William A. P. Smith

Recovering Facial Shape Using a Statistical Model of Surface Normal Direction

In this paper, we show how a statistical model of facial shape can be embedded within a shape-from-shading algorithm. We describe how facial shape can be captured using a statistical model of variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to Cartesian points on a local tangent plane. The distribution of surface normal directions is captured using the covariance matrix for the projected point positions. The eigenvectors of the covariance matrix define the modes of shape-variation in the fields of transformed surface normals. We show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by Lamberts law. We demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details. We assess the accuracy of the technique on a variety of images with ground truth and real-world images

Living on a high sugar diet: the fate of sucrose ingested by a phloem-feeding insect, the pea aphid Acyrthosiphon pisum.

The natural diet of aphids, plant phloem sap, generally contains high concentrations of sucrose. When pea aphids (Acyrthosiphon pisum) were fed on chemically defined diets containing sucrose radiolabelled in the glucose or fructose moiety, 2 to 12-fold and 87 to 110-fold more radioactivity was recovered from the tissues and honeydew, respectively, of aphids that ingested [U-(14)C-glucose]-sucrose than from those ingesting [U-(14)C-fructose]-sucrose. The total radioactivity recovered was 70% of the ingested [U-(14)C-glucose]-sucrose and <5% of ingested [U-(14)C-fructose]-sucrose. The dominant honeydew sugars produced by aphids feeding on 0.75 M sucrose diets were oligosaccharides comprising glucose. In vitro the guts of pea aphids had high sucrase activity, 1-5 U mg(-1) protein, generating equimolar glucose and fructose except at high sucrose concentrations where glucose production was inhibited (K(si)=0.1 M). These data suggest that the fructose moiety of ingested sucrose is assimilated very efficiently and may be preferentially respired by the aphid, and that the glucose moiety of sucrose is incorporated into oligosaccharides by the transglucosidase activity of the gut sucrase at high sucrose concentrations. These differences in the fate of sucrose-derived glucose and fructose are important elements in both the carbon nutrition and osmoregulation of aphids.

Inverse Rendering of Faces with a 3D Morphable Model

In this paper, we present a complete framework to inverse render faces with a 3D Morphable Model (3DMM). By decomposing the image formation process into geometric and photometric parts, we are able to state the problem as a multilinear system which can be solved accurately and efficiently. As we treat each contribution as independent, the objective function is convex in the parameters and a global solution is guaranteed. We start by recovering 3D shape using a novel algorithm which incorporates generalization error of the model obtained from empirical measurements. We then describe two methods to recover facial texture, diffuse lighting, specular reflectance, and camera properties from a single image. The methods make increasingly weak assumptions and can be solved in a linear fashion. We evaluate our findings on a publicly available database, where we are able to outperform an existing state-of-the-art algorithm. We demonstrate the usability of the recovered parameters in a recognition experiment conducted on the CMU-PIE database.

Semi-supervised feature selection for gender classification

We apply a semi-supervised learning method to perform gender determination. The aim is to select the most discriminating feature components from the eigen-feature representation of faces. By making use of the information provided by both labeled and unlabeled data, we successfully reduce the size of the labeled data set required for gender feature selection, and improve the classification accuracy. Instead of using 2D brightness images, we use 2.5D facial needle-maps which reveal more directly facial shape information. Principal geodesic analysis (PGA), which is a generalization of principal component analysis (PCA) from data residing in a Euclidean space to data residing on a manifold, is used to obtain the eigen-feature representation of the facial needle-maps. In our experiments, we achieve 90.50% classification accuracy when 50% of the data are labeled. This performance demonstrates the effectiveness of this method for gender classification using a small labeled set, and the feasibility of gender classification using the facial shape information.

3D morphable face models revisited

In this paper we revisit the process of constructing a high resolution 3D morphable model of face shape variation. We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more efficient and generalises to novel face surfaces more accurately than previous models. We also reformulate the probabilistic prior that the model provides on the distribution of parameter vector lengths. This distribution is determined solely by the number of model dimensions and can be used as a regularisation constraint in fitting the model to data without the need to empirically choose a parameter controlling the trade off between plausibility and quality of fit. As an example application of this improved model, we show how it may be fitted to a sparse set of 2D feature points (approximately 100). This provides a rapid means to estimate high resolution 3D face shape for a face in any pose given only a single face image. We present experimental results using ground truth data and hence provide absolute reconstruction errors. On average, the per vertex error of the reconstructed faces is less than 3.6 mm.

