Image analysis by circularly semi-orthogonal moments

• A kind of circular moments named circularly semi-orthogonal moment is proposed.
• It outperforms in image reconstruction over the circularly orthogonal moments.
• It performs better in invariant image recognition under noisy and smooth distortions.

Various types of circularly orthogonal moments have been widely used for image reconstruction and rotation invariant classification. However, they suffer from two errors namely numerical integration error and geometric error, which affect their reconstruction capability and pattern recognition accuracy. In this paper, a novel category of circular moments named circularly semi-orthogonal moments is proposed. In the proposed moment, a set of orthogonal basis functions modulated by a negative power exponential envelope is utilized as the radial basis function. For a given degree n, the radial basis function possesses more compact bandwidth, less cutoff frequency and more zeros compared with the frequently-used circularly orthogonal moments including Zernike and orthogonal Fourier–Mellin moments, and so the circularly semi-orthogonal moment calculated with the zeroth order approximation is more robust to numerical error than the frequently-used circularly orthogonal moments. Furthermore, the capability of the semi-orthogonal moment to describe high spatial frequency components of images is relatively higher than that of the frequently-used circularly orthogonal moments. Experimental results demonstrate that the semi-orthogonal moments calculated with the zeroth order approximation perform better than the frequently-used circularly orthogonal moments in terms of image reconstruction capability and invariant recognition accuracy in noise-free, noisy and smooth distortion conditions. It is also shown that the proposed high order moments are more numerically stable than the circularly orthogonal moments.