the complexity of mean payoff games on graphs abstract we study the complexity of finding the values and optimal strategies of mean payoff games on graphs a family of perfect information games introduced by ehrenfeucht and mycielski and considered by gurvich karzanov and khachiyan we describe a pseudo polynomial time algorithm for the solution of such games the decision problem for which is in np conp finally we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by condon these games are also known to be in np conp but no polynomial or pseudo polynomial time algorithm is known for them

clustered blockwise pca for representing visual data principal component analysis pca is extensively used in computer vision and image processing since it provides the optimal linear subspace in a least square sense it has been used for dimensionality reduction and subspace analysis in various domains however its scalability is very limited because of its inherent computational complexity we introduce a new framework for applying pca to visual data which takes advantage of the spatio temporal correlation and localized frequency variations that are typically found in such data instead of applying pca to the whole volume of data complete set of images we partition the volume into a set of blocks and apply pca to each block then we group the subspaces corresponding to the blocks and merge them together as a result we not only achieve greater efficiency in the resulting representation of the visual data but also successfully scale pca to handle large data sets we present a thorough analysis of the computational complexity and storage benefits of our approach we apply our algorithm to several types of videos we show that in addition to its storage and speed benefits the algorithm results in a useful representation of the visual data

kronecker basis representation based tensor sparsity and its applications to tensor recovery as a promising way for analyzing data sparse modeling has achieved great success throughout science and engineering it is well known that the sparsity low rank of a vector matrix can be rationally measured by nonzero entries number l 0 norm nonzero singular values number rank respectively however data from real applications are often generated by the interaction of multiple factors which obviously cannot be sufficiently represented by a vector matrix while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles unlike the vector matrix case constructing a rational high order sparsity measure for tensor is a relatively harder task to this aim in this paper we propose a measure for tensor sparsity called kronecker basis representation based tensor sparsity measure kbr briefly which encodes both sparsity insights delivered by tucker and candecomp parafac cp low rank decompositions for a general tensor then we study the kbr regularization minimization kbrm problem and design an effective admm algorithm for solving it where each involved parameter can be updated with closed form equations such an efficient solver makes it possible to extend kbr to various tasks like tensor completion and tensor robust principal component analysis a series of experiments including multispectral image msi denoising msi completion and background subtraction substantiate the superiority of the proposed methods beyond state of the arts

illumination recovery from image with cast shadows via sparse representation in this paper we propose using sparse representation for recovering the illumination of a scene from a single image with cast shadows given the geometry of the scene the images with cast shadows can be quite complex and therefore cannot be well approximated by low dimensional linear subspaces however it can be shown that the set of images produced by a lambertian scene with cast shadows can be efficiently represented by a sparse set of images generated by directional light sources we first model an image with cast shadows composed of a diffusive part without cast shadows and a residual part that captures cast shadows then we express the problem in an l1 regularized least squares formulation with nonnegativity constraints as light has to be non negative at any point in space this sparse representation enjoys an effective and fast solution thanks to recent advances in compressive sensing in experiments on synthetic and real data our approach performs favorably in comparison with several previously proposed methods

relative affine structure canonical model for 3d from 2d geometry and applications we propose an affine framework for perspective views captured by a single extremely simple equation based on a viewer centered invariant we call relative affine structure via a number of corollaries of our main results we show that our framework unifies previous work including euclidean projective and affine in a natural and simple way and introduces new extremely simple algorithms for the tasks of reconstruction from multiple views recognition by alignment and certain image coding applications

image representation by sign information image representation by sign data in its most general context is considered for the case when f is a two dimensional signal the authors study conditions under which f is determined by its sign or in other words by its quantization to 1 bit of information this study is carried out in two different directions first theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band limited image an interesting paradigm arising in theoretical computer vision is then posed are the zero crossing of f convolved with a laplacian of a gaussian at a single channel enough for unambiguously representing f second the problem of the completeness of the representation when the position of the zero crossings is known only approximately is addressed it is shown that when sign f is sampled significant ambiguities are introduced in the representation experimental results are presented which were obtained from an iterative algorithm devised to reconstruct real images from multiscale sign information

motion and structure from orthographic projections s ullman s classical 1979 results on motion structure from orthographic views are revisited specifically two results are presented 1 two orthographic views allow an uncountably infinite number of solutions to motion structure of a rigid body and 2 a linear algorithm for solving motion structure from four point correspondences over three views

