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25
Graph-spectral methods for Computer Vision
, 2003
"... This thesis describes a family of graph-spectral methods for computer vision that exploit the properties of the first eigenvector of the adjacency matrix of a weighted graph. The algorithms are applied to segmentation and grouping, shape-from-shading and graphmatching. In Chapter 3, we cast the prob ..."
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This thesis describes a family of graph-spectral methods for computer vision that exploit the properties of the first eigenvector of the adjacency matrix of a weighted graph. The algorithms are applied to segmentation and grouping, shape-from-shading and graphmatching. In Chapter 3, we cast the problem of grouping into an evidence combining setting where the number of clusters is determined by the modes of the adjacency matrix. With the number of clusters to hand, we model the grouping process using two sets of variables. These are the cluster memberships and the pairwise affinities or link-weights for the nodes of a graph. From a simple probability distribution for these parameters, we show how they may be estimated using the apparatus of the expectation-maximisation (EM) algorithm. The new method is demonstrated on the problems of line-segment grouping and gray-scale image segmentation. The method is shown to outperform a non-iterative eigenclustering method. In Chapter 4, we present a more direct graph-spectral method for segmentation and grouping by developing an iterative maximum likelihood framework for perceptual clustering. Here, we focuss in more detail on the likelihood function that results from the
Kernel bandwidth estimation in methods based on probability density function modeling
- in Proc. Int. Conf. Pattern Recognit
, 2008
"... In kernel density estimation methods, an approximation of the data probability density function is achieved by locating a kernel function at each data location. The smoothness of the functional approximation and the modelling ability are controlled by the kernel bandwidth. In this paper we propose a ..."
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In kernel density estimation methods, an approximation of the data probability density function is achieved by locating a kernel function at each data location. The smoothness of the functional approximation and the modelling ability are controlled by the kernel bandwidth. In this paper we propose a Bayesian estimation method for finding the kernel bandwidth. The distribution corresponding to the bandwidth is estimated from distributions characterizing the second order statistics estimates calculated from local neighbourhoods. The proposed bandwidth estimation method is applied in three different kernel density estimation based approaches: scale space, mean shift and quantum clustering. The third method is a novel pattern recognition approach using the principles of quantum mechanics. 1.
Generalised Perspective Shape from Shading in Spherical Coordinates
"... Abstract. In the last four decades there has been enormous progress in Shape from Shading (SfS) with respect to both modelling and numerics. In particular approaches based on advanced model assumptions such as perspective cameras and non-Lambertian surfaces have become very popular. However, regardi ..."
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Abstract. In the last four decades there has been enormous progress in Shape from Shading (SfS) with respect to both modelling and numerics. In particular approaches based on advanced model assumptions such as perspective cameras and non-Lambertian surfaces have become very popular. However, regarding the positioning of the light source, almost all recent approaches still follow the sim-plest geometric configuration one can think of: The light source is assumed to be located exactly at the optical centre of the camera. In our paper, we refrain from this unrealistic and severe restriction. Instead we consider a much more general SfS scenario based on a perspective camera, where the light source can be posi-tioned anywhere in the scene. To this end, we propose a novel SfS model that is based on a Hamilton-Jacobi equation (HJE) which in turn is formulated in terms of spherical coordinates. This particular choice of the modelling framework and the coordinate system comes along with two fundamental contributions: While on the modelling side, the spherical coordinate system allows us to derive a gener-alised brightness equation – a compact and elegant generalisation of the standard image irradiance equation to arbitrary configurations of the light source, on the numerical side, the formulation as Hamilton-Jacobi equation enables us to de-velop a specifically tailored variant of the fast marching (FM) method – one of the most efficient numerical solvers in the entire SfS literature. Results on syn-thetic and real-world data confirm our theoretical considerations. They clearly demonstrate the feasibility and efficiency of the generalised SfS approach.
