Multimedia Tools and Applications

, Volume 57, Issue 1, pp 29–48 | Cite as

On invariance analysis of Zernike moments in the presence of rotation with crop and loose modes

  • Shijun XiangEmail author


Zernike moments are widely applied in digital image processing fields based on many desirable properties, such as rotational invariance, noise robust and efficient representation of pattern. On the computational analysis of Zernike moment is challenging issue. From an algorithmic aspect, in this paper we investigate the effect of image rotation (including crop rotation and loose rotation) operations on Zernike moments in both theoretical and experimental ways. For the crop rotation, we suggest to extract the Zernike moments by mapping the image over a disc instead of inside a circle since the outside of an image after the crop rotation will be distorted. Referring to the loose rotation, we propose a preprocessing step (which is called image size normalization) to embed an image and its rotated versions into a predefined size of zero-value image in such a way that the effect of image size change due to loose rotation can be eliminated. By incorporating the proposed image size normalization operation, we introduce an effective extraction method of image Zernike moments against loose rotation operation. Experimental results show the validity of the proposed extraction method.


Digital image Loose rotation Crop rotation Zernike moments 



This work was supported in part by NSFC (No. 60903177), in part supported by Ph.D. Programs Foundation of Ministry of Education of China (No. 200805581048), the Fundamental Research Funds for the Central Universities (No. 21609412), and the Project-sponsored by SRF for ROCS, SEM (No. [2008]890). The author appreciates the anonymous reviewers for their valuable comments.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Electronic Engineering, School of Information Science and TechnologyJinan UniversityGuangzhouChina

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