Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of values, we are forced to sample densely from INRs to perform visualization tasks like iso-surface extraction which can be very computationally expensive. Recently, range analysis has shown promising results in improving the efficiency of geometric queries, such as ray casting and hierarchical mesh extraction, on INRs for 3D geometries by using arithmetic rules to bound the output range of the network within a spatial region. However, the analysis bounds are often too conservative for complex scientific data. In this paper, we present an improved technique for range analysis by revisiting the arithmetic rules and analyzing the probability distribution of the network output within a spatial region. We model this distribution efficiently as a Gaussian distribution by applying the central limit theorem. Excluding low probability values, we are able to tighten the output bounds, resulting in a more accurate estimation of the value range, and hence more accurate identification of iso-surface cells and more efficient iso-surface extraction on INRs. Our approach demonstrates superior performance in terms of the iso-surface extraction time on four datasets compared to the original range analysis method and can also be generalized to other geometric query tasks.

翻译：隐式神经表示（INR）通过建模将空间位置映射到数据值的函数，广泛应用于科学数据缩减与可视化。由于缺乏对数值空间分布的预先知识，我们被迫对INR进行密集采样以执行等值面提取等可视化任务，这可能导致极高的计算成本。近年来，范围分析通过使用算术规则约束网络在空间区域内的输出范围，在提升3D几何INR的几何查询（如光线投射与分层网格提取）效率方面展现出良好前景。然而，该分析对复杂科学数据的范围约束往往过于保守。本文通过重新审视算术规则并分析网络输出在空间区域内的概率分布，提出一种改进的范围分析技术。我们应用中心极限定理，将该分布高效建模为高斯分布。通过排除低概率值，我们能够收紧输出范围，从而更精确地估计数值范围，进而更准确地识别等值面单元并实现更高效的INR等值面提取。在四个数据集上，我们的方法在等值面提取时间方面均优于原始范围分析方法，且可泛化至其他几何查询任务。