shape estimation from shading defocus and correspondence using light field angular coherence light field cameras are quickly becoming commodity items with consumer and industrial applications they capture many nearby views simultaneously using a single image with a micro lens array thereby providing a wealth of cues for depth recovery defocus correspondence and shading in particular apart from conventional image shading one can refocus images after acquisition and shift one s viewpoint within the sub apertures of the main lens effectively obtaining multiple views we present a principled algorithm for dense depth estimation that combines defocus and correspondence metrics we then extend our analysis to the additional cue of shading using it to refine fine details in the shape by exploiting an all in focus image in which pixels are expected to exhibit angular coherence we define an optimization framework that integrates photo consistency depth consistency and shading consistency we show that combining all three sources of information defocus correspondence and shading outperforms state of the art light field depth estimation algorithms in multiple scenarios

inference of segmented overlapping surfaces from binocular stereo presents an integrated approach to the derivation of scene descriptions from a pair of stereo images where the steps of feature correspondence and surface reconstruction are addressed within the same framework special attention is given to the development of a methodology with general applicability in order to handle the issues of noise lack of image features surface discontinuities and regions that are visible in one image only we adopt a tensor representation for the data and introduce a robust computational technique called tensor voting for information propagation the key contributions of this paper are twofold first we introduce saliency instead of correlation scores as the criterion to determine the correctness of matches and the integration of feature matching and structure extraction second our tensor representation and voting as a tool enables us to perform the complex computations associated with the formulation of the stereo problem in 3d at a reasonable computational cost we illustrate the steps on an example then provide results on both random dot stereograms and real stereo pairs all processed with the same parameter set

stability for quadratic functional equation in the spaces of generalized functions in this paper we consider the general solution of quadratic functional equation f ax y f ax y f x y f x y 2 a2 1 f x for any integer a with a 1 0 1 moreover we reformulate and prove the hyers ulam rassias stability theorem of the above equation in the spaces of tempered distributions and fourier hyperfunctions the generalized hyers ulam stability originated from the th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

constructing a multivalued representation for view synthesis a fundamental problem in computer vision and graphics is that of arbitrary view synthesis for static 3 d scenes whereby a user specified viewpoint of the given scene may be created directly from a representation we propose a novel compact representation for this purpose called the multivalued representation mvr starting with an image sequence captured by a moving camera undergoing either unknown planar translation or orbital motion a mvr is derived for each preselected reference frame and may then be used to synthesize arbitrary views of the scene the representation itself is comprised of multiple depth and intensity levels in which the k th level consists of points occluded by exactly k surfaces to build a mvr with respect to a particular reference frame dense depth maps are first computed for all the neighboring frames of the reference frame the depth maps are then combined together into a single map where points are organized by occlusions rather than by coherent affine motions this grouping facilitates an automatic process to determine the number of levels and helps to reduce the artifacts caused by occlusions in the scene an iterative multiframe algorithm is presented for dense depth estimation that both handles low contrast regions and produces piecewise smooth depth maps reconstructed views as well as arbitrary flyarounds of real scenes are presented to demonstrate the effectiveness of the approach

generalization of ulam stability problem for euler lagrange quadratic mappings in 1968 s m ulam proposed the problem when is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true in 1978 p m gruber proposed the ulam type problem suppose a mathematical object satisfies a certain property approximately is it then possible to approximate this object by objects satisfying the property exactly in this paper we solve the generalized ulam stability problem for non linear euler lagrange quadratic mappings satisfying approximately a mean equation and an euler lagrange type functional equations in quasi banach spaces and p banach spaces

when is the shape of a scene unique given its light field a fundamental theorem of 3d vision the complete set of measurements that could ever be used by a passive 3d vision algorithm is the plenoptic function or light field we give a concise characterization of when the light field of a lambertian scene uniquely determines its shape and conversely when the shape is inherently ambiguous in particular we show that stereo computed from the light field is ambiguous if and only if the scene is radiating light of a constant intensity and color etc over an extended region

