Decomposition of Neural Discrete Representations for Efficient LiDAR Odometry and Mapping

In this paper, we introduce Decomposition-based Neural Mapping (DN-Map), a storage-efficient large-scale 3D mapping method that employs a quantized neural implicit representation based on a decomposition strategy. This decomposition strategy aims to efficiently capture repetitive and representative patterns of shapes by decomposing each discrete embedding into component vectors that are shared across the embedding space. Our DN-Map optimizes a set of component vectors, rather than entire discrete embeddings, and learns composition rather than indexing the discrete embeddings. By combining these representations with a shallow neural network and an efficient octree-based feature volume, our DN-Map successfully approximates signed distance functions and compresses the feature volume while preserving mapping quality. Furthermore, we extend the proposed representation to real-world scenarios without external pose input by integrating it into a LiDAR odometry and mapping (LOAM) framework, DN-LOAM. In the odometry module, signed distance values are directly retrieved from a pre-computed SDF lookup table, removing the need for neural decoders at inference. Extensive experiments demonstrate that DN-LOAM achieves a $16\times$ reduction in learned embedding storage, $2\times$ faster odometry estimation, and a substantial improvement in mapping accuracy compared to prior work.