Nonlinear 3D Face Morphable Model

As a classic statistical model of 3D facial shape and texture, 3D Morphable Model (3DMM) is widely used in facial analysis, e.g., model fitting, image synthesis. Conventional 3DMM is learned from a set of well-controlled 2D face images with associated 3D face scans, and represented by two sets of PCA basis functions. Due to the type and amount of training data, as well as the linear bases, the representation power of 3DMM can be limited. To address these problems, this paper proposes an innovative framework to learn a nonlinear 3DMM model from a large set of unconstrained face images, without collecting 3D face scans. Specifically, given a face image as input, a network encoder estimates the projection, shape and texture parameters. Two decoders serve as the nonlinear 3DMM to map from the shape and texture parameters to the 3D shape and texture, respectively. With the projection parameter, 3D shape, and texture, a novel analytically-differentiable rendering layer is designed to reconstruct the original input face. The entire network is end-to-end trainable with only weak supervision. We demonstrate the superior representation power of our nonlinear 3DMM over its linear counterpart, and its contribution to face alignment and 3D reconstruction. 1