Moments and moment invariants in the Radon space

•A framework of constructing moments and moment invariants in the Radon space is introduced.•A method to obtain RST and affine invariance of moments in the Radon space is proposed.•The implementation time of the proposed moments can be significantly reduced.•The recognition accuracy of the proposed moments can also be increased.

Radon transform has been acknowledged as the promising solution for image processing due to its high noise robustness and the ability of converting the rotation, scaling and translation operations on a pattern image into translations and scaling in the Radon image. Recently, several transforms widely employed in signal processing have been introduced in images׳ Radon space for pattern recognition. However, moments and especially moment invariants in the Radon space have not been thoroughly investigated. In this paper, we introduce a mathematical framework of constructing moments and moment invariants in the Radon space. First, rotational moments which represent non-orthogonal moments and Legendre–Fourier moments which represent orthogonal moments are introduced in the Radon space respectively. On this basis, we propose a method to obtain rotation, scaling and translation as well as affine invariance of these moments in the Radon space. Second, we prove that the proposed moments in the Radon space can be represented by a linear combination of classical geometric moments. With this property, the implementation time of the moments in the Radon space can be significantly reduced, and the recognition accuracy can also be greatly improved since no numerical approximation is involved. Theoretical and experimental analysis on invariant recognition accuracy, noise robustness, image blur distortion and computational time also shows the superiority of the proposed methods.