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Radon Transform

The radon function in the Image Processing Toolbox computes projections of an image matrix along specified directions. A projection of a two-dimensional 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, parallel-beam 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.

Parallel-Beam Projection at Rotation Angle Theta

For example, the line integral of f(x,y) in the vertical direction is the projection of f(x,y) onto the x-axis; the line integral in the horizontal direction is the projection of f(x,y) onto the y-axis. The following figure shows horizontal and vertical projections for a simple two-dimensional function.

Horizontal and Vertical Projections of a Simple Function

Projections can be computed along any angle theta. 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

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