  Aiming at drastic speedup for point-feature embeddings at test time, we
propose a new framework that uses a pair of multi-layer perceptrons (MLP) and a
lookup table (LUT) to transform point-coordinate inputs into high-dimensional
features. When compared with PointNet's feature embedding part realized by MLP
that requires millions of dot products, the proposed framework at test time
requires no such layers of matrix-vector products but requires only looking up
the nearest entities from the tabulated MLP followed by interpolation, defined
over discrete inputs on a 3D lattice that is substantially arranged
irregularly. We call this framework LUTI-MLP: LUT Interpolation ML that
provides a way to train end-to-end irregularly tabulated MLP coupled to a LUT
in a specific manner without the need for any approximation at test time.
LUTI-MLP also provides significant speedup for Jacobian computation of the
embedding function wrt global pose coordinate on Lie algebra $\mathfrak{se}(3)$
at test time, which could be used for point-set registration problems. After
extensive evaluation using the ModelNet40, we confirmed that the LUTI-MLP even
with a small (e.g., $4^3$) lattice yields performance comparable to that of the
MLP while achieving significant speedup: $100\times$ for the embedding,
$12\times$ for the approximate Jacobian, and $860\times$ for the canonical
Jacobian.