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

exploiting unsupervised and supervised constraints for subspace clustering data in many image and video analysis tasks can be viewed as points drawn from multiple low dimensional subspaces with each subspace corresponding to one category or class one basic task for processing such kind of data is to separate the points according to the underlying subspace referred to as subspace clustering extensive studies have been made on this subject and nearly all of them use unconstrained subspace models meaning the points can be drawn from everywhere of a subspace to represent the data in this paper we attempt to do subspace clustering based on a constrained subspace assumption that the data is further restricted in the corresponding subspaces e g belonging to a submanifold or satisfying the spatial regularity constraint this assumption usually describes the real data better such as differently moving objects in a video scene and face images of different subjects under varying illumination a unified integer linear programming optimization framework is used to approach subspace clustering which can be efficiently solved by a branch and bound bb method we also show that various kinds of supervised information such as subspace number outlier ratio pairwise constraints size prior and etc can be conveniently incorporated into the proposed framework experiments on real data show that the proposed method outperforms the state of the art algorithms significantly in clustering accuracy the effectiveness of the proposed method in exploiting supervised information is also demonstrated

a physics based analysis of image appearance models linear and multilinear models pca 3dmm aam asm and multilinear tensors of object shape appearance have been very popular in computer vision in this paper we analyze the applicability of these heuristic models from the fundamental physical laws of object motion and image formation we prove that under suitable conditions the image appearance space can be closely approximated to be multilinear with the illumination and texture subspaces being trilinearly combined with the direct sum of the motion and deformation subspaces this result provides a physics based understanding of many of the successes and limitations of the linear and multilinear approaches existing in the computer vision literature and also identifies some of the conditions under which they are valid it provides an analytical representation of the image space in terms of different physical factors that affect the image formation process numerical analysis of the accuracy of the physics based models is performed and tracking results on real data are presented

enhancing low rank subspace clustering by manifold regularization recently low rank representation lrr method has achieved great success in subspace clustering sc which aims to cluster the data points that lie in a union of low dimensional subspace given a set of data points lrr seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself however lrr only considers the global euclidean structure while the local manifold structure which is often important for many real applications is ignored in this paper to exploit the local manifold structure of the data a manifold regularization characterized by a laplacian graph has been incorporated into lrr leading to our proposed laplacian regularized lrr laplrr an efficient optimization procedure which is based on alternating direction method of multipliers admm is developed for laplrr experimental results on synthetic and real data sets are presented to demonstrate that the performance of lrr has been enhanced by using the manifold regularization

combined affine geometric transformations and spatially dependent radiometric deformations a decoupled linear estimation framework this paper considers the problem of registering two observations of the same object where the observations differ due to a combined effect of an affine geometric transformation and nonuniform illumination changes the problem of deriving new representations of the observations that are both invariant to geometric transformations and linear in the illumination model is analyzed in this framework we present a novel method for linear estimation of illumination changes in an affine invariant manner thus decoupling the original problem into two simpler ones the computational complexity of the method is low as it requires no more than solving a linear set of equations the prior step of illumination estimation is shown to improve the accuracy of state of the art registration techniques by a factor of two

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

duality between invariant spaces for max plus linear discrete event systems we extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max plus or tropical semiring we establish a duality theorem relating both notions which we use to construct dynamic observers these are useful in situations in which some of the system coefficients may vary within certain intervals the results are illustrated by an application to a manufacturing system

pathwise dynamic programming we present a novel method for deriving tight monte carlo confidence intervals for solutions of stochastic dynamic programming equations taking some approximate solution to the equation as an input we construct pathwise recursions with a known bias suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle we apply our method to three nonlinear option pricing problems pricing under bilateral counterparty risk under uncertain volatility and under negotiated collateralization

max plus a b invariant spaces and control of timed discrete event systems the concept of a b invariant subspace or controlled invariant of a linear dynamical system is extended to linear systems over the max plus semiring although this extension presents several difficulties which are similar to those encountered in the same kind of extension to linear dynamical systems over rings it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings sufficient conditions are given for computing the maximal a b invariant subspace contained in a given space and the existence of linear state feedbacks is discussed an application to the study of transportation networks which evolve according to a timetable is considered

