rectangular grid so that a level set of this function tracks the height contours of the shape the method imports techniques from differential geometry fluid dynamics and numerical analysis and provides an accurate shape from shading algorithm the method solves some topological problems and gracefully handles cases of non smooth surfaces that give rise to shocks in the propagating contours real and synthetic images of 3d profiles were submitted to the algorithm and the reconstructed surfaces are presented demonstrating the effectiveness of the proposed method

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

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

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

a theory of shape by space carving in this paper we consider the problem of computing the 3d shape of an unknown arbitrarily shaped scene from multiple photographs taken at known but arbitrarily distributed viewpoints by studying the equivalence class of all 3d shapes that reproduce the input photographs we prove the existence of a special member of this class the photo hull that 1 can be computed directly from photographs of the scene and 2 subsumes all other members of this class we then give a provably correct algorithm called space carving for computing this shape and present experimental results on complex real world scenes the approach is designed to 1 capture photorealistic shapes that accurately model scene appearance from a wide range of viewpoints and 2 account for the complex interactions between occlusion parallax shading and their view dependent effects on scene appearance

unique decipherability in formal languages abstract we consider several language theoretic aspects of various notions of unique decipherability or unique factorization in formal languages given a language l at some position within the chomsky hierarchy we investigate the language of words ud l in l that have unique factorization over l we also consider similar notions for weaker forms of unique decipherability such as numerically decipherable words nd l multiset decipherable words msd l and set decipherable words sd l although these notions of unique factorization have been considered before it appears that the languages of words having these properties have not been positioned in the chomsky hierarchy up until now we show that ud l nd l msd l and sd l need not be context free if l is context free in fact nd l and msd l need not be context free even if l is finite although ud l and sd l are regular in this case we show that if l is context sensitive then so are ud l nd l msd l and sd l we also prove that the membership problem resp emptiness problem for these classes is pspace complete resp undecidable we finally determine upper and lower bounds on the length of the shortest word of l not having the various forms of unique decipherability into elements of l

dynamic shape and appearance models we propose a model of the joint variation of shape and appearance of portions of an image sequence the model is conditionally linear and can be thought of as an extension of active appearance models to exploit the temporal correlation of adjacent image frames inference of the model parameters can be performed efficiently using established numerical optimization techniques borrowed from finite element analysis and system identification techniques

efficient photometric stereo using kernel regression photometric stereo estimates surface normals from multiple images captured under different light directions using a fixed camera to deal with non lambertian reflections the recent photometric stereo methods employ iterative or optimization frameworks that are computationally expensive this paper proposes an efficient photometric stereo method using kernel regression which can be transformed to an eigendecomposition problem the kernel parameter is variable for each surface point so that it can cope with the variety of general reflectances the best kernel parameter is automatically determined by leave one out cross validation to improve computational efficiency the leave one out process is accelerated by fast matrix computation and proper normal initialization the proposed photometric stereo method is extensively evaluated on synthetic and real surfaces with various reflectances experimental results validate that the method is computationally efficient and achieves the state of the art accuracy in surface normal estimation

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

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

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

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

a dynamical formalism of singular lagrangian system with higher derivatives the singular lagrangian system with higher derivatives is analyzed with the aid of the ostrogradski transformation and the dirac formalism the formulation of canonical theory is developed so that the equivalence between the lagrange formalism and the hamilton one is maintained as a practical example the acceleration dependent potentials appearing in the lagrangian of two point particles interacting gravitationally are dealt with and the equivalence between the two hamiltonians that follow from the two lagrangians which are related by the coordinate transformations is shown it is also shown when the constraints are all first class that a consistent generator of gauge transformation is constructed typical examples are given

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

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

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

multi view stereo reconstruction of dense shape and complex appearance we address the problem of estimating the three dimensional shape and complex appearance of a scene from a calibrated set of views under fixed illumination our approach relies on a rank condition that must be satisfied when the scene exhibits specular diffuse reflectance characteristics this constraint is used to define a cost functional for the discrepancy between the measured images and those generated by the estimate of the scene rather than attempting to match image to image directly minimizing such a functional yields the optimal estimate of the shape of the scene represented by a dense surface as well as its radiance represented by four functions defined on such a surface these can be used to generate novel views that capture the non lambertian appearance of the scene

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

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

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost