Proportional convolution filters - an alternative technique for non-distorted image enhancement

Abstract

This paper introduces a new class of spatial filters, here coined the proportional convolution filters. These filters are constructed in such way that the
values assigned to each kernel cell are weighted as a function of the trigonometric distance of the cells to the kernel centre. A set of high-pass and low-pass proportional
filters were designed using a specially tailored algorithm and a Delphi-based code that allows producing multi-dimensional filters. These filters underwent a twofold
test. Firstly, the filters were tested against an instructive digital image of a candle flame. This image was employed as it shows large and detailed variations in color tones
(low frequencies) and an assortment of possible boundaries between tones (high frequencies). Secondly, the filters were applied to a Landsat-5 TM image containing a
variety of landforms. Results showed the efficiency of the filters and the adequacy of an array of kernel sizes to enhance both tonal and edge variations in a digital image,
demonstrating that the proportional filters can benefit numerous applications in several fields of Geosciences.