  Deep neural representations of 3D shapes as implicit functions have been
shown to produce high fidelity models surpassing the resolution-memory
trade-off faced by the explicit representations using meshes and point clouds.
However, most such approaches focus on representing closed shapes. Unsigned
distance function (UDF) based approaches have been proposed recently as a
promising alternative to represent both open and closed shapes. However, since
the gradients of UDFs vanish on the surface, it is challenging to estimate
local (differential) geometric properties like the normals and tangent planes
which are needed for many downstream applications in vision and graphics. There
are additional challenges in computing these properties efficiently with a
low-memory footprint. This paper presents a novel approach that models such
surfaces using a new class of implicit representations called the closest
surface-point (CSP) representation. We show that CSP allows us to represent
complex surfaces of any topology (open or closed) with high fidelity. It also
allows for accurate and efficient computation of local geometric properties. We
further demonstrate that it leads to efficient implementation of downstream
algorithms like sphere-tracing for rendering the 3D surface as well as to
create explicit mesh-based representations. Extensive experimental evaluation
on the ShapeNet dataset validate the above contributions with results
surpassing the state-of-the-art.
