Radon Transform

R98229029 CHC

2-D Radon Transform

• R = radon(I, theta)

returns the Radon transform R of the intensity image I for the angle theta degrees.

2-D Radon Transform

2-D Radon Transform

2-D Radon Transform

2-D Radon Transform

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3-D Radon Transform

3-D Radon Transform

3-D Radon Transform• function [R,Xp,Yp]=radon3(I,theta,phi)• [yi,xi,zi]=size(I);• x=-floor(xi/2):floor(xi/2);• y=-floor(yi/2):floor(yi/2);• z=-floor(zi/2):floor(zi/2);• [X Y Z]=meshgrid(x,y,z);• theta=rad(theta);phi=rad(phi);• theta=theta/180*pi;phi=phi/180*pi;• X1=cos(phi)*X+sin(phi)*Y;• Y1=-cos(theta)*sin(phi)*X+cos(theta)*cos(phi)*Y+sin(theta)*Z;• Xr=round(X1(:));• Yr=round(Y1(:));• my=min(Yr)-1;• mx=min(Xr)-1;• R=zeros(max(Yr)-my,max(Xr)-mx);• for i=1:length(I(:));• R(Yr(i)-my,Xr(i)-mx)=R(Yr(i)-my,Xr(i)-mx)+I(i);• end• Xp=min(Xr):max(Xr);• Yp=min(Yr):max(Yr);