平稳随机场及其导数的不变联合分布：二维和三维的欧拉特征和临界点计数
The invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D
摘要：
给出了二维和三维各向同性随机场联合概率分布、梯度和Hessian不变量的全矩展开式。它允许显式表达ND中的欧拉特性和作为偏移集阈值和谱参数的函数的极值计数的计算，如模型示例所示。
英文摘要：
The full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian is presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and computation of extrema counts as functions of the excursion set threshold and the spectral parameter, as illustrated on model examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
