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# Thread: Implementing an algorithm, math error.

1. Junior Member
Join Date
Nov 2009
Posts
7

## 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:

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

2. Junior Member
Join Date
Nov 2009
Posts
7

## 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.

3. ## Re: Implementing an algorithm, math error.

cos^(-1) from the formula is not acos. you need 1/cos(...).

4. Elite Member Power Poster
Join Date
Aug 2000
Location
West Virginia
Posts
7,716

## 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

5. Junior Member
Join Date
Nov 2009
Posts
7

## 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))))));`

6. Elite Member Power Poster
Join Date
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Location
West Virginia
Posts
7,716

## Re: Implementing an algorithm, math error.

1) The inverse cosine is the arc-cosine ... you were correct on that.

2) see my previous post

7. Junior Member
Join Date
Nov 2009
Posts
7

## 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
}```

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