Wavelet transforms and edge detectors on digital images

K e y w o r d s W a v e l e t transforms, Image analysis, Edge detectors. 1. I N T R O D U C T I O N To help motivate this paper, we provide an introduction to some interesting problems in image processing. The second section introduces partial derivatives and how they are applied to the gray level values at the pixel locations. The third section introduces a few specific examples such as the vertical, horizontal, and Soble edge detecting techniques. Sections 4 and 5 introduces some fundamentals about wavelet transforms and leads into image edgers using wavelets. Section 6 provides the reader with a series of pictures that illustrate results in obtaining the edges within the image. 2. S O M E N O T I O N S A N D N O T A T I O N S A current 20 inch monitor displaying a black and white image currently contains pixel locations of 1600 rows and 1200 columns. Of course the number continues to increase everyday as technology progresses. Each pixel location is designated by a rectangular coordinate, (x l ,y l ) , and evaluates a gray level value at that coordinate location indicating the shade of gray. The values are traditionally on a scale of 0 to 255 whereby 0 corresponds to white and 255 correspond to black. The value of the gray level at this coordinate point, (xl,Yl), will be designated by f(xl,yl). 0895-7177/05/$ see front matter @ 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2004.12.002 Typeset by ~4A/tS-~X