genetic based stereo algorithm and disparity map evaluation in this paper a new genetic based stereo algorithm is presented our motivation is to improve the accuracy of the disparity map by removing the mismatches caused by both occlusions and false targets in our approach the stereo matching problem is considered as an optimization problem the algorithm first takes advantage of multi view stereo images to detect occlusions and therefore removes mismatches caused by visibility problems by optimizing the compatibility between corresponding points and the continuity of the disparity map using a genetic algorithm mismatches caused by false targets are removed the quadtree structure is used to implement the multi resolution framework since nodes at different level of the quadtree cover different number of pixels selecting nodes at different levels gives a similar effect as adjusting the window size at different locations of the image the experimental results show that our approach can generate more accurate disparity maps than two existing approaches in addition we introduce a new disparity map evaluation technique which is developed based on a similar technique employed in the image segmentation area comparing with two existing evaluation approaches the new technique can evaluate the disparity maps generated without additional knowledge of the scene such as the correct depth information or novel views

on the ulam stability of mixed type mappings on restricted domains in 1941 d h hyers solved the well known ulam stability problem for linear mappings in 1951 d g bourgin was the second author to treat the ulam problem for additive mappings in 1982 1998 we established the hyers ulam stability for the ulam problem of linear and nonlinear mappings in 1983 f skof was the first author to solve the ulam problem for additive mappings on a restricted domain in 1998 s m jung investigated the hyers ulam stability of additive and quadratic mappings on restricted domains in this paper we improve the bounds and thus the results obtained by s m jung in 1998 besides we establish the ulam stability of mixed type mappings on restricted domains finally we apply our recent results to the asymptotic behavior of functional equations of different types

applications of the brauer complex card shuffling permutation statistics and dynamical systems by algebraic group theory there is a map from the semisimple conjugacy classes of a finite group of lie type to the conjugacy classes of the weyl group picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the weyl group using the brauer complex it is proved that this measure agrees with a second measure on conjugacy classes of the weyl group induced by a construction of cellini using the affine weyl group formulas for cellini s measure in type a are found this leads to new models of card shuffling and has interesting combinatorial and number theoretic consequences an analysis of type c gives another solution to a problem of rogers in dynamical systems the enumeration of unimodal permutations by cycle structure the proof uses the factorization theory of palindromic polynomials over finite fields contact is made with symmetric function theory

a locally adaptive window for signal matching this article presents a signal matching algorithm that can select an appropriate window size adaptively so as to obtain both precise and stable estimation of correspondences matching two signals by calculating the sum of squared differences ssd over a certain window is a basic technique in computer vision given the signals and a window there are two factors that determine the difficulty of obtaining precise matching the first is the variation of the signal within the window which must be large enough relative to noise that the ssd values exhibit a clear and sharp minimum at the correct disparity the second factor is the variation of disparity within the window which must be small enough that signals of corresponding positions are duly compared these two factors present conflicting requirements to the size of the matching window since a larger window tends to increase the signal variation but at the same time tends to include points of different disparity a window size must be adaptively selected depending on local variations of signal and disparity in order to compute a most certain estimate of disparity at each point there has been little work on a systematic method for automatic window size selection the major difficulty is that while the signal variation is measurable from the input the disparity variation is not since disparities are what we wish to calculate we introduce here a statistical model of disparity variation within a window and employ it to establish a link between the window size and the uncertainty of the computed disparity this allows us to choose the window size that minimizes uncertainty in the disparity computed at each point this article presents a theory for the model and the resultant algorithm together with analytical and experimental results that demonstrate their effectiveness

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

shape from silhouette across time part i theory and algorithms shape from silhouette sfs is a shape reconstruction method which constructs a 3d shape estimate of an object using silhouette images of the object the output of a sfs algorithm is known as the visual hull vh traditionally sfs is either performed on static objects or separately at each time instant in the case of videos of moving objects in this paper we develop a theory of performing sfs across time estimating the shape of a dynamic object with unknown motion by combining all of the silhouette images of the object over time we first introduce a one dimensional element called a bounding edge to represent the visual hull we then show that aligning two visual hulls using just their silhouettes is in general ambiguous and derive the geometric constraints in terms of bounding edges that govern the alignment to break the alignment ambiguity we combine stereo information with silhouette information and derive a temporal sfs algorithm which consists of two steps 1 estimate the motion of the objects over time visual hull alignment and 2 combine the silhouette information using the estimated motion visual hull refinement the algorithm is first developed for rigid objects and then extended to articulated objects in the part ii of this paper we apply our temporal sfs algorithm to two human related applications 1 the acquisition of detailed human kinematic models and 2 marker less motion tracking

