Zernike moments are operators that are often used in the field of image analysis and pattern recognition. A certain number of retina chips that implement geometrical moment function have already beeen described in the litterature. However, the architectures of these circuits are not programmable so that their field of application is limited to position detection of an object and they are not suitable for pattern recognition.
In our paper, we propose a method and its implementation in a programmable retina circuit that allows us to compute, with the same circuit, Zernike moment values of different orders and repetitions. Our method is based on the measurement of the correlation value between two binary masks (memorized in memory devices integrated at the pixel level on the sensor) and an image to analyze, projected onto the sensor by optical means 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.
In the final paper we will also present the architecture of the CMOS retina circuit that implements the Zernike moment computation function as well as the simulation results. The circuit has been designed in standard 0.35µm CMOS technology and it is composed of an array of 180 x 180 pixels.