three dimensional face shape by local fitting to a single reference model the authors present a simple method to estimate the three dimensional shape of a face from an input image using a single reference model based on least squares between the output of the linear nonlinear ln neuronal model applied to blocks from an intensity image and blocks from a depth reference model the authors present the results obtained by varying the ln model parameters and estimate their best values which provide an acceptable reconstruction of each subject s depth the authors show that increasing the light source angle over the horizontal plane in the input image produces slight increases in reconstruction error but increasing the ambient light proportion produces greater increases in reconstruction error the authors applied the method to predict each subject s unknown depth using different individual reference models and an average reference model which provides the best results as a noise reduction technique the authors perform a point by point weighted averaging with the average reference model with weights equal to the fractions of the squares of the laplacian of a gaussian applied to the prediction and to the reference depth over the sum of both finally the authors present acceptable visual results obtained from external images of faces under arbitrary illumination having performed an illumination estimation previously

duality between smooth min and max entropies in classical and quantum information theory operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two entropy measures called smooth min entropy and smooth max entropy respectively while both entropies are equal to the von neumann entropy in certain special cases e g asymptotically for many independent repetitions of the given data their values can differ arbitrarily in the general case in this paper a recently discovered duality relation between nonsmooth min and max entropies is extended to the smooth case more precisely it is shown that the smooth min entropy of a system a conditioned on a system b equals the negative of the smooth max entropy of a conditioned on a purifying system c this result immediately implies that certain operational quantities such as the amount of compression and the amount of randomness that can be extracted from given data are related we explain how such relations have applications in cryptographic security proofs

a probabilistic framework for specular shape from shading one of the problems that hinders conventional methods for shape from shading is the presence of local specularities which may be misidentified as high curvature surface features in this paper we address the problem of estimating the proportions of lambertian and specular reflection components in order to improve the quality of surface normal information recoverable using shape from shading the framework for our study is provided by the iterated conditional modes algorithm we develop a maximum a posteriori probability map estimation method for estimating the mixing proportions for lambertian and specular reflectance and also for recovering local surface normals the map estimation scheme has two model ingredients first there are separate conditional measurement densities which describe the distributions of surface normal directions for the lambertian and specular reflectance components we experimentally compare three different models for the specular component the second ingredient is a smoothness prior which models the distribution of surface normal directions over local image regions we demonstrate the utility of method on real world data ground truth data is provided by imagery obtained with crossed polaroid filters this reveals not only that the method accurately estimates the proportion of specular reflection but that it also results in good surface normal reconstruction in the proximity of specular highlights

noise reduction in surface reconstruction from a given gradient field we present a gradient space technique for noise reduction in surfaces reconstructed from a noisy gradient field we first analyze the error sources in the recovered gradient field of a surface using a three image photometric stereo method based on this analysis we propose an additive noise model to describe the errors in the surface gradient estimates we then use a vector space formulation and construct a multiscale orthonormal expansion for gradient fields using the sparse representation properties of this expansion we develop techniques for reducing the gradient field noise by coefficient selection with thresholding the simulation results indicate that the proposed technique provides significant improvement on the noise levels of both the estimated gradient fields and the reconstructed surfaces under heavy noise levels furthermore the experiments using noisy photometric stereo image triplets of real range data suggest that the additive model remains viable after the nonlinear photometric stereo operation to provide accurate noise removal

the quantum capacity of channels with arbitrarily correlated noise we study optimal rates for quantum communication over a single use of a channel which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise the corresponding capacity is often referred to as the one shot quantum capacity in this paper we prove bounds on the one shot quantum capacity of an arbitrary channel this allows us to compute the quantum capacity of a channel with arbitrarily correlated noise in the limit of asymptotically many uses of the channel in the memoryless case we explicitly show that our results reduce to known expressions for the quantum capacity

leftover hashing against quantum side information the leftover hash lemma states that the output of a two universal hash function applied to an input with sufficiently high entropy is almost uniformly random in its standard formulation the lemma refers to a notion of randomness that is usually implicitly defined with respect to classical side information here a strictly more general version of the leftover hash lemma that is valid even if side information is represented by the state of a quantum system is shown our result applies to almost two universal families of hash functions the generalized leftover hash lemma has applications in cryptography e g for key agreement in the presence of an adversary who is not restricted to classical information processing

incompressible smoothed particle hydrodynamics for free surface flows a generalised diffusion based algorithm for stability and validations for impulsive flows and propagating waves the incompressible smoothed particle hydrodynamics isph method with projection based pressure correction has been shown to be highly accurate and stable for internal flows and importantly for many problems the pressure field is virtually noise free in contrast to the weakly compressible sph approach xu et al 2009 31 however for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels a new algorithm is presented which remedies this issue giving stable and accurate solutions to both internal and free surface flows generalising the particle shifting approach of xu et al 2009 31 the algorithm is based upon fick s law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability the algorithm is validated against analytical solutions for an internal flow at higher reynolds numbers than previously the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times the method is then validated for progressive regular waves with paddle motion defined by linear theory the accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels the test cases are thought to provide a more thorough quantitative validation than previously undertaken

