radon (Image Processing Toolbox User's Guide)

Image Processing Toolbox User's Guide

radon

Radon transform

Syntax

```
R = radon(I,theta)
[R,xp] = radon(...)
```

Description

R = radon(I,theta) returns the Radon transform R of the intensity image I for the angle theta degrees.

The Radon transform is the projection of the image intensity along a radial line oriented at a specific angle. If theta is a scalar, R is a column vector containing the Radon transform for theta degrees. If theta is a vector, R is a matrix in which each column is the Radon transform for one of the angles in theta. If you omit theta, it defaults to 0:179.

[R,xp] = radon(...) returns a vector xp containing the radial coordinates corresponding to each row of R.

The radial coordinates returned in xp are the values along the x'-axis, which is oriented at theta degrees counterclockwise from the x-axis. The origin of both axes is the center pixel of the image, which is defined as

```
floor((size(I)+1)/2)
```

For example, in a 20-by-30 image, the center pixel is (10,15).

Class Support

I can be of class double, logical, or any integer class. All other inputs and outputs are of class double.

Example

iptsetpref('ImshowAxesVisible','on')
I = zeros(100,100);
I(25:75, 25:75) = 1;
theta = 0:180;
[R,xp] = radon(I,theta);
imshow(R,[],'Xdata',theta,'Ydata',xp,...
            'InitialMagnification','fit')
xlabel('\theta (degrees)')
ylabel('x''')
colormap(hot), colorbar

See Also

fan2para, fanbeam, ifanbeam, iradon, para2fan, phantom

References

Bracewell, Ronald N., Two-Dimensional Imaging, Englewood Cliffs, NJ, Prentice Hall, 1995, pp. 505-537.

Lim, Jae S., Two-Dimensional Signal and Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1990, pp. 42-45.

Algorithm

The Radon transform of an image is the sum of the Radon transforms of each individual pixel, the superposition principle.

The algorithm first divides pixels in the image into four parts and projects each subdivision separately, as shown in the following figure.

Each pixel's contribution is proportionally split into the two nearest bins, according to the distance between the projected location and the bin centers. If the projection hits the center point of a bin, the bin on the axes gets the full .25 % weight of the pixel. If the projection hits the border between two bins, the bins share half the .25 %.

qtsetblk rangefilt