Digital image reconstruction using Zernike moments
Alfonso Padilla Vivanco, Areli Martinez-Ramirez, Fermin-Solomon S. Granados-Agustin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2004
It is well known that, a piecewise function can be expanded by an orthogonal set of functions. If the expansion coeficients are suitable for a large number of terms, the reconstruction of function can be achieved with high accuracy. However, for a few of them the reconstruction of the input function, in general, is poor. In this work, we reconstruct discrete image functions using the complex Zernike polynomials. We compare the reconstruction of the input image function in two cases. When the input image is mapped inside or outside an unit circle for several expansion orders. To measure the reconstruction we use the relative error between the input and reconstructed images. Also, we show that the relative error can be reduced if the module of the complex discrete distribution of the reconstruction is squared.