A summed [[Area]] tabled is a [[Data Structure]] for getting the sum of values in a rectangular [[Subset|subet]] of a grid, typically an [[Image]]. The recursive definnition to preprocess a summed area table is defined as the following: $\huge S(u,v) = \sum_{i=0}^{u-1}T(i,v) + \sum_{j=0}^{v-1}T(u,j) + S(u-1,v-1) $ $\huge \begin{align} S(u,v) &= \sum_{i=0}^{u-1}T(i,v) + \sum_{j=0}^{v-1}T(u,j) + S(u-1,v-1) \end{align} $ Where $T(i, j)$ is the [[Texel]] [[Vector]] at coordinates $\braket{i,j}$. Where the recursive base case for $S$ is: $\huge S(0,0) = T(0, 0) $ The final table will have the same dimensions as the original image. ![[Pasted image 20251029170645.png|invert_Sepia|300]]