Line integral with given midpoint and radius of a circle. Daugmans algorithm

Question

I am trying to realize the daugman algorithm in java code. While reviewing the formula I found a line integral with a mid point and a radius as parameters. Now I am trying to understand how to calculate this integral. $$ \oint\limits_{x0, y0, r}^{} \frac{I(x,y)}{2πr} ds $$ (x0,y0) is the center and r the radius. I(x,y) is the Image with pixelvalues. Can anyone explain how to calculate this?

Answer 1

$$ \mathop{\oint}_{s(t)=(x_0+i y_0)+re^{it}}\frac{I(x,y)}{2\pi r}ds=\\ \frac{1}{2\pi r}\int_0^{2\pi} I\bigg(g(t),h(t)\bigg)\sqrt{(g')^2+(h')^2}dt $$ where $g(t)=\text{Re}[s(t)]$ and $h(t)=\text{Im}[s(t)]$.