Neural 3D implicit representations learn priors that are useful for diverse applications, such as single- or multiple-view 3D reconstruction. A major downside of existing approaches while rendering an image is that they require evaluating the network multiple times per camera ray so that the high computational time forms a bottleneck for downstream applications. We address this problem by introducing a novel neural scene representation that we call the directional distance function (DDF). To this end, we learn a signed distance function (SDF) along with our DDF model to represent a class of shapes. Specifically, our DDF is defined on the unit sphere and predicts the distance to the surface along any given direction. Therefore, our DDF allows rendering images with just a single network evaluation per camera ray. Based on our DDF, we present a novel fast algorithm (FIRe) to reconstruct 3D shapes given a posed depth map. We evaluate our proposed method on 3D reconstruction from single-view depth images, where we empirically show that our algorithm reconstructs 3D shapes more accurately and it is more than 15 times faster (per iteration) than competing methods.

翻译：神经3D隐式表示能够学习适用于多种应用（如单视图或多视图3D重建）的先验知识。现有方法在渲染图像时的主要缺陷在于，每条相机光线需要多次评估网络，导致高计算开销成为下游应用的瓶颈。针对此问题，我们提出了一种新型神经场景表示——方向距离函数（DDF）。我们通过联合学习符号距离函数（SDF）与DDF模型来表征形状类别。具体而言，DDF定义在单位球面上，可预测任意给定方向到表面的距离，因此每条相机光线仅需一次网络评估即可完成图像渲染。基于所提出的DDF，我们进一步设计了快速算法（FIRe），用于从带姿态的深度图中重建3D形状。在单视图深度图像三维重建任务上的实验表明，本算法不仅能更精确地重建3D形状，且每轮迭代速度较竞争方法提升15倍以上。