Image Processing Toolbox User's Guide 
Radon Transform
The radon
function in the Image Processing Toolbox computes projections of an image matrix along specified directions. A projection of a twodimensional function f(x,y) is a set of line integrals. The radon
function computes the line integrals from multiple sources along parallel paths, or beams, in a certain direction. The beams are spaced 1 pixel unit apart. To represent an image, the radon
function takes multiple, parallelbeam projections of the image from different angles by rotating the source around the center of the image. The following figure shows a single projection at a specified rotation angle.
ParallelBeam Projection at Rotation Angle Theta
Note
For information about creating projection data from line integrals along paths that radiate from a single source, called fanbeam projections, see FanBeam Projection Data. To convert parallelbeam projection data to fanbeam projection data, use the para2fan function.

For example, the line integral of f(x,y) in the vertical direction is the projection of f(x,y) onto the xaxis; the line integral in the horizontal direction is the projection of f(x,y) onto the yaxis. The following figure shows horizontal and vertical projections for a simple twodimensional function.
Horizontal and Vertical Projections of a Simple Function
Projections can be computed along any angle . In general, the Radon transform of f(x,y) is the line integral of f parallel to the y´axis
The following figure illustrates the geometry of the Radon transform.
Geometry of the Radon Transform
DCT and Image Compression  Plotting the Radon Transform 
© 19942005 The MathWorks, Inc.