On the connection between the Zernike moments and Radon transform of an image

Authors:
Ned C. Rouze;Victor C. Soon;Gary D. Hutchins
Affiliations:
Indiana University School of Medicine, Department of Radiology, Division of Imaging Science, 950 W. Walnut, R2 E124, Indianapolis, IN 46202, USA;Indiana University School of Medicine, Department of Radiology, Division of Imaging Science, 950 W. Walnut, R2 E124, Indianapolis, IN 46202, USA;Indiana University School of Medicine, Department of Radiology, Division of Imaging Science, 950 W. Walnut, R2 E124, Indianapolis, IN 46202, USA
Venue:
Pattern Recognition Letters
Year:
2006

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Abstract

We describe a simple and direct method to calculate the Zernike moments of an image from its Radon transform using a polynomial transform in the position coordinate and a Fourier transform in the angular coordinate. The transform allows the estimation of image moments from measured sinogram data without the need for matrix inversion or the intermediate step of image reconstruction. The transform is invertible and, thereby, gives insight into the connection between image moments and tomographic image reconstruction. It also suggests an alternative method for the efficient computation of Zernike moments of an image.