MASH: Masked Anchored SpHerical Distances
for 3D Shape Representation and Generation
MASH represents a 3D shape by fitting a set of Masked Anchored SpHerical distance functions as observed from the perspective of a fixed number of anchor points in 3D space. Left shows an iterative optimization of MASH parameters, from an unoriented point cloud, leading to closer and closer approximations to the ground-truth shape surface. Middle and right show the versatility of MASH in enabling a variety of downstream applications including shape completion, blending, and conditional 3D generation from multi-modal inputs including text prompts, point clouds, and single-view images.
We introduce Masked Anchored SpHerical Distances (MASH), a novel multi-view and parametrized representation of 3D shapes. Inspired by multi-view geometry and motivated by the importance of perceptual shape understanding for learning 3D shapes, MASH represents a 3D shape as a collection of observable local surface patches, each defined by a spherical distance function emanating from an anchor point. We further leverage the compactness of spherical harmonics to encode the MASH functions, combined with a generalized view cone with a parameterized base that masks the spatial extent of the spherical function to attain locality. We develop a differentiable optimization algorithm capable of converting any point cloud into a MASH representation accurately approximating ground-truth surfaces with arbitrary geometry and topology. Extensive experiments demonstrate that MASH is versatile for multiple applications including surface reconstruction, shape generation, completion, and blending, achieving superior performance thanks to its unique representation encompassing both implicit and explicit features.
