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中心极限定理型随机场的倾斜欧拉示性数密度及其“bubbles”数据应用AI 解读

Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level u chosen to control the tail probability or p-value of its maximum. This p-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above u, denoted $\mathbb{E}\varphi(A_{u})$. Under isotropy, one can use the expansion $\mathbb{E}\varphi(A_{u})=\sum_{k}\mathcal{V}_{k}\rho_{k}(u)$, where $\mathcal{V}_{k}$…

离散采样随机场的最大值及其在面部识别“气泡”技术中的应用AI 解读

A smooth Gaussian random field with zero mean and unit variance is sampled on a discrete lattice, and we are interested in the exceedance probability or P-value of the maximum in a finite region. If the random field is smooth relative to the mesh size, then the P-value can be well approximated by results for the continuously sampled smooth random field (Adler, 1981; Worsley, 1995a; Taylor & Adler, 2003; Adler & Taylor, 2007). If the random field is not smooth, so that…