论文标题
部分可观测时空混沌系统的无模型预测
Neural Distortion Fields for Spatial Calibration of Wide Field-of-View Near-Eye Displays
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We propose a spatial calibration method for wide Field-of-View (FoV) Near-Eye Displays (NEDs) with complex image distortions. Image distortions in NEDs can destroy the reality of the virtual object and cause sickness. To achieve distortion-free images in NEDs, it is necessary to establish a pixel-by-pixel correspondence between the viewpoint and the displayed image. Designing compact and wide-FoV NEDs requires complex optical designs. In such designs, the displayed images are subject to gaze-contingent, non-linear geometric distortions, which explicit geometric models can be difficult to represent or computationally intensive to optimize. To solve these problems, we propose Neural Distortion Field (NDF), a fully-connected deep neural network that implicitly represents display surfaces complexly distorted in spaces. NDF takes spatial position and gaze direction as input and outputs the display pixel coordinate and its intensity as perceived in the input gaze direction. We synthesize the distortion map from a novel viewpoint by querying points on the ray from the viewpoint and computing a weighted sum to project output display coordinates into an image. Experiments showed that NDF calibrates an augmented reality NED with 90$^{\circ}$ FoV with about 3.23 pixel (5.8 arcmin) median error using only 8 training viewpoints. Additionally, we confirmed that NDF calibrates more accurately than the non-linear polynomial fitting, especially around the center of the FoV.