Face Shape Recovery from a Single Image View
, 2006
"... 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 shape-from-shading (SFS) is appealing since it is a non-invasive 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 shape-from-shading (SFS) is appealing since it is a non-invasive 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 data-closeness and integrabil-ity in Shape-from-Shading. 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 local-shape 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
Contents lists available at ScienceDirect Image and Vision Computing
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Statistical Methods For Facial Shape-from-shading and Recognition
"... This thesis presents research aimed at improving the quality of facial shape information that can be recovered from single intensity images using shape-from-shading, with the aim of exploiting this information for the purposes of face recognition and view synthesis. The common theme throughout this ..."
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This thesis presents research aimed at improving the quality of facial shape information that can be recovered from single intensity images using shape-from-shading, with the aim of exploiting this information for the purposes of face recognition and view synthesis. The common theme throughout this thesis is the use of statistical methods to offer enhanced accuracy and robustness over existing techniques for facial shape-from-shading. The work presented goes some way to reinstating shape-from-shading as a viable means to recover facial shape from single, real world images. In Chapter 2 we thoroughly survey the existing literature in the areas of face recognition, shape recovery and skin reflectance modelling. We draw from this review a number of important observations. The first is that existing solutions to the general shape-fromshading problem prove incapable of recovering accurate facial shape from real world images. The second is that statistical models have been shown to be highly effective in modelling facial appearance and shape variation and have been applied successfully to the problem of face recognition. Finally, we highlight the complex nature of light interaction with skin and note that previous attempts to apply shape-from-shading to real world face
1 A Graph-Spectral Approach to Shape-from-shading
"... Abstract — In this paper we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterise the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalise large c ..."
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Abstract — In this paper we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterise the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalise large change 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 maximises the sum of curvature dependent 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 real-world imagery. Index Terms — Shape-from-shading, graph seriation, graphspectral methods.
Abstract ARTICLE IN PRESS Pattern Recognition ( ) – Vector transport for shape-from-shading
, 2004
"... In this paper we describe a new shape-from-shading method. We show how the parallel transport of surface normals can be used to impose curvature consistency and also to iteratively update surface normal directions so as to improve the brightness error. We commence by showing how to make local estima ..."
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In this paper we describe a new shape-from-shading method. We show how the parallel transport of surface normals can be used to impose curvature consistency and also to iteratively update surface normal directions so as to improve the brightness error. We commence by showing how to make local estimates of the Hessian matrix from surface normal information. With the local Hessian matrix to hand, we develop an “EM-like ” algorithm for updating the surface normal directions. At each image location, parallel transport is applied to the neighbouring surface normals to generate a sample of local surface orientation predictions. From this sample, a local weighted estimate of the image brightness is made. The transported surface normal which gives the brightness prediction which is closest to this value is selected as the revised estimate of surface orientation. The revised surface normals obtained in this way may in turn be used to re-estimate the Hessian matrix, and the process iterated until stability is reached. We experiment with the method on a variety of real world and synthetic data. Here we explore the properties of the fields of surface normals and the height data delivered by the method. � 2005 Published by Elsevier Ltd on behalf of Pattern Recognition Society.
Bayesian Estimation of Kernel Bandwidth for
"... Abstract. Kernel density estimation (KDE) has been used in many computational intelligence and computer vision applications. In this paper we propose a Bayesian estimation method for finding the bandwidth in KDE applications. A Gamma density function is fitted to distributions of variances of K-near ..."
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Abstract. Kernel density estimation (KDE) has been used in many computational intelligence and computer vision applications. In this paper we propose a Bayesian estimation method for finding the bandwidth in KDE applications. A Gamma density function is fitted to distributions of variances of K-nearest neighbours data populations while uniform distribution priors are assumed for K. A maximum log-likelihood approach is used to estimate the parameters of the Gamma distribution when fitted to the local data variance. The proposed methodology is applied in three different KDE approaches: kernel sum, mean shift and quantum clustering. The third method relies on the Schrödinger partial differential equation and uses the analogy between the potential function that manifests around particles, as defined in quantum physics, and the probability density function corresponding to data. The proposed algorithm is applied to artificial data and to segment terrain images.
