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.
翻译:清晰的神经表面表层显示能够以任意的精确度精确和精确度精确和高效地提取编码的表面表面,以及分析地衍生不同的几何特性,例如表面正常度和曲度。这些可取的特性,在其隐含对应物中不存在,使它在计算机视觉、图形和机器人方面的各种应用成为理想。然而,SOTA的工程在它能够有效描述的地形学方面是有限的,它为重建复杂的表面和模型效率而引入的。在这项工作中,我们展示了一个以新颖的星系为基础的神经图集,这是一个新的星系直露的神经表面表层表示。核心是一个完全可以学习的准参数领域,其特点是在参数空间的开放方形上界定了一个隐含的概率占用场。相比之下,先前的工程通常预设了参数域。增加的灵活性使图表能够接受任意的地形学和界限。因此,我们的代表可以学习一个小于三个海图的最小的地图集,其中含有扭曲-最小的参数,包括封闭和开放的表面与任意连接的部件。我们的实验支持各种假设,并显示我们的地理测量学上最精确地貌。