Quantitative Assessment of the Accuracy of 3D Face Shape Reconstruction

This paper addresses the question of the accuracy of reconstruction of 3D face surfaces from single 2D face images. Shape reconstruction from 2D face images is an approximation process, and quantitative analysis of reconstruction accuracy is essential in order to validate the results. Recently 3D synthesis techniques using morphable models have become quite popular, however, they have only been shown to reconstruct accurately in a qualitative fashion. Different methods vary in performance, and it is very difficult to compare them using just qualitative results. This paper evaluates a shape reconstruction algorithm, based on the well known analysis by synthesis approach, which works on single 2D images with unknown intrinsic camera parameters. The evaluation of the reconstructed models is carried out using a quantitative approach based on geometric similarity and a weighted eigen distance. The algorithm proposes the use of a texture mapped shape model. The shape model is created in advance from a representative set of 3D face surfaces. A dense correspondence, which is essential for encoding 3D shape information, is established using rigid and non-rigid registration. The reconstruction is carried out by optimising over the shape parameters with an objective function that minimises differences between the 2D image and the corresponding projection of the 3D image. The accuracy of reconstruction is improved by using an annealing based approach to overcome the problems of multiple local minima due to the non-convexity of the search space. The algorithm was tested using three different face databases in order to assess the broader applicability of the proposed method.