MATLAB CODE:
figure,imshow(HSI);title('HSI Image');
%Obtain the Hue, Saturation and Intensity components
H1=HSI(:,:,1);
S1=HSI(:,:,2);
I1=HSI(:,:,3);
%Multiply Hue by 360 to represent in the range [0 360]
H1=H1*360;
%Preallocate the R,G and B components
R1=zeros(size(H1));
G1=zeros(size(H1));
B1=zeros(size(H1));
RGB1=zeros([size(H1),3]);
%RG Sector(0<=H<120)
%When H is in the above sector, the RGB components equations are
B1(H1<120)=I1(H1<120).*(1-S1(H1<120));
R1(H1<120)=I1(H1<120).*(1+((S1(H1<120).*cosd(H1(H1<120)))./cosd(60-H1(H1<120))));
G1(H1<120)=3.*I1(H1<120)-(R1(H1<120)+B1(H1<120));
%GB Sector(120<=H<240)
%When H is in the above sector, the RGB components equations are
%Subtract 120 from Hue
H2=H1-120;
R1(H1>=120&H1<240)=I1(H1>=120&H1<240).*(1-S1(H1>=120&H1<240));
G1(H1>=120&H1<240)=I1(H1>=120&H1<240).*(1+((S1(H1>=120&H1<240).*cosd(H2(H1>=120&H1<240)))./cosd(60-H2(H1>=120&H1<240))));
B1(H1>=120&H1<240)=3.*I1(H1>=120&H1<240)-(R1(H1>=120&H1<240)+G1(H1>=120&H1<240));
%BR Sector(240<=H<=360)
%When H is in the above sector, the RGB components equations are
%Subtract 240 from Hue
H2=H1-240;
G1(H1>=240&H1<=360)=I1(H1>=240&H1<=360).*(1-S1(H1>=240&H1<=360));
B1(H1>=240&H1<=360)=I1(H1>=240&H1<=360).*(1+((S1(H1>=240&H1<=360).*cosd(H2(H1>=240&H1<=360)))./cosd(60-H2(H1>=240&H1<=360))));
R1(H1>=240&H1<=360)=3.*I1(H1>=240&H1<=360)-(G1(H1>=240&H1<=360)+B1(H1>=240&H1<=360));
%Form RGB Image
RGB1(:,:,1)=R1;
RGB1(:,:,2)=G1;
RGB1(:,:,3)=B1;
%Represent the image in the range [0 255]
RGB1=im2uint8(RGB1);
figure,imshow(RGB1);title('RGB Image');
Explanation
