cv.COLOR_BGR2LAB gives wrong range

Question

within the following code, I use a png image 4096*4096 pixels which includes every possible RGB colors (not twice the same pixel, can be found here http://allrgb.com/starry-night) Then I convert the RGB values to LAB values and I check the range of each of the channels

import cv2 as cv
import numpy as np

im=cv.imread('allrgb.png')


im=im.astype(np.uint8)

colors_lab=cv.cvtColor(im,cv.COLOR_BGR2LAB)

m=np.amin(colors_lab[...,...,0])    

The results are the following :

if the original image has type uint8, R[0,255],G[0,255],B[0,255] gives L[0,255],A[42,226],B[20,223]

if the original image has type float32, R[0,1],G[0,1],B[0,1] gives L[0,100],A[-86.1813,98.2351],B[-107.862,94.4758]

In any case, the Lab range is never the expected one, which is given by open CV documentation

Any idea how to explain that ?

Answer 1

The LAB values returned from OpenCV will never lie outside the ranges 0 ≤ L ≤ 100, -127 ≤ a ≤ 127, -127 ≤ b ≤ 127 when converting float images (OpenCV color conversions). When converting 8-bit images, the range of L is multiplied by 255/100, and a and b get an offset of 128 to fill out the 8-bit range.

But no matter the image data type: the LAB color space's gamut exceeds the one of RGB color spaces, see for example the second paragraph in the wikipedia article on LAB.

Thus, when you convert from RGB/BGR to LAB, you will never get the full LAB range, as LAB contains colors that can't be represented in RGB.