IJPAM: Volume 46, No. 2 (2008)

Invited Lecture Delivered at
Forth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)


John Schmeelk
Department of Mathematical Sciences
Virginia Commonwealth University
P.O. Box 8095, Doha, QATAR
e-mail: jschmeelk@qatar.vcu.edu

Abstract.This is an expansion of my previous presentation in our Third International Conference of Applied Mathematics and Computing in 2006 in Plovdiv. Again, filter design is an integral component to enhance desired aspects within an image such as clarity of edges. This paper provides an introduction to filter design and image edge detection using matrices, partial derivatives, convolutions and frequencies that enter into identifying components in the problem. We are especially addressing the notion of edge detection, which has far reaching applications in all areas of research, including medical research. For example a patient can be diagnosed as having an aneurysm by studying an angiogram. An angiogram is the visual view of the blood vessels whereby the edges are highlighted. This process is completed through convolution, filters and special frequency techniques using the software, MATLAB 7.2 (2006). Some illustrations included will be vertical, horizontal and Sobel Edge Detectors together with some wavelet transforms to locate the edges in an image. We also include the Fast Fourier Transform to obtain the frequency space together with filtering such as the use of the Ideal Filter, Butterworth Filter and Bessel Function Filter.

Received: August 17, 2007

AMS Subject Classification: 68U10

Key Words and Phrases: edge detection in images, filter design, wavelet transforms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2