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24
A graphspectral approach to shapefromshading
 IEEE Transactions on Image Processing
, 2004
"... Abstract—In this paper, we explore how graphspectral methods can be used to develop a new shapefromshading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large ch ..."
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Abstract—In this paper, we explore how graphspectral methods can be used to develop a new shapefromshading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvaturedependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert’s law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and realworld imagery. Index Terms—Graph seriation, graphspectral methods, shapefromshading. I.
Recursive photometric stereo when multiple shadows and highlights are present, in
 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition
"... We present a recursive algorithm for 3D surface reconstruction based on Photometric Stereo in the presence of highlights, and self and cast shadows. We assume that the surface reflectance outside the highlights can be approximated by the Lambertian model. The algorithm works with as few as three lig ..."
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Cited by 11 (2 self)
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We present a recursive algorithm for 3D surface reconstruction based on Photometric Stereo in the presence of highlights, and self and cast shadows. We assume that the surface reflectance outside the highlights can be approximated by the Lambertian model. The algorithm works with as few as three light sources, and it can be generalised for N without any difficulties. Furthermore, this reconstruction method is able to identify areas where the majority of the lighting directions result in unreliable pixel intensities, providing the capability to adjust a reconstruction algorithm and improve its performance avoiding the unreliable sources. We report results for both artificial and real images and compare them with the results of other state of the art photometric stereo algorithms. 1.
A graphspectral method for surface height recovery
 PATTERN RECOGNITION
, 2004
"... This paper describes a graphspectral method for 3D surface integration. The algorithm takes as its input a 2D field of surface normal estimates,delivered,for instance,by a shapefromshading or shapefromtexture procedure. We commence by using the surface normals to obtain an affinity weight matri ..."
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Cited by 9 (4 self)
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This paper describes a graphspectral method for 3D surface integration. The algorithm takes as its input a 2D field of surface normal estimates,delivered,for instance,by a shapefromshading or shapefromtexture procedure. We commence by using the surface normals to obtain an affinity weight matrix whose elements are related to the surface curvature. The weight matrix is used to compute a rownormalized transition probability matrix,and we pose the recovery of the integration path as that of finding the steadystate random walk for the Markov chain defined by this matrix. The steadystate random walk is given by the leading eigenvector of the original affinity weight matrix. By threading the surface normals together along the path specified by the magnitude order of the components of the leading eigenvector we perform surface integration. The height increments along the path are simply related to the traversed path length and the slope of the local tangent plane. The method is evaluated on needlemaps delivered by a shapefromshading algorithm applied to realworld data and also on synthetic data. The method is compared with the local geometric height reconstruction method of Bors,Hancock and Wilson, and the global methods of Horn and Brooks and Frankot and Chellappa.
Surface Radiance Correction for Shape from Shading
 Pattern Recognition
, 2005
"... It is well known that many surfaces exhibit reflectance that is not well modelled by Lambert’s law. This is the case not only for surfaces that are rough or shiny, but also those that are matte and composed of materials that are particle suspensions. As a result, standard Lambertian shapefromshadi ..."
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Cited by 6 (1 self)
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It is well known that many surfaces exhibit reflectance that is not well modelled by Lambert’s law. This is the case not only for surfaces that are rough or shiny, but also those that are matte and composed of materials that are particle suspensions. As a result, standard Lambertian shapefromshading methods can not be applied directly to the analysis of rough and shiny surfaces. In order to overcome this difficulty, in this paper, we consider how to reconstruct the Lambertian component for rough and shiny surfaces when the object is illuminated in the viewing direction (retroreflection). To do this we make use of the diffuse reflectance models described by Oren and Nayar, and by Wolff. Our experiments with synthetic and realworld data reveal the effectiveness of the correction method, leading to improved surface normal and height recovery. 1
Kernelbased classification using quantum mechanics
, 2007
"... This paper introduces a new nonparametric estimation approach inspired from quantum mechanics. Kernel density estimation associates a function to each data sample. In classical kernel estimation theory the probability density function is calculated by summing up all the kernels. The proposed approac ..."
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Cited by 5 (2 self)
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This paper introduces a new nonparametric estimation approach inspired from quantum mechanics. Kernel density estimation associates a function to each data sample. In classical kernel estimation theory the probability density function is calculated by summing up all the kernels. The proposed approach assumes that each data sample is associated with a quantum physics particle that has a radial activation field around it. Schrödinger differential equation is used in quantum mechanics to define locations of particles given their observed energy level. In our approach, we consider the known location of each data sample and we model their corresponding probability density function using the analogy with the quantum potential function. The kernel scale is estimated from distributions of Knearest neighbours statistics. In order to apply the proposed algorithm to pattern classification we use the local Hessian for detecting the modes in the quantum potential hypersurface. Each mode is assimilated with a nonparametric class which is defined by means of a region growing algorithm. We apply the proposed algorithm on artificial data and for the topography segmentation from radar images of terrain.
