physically based adaptive preconditioning for early vision several problems in early vision have been formulated in the past in a regularization framework these problems when discretized lead to large sparse linear systems in this paper we present a novel physically based adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to dramatically improve the speed of convergence for solving the aforementioned linear systems a preconditioner based on the membrane spline or the thin plate spline or a convex combination of the two is termed a physically based preconditioner for obvious reasons the adaptation of the preconditioner to an early vision problem is achieved via the explicit use of the spectral characteristics of the regularization filter in conjunction with the data this spectral function is used to modulate the frequency characteristics of a chosen wavelet basis and these modulated values are then used in the construction of our preconditioner we present the preconditioner construction for three different early vision problems namely the surface reconstruction the shape from shading and the optical flow computation problems performance of the preconditioning scheme is demonstrated via experiments on synthetic and real data sets

fast surface interpolation using hierarchical basis functions an alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented conjugate gradient descent is used in conjunction with a hierarchical multiresolution set of basis functions the resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed simulation results showing the speed of convergence and its dependence on the choice of interpolator the number of smoothing levels and other factors are presented the relationship of this approach to other multiresolution relaxation and representation schemes is also discussed

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

strong converse for the classical capacity of optical quantum communication channels we establish the classical capacity of optical quantum channels as a sharp transition between two regimes one which is an error free regime for communication rates below the capacity and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity this result is obtained by proving a strong converse theorem for the classical capacity of all phase insensitive bosonic gaussian channels a well established model of optical quantum communication channels such as lossy optical fibers amplifier and free space communication the theorem holds under a particular photon number occupation constraint which we describe in detail in this paper our result bolsters the understanding of the classical capacity of these channels and opens the path to applications such as proving the security of noisy quantum storage models of cryptography with optical links

a fast scalable algorithm for discontinuous optical flow estimation multiple moving objects partially occluded objects or even a single object moving against the background gives rise to discontinuities in the optical flow field in corresponding image sequences while uniform global regularization based moderately fast techniques cannot provide accurate estimates of the discontinuous flow field statistical optimization based accurate techniques suffer from excessive solution time a weighted anisotropic smoothness based numerically robust algorithm is proposed that can generate discontinuous optical flow field with high speed and linear computational complexity weighted sum of the first order spatial derivatives of the flow field is used for regularization less regularization is performed where strong gradient information is available the flow field at any point is interpolated more from those at neighboring points along the weaker intensity gradient component such intensity gradient weighted regularization leads to euler lagrange equations with strong anisotropies coupled with discontinuities in their coefficients a robust multilevel iterative technique that recursively generates coarse level problems based on intensity gradient weighted smoothing weights is employed to estimate discontinuous optical flow field experimental results are presented to demonstrate the efficacy of the proposed technique

variational image reconstruction from arbitrarily spaced samples a fast multiresolution spline solution we propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations we adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms 1 the sum of squared errors at the specified points and 2 a quadratic functional that penalizes the lack of smoothness we search for a solution that is a uniform spline and show how it can be determined by solving a large sparse system of linear equations we interpret the solution of our approach as an approximation of the analytical solution that involves radial basis functions and demonstrate the computational advantages of our approach using the two scale relation for b splines we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution we use this relation to develop a fast multigrid algorithm we demonstrate the effectiveness of our approach on some image reconstruction examples

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

a strain energy approach to regularization in displacement field fits of elastically deforming bodies current methods for regularizing displacement fields in deformation fitting problems are sensitive to rotation we propose a rotation insensitive regularization functional which is the true strain energy for a rubber like material the deformation fitting problem is solved iteratively using successive approximations of the body s rotation which may be non uniform

a note on a goal programming model for incomplete interval multiplicative preference relations and its application in group decision making abstract in a recently published paper by liu et al liu f zhang w g wang z x 2012 a goal programming model for incomplete interval multiplicative preference relations and its application in group decision making european journal of operational research 218 747 754 two equations are introduced to define consistency of incomplete interval multiplicative preference relations imprs and employed to develop a goal programming model for estimating missing values this note illustrates that such consistency definition and estimation model are technically incorrect new transitivity conditions are proposed to define consistent imprs and a two stage goal programming approach is devised to estimate missing values for incomplete imprs

