Modern
imaging relies heavily on digital image manipulation.
The algorithms to enhance pictures or to automatically
detect items in pictures are all inherently
mathematical.
Jean Baptiste Joseph Fourier(French,
1768-1830) lends his name to one
of the most important techniques in image
processing, Fourier Transforms, which
converts images (or signals in general)
into frequency representations. This alternate
view of images makes it easier to analyze
and manipulate the data mathematically.
The general one-dimensional Fourier ransform
of a function x(t) is:
For image processing,
we require a two-dimensional variation:
Fast Fourier
Transforms (FFT) are versions of the general
Fourier Transforms where the mathematics
is broken into portions (discretized)
to allow efficient computation on computers.
Euclid
of Alexandria(Greek, 325
– 265 BC) wrote the earliest
book on Geometric Optics (300 BC). His
principles still survive today.
