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We address the problem of generating a high-resolution surface reconstructionfrom 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 unitsphere) and maps each sample to a local tangent plane on the 3D reconstructionof the object. Each tangent plane is represented as an origin point and anormal vector at that point. By efficiently learning a continuous mappingfunction, the surface can be generated at arbitrary resolution in contrast toother methods which generate fixed resolution outputs. We present the SurfaceHOF in which both the higher order function and the mapping function arerepresented as neural networks, and train the networks to generatereconstructions of PointNet objects. Experiments show that Surface HOF is moreaccurate and uses more efficient representations than other state of the artmethods for surface reconstruction. Surface HOF is also easier to train: itrequires minimal input pre-processing and output post-processing and generatessurface representations that are more parameter efficient. Its accuracy andconvenience make Surface HOF an appealing method for single imagereconstruction.

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