Convert RGB to HSI

I am looking for the values in the first row of S of an HSI color model. Unfortunately, I do not get the desired values. I assume it is my conversion from rgb to hsi. Instead I use rgb2hsv. Does this make any difference?

R = [ 120 20 30;
   170 20 70;
  120 140 70 ]

G = [ 40 150 20;
   20 110 20;
   25 20 20 ]

B = [20 60 150;
    190 20 250;
    20 30 40]

I = zeros(3,3,3);
I(:, :, 1) = R;
I(:, :, 2) = G;
I(:, :, 3) = B;

Ir = rgb2hsv(I);
S = Ir(1,:,2)

% Desired output:
% [0.67 0.74 0.70]

%My output:
% [0.83 0.87 0.87 ]

Answer 1

[DGM]

Yes, it makes a difference. Compare the results for HSI, HSL and HSV:

R = [ 120 20 30;
    170 20 70;
    120 140 70 ];
G = [ 40 150 20;
    20 110 20;
    25 20 20 ];
B = [20 60 150;
    190 20 250;
    20 30 40];

rgb = uint8(cat(3,R,G,B));
hsi = rgb2hsi(rgb);
hsl = rgb2hsl(rgb);
hsv = rgb2hsv(rgb);

% the vector of interest
hsi(1,:,2)

ans =

0.6667 0.7391 0.7000

hsl(1,:,2)

ans =

0.7143 0.7647 0.7647

hsv(1,:,2)

ans =

0.8333 0.8667 0.8667

MATLAB/IPT does not have tools for HSI or HSL conversions. The HSI/HSL conversion tools I used are found here. There are also others on the File Exchange, though be aware that Pascal Getreuer's popular Colorspace Transformations has a bug in the HSI path and will give the incorrect results.