numpy transforming RGB image to YIQ color space

Question

For a class, I need to transform RGB image into YIQ. We have been told that the conversion can be made by:

I started to write a messy code with loops to have the matrix multiplication and then I found out a function

 skimage.color.yiq2rgb(imYIQ)

and when I looked inside to see what they were doing I saw the following (I'm copying stuff so it will be more clear):

yiq_from_rgb = yiq_from_rgb = np.array([[0.299,      0.587,        0.114],
                                 [0.59590059, -0.27455667, -0.32134392],
                                 [0.21153661, -0.52273617, 0.31119955]])
return np.dot(arr, yiq_from_rgb.T.copy())

when arr is just the RGB pic as a matrix

I'm trying to understand why this works? why do they take the Transpose matrix? (.T) And how exactly does the dot product work when the arr shape is different than the yiq_from_rgb?

Answer 1

In your reference figure containing the matrix for the conversion, the transformation matrix is on the left of the RGB channels. So, for the first pixel in your RGB image, let's call it (p1r, p1g, p1b) corresponding to R, G, B channels respectively, we need to multiply with the transformation matrix and sum the results like:

y1y = (0.299*p1r + 0.587*p1g + 0.114*p1b)
y1i = (0.596*p1r - 0.275*p1g - 0.321*p1b)
y1q = (0.212*p1r - 0.523*p1g + 0.311*p1b)

where (y1y,y1i,y1q) is the value for the first pixel in the resulting YIQ image, after rounding/taking int. We do the same kind of multiplication for all the pixels in the whole RGB image and obtain the desired YIQ image.

Now, since they do this whole implementation using np.dot(arr, yiq_from_rgb.T), to have the weighting work out correctly the transformation matrix needs to be transposed. And copy is just to have a dedicated of the transposed transformation matrix for the purpose of this conversion.

Also, notice that contrary to your figure, in np.dot() the RGB array is on the left of transformation matrix.