i'm reading a paper Polynomial Shape from Shading about the SFS problem. And it's written in this paper as the following: the discrete partial derivatives.
it makes me confused since we know that: $$\begin{align}&\frac{\partial f(x,y)}{\partial x}\approx \frac{f(x+\delta x,y)-f(x,y)}{\delta x},\\&\frac{\partial f(x,y)}{\partial y}\approx \frac{f(x,y+\delta y)-f(x,y)}{\delta y}.\end{align}$$ So i searched its references and found that in Shape from shading using linear approximation: discrete approximations .
My problem is: why don't the formulas in these two paper divide by $\delta x$ or $\delta y$? Since it's pixel coordinates?