Continuous Signed Distance Functions for 3D Vision

We explore the use of continuous signed distance functions as an object representation for 3D vision. Popularized in procedural computer graphics, this representation defines 3D objects as geometric primitives combined with constructive solid geometry and transformed by nonlinear deformations, scaling, rotation or translation. Unlike its discretized counterpart, that has become important in dense 3D reconstruction, the continuous distance function is not stored as a sampled volume, but as a closed mathematical expression. We argue that this representation can have several benefits for 3D vision, such as being able to describe many classes of indoor and outdoor objects at the order of hundreds of bytes per class, getting parametrized shape variations for free. As a distance function, the representation also has useful computational aspects by defining, at each point in space, the direction and distance to the nearest surface, and whether a point is inside or outside the surface.