Surface HOF: Surface Reconstruction from a Single Image Using Higher Order Function Networks

We address the problem of generating a high-resolution surface reconstruction from a single image. Our approach is to learn a Higher Order Function (HOF) which takes an image of an object as input and generates a mapping function. The mapping function takes samples from a canonical domain (e.g. the unit sphere) and maps each sample to a local tangent plane on the 3D reconstruction of the object. Each tangent plane is represented as an origin point and a normal vector at that point. By efficiently learning a continuous mapping function, the surface can be generated at arbitrary resolution in contrast to other methods which generate fixed resolution outputs. We present the Surface HOF in which both the higher order function and the mapping function are represented as neural networks, and train the networks to generate reconstructions of PointNet objects. Experiments show that Surface HOF is more accurate and uses more efficient representations than other state of the art methods for surface reconstruction. Surface HOF is also easier to train: it requires minimal input pre-processing and output post-processing and generates surface representations that are more parameter efficient. Its accuracy and convenience make Surface HOF an appealing method for single image reconstruction.