affine shuffles shuffles with cuts the whitehouse module and patience sorting abstract type a affine shuffles are compared with riffle shuffles followed by a cut although these probability measures on the symmetric group s n are different they both satisfy a convolution property strong evidence is given that when the underlying parameter q satisfies gcd n q 1 1 the induced measures on conjugacy classes of the symmetric group coincide this gives rise to interesting combinatorics concerning the modular equidistribution by major index of permutations in a given conjugacy class and with a given number of cyclic descents using representation theoretic work on the whitehouse module a formula is obtained for the cycle structure of a riffle shuffle followed by a cut it is proved that the use of cuts does not speed up the convergence rate of riffle shuffles to randomness generating functions for the first pile size in patience sorting from decks with repeated values are derived this relates to random matrices

stereo matching using genetic algorithm with adaptive chromosomes abstract a new stereo matching scheme using a genetic algorithm is presented to improve the depth reconstruction method of stereo vision systems genetic algorithms are efficient search methods based on principles of population genetics i e mating chromosome crossover gene mutation and natural selection the proposed approach considers the matching environment as an optimization problem and finds the optimal solution by using an evolutionary strategy accordingly genetic operators are adapted for the circumstances of stereo matching 1 an individual is a disparity set 2 a chromosome has a 2d structure for handling image signals efficiently and 3 a fitness function is composed of certain constraints which are commonly used in stereo matching since the fitness function consists of intensity similarity and disparity smoothness the matching and relaxation processes are considered at the same time in each generation in order to acquire a disparity map consistent with the image appearance a region of the input image divided by zero crossing points is extracted and used in the determination of the chromosome shape as a result all chromosomes contain the external image form and the disparity output coincides with the input image without any modification of the matching algorithm in addition an informed gene generation based on intensity difference is applied to reduce the searching space of the genetic operations

enriched p partitions and peak algebras abstract we develop a more general view of stembridge s enriched p partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group initially we focus on commutative peak algebras spanned by sums of permutations with the same number of peaks where we consider several variations on the definition of peak whereas stembridge s enriched p partitions are related to quasisymmetric functions the dual coalgebra of solomon s type a descent algebra our generalized enriched p partitions are related to type b quasisymmetric functions the dual coalgebra of solomon s type b descent algebra using these functions we move on to explore non commutative peak algebras spanned by sums of permutations with the same set of peaks while some of these algebras have been studied before our approach gives explicit structure constants with a combinatorial description

multiframe image point matching and 3 d surface reconstruction this paper presents two new methods the joint moment method jmm and the window variance method wvm for image matching and 3 d object surface reconstruction using multiple perspective views the viewing positions and orientations for these perspective views are known a priori as is usually the case for such applications as robotics and industrial vision as well as close range photogrammetry like the conventional two frame correlation method the jmm and wvm require finding the extrema of 1 d curves which are proved to theoretically approach a delta function exponentially as the number of frames increases for the jmm and are much sharper than the two frame correlation function for both the jmm and the wvm even when the image point to be matched cannot be easily distinguished from some of the other points the theoretical findings have been supported by simulations it is also proved that jmm and wvm are not sensitive to certain radiometric effects if the same window size is used the computational complexity for the proposed methods is about n 1 times that for the two frame method where n is the number of frames simulation results show that the jmm and wvm require smaller windows than the two frame correlation method with better accuracy and therefore may even be more computationally feasible than the latter since the computational complexity increases quadratically as a function of the window size

motion estimation with quadtree splines this paper presents a motion estimation algorithm based on a new multiresolution representation the quadtree spline this representation describes the motion field as a collection of smoothly connected patches of varying size where the patch size is automatically adapted to the complexity of the underlying motion the topology of the patches is determined by a quadtree data structure and both split and merge techniques are developed for estimating this spatial subdivision the quadtree spline is implemented using another novel representation the adaptive hierarchical basis spline and combines the advantages of adaptively sized correlation windows with the speedups obtained with hierarchical basis preconditioners results are presented on some standard motion sequences

similarity measures for image matching despite occlusions in stereo vision in the context of computer vision matching can be done with similarity measures this paper presents the classification of these measures into five families in addition 18 measures based on robust statistics previously proposed in order to deal with the problem of occlusions are studied and compared to the state of the art a new evaluation protocol and new analyses are proposed and the results highlight the most efficient measures first near occlusions the smooth median powered deviation and second near discontinuities a non parametric transform based measure census

