# Implementing an algorithm, math error.

• November 5th, 2009, 08:23 AM
tmaneo
Implementing an algorithm, math error.
Hi, im making a program that can convert RGB to HSI. Hue, Saturation and Intensity.
HSI is abit more complex than HSV and HSB.
Im using OpenCV for doing it. But i however cant used the premade funcs in opencv.

Im loading my input image into a matrix, and im dragging out the rgb-info i want.
Done in a loop for x,y.

i have succesfully made the conversion of S and I, but im stuggling alot with H.

This is the formulas for the conversion:
http://www.xplanet.dk/hsi.jpg

Code equivalent:
Code:

```float H, S, I; I = ((R+G+B)/3); float min=R; if (min>G) min=G; if (min>B) min=B; S = 1-(3*(min/(R+G+B)));```
H, is more complex though. It rely on whether (G>=B) is true or false.
Code:

```if (G>=B) { H = acos((1/2)*(((R-G)+(R-B))/(sqrt(((R-G)*(R-G))+((R-B)*(G-B)))))); cout << "without 360-part H = " << H << endl; //writes the S value } else { H = 360-(acos((1/2)*(((R-G)+(R-B))/(sqrt(((R-G)*(R-G))+((R-B)*(G-B))))))); cout << "360-part H = " << H << endl; //writes the S value }```
when i manually plug in some static RGB values to test if the results is correct, then with (0,255,0) Green i get this:
I=85
S=1
H=1.5708
and the correct results would be:
I=85
S=1
H=120

so my question is, have I implemented it wrong in c++ ?
and how is the right way?

also i have found another formula of the H-part, but i think its the same, though im not sure how to implement the squared part. but its on this link: http://www5.informatik.tu-muenchen.d...csc/COL_24.htm
• November 5th, 2009, 08:28 AM
tmaneo
Re: Implementing an algorithm, math error.
Im using codeblocks though, but quite sure it has nothing to do with the program, but error in the c++ language ive made.
• November 5th, 2009, 08:29 AM
Alex F
Re: Implementing an algorithm, math error.
cos^(-1) from the formula is not acos. you need 1/cos(...).
• November 5th, 2009, 08:38 AM
Philip Nicoletti
Re: Implementing an algorithm, math error.
1) You do the following:

Code:

`(1/2)`
This will do integer arithmetic (giving a value of 0). Change to:
Code:

`1.0 / 2.0  (or 0.5)`
2) acos returns the value in radians , not degrees
Code:

```H = acos((1.0/2.0)*(((R-G)+(R-B))/(sqrt(((R-G)*(R-G))+((R-B)*(G-B)))))); H = H *180 / 3.14159; cout << "without 360-part H = " << H << endl; //writes the S value```
The second part will have a similar problem
• November 5th, 2009, 08:40 AM
tmaneo
Re: Implementing an algorithm, math error.
if i write "1/cos" it just returns "1" on a 0,255,0 green. Where it should return a 120 value.
Code:

`H = 1/cos((1/2)*(((R-G)+(R-B))/(sqrt(((R-G)*(R-G))+((R-B)*(G-B))))));`
• November 5th, 2009, 08:45 AM
Philip Nicoletti
Re: Implementing an algorithm, math error.
1) The inverse cosine is the arc-cosine ... you were correct on that.

2) see my previous post
• November 5th, 2009, 08:51 AM
tmaneo
Re: Implementing an algorithm, math error.
Yes, i crossposted, but thanks alot. Changing the &#189; to your suggestions and making radians to degrees did the trick.
Code:

```//Calculating "H" Hue if (G>=B) { H = acos((1.0/2.0)*(((R-G)+(R-B))/(sqrt(((R-G)*(R-G))+((R-B)*(G-B)))))); H = H *180 / 3.14159; cout << "without 360-part H = " << H << endl; //writes the S value } else { H = (acos((1.0/2.0)*(((R-G)+(R-B))/(sqrt(((R-G)*(R-G))+((R-B)*(G-B))))))); H = 360-(H *180 / 3.14159); cout << "360-part H = " << H << endl; //writes the S value }```