I have the following weighting function:
$$ w(\rho) = k \cdot(\rho^\alpha)\cdot(1-\rho)^\beta,$$
where $\rho$ represents a pixel value expressed as a
double, i.e., it ranges from $0$ to $1$, and $ 1\le \alpha \le \beta$.
How can I convert this function so that it shows a curve similar to the given one but works for pixel values expressed as
uint8, i.e., ranging from $0$ to $255$?
In the following example of the function I take values $\alpha = 1$; $\beta =6$ and $k =17.6$.