structure from motion beyond the epipolar constraint the classic approach to structure from motion entails a clear separation between motion estimation and structure estimation and between two dimensional 2d and three dimensional 3d information for the recovery of the rigid transformation between different views only 2d image measurements are used to have available enough information most existing techniques are based on the intermediate computation of optical flow which however poses a problem at the locations of depth discontinuities if we knew where depth discontinuities were we could using a multitude of approaches based on smoothness constraints accurately estimate flow values for image patches corresponding to smooth scene patchess but to know the discontinuities requires solving the structure from motion problem first this paper introduces a novel approach to structure from motion which addresses the processes of smoothing 3d motion and structure estimation in a synergistic manner it provides an algorithm for estimating the transformation between two views obtained by either a calibrated or uncalibrated camera the results of the estimation are then utilized to perform a reconstruction of the scene from a short sequence of images the technique is based on constraints on image derivatives which involve the 3d motion and shape of the scene leading to a geometric and statistical estimation problem the interaction between 3d motion and shape allows us to estimate the 3d motion while at the same time segmenting the scene if we use a wrong 3d motion estimate to compute depth we obtain a distorted version of the depth function the distortion however is such that the worse the motion estimate the more likely we are to obtain depth estimates that vary locally more than the correct ones since local variability of depth is due either to the existence of a discontinuity or to a wrong 3d motion estimate being able to differentiate between these two cases provides the correct motion which yields the least varying estimated depth as well as the image locations of scene discontinuities we analyze the new constraints show their relationship to the minimization of the epipolar constraint and present experimental results using real image sequences that indicate the robustness of the method

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

semisimple conjugacy classes and classes in the weyl group abstract we discuss a map from the semisimple conjugacy classes of a finite group gf of lie type to the f conjugacy classes of its weyl group we obtain two expressions for the number of semisimple classes mapped by into a given f conjugacy class of w the first involves distinguished coset representatives in the affine weyl group and the second is the number of elements in the coroot lattice satisfying certain conditions the brauer complex plays a key role in the proof the map has recently proved of interest in connection with probabilistic and combinatorial group theory

view generation for three dimensional scenes from video sequences this paper focuses on the representation and view generation of three dimensional 3 d scenes in contrast to existing methods that construct a full 3 d model or those that exploit geometric invariants our representation consists of dense depth maps at several preselected viewpoints from an image sequence furthermore instead of using multiple calibrated stationary cameras or range scanners we derive our depth maps from image sequences captured by an uncalibrated camera with only approximately known motion we propose an adaptive matching algorithm that assigns various confidence levels to different regions in the depth maps nonuniform bicubic spline interpolation is then used to fill in low confidence regions in the depth maps once the depth maps are computed at preselected viewpoints the intensity and depth at these locations are used to reconstruct arbitrary views of the 3 d scene specifically the depth maps are regarded as vertices of a deformable 2 d mesh which are transformed in 3 d projected to 2 d and rendered to generate the desired view experimental results are presented to verify our approach

multilevel enhancement and detection of stereo disparity surfaces abstract the problem of stereo vision has been of increasing interest to the computer vision community over the past decade this paper presents a new computational framework for matching a pair of stereo images arising from viewing the same object from two different positions in contrast to previous work this approach formulates the matching problem as detection of a bright coherent disparity surface in a 3d image called the spatio disparity space sds image the sds images represents the goodness of each and every possible match a nonlinear filter is proposed for enhancing the disparity surface in the sds image and for suppressing the noise this filter is used to construct a hyperpyramid representation of the sds image then the disparity surface is detected using a coarse to fine control structure the proposed method is robust to photometric and geometric distortions in the stereo images and has a number of computational advantages it produces good results for complex scenes

consistent depth maps recovery from a video sequence this paper presents a novel method for recovering consistent depth maps from a video sequence we propose a bundle optimization framework to address the major difficulties in stereo reconstruction such as dealing with image noise occlusions and outliers different from the typical multi view stereo methods our approach not only imposes the photo consistency constraint but also explicitly associates the geometric coherence with multiple frames in a statistical way it thus can naturally maintain the temporal coherence of the recovered dense depth maps without over smoothing to make the inference tractable we introduce an iterative optimization scheme by first initializing the disparity maps using a segmentation prior and then refining the disparities by means of bundle optimization instead of defining the visibility parameters our method implicitly models the reconstruction noise as well as the probabilistic visibility after bundle optimization we introduce an efficient space time fusion algorithm to further reduce the reconstruction noise our automatic depth recovery is evaluated using a variety of challenging video examples

