A Deep Signed Directional Distance Function for Shape Representation

Predicting accurate observations efficiently from novel views is a key requirement for several robotics applications. Existing shape and surface representations, however, either require expensive ray-tracing operations, e.g., in the case of meshes or signed distance functions (SDFs), or offer only a coarse view, e.g., in the case of quadrics or point clouds. We develop a new representation that captures viewing direction and enables fast novel view synthesis. Our first contribution is a signed directional distance function (SDDF) that extends the SDF definition by measuring distance in a desired viewing direction rather than to the nearest point. As a result, SDDF removes post-processing steps for view synthesis required by SDF, such as surface extraction via marching cubes or rendering via sphere tracing, and allows ray-tracing through a single function call. SDDF also encodes by construction the property that distance decreases linearly along the viewing direction. We show that this enables dimensionality reduction in the function representation and guarantees the prediction accuracy independent of the distance to the surface. Recent advances demonstrate impressive performance of deep neural networks for shape learning, including IGR for SDF, Occupancy Networks for occupancy, AtlasNet for meshes, and NeRF for density. Our second contribution, DeepSDDF, is a deep neural network model for SDDF shape learning. Similar to IGR, we show that DeepSDDF can model whole object categories and interpolate or complete shapes from partial views.