python: how to compute the sharpness features of image

Question

I am extracting the sharpness features of image as shown in the following image mentioned in a paper.

I have done with the following code. Firstly, use the open cv convert the RGB to HSL (luminance is L mentioned in the paper), then get L array. and then used the Laplacian operator to get the LP. Finally, obtain the sharpness value of image based on mathematical form in the paper.

img_HLS = cv2.cvtColor(image, cv2.COLOR_BGR2HLS)
L = img_HLS[:, :, 1]
u = np.mean(L)
LP = cv2.Laplacian(L, cv2.CV_16S, ksize = 3)  
s = np.sum(LP/u) 

I don't know my solution is right or wrong, if there is problem, please help me correct it. Thank!

Answer 1

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.