Problem Set No. 2
By Alan Daniels

Introduction

• A picture of a steel rod.
• The same picture, filtered with a 7x7 Gaussian matrix.
• The same picture, with added Gaussian noise, and then filtered.
• The same picture, with Gaussian noise, but no filtering.

• The two 1x2 simple gradients (rightward and downward).
• Two two 2x2 simple gradients (rightward and downward).
• The Roberts cross operator.
• The Sobel operator.
• The Prewitt operator.

Here is the MATLAB code used to generate all of the pictures you see below.

• ps2.m.
• clip.m.

The Results

This assignment was pretty straightforward, so I'll let the results speak for themselves. I've deliberately set up the matrices myself, rather than using the standard MATLAB "edge" function with arguments, since the "edge" function gives binary results, and I wanted to see the grayscale version. In each case, I set up the convolution matrix manually, used the absolute value of the convolution, and scaled the result by five or 10 to make the results more visible. I've arranged everything into a grid to make the comparison easier.

	Original	Filter	Noise + Filter	Noise Only
Originals
Gradient Downward 1 By 2
Gradient Downward 2 By 2
Gradient Rightward 1 By 2
Gradient Rightward 2 By 2
Roberts
Sobel
Prewitt

Conclusion

As is obvious, each of the edge detection algorithms are very intolerant of noise, much more than I thought it would be originally. Also, standard Gaussian filtering was mildly helpful, but not nearly enough to make up for any noise introduced into the picture.