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

where and why local shading analysis works an apparent contradiction in the shape from shading literature is examined although practical experience suggests that shape can be inferred from the local analysis of shading mathematical analyses support the opposite a criterion for exact surface recovery is derived and it is shown that as a result of surface geometry elliptic hyperbolic and doubly curved surfaces could be recovered to reasonable accuracy provided that surface curvature and or foreshortening were limited in other words by relaxing the requirement that surfaces be recovered exactly it is found that local analysis of shading can provide useful descriptions of shape as evidenced by the results presented

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

surface reconstruction in gradient field domain using compressed sensing surface reconstruction from measurements of spatial gradient is an important computer vision problem with applications in photometric stereo and shape from shading in the case of morphologically complex surfaces observed in the presence of shadowing and transparency artifacts a relatively large dense gradient measurements may be required for accurate surface reconstruction consequently due to hardware limitations of image acquisition devices situations are possible in which the available sampling density might not be sufficiently high to allow for recovery of essential surface details in this paper the above problem is resolved by means of derivative compressed sensing dcs dcs can be viewed as a modification of the classical cs which is particularly suited for reconstructions involving image surface gradients in dcs a standard cs setting is augmented through incorporation of additional constraints arising from some intrinsic properties of potential vector fields we demonstrate that using dcs results in reduction in the number of measurements as compared with the standard dense sampling while producing estimates of higher accuracy and smaller variability as compared with cs based estimates the results of this study are further supported by a series of numerical experiments

inflow outflow with dirichlet boundary conditions for pressure in isph in the present work we propose a new algorithm for open boundary treatment in isph in the literature a few models for open boundary conditions are available but most of them are applied to weakly compressible sph wcsph only in our method the inflow outflow is driven by true dirichlet boundary conditions of the projected pressure field we ensure the dirichlet boundary condition by a particle mirroring technique at the open boundary to compute the pressure field this procedure enables us to handle variable inlet velocities across the open boundary the dirichlet boundary conditions are introduced for the projected pressure matrix we apply an error analysis for a hagenpoiseuille flow driven by a pressure gradient and demonstrate the robustness and accuracy with a flow around a cylinder and an oscillating flow where inlet and outlet conditions periodically change additionally a volume flux controller is presented in combination with variable pressure boundary conditions finally the new open boundary treatment is applied to a bubble formation process during gas injection and validated with experimental results

pressure boundary conditions for computing incompressible flows with sph in smoothed particle hydrodynamics sph methods for fluid flow incompressibility may be imposed by a projection method with an artificial homogeneous neumann boundary condition for the pressure poisson equation this is often inconsistent with physical conditions at solid walls and inflow and outflow boundaries for this reason open boundary flows have rarely been computed using sph in this work we demonstrate that the artificial pressure boundary condition produces a numerical boundary layer that compromises the solution near boundaries we resolve this problem by utilizing a rotational pressure correction scheme with a consistent pressure boundary condition that relates the normal pressure gradient to the local vorticity we show that this scheme computes the pressure and velocity accurately near open boundaries and solid objects and extends the scope of sph simulation beyond the usual periodic boundary conditions

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

direct analytical methods for solving poisson equations in computer vision problems direct analytical methods are discussed for solving poisson equations of the general form delta u f on a rectangular domain some embedding techniques that may be useful when boundary conditions obtained from stereo and occluding boundary are defined on arbitrary contours are described the suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms applications to shape from shading lightness and optical flow problems are also discussed a proof for the existence and convergence of the flow estimates is given experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations

a new open boundary formulation for incompressible sph abstract in this work a new formulation for inflow outflow boundary conditions in an incompressible smoothed particles hydrodynamics isph model is proposed it relies on the technique of unified semi analytical boundary conditions that was first proposed for wall boundary conditions in 2013 then extended to open boundaries in the framework of weakly compressible sph wcsph an isph model relying on that formulation for solid boundaries was then proposed which is the one considered here it includes a buoyancy model for temperature effects and a k turbulence closure there are two main requirements for the imposition of open boundaries in isph an algorithm to let particles enter and leave the domain and the correct imposition of open boundary conditions on the fields regarding the algorithm for particles creation destruction it relies on the variation of mass of the particles located at the open boundaries when the mass of such a particle reaches a threshold a new particle is released on the other hand the imposition of open boundary conditions on the fields is done by prescribing the value of the boundary terms appearing in the semi analytical formulation the formulation was first validated in 2 d on a cut dam break a case of propagation of a solitary wave and a creager weir it was then extended to 3 d and tested on a 3 d circular pipe a preliminary application case consisting of two connected pipes at different temperatures was then simulated the results are promising since in all cases the fluid enters and leaves the domain as prescribed and generating none or very few reflected waves

