Pyramid of Filters - Fast Image Filtering without FFT

Abstract

Methods of computer graphics which had already become common in design of new optical systems and materials find currently new applications such as stomatology and ophthalmology. Some modern imaging systems are now designed in conjunction with the human vision system which is at their end. Asa result simulation of the effects of human vision becomes necessary. These include partial defocusing and resulting "blur" of image, scattering and halo/corona and so on. Such effects are usually simulated convolving the original, "ideal" image with the pixel spread function. The latter frequently has size about that of the source image, so straightforward calculation of convolution would take a giant number of operations. Therefore in case of high resolution a decent speedis usually achieved by using the Fast Fourier Transform (FFT) for convolution,but since FFT operates periodic functions on a lattice with resolution being an integer power of a prime numbers, the required working resolution may considerably increase that of the original image and required memory becomes inadmissible. This paper presents an alternative method that allows calculations in much smaller memory avoiding overheads introduced by FFT requirements.