Résumé
Indeed, if we consider the real and imaginary parts of the Zernick polynomial of order p and repetition q as two images, then we can notice that there is a close relationship between the correlation value of two images and the expression of the real and imaginary parts of the Zernick moments of an image. Thus, the value of the Zernick moment of an image can be obtained by computing the correlation value between the image under analysis and two other images, one for the real part and another one for the imaginary part. The latter two images that depend on the order p and repetition q of the Zernick moment to compute are gray level images that need to be memorized in the retina. In order to reduce hardware implementation cost they are transformed into binary images or masks using a dithering algorithm. In this way only a 2-bit memory device is required per pixel to memorize the two masks (on bit per mask). Using the binary masks instead of the gray level images only gives an approximate value of the Zernick moments. However, we will show that the approximated values are still a good representation of the analyzed image (and thus can be used in a pattern recognition application). To do so, the exact and approximate values of the Zernick moments for values of p and q ranging from 0 to 30 have been computed and the images reconstructed from these values compared to the original one. The relative errors between the respective reconstructed images (exact and approximated Zernick moments) and the original image have been plotted against the orders of the Zernick moments used in the reconstruction. We have noticed that the evolutions of the error curves are quite similar.