a simple stereo algorithm to recover precise object boundaries and smooth surfaces in area based stereo matching there is a problem called boundary overreach i e the recovered object boundary turns out to be wrongly located away from the real one this is especially harmful to segmenting objects using depth information a few approaches have been proposed to solve this problem however these techniques tend to degrade on smooth surfaces that is there seems to be a trade off problem between recovering precise object edges and obtaining smooth surfaces in this paper we propose a new simple method to solve this problem using multiple stereo pairs and multiple windowing our method detects the region where the boundary overreach is likely to occur let us call it bo region and adopts appropriate methods for the bo and non bo regions although the proposed method is quite simple the experimental results have shown that it is very effective at recovering both sharp object edges at their correct locations and smooth object surfaces

depth estimation using a sliding camera image based 3d reconstruction technology is widely used in different fields the conventional algorithms are mainly based on stereo matching between two or more fixed cameras and high accuracy can only be achieved using a large camera array which is very expensive and inconvenient in many applications another popular choice is utilizing structure from motion methods for arbitrarily placed camera s however due to too many degrees of freedom its computational cost is heavy and its accuracy is rather limited in this paper we propose a novel depth estimation algorithm using a sliding camera system by analyzing the geometric properties of the camera system we design a camera pose initialization algorithm that can work satisfyingly with only a small number of feature points and is robust to noise for pixels corresponding to different depths an adaptive iterative algorithm is proposed to choose optimal frames for stereo matching which can take advantage of continuously pose changing imaging and save the time consumption amazingly too the proposed algorithm can also be easily extended to handle less constrained situations such as using a camera mounted on a moving robot or vehicle experimental results on both synthetic and real world data have illustrated the effectiveness of the proposed algorithm

solution of the ulam stability problem for euler lagrange quadratic mappings abstract in 1940 s m ulam proposed at the university of wisconsin theproblem give conditions in order for a linear mapping near an approximately linear mapping to exist in 1968 s u ulam proposed the moregeneral problem when is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true in 1978 p m gruber proposed theulam type problem suppose a mathematical object satisfies a certain property approximately is it then possible to approximate this object by objects satisfying the property exactly according to p m gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types in 1982 1996 we solved the above ulam problem or equivalently the ulam type problem for linear mappings and established analogous stability problems in this paper we first introduce new quadratic weighted means and fundamental functional equations and then solve the ulam stability problem for non linear euler lagrange quadratic mappings q x y satisfying a mean equation and functional equation formula for all 2 dimensional vectors x1 x2 x2 withxa normed linear space y a real complete normed linear space and any fixed pair a1 a2 of realsaiand any fixed pair m1 m2 of positive realsmi i 1 2 formula

hybrid stereo matching with a new relaxation scheme of preserving disparity discontinuity abstract a hybrid stereo matching algorithm using a combined edge and region based method is proposed to take the advantage of each technique i e an exactly matched point and a full resolution disparity map region based matching is typically more efficient than edge based matching however a region based matcher lacks the capability of generating an accurate fine resolution disparity map the generation of such a map can be better accomplished by using edge based techniques accordingly regions and edges both play important and complimentary roles in a binocular stereo process since it is crucial that an efficient and robust stereo system utilizes the most appropriate set of primitives a nonlinear laplacian filter is modified to extract proper primitives since each pixel value of a second order differentiated image includes important information for the intensity profile information such as edge signed and zero pixels obtained by the modified nonlinear laplacian filter is used to determine the matching strategy consequently the proposed matching algorithm consists of edge signed and zero or residual pixel matching different matching strategies are adopted in each matching step adaptive windows with variable sizes and shapes are also used to consider the local information of the pixels in addition a new relaxation scheme based on the statistical distribution of matched errors and constraint functions which contain disparity smoothness uniqueness and discontinuity preservation is proposed to efficiently reduce mismatched points in unfavorable conditions unlike conventional relaxation schemes the erosion in an abrupt area of a disparity map is considerably reduced because a discontinuity preservation factor based on a survival possibility function is added to the proposed relaxation the relaxation scheme can be applied to various methods such as block feature region object based matching methods and so on by modifying the excitatory set of the smoothness constraint function experimental results show that the proposed matching algorithm is effective for various images even if the image has a high content of noise and repeated patterns the convergence rate of the relaxation and the output quality are both improved