segmented linear subspaces for illumination robust face recognition all images of a convex lambertian surface captured with a fixed pose under varying illumination are known to lie in a convex cone in the image space that is called the illumination cone since this cone model is too complex to be built in practice researchers have attempted to approximate it with simpler models in this paper we propose a segmented linear subspace model to approximate the cone our idea of segmentation is based on the fact that the success of low dimensional linear subspace approximations of the illumination cone increases if the directions of the surface normals get close to each other hence we propose to cluster the image pixels according to their surface normal directions and to approximate the cone with a linear subspace for each of these clusters separately we perform statistical performance evaluation experiments to compare our system to other popular systems and demonstrate that the performance increase we obtain is statistically significant

an algorithm to describe the solution set of any tropical linear system a x b x abstract an algorithm to give an explicit description of all the solutions to any tropical linear system a x b x is presented the given system is converted into a finite rather small number p of pairs s t of classical linear systems a system s of equations and a system t of inequalities the notion introduced here that makes p small is called compatibility the particular feature of both s and t is that each item equation or inequality is bivariate i e it involves exactly two variables one variable with coefficient 1 and the other one with 1 s is solved by gaussian elimination we explain how to solve t by a method similar to gaussian elimination to achieve this we introduce the notion of sub special matrix the procedure applied to t is therefore called sub specialization

the equation a x b y over max for the two sided homogeneous linear equation system a x b y over max with no infinite rows or columns in a or b an algorithm is presented which converges to a finite solution from any finite starting point whenever a finite solution exists if the finite elements of a b are all integers convergence is in a finite number of steps for which a precise bound can be calculated if moreover one of a b has only finite elements the algorithm is thus pseudopolynomial in complexity

appearance sampling of real objects for variable illumination the appearance of an object greatly changes under different lighting conditions even so previous studies have demonstrated that the appearance of an object under varying illumination conditions can be represented by a linear subspace a set of basis images spanning such a linear subspace can be obtained by applying the principal component analysis pca for a large number of images taken under different lighting conditions since little is known about how to sample the appearance of an object in order to correctly obtain its basis images it was a common practice to use as many input images as possible in this study we present a novel method for analytically obtaining a set of basis images of an object for varying illumination from input images of the object taken properly under a set of light sources such as point light sources or extended light sources our proposed method incorporates the sampling theorem of spherical harmonics for determining a set of lighting directions to efficiently sample the appearance of an object we further consider the issue of aliasing caused by insufficient sampling of the object s appearance in particular we investigate the effectiveness of using extended light sources for modeling the appearance of an object under varying illumination without suffering the aliasing caused by insufficient sampling of its appearance

difference subspace and its generalization for subspace based methods subspace based methods are known to provide a practical solution for image set based object recognition based on the insight that local shape differences between objects offer a sensitive cue for recognition this paper addresses the problem of extracting a subspace representing the difference components between class subspaces generated from each set of object images independently of each other we first introduce the difference subspace ds a novel geometric concept between two subspaces as an extension of a difference vector between two vectors and describe its effectiveness in analyzing shape differences we then generalize it to the generalized difference subspace gds for multi class subspaces and show the benefit of applying this to subspace and mutual subspace methods in terms of recognition capability furthermore we extend these methods to kernel ds kds and kernel gds kgds by a nonlinear kernel mapping to deal with cases involving larger changes in viewing direction in summary the contributions of this paper are as follows 1 a ds kds between two class subspaces characterizes shape differences between the two respectively corresponding objects 2 the projection of an input vector onto a ds kds realizes selective visualization of shape differences between objects and 3 the projection of an input vector or subspace onto a gds kgds is extremely effective at extracting differences between multiple subspaces and therefore improves object recognition performance we demonstrate validity through shape analysis on synthetic and real images of 3d objects as well as extensive comparison of performance on classification tests with several related methods we study the performance in face image classification on the yale face database b and the cmu multi pie database and hand shape classification of multi view images

on the steady state control of timed event graphs with firing date constraints two algorithms for solving a specific class of steady state control problems for timed event graphs are presented in the first asymptotic convergence to the desired set is guaranteed the second algorithm which builds on from the recent developments in the spectral theory of min max functions guarantees lyapunov stability since the distance between the actual state and the desired set never increases simulation results show the efficiency of the proposed approach in a problem of moderate complexity

