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：神经隐式曲面表示作为一种以低内存成本实现高保真曲面重建的方法，目前正受到广泛关注。然而，现有方法仍面临内存使用过度和曲面不平滑的问题，这在稀疏输入的大规模应用场景（如机器人领域常见情况）中尤为突出。为解决这些问题，我们首先引入一种稀疏结构——三叉四叉树，该结构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进行拼接。随后，通过一个小型多层感知器将组合特征解码为符号距离值。我们证明，该方法有助于实现更平滑的重建，具有更高的完整率和更少的空洞。与近期两个基线方法（一个基于隐式表示，一个基于显式表示）相比，我们的方法仅需其10%–50%的内存消耗，同时达到具有竞争力的重建质量。