Kernel Bandwidth Estimation for Nonparametric Modeling
, 2009
"... Kernel density estimation is a nonparametric procedure for probability density modeling, which has found several applications in various fields. The smoothness and modeling ability of the functional approximation are controlled by the kernel bandwidth. In this paper, we describe a Bayesian estimati ..."
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Cited by 4 (1 self)
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Kernel density estimation is a nonparametric procedure for probability density modeling, which has found several applications in various fields. The smoothness and modeling ability of the functional approximation are controlled by the kernel bandwidth. In this paper, we describe a Bayesian estimation method for finding the bandwidth from a given data set. The proposed bandwidth estimation method is applied in three different computationalintelligence methods that rely on kernel density estimation: 1) scale space; 2) mean shift; and 3) quantum clustering. The third method is a novel approach that relies on the principles of quantum mechanics. This method is based on the analogy between data samples and quantum particles and uses the Schrödinger potential as a cost function. The proposed methodology is used for blindsource separation of modulated signals and for terrain segmentation based on topography information.
Toward Spatial Reasoning about "Natural" Objects 13
 Computer Vision and Image Understanding
, 2006
"... This paper describes work aimed at developing a practical scheme for face analysis using shapefromshading. Existing methods have a tendency to recover surfaces in which convex features such as the nose are imploded. This is a result of the fact that subtle changes in the elements of the field of s ..."
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Cited by 3 (1 self)
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This paper describes work aimed at developing a practical scheme for face analysis using shapefromshading. Existing methods have a tendency to recover surfaces in which convex features such as the nose are imploded. This is a result of the fact that subtle changes in the elements of the field of surface normals can cause significant changes in the corresponding integrated surface. To overcome this problem, in this paper we describe a localshape based method for imposing convexity constraints. We show how to modify the orientations in the surface gradient field using critical points on the surface and local shape indicators. The method is applied to both surface height recovery and face reillumination. Experiments show that altering the field of surface normals so as to impose convexity results in greatly improved height reconstructions and more realistic reilluminations. 2 1
Finding the Number of Clusters for Nonparametric Segmentation
"... Abstract. Nonparametric data representation can be done by means of a potential function. This paper introduces a methodology for finding modes of the potential function. Two different methods are considered for the potential function representation: by using summations of Gaussian kernels, and by ..."
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Abstract. Nonparametric data representation can be done by means of a potential function. This paper introduces a methodology for finding modes of the potential function. Two different methods are considered for the potential function representation: by using summations of Gaussian kernels, and by employing quantum clustering. In the second case each data sample is associated with a quantum physics particle that has a radial energy field around its location. Both methods use a scaling parameter (bandwidth) to model the strength of the influence around each data sample. We estimate the scaling parameter as the mean of the Gamma distribution that models the variances of Knearest data samples to any given data. The local Hessian is used afterwards to find the modes of the resulting potential function. Each mode is associated with a cluster. We apply the proposed algorithm for blind signal separation and for the topographic segmentation of radar images of terrain. 1
Face Shape Recovery from a Single Image View
"... The problem of acquiring surface models of faces is an important one with potentially significant applications in biometrics, computer games and production graphics. For such task, the use of shapefromshading (SFS) is appealing since it is a noninvasive method that mimics the capabilities of the ..."
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The problem of acquiring surface models of faces is an important one with potentially significant applications in biometrics, computer games and production graphics. For such task, the use of shapefromshading (SFS) is appealing since it is a noninvasive method that mimics the capabilities of the human visual system. In this thesis, our interest lies on the recovery of facial shape from single image views. We make four novel contributions to this area. We commence by describing an algorithm for ensuring datacloseness and integrability in ShapefromShading. The combination of these constraints is aimed to overcome the problem of high dependency on the image irradiance. Next, we focus on developing a practical scheme for face analysis using SFS. We describe a localshape based method for imposing a novel convexity constraint. We show how to modify the orientations in the surface gradient field using critical points on the surface and local shape indicators. Then, we explore the use of statistical models that can be used in conjunction with SFS to reconstruct facial shape. We describe four different ways of constructing the 3D
NONPARAMETRIC CLUSTERING USING QUANTUM MECHANICS
"... This paper introduces a new nonparametric estimation approach that can be used for data that is not necessarily Gaussian distributed. The proposed approach employs the Shrödinger partial differential equation. We assume that each data sample is associated with a quantum physics particle that has a r ..."
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Cited by 1 (1 self)
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This paper introduces a new nonparametric estimation approach that can be used for data that is not necessarily Gaussian distributed. The proposed approach employs the Shrödinger partial differential equation. We assume that each data sample is associated with a quantum physics particle that has a radial field around its value. We consider a statistical estimation approach for finding the size of the influence field around each data sample. By implementing the Shrödinger equation we obtain a potential field that is assimilated with the data density. The regions of minima in the potential are determined by calculating the local Hessian on the potential hypersurface. The quantum clustering approach is applied for blind separation of signals and for segmenting SAR images of terrain based on surface normal orientation. 1.