  We introduce CN-DHF (Compact Neural Double-Height-Field), a novel hybrid
neural implicit 3D shape representation that is dramatically more compact than
the current state of the art. Our representation leverages Double-Height-Field
(DHF) geometries, defined as closed shapes bounded by a pair of oppositely
oriented height-fields that share a common axis, and leverages the following
key observations: DHFs can be compactly encoded as 2D neural implicits that
capture the maximal and minimal heights along the DHF axis; and typical closed
3D shapes are well represented as intersections of a very small number (three
or fewer) of DHFs. We represent input geometries as CNDHFs by first computing
the set of DHFs whose intersection well approximates each input shape, and then
encoding these DHFs via neural fields. Our approach delivers high-quality
reconstructions, and reduces the reconstruction error by a factor of 2:5 on
average compared to the state-of-the-art, given the same parameter count or
storage capacity. Compared to the best-performing alternative, our method
produced higher accuracy models on 94% of the 400 input shape and parameter
count combinations tested.
