Math of Image processing

Intro

Digital image processing is almost everywhere, from smartphones to computers, with installed programs or online services. Images can be reszied, their contrast and brightness can be changed and much more. Behind many of these algorithms is rather simple mathematics.

Images are composed of pixels, tiny squares that have the same colour. In gray scale images every pixel has just one brightnessvalue that can be described by a number: Usually 0 stands for black and 100 (in this page) or 255 (in many computer programs) stands for white, with values in between for different shades of grey.

For some operations one needs to know about the coordinate system to find the place of a particular pixel.

Algorithms

The following distinguishes several types of image processing algorithms.

One-Pixel-Algorithms: Each pixel stays at its place and only its brightness/colour is modified. [One Pixel] , [Colour version]
Transformationen: Pixels on the move. [Transformation]
Convolution. Taking neighbouring pixels into account. [Convolution]
Combination: Two images are combined. [Combination]
Function composition. Two functions are applied in turn [Composition]
Animationen. Time depened pictures. [Animationen - one Pixel] , [Animationen - Colour] , [Animationen Transformation]

Image stream of a wewbcam

The stream of a WebCam is a function that assigns each time t an image B(t) .
HTML5-Applet: Webcam stream .

Information

Idea: Reinhard Oldenburg, Programming: Reinhard Oldenburg and Niklas Ahlers