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

interpolation using wavelet bases efficient solutions to regularization problems can be obtained using orthogonal wavelet bases for preconditioning good approximate solutions can be obtained in only two or three iterations with each iteration requiring only o n operations and o n storage locations two and three dimensional examples are shown using both synthetic and real range data

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

generalized capacitance matrix theorems and algorithm for solving linear systems the capacitance matrix method has been widely used as an efficient numerical tool for solving the boundary value problems on irregular regions initially this method was based on the sherman morrison woodbury formula an expression for the inverse of the matrix a uvt with bf a in re n times n and bf u v in re n times p extensions of this method reported in literature have made restrictive assumptions on the matrices a and a uvt in this paper we present several theorems which are generalizations of the capacitance matrix theorem in cite buzbee and are suited for very general matrices a and a uvt a generalized capacitance matrix algorithm is developed from these theorems and holds the promise of being applicable to more general problems in addition it gives ample freedom to choose the matrix a for developing very efficient numerical algorithms we demonstrate the usefulness of our generalized capacitance matrix algorithm by applying it to efficiently solve large sparse linear systems in several computer vision problems namely the surface reconstruction and interpolation and the shape from orientation problem

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

recovering the position and orientation of free form objects from image contours using 3d distance maps the accurate matching of 3d anatomical surfaces with sensory data such as 2d x ray projections is a basic problem in computer and robot assisted surgery in model based vision this problem can be formulated as the estimation of the spatial pose position and orientation of a 3d smooth object from 2d video images the authors present a new method for determining the rigid body transformation that describes this match the authors method performs a least squares minimization of the energy necessary to bring the set of the camera contour projection lines tangent to the surface to correctly deal with projection lines that penetrate the surface the authors consider the minimum signed distance to the surface along each line i e distances inside the object are negative to quickly and accurately compute distances to the surface the authors introduce a precomputed distance map represented using an octree spline whose resolution increases near the surface this octree structure allows the authors to quickly find the minimum distance along each line using best first search experimental results for 3d surface to 2d projection matching are presented for both simulated and real data the combination of the authors problem formulation in 3d their computation of line to surface distances with the octree spline distance map and their simple minimization technique based on the levenberg marquardt algorithm results in a method that solves the 3d 2d matching problem for arbitrary smooth shapes accurately and quickly

matching 3 d anatomical surfaces with non rigid deformations using octree splines presents a new method for determining the minimal nonrigid deformation between two 3d surfaces such as those which describe anatomical structures in 3d medical images although the authors match surfaces they represent the deformation as a volumetric transformation their method performs a least squares minimization of the distance between the two surfaces of interest to quickly and accurately compute distances between points on the two surfaces the authors use a precomputed distance map represented using an octree spline whose resolution increases near the surface to quickly and robustly compute the deformation the authors use a second octree spline to model the deformation function the coarsest level of the deformation encodes the global e g affine transformation between the two surfaces while finer levels encode smooth local displacements which bring the two surfaces into closer registration the authors present experimental results on both synthetic and real 3d surfaces

multiscale modeling and estimation of motion fields for video coding we present a systematic approach to forward motion compensated predictive video coding the first step is the definition of a flexible model that compactly represents motion fields the inhomogeneity and spatial coherence properties of motion fields are captured using linear multiscale models one possible design is based on linear finite elements and yields a multiscale extension of the triangle motion compensation tmc method the second step is the choice of a computational technique that identifies the coefficients of the linear model we study a modified optical flow technique and minimize a cost function closely related to horn and schunck s 1981 criterion the cost function balances accuracy and complexity of the motion compensated predictor and is viewed as a measure of goodness of the motion field it determines not only the coefficients of the model but also the quantization method we formulate the estimation and quantization problems jointly as a discrete optimization problem and solve it using a fast multiscale relaxation algorithm a hierarchical extension of the algorithm allows proper handling of large displacements simulations on a variety of video sequences have produced improvements over tmc and over the half pel accuracy full search block matching algorithm in excess of 0 5 db in average the results are visually superior as well in particular the reconstructed video is entirely free of blocking artifacts

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