Facial Shape-from-shading and Recognition Using Principal Geodesic Analysis and Robust Statistics

Abstract The aim in this paper is to use principal geodesic analysis to model the statistical variations for sets of facial needle maps. We commence by showing how to represent the distribution of surface normals using the exponential map. Shape deformations are described using principal geodesic analysis on the exponential map. Using ideas from robust statistics we show how this deformable model may be fitted to facial images in which there is significant self-shadowing. Moreover, we demonstrate that the resulting shape-from-shading algorithm can be used to recover accurate facial shape and albedo from real world images. In particular, the algorithm can effectively fill-in the facial surface when more than 30% of its area is subject to self-shadowing. To investigate the utility of the shape parameters delivered by the method, we conduct experiments with illumination insensitive face recognition. We present a novel recognition strategy in which similarity is measured in the space of the principal geodesic parameters. We also use the recovered shape information to generate illumination normalized prototype images on which recognition can be performed. Finally we show that, from a single input image, we are able to generate the basis images employed by a number of well known illumination-insensitive recognition algorithms. We also demonstrate that the principal geodesics provide an efficient parameterization of the space of harmonic basis images.

A Coupled Statistical Model for Face Shape Recovery From Brightness Images

We focus on the problem of developing a coupled statistical model that can be used to recover facial shape from brightness images of faces. We study three alternative representations for facial shape. These are the surface height function, the surface gradient, and a Fourier basis representation. We jointly capture variations in intensity and the surface shape representations using a coupled statistical model. The model is constructed by performing principal components analysis on sets of parameters describing the contents of the intensity images and the facial shape representations. By fitting the coupled model to intensity data, facial shape is implicitly recovered from the shape parameters. Experiments show that the coupled model is able to generate accurate shape from out-of-training-sample intensity images

Systolic loop methods for molecular dynamics simulation using multiple transputers

Abstract The implementation of molecular dynamics simulation on parallel computers needs a method which distributes over the processors both the evaluation of pair interactions and the integration of particle motions. This paper introduces several ways to achieve this, all based on the systolic loop concept. Each particle has a home processor which integrates its motion. In the evaluation of the interactions, the particle data circulate around the ring of processors in such a way that every particle meets every other particle, enabling all the pair interactions to be evaluated. The methods are suitable for use with a spherical cut-off or with a neighbour list. Three possible sources of inefficiency are discussed in detail. These are: imperfect load balancing during the force evaluation; communication delays during the force evaluation; and communication delays in accumulating thermodynamic quantities. In each case the loss of efficiency is only significant if the number of processors approaches the number of particles, which is unlikely to be the case in practice. Also, if the parallel computer is constructed from transputers, their ability to simultaneously calculate and communicate can reduce communication delays in the force evaluation. The methods have been tested on systems of up to 130 transputers.

Recovering facial shape and albedo using a statistical model of surface normal direction

This paper describes how facial shape can be modelled using a statistical model that captures variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map surface normals from the unit sphere to points on a local tangent plane. The variations in surface normal direction are captured using the covariance matrix for the projected point positions. This allows us to model variations in face shape using a standard point distribution model. We train the model on fields of surface normals extracted from range data and show how to fit the model to intensity data using constraints on the surface normal direction provided by Lamberts law. We demonstrate that this process yields accurate facial shape recovery and allows an estimate of the albedo map to be made from single, real world face images.

Gender Classification using Shape from Shading

The aim in this paper is to show how to use the 2.5D facial surface normals (needle-maps) recovered using shape from shading (SFS) to improve the performance of gender classification. We incorporate principal geodesic analysis (PGA) into SFS to guarantee the recovered needle-maps is a possible example defined by a statistical model. Because the recovered facial needlemaps satisfy data-closeness constraint, they not only give the facial shape information, but also combine the image intensity implicitly. Experiments show that this combination gives better gender classification performance than using facial shape or texture information alone.