[Paper Review] Closed-form Solution for IMU based LSD-SLAM Point Cloud Conversion into the Scaled 3D World Environment

Sergey Triputen, Kristiaan Schreve+2 more|arXiv (Cornell University)|Jul 19, 2017

Robotics and Sensor-Based Localization4 references3 citations

TL;DR

This paper presents a closed-form solution to convert LSD-SLAM's monocular, unscaled point cloud into a metrically accurate 3D world coordinate system using IMU data. By aligning camera trajectory and point cloud through a transformation that corrects scale and orientation errors, the method achieves precise, real-world-aligned 3D reconstructions suitable for robotics applications like path planning.

ABSTRACT

SLAM is a very popular research stream in computer vision and robotics nowadays. For more effective SLAM implementation it is necessary to have reliable informa- tion about the environment, also the data should be aligned and scaled according to the real world coordinate system. Monocular SLAM research is an attractive sub-stream, because of the low equipment cost, size and weight. In this paper we present a way to build a conversion from LSD-SLAM coordinate space to the real world coordinates using a true metric scale with IMU sensor data implementation. The causes of differences between the real and calculated spaces are explained and the possibility of conversions between the spaces is proved. Additionally, a closed-form solution for inter space trans- formation calculation is presented. The synthetic method of generating high level accurate and well controlled input data for the LSD-SLAM algorithm is presented. Finally, the reconstructed 3D environment representation is delivered as an output of the implemented conversion.

Motivation & Objective

• Address the lack of metric scale in monocular SLAM systems like LSD-SLAM, which limits integration with real-world robotic systems.
• Overcome the challenge of converting LSD-SLAM's relative, unscaled 3D point cloud into a globally aligned, metrically accurate representation.
• Enable reliable 3D environment reconstruction for path planning and obstacle detection by fusing IMU data with LSD-SLAM output.
• Develop a synthetic simulation framework using Blender to generate controlled, high-fidelity input data for algorithm validation.
• Provide a closed-form transformation to correct scale and orientation discrepancies between LSD-SLAM's internal coordinate system and the real world.

Proposed method

• Use a synthetic 3D environment in Blender to generate realistic image sequences with controlled textures, lighting, and motion for LSD-SLAM input.
• Simulate IMU data (acceleration and angular rates) to provide ground truth motion information for camera trajectory estimation.
• Apply a closed-form transformation derived from the IMU data and LSD-SLAM's estimated trajectory to correct scale and orientation.
• Use the transformation to reproject LSD-SLAM's point cloud into the real-world coordinate system, aligning axes and scale with the ground truth.
• Validate the method by comparing the transformed point cloud against the known Blender-generated ground truth in MATLAB.
• Represent the final output as an octree mesh for efficient spatial representation and downstream robotic use.

Experimental results

Research questions

• RQ1 Can a closed-form transformation be derived to convert LSD-SLAM’s unscaled, relative 3D point cloud into a metrically accurate 3D world coordinate system?
• RQ2 How accurately can IMU data be used to correct the scale and orientation of LSD-SLAM’s output in a synthetic environment?
• RQ3 What is the impact of initialization dynamics on scale convergence, and how can stabilization be achieved?
• RQ4 To what extent does the transformation preserve geometric fidelity and alignment with the real-world environment?
• RQ5 Can the method reliably produce a metrically scaled 3D reconstruction suitable for robotics tasks like path planning?

Key findings

• The proposed closed-form transformation successfully aligns LSD-SLAM’s point cloud with the real-world coordinate system, achieving correct scale and orientation.
• The scale factor converges after approximately 4,300 frames, with stable performance observed beyond that point despite minor bursts.
• The ground truth path length in Blender was 195.12 meters, while LSD-SLAM’s estimated path was only 12.6 units, indicating a significant scale discrepancy before correction.
• After conversion, the point cloud geometry and camera path were accurately aligned with the Blender-generated ground truth, as verified in MATLAB.
• The method enables reliable 3D reconstruction suitable for downstream robotics applications such as path planning and obstacle avoidance.
• The scale coefficient is not constant over time and requires dynamic adjustment, especially during repeated or looped trajectories.