Sobel Edge Detection Filter
Submitted by: Aaron Brooks - Brent Bolton - Jason O'Kane
Algorithm
| Horizontal Kernel |
| -1 |
-2 |
-1 |
0 |
0 |
0 |
| +1 |
+2 |
+1 |
| Vertical Kernel |
| -1 |
0 |
+1 |
-2 |
0 |
+2 |
| -1 |
0 |
+1 |
Two 3x3 convolution masks are applied to each pixel, one color at a
time - one with a horizontal trend and one with a vertical trend. The
result of the each convolution is treated a vector representing the
edge through the current pixel. If the magnitude of the sum of these
two orthogonal vectors is greater than some user-specified threshold,
the pixel is marked in black as an edge. Otherwise, the pixel is set
to white.
Run Time Assessment
| |
Hardware |
Approximate Run Time |
| Bolton, Brooks, and O'Kane |
CSS Linux workstation |
11 sec |
| Digital Darkroom, IP Toolkit |
CSS Multimedia workstation |
7 sec |
Understandably, this filter runs slowly. At each pixel, two 3x3
convolutions (requiring 9 multiplications each) are made, followed by an
expensive square root calculation.
Results
The algorithm works well - the main edges of the image can be seen
clearly. However, some possibly undesirable features can be seen on
the can itself - probably resulting from the droplets of condensed
water in the original image. These might possibly be eliminated by
adjusting the threshold.
Several factors account for the differences seen between our results
and the results from the IP tooklit:
- The IP Toolkit filter seems to be marking edges in the color of
the original image. In deference to the assignment description,
our filter marks edges in black.
- It's likely that the IP Toolkit uses a different threshold than
70 - the threshold used to generate our test image.
Our filter begins by converting the image to grey-scale. The
approach taken by the IP Toolkit filter is not known. One
possibility is to convert the image to an HSI representation and
perform processing on the I value. It is also reasonable to detect
edges in the H or S values as well. The precise approach chosen
should depend on the type of image being processed and the nature
of the edges being detected.
Source Code
Test Images
Original Image
After edge detection (Bolton, Brooks, and O'Kane)
After edge detection (Digital Darkroom, IP Tooklit)
