Special Functions

cyl(r)cone(r)exponential(r)gauss(r)
airy(r)sinc(r)^2(sinc(x)*sinc(y))^2tri(x)*tri(y)

source code: imdemo.cpp

The domain of these images is -2 <= (x, y) < 2

log image display

The sinc and airy functions above have a ring structure which can be seen more clearly by taking the logarithm of the image. The method is

v = (v>0.0? 1.0+log10(v)/decades: 0.0);

where v is a pixel value and decades is the number of decades to stretch.

The images below were stretched with decades = 3

airy(r)sinc(r)^2(sinc(x)*sinc(y))^2

source code for logarithmic enhancement: logim.cpp

expanded range

The ring structure in the above images extends much further than the domain of those images. We can use imdemo to produce images over a larger range. We also make the images themselves bigger. For the airy function, the following commands were used.

imdemo 4 bigdemo4.img 256 10
logim bigdemo4.img 3

The domain is now -5 <= (x, y) < 5

airy(r)sinc(r)^2(sinc(x)*sinc(y))^2


Written by: John Loomis
E-Mail address: John.Loomis@notes.udayton.edu
Last updated: 17 Oct 1996