On Representation of 3D Rotation in the Context of Deep Learning

TL;DR

In line with previous research, it was found that networks using the continuous 5D and 6D representations performed better than the discontinuous ones.

Abstract

This paper investigates various methods of representing 3D rotations and their impact on the learning process of deep neural networks. We evaluated the performance of ResNet18 networks for 3D rotation estimation using several rotation representations and loss functions on both synthetic and real data. The real datasets contained 3D scans of industrial bins, while the synthetic datasets included views of a simple asymmetric object rendered under different rotations. On synthetic data, we also assessed the effects of different rotation distributions within the training and test sets, as well as the impact of the object's texture. In line with previous research, we found that networks using the continuous 5D and 6D representations performed better than the discontinuous ones.

Figures (13)

• Figure 1.1: Illustration of the definition of a continuous representation on a 2D space. The region of discontinuity is shown in turquoise. In red is illustrated the problem when the size of the angle $\varphi$ differs in reality and in the representation: in reality it is small, but in the representation it is large.
• Figure 1.2: Rendered images of the designed object under varying rotations.
• Figure 1.3: Random Distribution. Theoretical area on the left, actual samples in the dataset on the right.
• Figure 1.4: Big Hole Distribution. Theoretical area on the left, actual samples in dataset on the right.
• Figure 1.5: Many Holes Distribution. Theoretical area on the left, actual samples in dataset on the right.