How to calculate the angular error

     The angular error ε is defined as the angular distance between the algorithm’s estimate of the light source (ee) and the true illuminant vector (el) in normalized

     ε= Cos -1(el . ee ) this is the formula for calculation of angular error

This is the formula for calculate the angular error please give the code for that

thanking you

Answer 1

[Roger Stafford]

Apparently you have two 3D vectors, each of unit magnitude, el and ee, and you wish to find the angle between them. One formula would be:

 e = acos(dot(el,ee));

which gives e in radians. Another formula is:

 e = atan2(norm(cross(el,ee)),dot(el,ee));

which also gives e in radians. Furthermore it doesn't require that el and ee have unit magnitude. It is more accurate when e is near 0 or pi where the 'acos' function suffers larger rounding errors.

[Jan]

While I agree with you, the shown formula of Fathima looks more like:

e = cos(-dot(e1, ee))

[Roger Stafford]

No, Jan, I think it is a badly copied minus one superscript and refers to the inverse of the cosine function. It is the only thing that makes sense here.

[Jan]

Thanks, Roger. I've said already, that I agree that your suggestion make sense. But now your explanation where the minus comes from is such obvious that I cannot understand, why it was not clear to me initially.