Three-Dimensional Face Shape by Local Fitting to a Single Reference Model

Abstract

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.