Deep Imbalanced Multi-Target Regression: 3D Point Cloud Voxel Content Estimation in Simulated Forests

Voxelization is an effective approach to reduce the computational cost of processing Light Detection and Ranging (LiDAR) data, yet it results in a loss of fine-scale structural information. This study explores whether low-level voxel content information, specifically target occupancy percentage within a voxel, can be inferred from high-level voxelized LiDAR point cloud data collected from Digital Imaging and remote Sensing Image Generation (DIRSIG) software. In our study, the targets include bark, leaf, soil, and miscellaneous materials. We propose a multi-target regression approach in the context of imbalanced learning using Kernel Point Convolutions (KPConv). Our research leverages cost-sensitive learning to address class imbalance called density-based relevance (DBR). We employ weighted Mean Saquared Erorr (MSE), Focal Regression (FocalR), and regularization to improve the optimization of KPConv. This study performs a sensitivity analysis on the voxel size (0.25 - 2 meters) to evaluate the effect of various grid representations in capturing the nuances of the forest. This sensitivity analysis reveals that larger voxel sizes (e.g., 2 meters) result in lower errors due to reduced variability, while smaller voxel sizes (e.g., 0.25 or 0.5 meter) exhibit higher errors, particularly within the canopy, where variability is greatest. For bark and leaf targets, error values at smaller voxel size datasets (0.25 and 0.5 meter) were significantly higher than those in larger voxel size datasets (2 meters), highlighting the difficulty in accurately estimating within-canopy voxel content at fine resolutions. This suggests that the choice of voxel size is application-dependent. Our work fills the gap in deep imbalance learning models for multi-target regression and simulated datasets for 3D LiDAR point clouds of forests.

Sparse canonical correlation analysis

Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vectors and show how to solve it efficiently using linearized alternating direction method of multipliers (ADMM) and using TFOCS as a black box. We illustrate this idea on simulated data.