Neural implicit surface representations are currently receiving a lot of interest as a means to achieve high-fidelity surface reconstruction at a low memory cost, compared to traditional explicit representations.However, state-of-the-art methods still struggle with excessive memory usage and non-smooth surfaces. This is particularly problematic in large-scale applications with sparse inputs, as is common in robotics use cases. To address these issues, we first introduce a sparse structure, \emph{tri-quadtrees}, which represents the environment using learnable features stored in three planar quadtree projections. Secondly, we concatenate the learnable features with a Fourier feature positional encoding. The combined features are then decoded into signed distance values through a small multi-layer perceptron. We demonstrate that this approach facilitates smoother reconstruction with a higher completion ratio with fewer holes. Compared to two recent baselines, one implicit and one explicit, our approach requires only 10\%--50\% as much memory, while achieving competitive quality.

翻译：神经隐式表面表示因其能以较低内存成本实现高保真表面重建而备受关注，相较于传统显式表示方法具有显著优势。然而，现有先进方法仍面临内存占用过高和表面不光滑等挑战，这在大规模稀疏输入场景（如机器人应用中常见）中尤为突出。针对这些问题，我们首先提出一种稀疏结构——三叉四叉树，通过存储在三个平面四叉树投影中的可学习特征来表示环境。其次，我们将可学习特征与傅里叶特征位置编码相级联，并通过小型多层感知器将联合特征解码为符号距离值。实验表明，该方法能实现更平滑的重建，并具有更高的补全率和更少的空洞。与两种近期基线方法（一种隐式方法、一种显式方法）相比，我们的方法在保持竞争性质量的同时，内存占用仅需其10%至50%。