refinements of generalized triangle inequalities abstract in this paper we discuss refinements of the well known triangle inequality and it is reverse inequality for strongly integrable functions with values in a banach space x we also discuss refinement of a generalized triangle inequality of the second kind for l p functions for both cases the attainability of the equality is also investigated

on the stability of euler lagrange type cubic mappings in quasi banach spaces abstract in this paper we solve the generalized hyers ulam rassias stability problem for euler lagrange type cubic functional equations f a x y f x a y a 1 a 1 2 f x f y a a 1 f x y for mappings f x y in quasi banach spaces and for fixed integers a with a 0 1 in addition we also present a counterexample that does not satisfy the stability based on ulam s question

extracting view dependent depth maps from a collection of images stereo correspondence algorithms typically produce a single depth map in addition to the usual problems of occlusions and textureless regions such algorithms cannot model the variation in scene or object appearance with respect to the viewing position in this paper we propose a new representation that overcomes the appearance variation problem associated with an image sequence rather than estimating a single depth map we associate a depth map with each input image or a subset of them our representation is motivated by applications such as view interpolation and depth based segmentation for model building or layer extraction we describe two approaches to extract such a representation from a sequence of images the first approach which is more classical computes the local depth map associated with each chosen reference frame independently the novelty of this approach lies in its combination of shiftable windows temporal selection and graph cut optimization the second approach simultaneously optimizes a set of self consistent depth maps at multiple key frames since multiple depth maps are estimated simultaneously visibility can be modeled explicitly and disparity consistency imposed across the different depth maps results which include a difficult specular scene example show the effectiveness of our approach

stereo matching with linear superposition of layers in this paper we address stereo matching in the presence of a class of non lambertian effects where image formation can be modeled as the additive superposition of layers at different depths the presence of such effects makes it impossible for traditional stereo vision algorithms to recover depths using direct color matching based methods we develop several techniques to estimate both depths and colors of the component layers depth hypotheses are enumerated in pairs one from each layer in a nested plane sweep for each pair of depth hypotheses matching is accomplished using spatial temporal differencing we then use graph cut optimization to solve for the depths of both layers this is followed by an iterative color update algorithm which we proved to be convergent our algorithm recovers depth and color estimates for both synthetic and real image sequences

ulam stability problem for quadratic mappings of euler lagrange abstract the purpose of this paper is to solve the stability problem of ulam for an approximate mapping f a b of the following quadratic functional equation of euler lagrange a b aq x a b bq y q ax by abq x y for all x y a with a and b linear spaces

stochastic stereo matching over scale a stochastic optimization approach to stereo matching is presented unlike conventional correlation matching and feature matching the method provides a dense array of disparities eliminating the need for interpolation first the stereo matching problem is defined in terms of finding a disparity map that satisfies two competing constraints 1 matched points should have similar image intensity and 2 the disparity map should vary as slowly as possible these constraints are interpreted as specifying the potential energy of a system of oscillators ground states are approximated by a new variant of simulated annealing which has two important features first the microcanonical ensemble is simulated using a new algorithm that is more efficient and more easily implemented than the familiar metropolis algorithm which simulates the canonical ensemble secondly it uses a hierarchical coarse to fine control structure employing gaussian or laplacian pyramids of the stereo images in this way quickly computed results at low resolutions are used to initialize the system at higher resolutions

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

the peak algebra of the symmetric group revisited abstract the linear span p n of the sums of all permutations in the symmetric group sn with a given set of peaks is a sub algebra of the symmetric group algebra due to nyman this peak algebra is a left ideal of the descent algebra d n and the direct sum p of all p n is a hopf sub algebra of the direct sum d of all d n dual to the stembridge algebra of peak functions in our self contained approach peak counterparts of several results on the descent algebra are established including a simple combinatorial characterization of the algebra p n an algebraic characterization of p n based on the action on the poincare birkhoff witt basis of the free associative algebra the display of peak variants of the classical lie idempotents an eulerian type sub algebra of p n a description of the jacobson radical of p n and its nil potency index of the principal indecomposable and irreducible p n modules and of the cartan matrix of p n furthermore it is shown that the primitive lie algebra of p is free and that p is its enveloping algebra

visual modeling with a hand held camera in this paper a complete system to build visual models from camera images is presented the system can deal with uncalibrated image sequences acquired with a hand held camera based on tracked or matched features the relations between multiple views are computed from this both the structure of the scene and the motion of the camera are retrieved the ambiguity on the reconstruction is restricted from projective to metric through self calibration a flexible multi view stereo matching scheme is used to obtain a dense estimation of the surface geometry from the computed data different types of visual models are constructed besides the traditional geometry and image based approaches a combined approach with view dependent geometry and texture is presented as an application fusion of real and virtual scenes is also shown

