Clarification needed for RGB -> YCbCr -> RGB conversion

[anandkumarcr]

HI,

I needed a clarification in the conversion of RGB -> YCbCr and resulting YCbCr back to RGB.

The following is the formula I am using to convert RGB -> YCbCr.

Y = (0.257 * R) + (0.504 * G) + (0.098 * B) + 16..................(1)

Cb = -(0.148 * R) - (0.291 * G) + (0.439 * B) + 128..................(2)

Cr = (0.439 * R) - (0.368 * G) - (0.071 * B) + 128....................(3)

And to get back the original RGB from YCbCr I am using the following :-

R = 1.164(Y - 16) + 1.596(Cr - 128)..........................(4)

G = 1.164(Y - 16) - 0.813(Cr - 128) - 0.391(Cb - 128).................(5)

B = 1.164(Y - 16) + 2.018(Cb - 128)....................(6)


However I am getting the following outputs for the following inputs:-

Original R = 187
Original G = 146
Original B = 69

From equations (1),(2),(3) above

Y = 144
Cb = 37
Cr = 51

And on reverting back the YCbCr to obtain the original RGB according to equations (4),(5),(6) -I am getting

Obtained R = 185
Obtained G = 165
Obtained B = -34

Though the obtained RGB is correct according to the calculations, it does not make any sense that it is not equal to the original RGB input and even worse - obtained RGB attains negative values at times.

Could anybody please point out any mistakes or any steps that need to be corrected ?

Thank you

 

[emresel]

Hi;
It seems to me your calculation is somehow wrong. Otherwise equations should be OK.
Could you please share your code? It is Matlab or C?

 

[anandkumarcr]

Hi emresel,

I suppose I have after all made a mistake in equation (2) due to oversight.
Cb = -(0.148 * R) - (0.291 * G) + (0.439 * B) + 128..................(2)
The one marked in red, I had taken it as 0.418 instead of 0.148. So now after rectifying it I seem to be getting the right result.

However I had another question, what is the acceptable range of error in RGB->YCbCr ->RGB conversion. I seem to be getting about a difference of 2-3 units of intensity difference on an average.

Is the error measured in terms of Quantization Error ? Or is there any other metric ?

Thank you.

 

[emresel]

Hi;
If you substitute Y and Cb equations (1 and 3) in equation 4 (reverse R calculation) you can obtain R=R.
(I mean on paper there shouldn’t be any difference like that).
If you consider in matrix form [YCbCr]=A*[RGB], and [RGB]=B*[YCbCr], here B is inv(A). See it.

So may be some kind of rounding error appears in your code.
i.e. check variable types, select them as floating not integer.