python: how to compute the sharpness features of image
What you have implemented is not what the formula denotes, but what you have implemented will return an indication of Sharpness, possibly with some minor modifications.

The formula produces a single $\mathbb{R}$eal number as the ratio of the local sum of laplacians divided by the local mean. "Local" here refers to a square image patch (of some dimensions) centred around pixel $(x,y)$.

If you forget about the division by $\mu$ for a minute, the $LP(x,y)$ is the sum of the "local" second derivatives. This is a $\mathbb{R}$eal number.

The way you have implemented it, the sum operates over the Laplacian of the whole image.

Furthermore, as the Laplacian is a $\mathbb{R}$eal number and the image is a $\mathbb{N}$atural (bounded) number (a.k.a a non-negative integer), you may experience rounding errors. I say "may" because the matrix used by opencv is also based on integers, so the rounding comes into play at a different region.

Evaluating the Laplacian over the whole image is not so much of a "problem" if that sum you used operates across both dimensions. Usually, in platforms such as GNU Octave, MATLAB and others, a single sum over some matrix, operates across one dimension (usually it sums the columns). Therefore, your s would become a vector...not a $\mathbb{R}$eal number.

Hope this helps.