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

photometric stereo via expectation maximization this paper presents a robust and automatic approach to photometric stereo where the two main components namely surface normals and visible surfaces are respectively optimized by expectation maximization em a dense set of input images is conveniently captured using a digital video camera while a handheld spotlight is being moved around the target object and a small mirror sphere in our approach the inherently complex optimization problem is simplified into a two step optimization where em is employed in each step 1 using the dense input the weight or importance of each observation is alternately optimized with the normal and albedo at each pixel and 2 using the optimized normals and employing the markov random fields mrfs surface integrabilities and discontinuities are alternately optimized in visible surface reconstruction our mathematical derivation gives simple updating rules for the em algorithms leading to a stable practical and parameter free implementation that is very robust even in the presence of complex geometry shadows highlight and transparency we present high quality results on normal and visible surface reconstruction where fine geometric details are automatically recovered by our method

open boundary conditions for isph and their application to micro flow open boundary conditions for incompressible smoothed particle hydrodynamics isph are rare for stable simulations with open boundary conditions one needs to specify all boundary conditions correctly in the pressure force as well as in the linear equation system for pressure calculation especially for homogeneous or non homogeneous dirichlet boundary conditions for pressure there exist several possibilities but only a few lead to stable results however this isn t trivial for open boundary conditions we introduce a new approach for open boundary conditions for isph to enable stable simulations in contrast to existing models for weakly compressible sph we can specify open pressure boundary conditions because in isph pressure can be calculated independently of the density the presented approach is based on the mirror particle approach already introduced for solid wall boundary conditions here we divide the mirror axis in several segments with time dependent positions we validate the presented approach for the example of poiseuille flow and flow around a cylinder at different reynolds numbers and show that we get good agreement with references then we demonstrate that the approach can be applied to free surface flows finally we apply the new approach to micro flow through a random porous medium with a different number of in and outlets and demonstrate its benefits

a theory of photometric stereo for a class of diffuse non lambertian surfaces a theory of photometric stereo is proposed for a large class of non lambertian reflectance maps the authors review the different reflectance maps proposed in the literature for modeling reflection from real world surfaces from this they obtain a mathematical class of reflectance maps to which the maps belong they show that three lights can be sufficient for a unique inversion of the photometric stereo equation for the entire class of reflectance maps they also obtain a constraint on the positions of light sources for obtaining this solution they investigate the sufficiency of three light sources to estimate the surface normal and the illuminant strength the issue of completeness of reconstruction is addressed they show that if k lights are sufficient for a unique inversion 2k lights are necessary for a complete inversion

an incompressible multi phase sph method an incompressible multi phase sph method is proposed in this method a fractional time step method is introduced to enforce both the zero density variation condition and the velocity divergence free condition at each full time step to obtain sharp density and viscosity discontinuities in an incompressible multi phase flow a new multi phase projection formulation in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed numerical examples for taylor green flow capillary waves drop deformation in shear flows and for rayleigh taylor instability are presented and compared to theoretical solutions or references from literature the results suggest good accuracy and convergence properties of the proposed method

randomness extraction via a quantum generalization of the conditional collision entropy randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information this paper provides randomness extraction against quantum side information whose extractable key length is given by a quantum generalization of the collision entropy which is smoothed and conditioned differently from how this is done in existing schemes based on the fact that the collision entropy is not subadditive its optimization with respect to additional side information is introduced and is shown to be asymptotically optimal the lower bound derived there for general states is expressed as the difference between two unconditional entropies and its evaluation reduces to an eigenvalue problem of two states which are the entire state and the marginal state of side information

