Max Zhao

The name is terrain: $f = 1 - 0.62\,(G_{\sigma_1} * L) - 0.30\,(G_{\sigma_2} * L) + \eta$, where $L$ is the letter mask, $G_\sigma$ a Gaussian blur, and $\eta(\mathbf{x}) = \sum_{\mathbf{k}} a_{\mathbf{k}} \cos(\mathbf{k} \cdot \mathbf{x}) + b_{\mathbf{k}} \sin(\mathbf{k} \cdot \mathbf{x})$ a random field whose coefficients follow Ornstein–Uhlenbeck processes, $da_{\mathbf{k}} = -\theta\, a_{\mathbf{k}}\,dt + \sigma\,dW$. Water fills the sublevel set $\{\mathbf{x} : f(\mathbf{x}) \le t\}$, the pixel filtration my flood detection paper runs on radar images. The inset is its persistence diagram, recomputed every frame by union-find: dots are pools ($H_0$), rings are islands ($H_1$), and $\beta_0, \beta_1$ count those alive at the current level $t$. Dragging across the name subtracts a Gaussian from $f$, digging channels and rings.