20-10-2012, 06:05 PM
Edge Detectors in Image Processing
Edge Detectors.pdf (Size: 678.55 KB / Downloads: 71)
Abstract
Image edge detection is an integral
component of image processing to enhance the clarity
of edges and the type of edges. My previous paper15
began to discuss the issues regarding edge techniques.
This paper provides a deeper analysis regarding image
edge detection using matrices, partial derivatives,
convolutions and the software’s, MATLAB 7.9.0 and
the MATLAB Image Processing Toolbox 6.4. Edge
detection has applications in all areas of research such
as medicine. A patient can be diagnosed with an
aneurysm, by studying an angiogram. An angiogram
is the visual view of the blood vessels and illustrated
in Figure 1(VascularWeb image). The previous paper
15 studied alphabets using vertical, horizontal and
Sobel transforms. This paper will study images to
include the alphabet O and two images, Cameraman
and Rice included in the Image Processing Toolbox
6.4. We then compare the techniques implemented in
the previous paper15 and the images, alphabet O,
Cameraman and Rice using vertical, horizontal, Sobel,
and Canny transforms implementing the software’s
MATLAB 7.9.0 and the Image Processing Toolbox
6.4.
Introduction
To help motivate this paper, we provide an
introduction to the edger problem in image processing
implementing matrix techniques, partial derivatives
and convolutions. Section (2) provides an introduction
to matrix and partial derivatives and how they are
applied to the pixels to obtain the gray level value in
black and white images. Section (3) introduces the
mathematical requirements for a few specific
examples such as the vertical, horizontal and Sobel
edge detectors. Section (4) provides the reader with a
series of illustrations that demonstrate edging
techniques in a three-dimensional image, and images
directly taken from a camera. We compare results
developing mathematical procedures to include
convolutions using MATLAB 7.9.0 vs using. the
Image Processing Toolbox 6.4.
Some Notions and Notations
A current laptop in advertisements displays an image
using 1680 x1050 pixels. The number of pixels
continues to increase everyday as technology
progresses. Therefore the resolution of the images
continues to improves. Each pixel location designated
by the coordinates, (x1, y1), contains a gray level value
indicating the shade of gray within the image at that
point. The values are 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 lattice point, (x1, y1),
will be designated by f(x1, y1). Before we continue
with the edge detection analysis, we briefly review a
few matrix and calculus techniques.
Conclusion
As seen by the previous images the mathematical development techniques briefly discussed in sections 3-4 illustrated strong edges. The image toolkit without any further enhancement techniques included in the tool kit somewhat submerges the clarity of the edges. However the particular application being used by the researcher must review both techniques to identify the appropriate results for the required goal.