dense photometric stereo a markov random field approach we address the problem of robust normal reconstruction by dense photometric stereo in the presence of complex geometry shadows highlight transparencies variable attenuation in light intensities and inaccurate estimation in light directions the input is a dense set of noisy photometric images conveniently captured by using a very simple set up consisting of a digital video camera a reflective mirror sphere and a handheld spotlight we formulate the dense photometric stereo problem as a markov network and investigate two important inference algorithms for markov random fields mrfs graph cuts and belief propagation to optimize for the most likely setting for each node in the network in the graph cut algorithm the mrf formulation is translated into one of energy minimization a discontinuity preserving metric is introduced as the compatibility function which allows a expansion to efficiently perform the maximum a posteriori map estimation using the identical dense input and the same mrf formulation our tensor belief propagation algorithm recovers faithful normal directions preserves underlying discontinuities improves the normal estimation from one of discrete to continuous and drastically reduces the storage requirement and running time both algorithms produce comparable and very faithful normals for complex scenes although the discontinuity preserving metric in graph cuts permits efficient inference of optimal discrete labels with a theoretical guarantee our estimation algorithm using tensor belief propagation converges to comparable results but runs faster because very compact messages are passed and combined we present very encouraging results on normal reconstruction a simple algorithm is proposed to reconstruct a surface from a normal map recovered by our method with the reconstructed surface an inverse process known as relighting in computer graphics is proposed to synthesize novel images of the given scene under user specified light source and direction the synthesis is made to run in real time by exploiting the state of the art graphics processing unit gpu our method offers many unique advantages over previous relighting methods and can handle a wide range of novel light sources and directions

one shot classical quantum capacity and hypothesis testing the one shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold in this work we show that this capacity is well approximated by a relative entropy type measure defined via hypothesis testing combined with a quantum version of stein s lemma our results give a conceptually simple proof of the well known holevo schumacher westmoreland theorem for the capacity of memoryless channels more generally we obtain tight capacity formulas for arbitrary not necessarily memoryless channels

privacy amplification for quantum key distribution this paper examines classical privacy amplification using a universal family of hash functions in quantum key distribution the adversary s measurement can wait until the choice of hash functions is announced and so the adversary s information may depend on the choice therefore the existing result on classical privacy amplification which assumes the independence of the choice from the other random variables is not applicable to this case this paper provides a security proof of privacy amplification which is valid even when the adversary s information may depend on the choice of hash functions the compression rate of the proposed privacy amplification can be taken to be the same as that of the existing one with an exponentially small loss in secrecy of a final key

on the imaging of fractal surfaces an analysis is presented of the imaging of surfaces modeled by fractal brownian elevation functions of the sort used in computer graphics it is shown that if lambertian reflectance modest surface slopes and the absence of occlusions and self shadowing are assumed a fractal surface with fourier power spectrum proportional to f sup beta produces an image with power spectrum proportional to f sup 2 beta here f is the spatial frequency and beta is related to the fractional dimension value this allows one to use the spectral falloff of the images to predict the fractal dimension of the surface

analysis of the incompressibility constraint in the smoothed particle hydrodynamics method summary smoothed particle hydrodynamics sph is a particle based fully lagrangian method for fluid flow simulations in this work fundamental concepts of the method are first briefly recalled then we present a thorough comparison of two different incompressibility treatments in sph the weakly compressible approach where a suitably chosen equation of state is used and the truly incompressible method in two basic variants where the velocity field projection onto a divergence free space is performed a noteworthy aspect of the study is that in each incompressibility treatment the same boundary conditions are used and further developed that allows a direct comparison to be made two dimensional and three dimensional validation cases are studied problems associated with the numerical setup are discussed and an optimal choice of the computational parameters is proposed and verified the efficiency issues of the incompressibility treatments are considered and the speed up features are highlighted the results show that the present state of the art truly incompressible methods based on a velocity correction suffer from density accumulation errors to address this issue an algorithm based on a correction for both particle velocities and positions is presented the usefulness of this density correction is examined and demonstrated copyright 2012 john wiley sons ltd

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

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

second order asymptotics in fixed length source coding and intrinsic randomness there is a difference between the optimal rates of fixed length source coding and intrinsic randomness when we care about the second order asymptotics we prove this difference for general information sources and then investigate independent and identically distributed i i d random variables and markovian variables as examples the difference is demonstrated through an investigation of the second order asymptotic behavior of the rates a universal fixed length source code attaining the second order optimal rate is also proposed the difference between the rates of fixed length source coding and intrinsic randomness proves that the outputs of fixed length source codes are not uniformly distributed

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

one shot rates for entanglement manipulation under non entangling maps we obtain expressions for the optimal rates of one shot entanglement manipulation under operations which generate a negligible amount of entanglement as the optimal rates for entanglement distillation and dilution in this paradigm we obtain the max and min relative entropies of entanglement the two logarithmic robustnesses of entanglement and smoothed versions thereof this gives a new operational meaning to these entanglement measures moreover by considering the limit of many identical copies of the shared entangled state we partially recover the recently found reversibility of entanglement manipulation under the class of operations which asymptotically do not generate entanglement