Implementing an algorithm, math error.
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  1. #1
    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. #2
    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. #3
    Join Date
    Jul 2002
    Posts
    2,512

    Re: Implementing an algorithm, math error.

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

  4. #4
    Join Date
    Aug 2000
    Location
    West Virginia
    Posts
    7,564

    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. #5
    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. #6
    Join Date
    Aug 2000
    Location
    West Virginia
    Posts
    7,564

    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. #7
    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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