cvtColor: CV_RGB2HSV_FULL is inaccurate (Bug #938)

Hi,

I've read the rgb to hsv conversion code, and found some inaccuracies especially with the _FULL mode that uses 0..255 as H range. After doing some tests, I found the biggest error at rgb=(251,2,255), giving an exact h value of 212.66, but computes to 208 by OpenCV.

Some more in-detail code analysis: In color.cpp, function cvtColor():

int hrange = depth CV_32F ? 360 : code CV_BGR2HSV || code CV_RGB2HSV ||
code CV_BGR2HLS || code == CV_RGB2HLS ? 180 : 255;

For _FULL, hrange should be 256 not 255. The actual range will be 0..hrange-1.

See also color.cpp, RGB2HSV_b::operator():

h += h < 0 ? hr : 0;

This should add 256 to negative values. (And could be replaced by h=uchar(h) in this case.)

int hr = hrange, hscale = hr == 180 ? 15 : 21;
...
h = (h * div_table[diff] * hscale + (1 << (hsv_shift + 6))) >> (7 + hsv_shift);

hscale is actually hrange*128/6/255, which evaluates to acceptable 15.05 for hrange=180, but 21.42 for hrange=256, which introduces serious rounding errors. This is the main source of h inaccuracy. Worst case error here is 5*diff*0.42/128, which can be up to +4.18 for the h component.

This can be avoided by using another division table
table[diff] = Round((hrange << shift)/(6.0*diff)), and
h = (h * table[diff] + (1 << (shift-1))) >> shift.
This will also be faster.

In color.cpp, RGB2HSV_b::operator():

s = diff * div_table[v] >> hsv_shift;

This should use rounding, eg. +(1<<(hsv_shift-1)) to avoid embarrassing rounding errors, like rgb=(0,0,9) having saturation 254 instead of 255.