20250331_D&A

Image segmentation

E (R) = \sum_{s \in R} (y_{s} - μ_{R})^{2}

with

\begin{aligned} (y_{s} - μ_{R})^{2} & = y_{s}^{2} - 2 y_{s} m y_{R} + μ_{R}^{2} \end{aligned}

\begin{aligned} \sum_{s \in R} (y_{s} - μ_{R})^{2} & = \sum_{s \in R} y_{s}^{2} - 2 \sum_{s \in R} y_{s} m y_{R} + \sum_{s \in R} μ_{R}^{2} \\ = area_square_sum - 2 \cdot mean \cdot area + {mean}^{2} \cdot area \end{aligned}