Efficient and Robust Registration on the 3D Special Euclidean Group

TL;DR

This work presents a robust, fast and accurate method for registration of 3D scans that optimizes a robust cost function on the intrinsic representation of rigid motions, i.e., the Special Euclidean group SE(3).

Abstract

We present an accurate, robust and fast method for registration of 3D scans. Our motion estimation optimizes a robust cost function on the intrinsic representation of rigid motions, i.e., the Special Euclidean group $\mathbb{SE}(3)$. We exploit the geometric properties of Lie groups as well as the robustness afforded by an iteratively reweighted least squares optimization. We also generalize our approach to a joint multiview method that simultaneously solves for the registration of a set of scans. We demonstrate the efficacy of our approach by thorough experimental validation. Our approach significantly outperforms the state-of-the-art robust 3D registration method based on a line process in terms of both speed and accuracy. We also show that this line process method is a special case of our principled geometric solution. Finally, we also present scenarios where global registration based on feature correspondences fails but multiview ICP based on our robust motion estimation is successful.

Figures (8)

• Figure 1: Reconstruction of the livingroom 2 sequence from the Augmented ICL-NUIM dataset, as given by our method with the $L_{\frac{1}{2}}$ loss function
• Figure 2: Comparison of the line process solution with our method for different $K_{IRLS}$. For ease of visualization, we show performance only for the iterations between $2$ and $10$.
• Figure 3: Number of iterations $K_{outer}$ taken by each method to reach each convergence criterion $\epsilon$
• Figure 4: 3D reconstruction of a statue of Mahatma Gandhi. The close-up on the top left shows that joint multiview registration using FPFH features fails whereas the close-up on the bottom left shows successful registration using our robust pairwise motion estimation within a multiview ICP routine. The full reconstruction is shown on the right.
• Figure 5: Reconstruction of the livingroom 1 sequence from the Augmented ICL-NUIM dataset, as given by our method with the $L_{\frac{1}{2}}$ loss function