Deep Medial Fields

Daniel Rebain, Ke Li, Vincent Sitzmann, Soroosh Yazdani, Kwang Moo Yi, Andrea Tagliasacchi

Abstract:

Implicit representations of geometry, such as occupancy fields or signed
distance fields (SDF), have recently re-gained popularity in encoding 3D
solid shape in a functional form. In this work, we introduce medial fields:
a field function derived from the medial axis transform (MAT) that makes
available information about the underlying 3D geometry that is immediately
useful for a number of downstream tasks. In particular, the medial field
encodes the local thickness of a 3D shape, and enables O(1) projection of a
query point onto the medial axis. To construct the medial field we require
nothing but the SDF of the shape itself, thus allowing its straightforward
incorporation in any application that relies on signed distance fields. Working in unison with the O(1) surface projection supported by the SDF, the
medial field opens the door for an entirely new set of efficient, shape-aware
operations on implicit representations. We present three such applications,
including a modification to sphere tracing that renders implicit representations with better convergence properties, a fast construction method for
memory-efficient rigid-body collision proxies, and an efficient approximation of ambient occlusion that remains stable with respect to viewpoint
variations.