Reply to ”Comments on Image Compression and Kriging”, by P. Delfiner

Abstract

A computer image is digital with resolution the resolution imposed by the hardware. Computer images are generated either by scanning an analog image, or by using a camera as input device, or by drawing an image to a pad, or several other means. Appropriate hardware firmware and software is available today by manufactures for converting an analog image to digital. It is well recognized that such a conversion could create aliasing, a phenomenon whereby lines have a staircase syndrome (here by lines we mean straight lines and other lines), and pixels representing small areas of the original analog picture, have undesirable discontinuities. In order for these undesirable discontinuities which are referred to as aliasing, or the phenomenon of aliasing, to be corrected special mathematical filters are applied. These filters take into consideration the fact that pixels are autocorrelated. The filters replace the intensity, or color and intensity, of the pixel with a new color and intensity. The phenomenon of aliasing is common not only when one converts images from analog to digital by inputing them in the computer by some method, but also by using mathematical methods to draw lines or surfaces in the computer, since our mathematical methods usually have as a domain and range a continuous space, but we use the computer screen, which is limited by the number of pixels available and therefore is very discrete, to represent these continuous phenomena. So aliasing is the staircase phenomenon or the undesirable discontinuities created by mapping continuous images into a discrete space. Antialiasing is a mathematical method used to correct for aliasing. Antialiasing methods usually use the values of neighboring pixels to calculate a new value for a pixel. In the space domain the process of antialiasing results in a convolution which if transformed by a Z-transform, or a Fourier transform it becomes a product. Thus it is easier from both the algebraic and computational point of view to deal with antialiasing in the frequency domain, rather than the space domain. The interesting reader could find this information in any signal processing or computer graphics book published after the mid-eighties. What we like to impress upon our readers here is that the antialiasing is a process of improving a digital image and this process has nothing to do with compression, at least as far as we are concerned and the way we use compression in our lab. We hope that our reader agrees that if we continue to use antialiasing in the already antialiased image after a few repetitions all the pixels will converge to the same value.