Vectorized Computation of Euler Characteristic Functions and Transforms
Jessi Cisewski-Kehe, Brittany Terese Fasy, Alexander McCleary, Eli Quist, Jack Ruder
加权欧拉特性变换(WECT)和欧拉特性函数(ECF)已被证明是各种应用中有用的工具。 然而,目前计算这些函数的方法既没有针对速度进行优化,也没有扩展到更高维度的设置。 在这项工作中,我们提出了使用张量运算计算此类拓扑变换的矢量化框架,该框架针对GPU架构进行了高度优化,并在任意维度的几何简单复合物(或立方体复合物)中完全通用地工作。 在实验上,该框架在计算各种图像数据集的WECT和ECF时,比现有方法显示出显着的加速(高达180×)。 这些变换的计算是在一个名为pyECT的公开可用的Python包中实现的。
The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are neither optimized for speed nor do they scale to higher-dimensional settings. In this work, we present a vectorized framework for computing such topological transforms using tensor operations, which is highly optimized for GPU architectures and works in full generality across geometric si...