Discrete Fourier Transform-based Point Cloud Compression for Efficient SLAM in Featureless Terrain

TL;DR

This work addresses the data bottleneck in SLAM by introducing a DFT-based compression pipeline that converts 3D point clouds into a 2D DEM, performs a 2D DFT, and retains low-frequency content via a circular low-pass filter defined by $f_c = 1 - \frac{r}{r_M}$. Reconstruction uses the inverse DFT, enabling substantial data-size reduction with limited degradation for gradually varying terrains, such as planetary deserts or lunar surfaces. The approach is evaluated on MADMAX terrain sequences using RMSE and bits-per-point, revealing a clear trade-off: higher data reduction increases reconstruction error, with gentler slopes suffering less severely. The results suggest practical applicability for resource-constrained SLAM scenarios, while highlighting the need for real-time performance and terrain-aware cutoff selection in future work.

Abstract

Simultaneous Localization and Mapping (SLAM) is an essential technology for the efficiency and reliability of unmanned robotic exploration missions. While the onboard computational capability and communication bandwidth are critically limited, the point cloud data handled by SLAM is large in size, attracting attention to data compression methods. To address such a problem, in this paper, we propose a new method for compressing point cloud maps by exploiting the Discrete Fourier Transform (DFT). The proposed technique converts the Digital Elevation Model (DEM) to the frequency-domain 2D image and omits its high-frequency components, focusing on the exploration of gradual terrains such as planets and deserts. Unlike terrains with detailed structures such as artificial environments, high-frequency components contribute little to the representation of gradual terrains. Thus, this method is effective in compressing data size without significant degradation of the point cloud. We evaluated the method in terms of compression rate and accuracy using camera sequences of two terrains with different elevation profiles.

Figures (6)

• Figure 1: Our technique employs Discrete Fourier Transform (DFT) to remove high-frequency components to compress the data size of the point cloud generated by SLAM. In the case of gradual terrains, the removal of high-frequency components has minimal impact, enabling the minimum error in the reconstructed point cloud after the reduction.
• Figure 2: Overview of DEM creation. The projection plane passes through the centroid of the point cloud.
• Figure 3: Frequency-domain image as the output of DFT. $r_M$ is a fixed value for the point cloud, while $r$, the parameter to define the reduction ratio, can take arbitrary values. By varying the value of $r$, the frequency threshold for data reduction can be determined.
• Figure 4: Representative snaps in the MADMAX dataset. (a) A flat sandy terrain with almost no undulations. (b) A terrain with undulations caused by rocks.
• Figure 5: Point cloud maps and robot trajectories are generated for both terrains. From left to right: Original, Cutoff ratio $=$ 0.8, and Cutoff ratio $=$ 0.95. (b) shows an enlarged view of a specific location.