论文标题
最小神经图集：具有最小图表和失真的参数化复杂表面
Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion
论文作者
论文摘要
明确的神经表面表示可以以任意精度准确有效地提取编码的表面，以及分析衍生的差异几何特性，例如表面正常和曲率。这种理想的属性在其隐式对应物中没有，它使其非常适合计算机视觉，图形和机器人技术中的各种应用。但是，SOTA的作品在可以有效描述的拓扑的角度受到限制，它引入了重建复杂表面和模型效率的失真。在这项工作中，我们提出了最小的神经图集，这是一种基于ATLA的新型显式神经表面表示。其核心是一个完全可学习的参数域，由在参数空间的开放正方形上定义的隐式概率占用字段给出。相比之下，先前的工作通常预先定义参数域。附加的灵活性使图表能够接收任意拓扑和边界。因此，我们的表示形式可以学习3个图表的最小地图集，这些图表具有任意拓扑表面（包括具有任意连接组件的闭合和开放表面）的最低限度参数化。我们的实验支持了这一假设，并表明，由于对拓扑和几何形状的关注，我们的重建在整体几何形状方面更为准确。
Explicit neural surface representations allow for exact and efficient extraction of the encoded surface at arbitrary precision, as well as analytic derivation of differential geometric properties such as surface normal and curvature. Such desirable properties, which are absent in its implicit counterpart, makes it ideal for various applications in computer vision, graphics and robotics. However, SOTA works are limited in terms of the topology it can effectively describe, distortion it introduces to reconstruct complex surfaces and model efficiency. In this work, we present Minimal Neural Atlas, a novel atlas-based explicit neural surface representation. At its core is a fully learnable parametric domain, given by an implicit probabilistic occupancy field defined on an open square of the parametric space. In contrast, prior works generally predefine the parametric domain. The added flexibility enables charts to admit arbitrary topology and boundary. Thus, our representation can learn a minimal atlas of 3 charts with distortion-minimal parameterization for surfaces of arbitrary topology, including closed and open surfaces with arbitrary connected components. Our experiments support the hypotheses and show that our reconstructions are more accurate in terms of the overall geometry, due to the separation of concerns on topology and geometry.
