3D shape classification using the R-transform

The rapid transform is invariant under cyclic shifts. It is used for 3D shape classification. A 3D shape is described by a library of projected views in 2D. Contour points are approximated by piecewise linear segments, and the segment lengths are considered as contour features. The transform coefficients of contour features are invariant under shape translation and rotation, since a rotation in 2D produces a cyclic shift on the feature vector components. This approach makes it possible to compare shape boundaries without the need to generate an exhaustive search to align their feature vectors. The matching algorithm is tested on six classes of aircraft patterns under various resolutions. Computation of the transform involves additions and subtractions, and its complexity is of order n ln(n). The algorithm can easily be implemented in a parallel processor architecture.<>