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

surface dependent representations for illumination insensitive image comparison we consider the problem of matching images to tell whether they come from the same scene viewed under different lighting conditions we show that the surface characteristics determine the type of image comparison method that should be used previous work has shown the effectiveness of comparing the image gradient direction for surfaces with material properties that change rapidly in one direction we show analytically that two other widely used methods normalized correlation of small windows and comparison of multiscale oriented filters essentially compute the same thing then we show that for surfaces whose properties change more slowly comparison of the output of whitening filters is most effective this suggests that a combination of these strategies should be employed to compare general objects we discuss indications that gabor jets use such a mixed strategy effectively and we propose a new mixed strategy we validate our results on synthetic and real images

projective structure from uncalibrated images structure from motion and recognition address the problem of reconstructing 3 d space in a projective framework from two or more views and the problem of artificially generating novel views of the scene from two given views reprojection the author describes an invariance relation that provides a new description of structure which the author calls projective depth that is captured by a single equation relating image point correspondences across two or more views and the homographics of two arbitrary virtual planes the framework is based on knowledge of correspondence of features across views is linear and extremely simple and the computations of structure readily extend to overdetermination using multiple views experimental results demonstrate a high degree of accuracy in both tasks reconstruction and reprojection

max plus control design for temporal constraints meeting in timed event graphs the aim of the presented work is the control of timed event graph to meet tight temporal constraints the problem of temporal constraints is formulated in terms of control of linear max plus models first the synthesis of a control law that ensures the satisfaction of a single constraint for a single input system is presented then the single input multi constraints problem is tackled and finally the method is extended to the multi inputs multi constraints problem the proposed method is illustrated on the example of a simple production process

image representation using laplacian regularized nonnegative tensor factorization tensor provides a better representation for image space by avoiding information loss in vectorization nonnegative tensor factorization ntf whose objective is to express an n way tensor as a sum of k rank 1 tensors under nonnegative constraints has recently attracted a lot of attentions for its efficient and meaningful representation however ntf only sees euclidean structures in data space and is not optimized for image representation as image space is believed to be a sub manifold embedded in high dimensional ambient space to avoid the limitation of ntf we propose a novel laplacian regularized nonnegative tensor factorization lrntf method for image representation and clustering in this paper in lrntf the image space is represented as a 3 way tensor and we explicitly consider the manifold structure of the image space in factorization that is two data points that are close to each other in the intrinsic geometry of image space shall also be close to each other under the factorized basis to evaluate the performance of lrntf in image representation and clustering we compare our algorithm with nmf ntf ncut and gnmf methods on three standard image databases experimental results demonstrate that lrntf achieves better image clustering performance while being more insensitive to noise

the quadric reference surface theory and applications the conceptual component of this work is about reference surfaces which are the analogous to reference frames often used for shape representation purposes the theoretical component of this work involves the question of whether one can find a unique and simple mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3d given i few corresponding points in the two views or ii the outline conic of the surface in one view only and few corresponding points in the two views the practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects

analytic pca construction for theoretical analysis of lighting variability in images of a lambertian object we analyze theoretically the subspace best approximating images of a convex lambertian object taken from the same viewpoint but under different distant illumination conditions we analytically construct the principal component analysis for images of a convex lambertian object explicitly taking attached shadows into account and find the principal eigenmodes and eigenvalues with respect to lighting variability our analysis makes use of an analytic formula for the irradiance in terms of spherical harmonic coefficients of the illumination and shows under appropriate assumptions that the principal components or eigenvectors are identical to the spherical harmonic basis functions evaluated at the surface normal vectors our main contribution is in extending these results to the single viewpoint case showing how the principal eigenmodes and eigenvalues are affected when only a limited subset the upper hemisphere of normals is available and the spherical harmonics are no longer orthonormal over the restricted domain our results are very close both qualitatively and quantitatively to previous empirical observations and represent the first essentially complete theoretical explanation of these observations

signal reconstruction from fourier transform sign information in this paper we present new results on the reconstruction of signals from only the sign of the real part of the fourier transform specifically we develop new theoretical results which state conditions under which two dimensional signals are uniquely specified to within a scale factor with this information and show that these conditions include a broad class of signals furthermore we apply this result to the problem of reconstructing two dimensional signals from their zero crossings we also present two algorithms for reconstructing a signal from sign information in either the time or frequency domain