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

Irregularly Tabulated MLP for Fast Point Feature Embedding