3DTI-Net: Learn 3D Transform-Invariant Feature Using Hierarchical Graph CNN

Abstract

Recently, emerging point cloud dedicated deep learning frameworks, such as PointNet and PointNet++, have achieved remarkable advantage in both accuracy and speed over traditional handcrafted ones. However, since the point coordinates of point clouds are represented in various local coordinate systems, most existing methods require additional preprocessing on raw point clouds. In this work, we design an efficient transform-invariant framework (named 3DTI-Net) for point cloud processing without the need of such preprocessing. 3DTI-Net consists of a transform invariant feature encoder as the front-end and a hierarchical graph convolutional neural network as the back-end. It achieves transform invariant feature extraction by learning inner 3D geometry information based on local graph representation. Experiments results on various classification and retrieval tasks show that, 3DTI-Net is able to learn 3D feature efficiently and can achieve state-of-the-art performance in rotated 3D object classification and retrieval.

A Appendix

1.1 A.1 Proof of Property 1

Proof

Translation invariance can be easily achieved by the re-centering operation, To prove rotation invariance, let ${R} \in \mathbb {R}^{3 \times 3}$ be an arbitrary rotation matrix, and the rotated point cloud coordinates is XR. Then, the i-th feature satisfies:

$$\begin{aligned} \begin{aligned} f_i (X R )&= \left\| \left( h(L) X R \right) _i \right\| _2^2 \\&= \left\| \left( h(L) \right) _i X R \right\| _2^2 \\&= \left( h(L) \right) _i X R R^T X^T \left( h(L) \right) _i ^T \\&= \left( h(L) \right) _i X X^T \left( h(L) \right) _i ^T \\&= \left\| \left( h(L) X \right) _i \right\| _2^2 \ = \ f_i ( X ). \end{aligned} \end{aligned}$$

(4)

$\square$