Mapping of Sparse 3D Data using Alternating Projection

TL;DR

This paper introduces a new method for registering sparse, texture-less 3D scans by re-parameterizing point clouds with line segments and using an alternating projection algorithm to satisfy intersection and rigidity constraints.

Contribution

The paper presents a novel registration technique that works effectively on sparse 3D data without relying on dense point clouds or RGB information.

Findings

Outperforms existing algorithms on Kinect and LiDAR datasets.

Effective with 100X downsampled sparse data in Kinect.

Achieves better accuracy than methods using full-resolution data.

Abstract

We propose a novel technique to register sparse 3D scans in the absence of texture. While existing methods such as KinectFusion or Iterative Closest Points (ICP) heavily rely on dense point clouds, this task is particularly challenging under sparse conditions without RGB data. Sparse texture-less data does not come with high-quality boundary signal, and this prohibits the use of correspondences from corners, junctions, or boundary lines. Moreover, in the case of sparse data, it is incorrect to assume that the same point will be captured in two consecutive scans. We take a different approach and first re-parameterize the point-cloud using a large number of line segments. In this re-parameterized data, there exists a large number of line intersection (and not correspondence) constraints that allow us to solve the registration task. We propose the use of a two-step alternating projection algorithm by formulating the registration as the simultaneous satisfaction of intersection and rigidity constraints. The proposed approach outperforms other top-scoring algorithms on both Kinect and LiDAR datasets. In Kinect, we can use 100X downsampled sparse data and still outperform competing methods operating on full-resolution data.