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

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

multi image matching for a general motion stereo camera model abstract this paper presents an accurate and robust motion stereo algorithm employing multiple images taken under a general motion the object functions for individual stereo pairs are represented in terms of the depth then these object functions are integrated considering the positions of cameras and the shape of the object functions by integrating the general motion stereo images we not only reduce the ambiguities in correspondence but also improve the accuracy of reconstruction also by introducing a weight for each object function and selecting only reliable object functions we can improve the accuracy greatly and eliminate false matches caused by occlusion or noise experimental results on the synthetic and real data sets are presented to demonstrate the performance of the proposed algorithm

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

stereo matching algorithm based on modified wavelet decomposition process multiresolutional representation such as pyramidal structures is useful for stereo matching as coarse to fine strategy however conventional pyramidal structures using gaussian or laplacian filters lose much information due to their low pass filtering characteristics and also cannot obtain any spatial orientation selectivity the adoption of wavelet transform can remedy these problems but at the time of image translation it changes wavelet coefficients in this paper a pyramid using modified wavelet decomposition process is proposed to have translation invariance the image transformed by the proposed method is converted into appropriate multiple features without loss of information since the importance of each feature is determined heuristically in the multiple feature based stereo matching method it is very difficult to fuse them adequately in the proposed algorithm the weight of each feature that is the relative importance of each feature is decided from the similarity between the intensities in the local region of each left and right wavelet channels since the window size used for the decision of weight and disparity values greatly influences the processed result the window is adaptively determined from the disparities estimated in the coarse resolution and low varying channel of fine resolution the window size must be large enough to obtain signal to noise ratio but not too large as to induce the effects of projective distortion also a new relaxation algorithm which can reduce false matches without blurring the disparity edge is proposed by integrating adaptive weight variable window selection method and relaxation process an accurate and stable disparity map is obtained experimental results for various images show that the proposed algorithm has good performance even if the image has the unfavorable conditions

characterization of a generalized triangle inequality in normed spaces abstract for a normed linear space x and p 0 we characterize all n tuples 1 n r n for which the generalized triangle inequality of the second type x 1 x n p x 1 p 1 x n p n holds for any x 1 x n x we also characterize 1 n r n for which the reverse of the inequality above holds

spline based image registration the problem of image registration subsumes a number of problems and techniques in multiframe image analysis including the computation of optic flow general pixel based motion stereo correspondence structure from motion and feature tracking we present a new registration algorithm based on spline representations of the displacement field which can be specialized to solve all of the above mentioned problems in particular we show how to compute local flow global parametric flow rigid flow resulting from camera egomotion and multiframe versions of the above problems using a spline based description of the flow removes the need for overlapping correlation windows and produces an explicit measure of the correlation between adjacent flow estimates we demonstrate our algorithm on multiframe image registration and the recovery of 3d projective scene geometry we also provide results on a number of standard motion sequences

shape and the stereo correspondence problem we examine the implications of shape on the process of finding dense correspondence and half occlusions for a stereo pair of images the desired property of the disparity map is that it should be a piecewise continuous function which is consistent with the images and which has the minimum number of discontinuities to zeroth order piecewise continuity becomes piecewise constancy using this approximation we first discuss an approach for dealing with such a fronto parallel shapeless world and the problems involved therein we then introduce horizontal and vertical slant to create a first order approximation to piecewise continuity in particular we emphasize the following geometric fact a horizontally slanted surface i e having depth variation in the direction of the separation of the two cameras will appear horizontally stretched in one image as compared to the other image thus while corresponding two images n pixels on a scanline in one image may correspond to a different number of pixels m in the other image this leads to three important modifications to existing stereo algorithms a due to unequal sampling existing intensity matching metrics must be modified b unequal numbers of pixels in the two images must be allowed to correspond to each other and c the uniqueness constraint which is often used for detecting occlusions must be changed to an interval uniqueness constraint we also discuss the asymmetry between vertical and horizontal slant and the central role of non horizontal edges in the context of vertical slant using experiments we discuss cases where existing algorithms fail and how the incorporation of these new constraints provides correct results

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs