Image matching for translation, rotation and uniform scaling by the radon transform

A new technique for matching a 2-D or 3-D image to a translated, rotated, and uniformly scaled reference image is proposed. This method comprises three steps: (1) calculating the Radon transform of the reference image and the images to be matched, (2) calculating the Fourier invariant (FI) descriptor for each 1-D projection image, and (3) matching the FI descriptor in the projection space. The theory shows that information about translation, rotation and uniform scaling of a 2-D or 3-D image can be represented in its 1-D projections; thus a 2-D or 3-D matching can be accomplished as a set of 1-D operations. In particular, the presented technique provides a way to address the 3-D recognition problem when rigid motion is assumed.