CSC 520

Homework Instructions: All homework must be completed in legible writing. The professor will not attempt to decipher handwriting. If your handwriting is suspect, the professor suggests that the student type up his/her homework.

Homework that is late will be penalized 10% per10. Homework should always be turned in at the beginning of class unless otherwise instructed.

1. Provide two synonyms for "spatial filtering".

2. Write the equation for spatial correlation and convolution as presented in class.

3. Provide a succent discussion on the use of smoothing filters. Give an example of a 3x3 smoothing filter.

4. Write the kernel for a 3x3 45 degree isotropic Laplacian filter. Name some uses for this type of kernel.

5. Write all the kernels for the Prewitt and Sobel edge masks. What feature does the Sobel kernels implicitly perform over the Prewitt kernels? Hint: it has to do with the center weightings.

6. List the three properties required for the "approximation of the first derivative".

7. Apply the Sobel's vertical and horizontal mask to image 1 from above to create the gradient image (use the approximation form for the gradient |gx|+|gy|) and the direction of gradient image. Note: This is a hand calculation problem, hence, scaling is not necessary. But, to visualize the gradient information and use in an image one would need to rescale.

8. Compute the Marr-Hildreth edge detection on image 1. Contrast the Marr-Hildreth results with that of problem 7 (Sobel). NOTE: in comparing the edges produced rescaling the resultant images will be beneficial. In comparing the techniques look at the original image to gain some idea of the the edge information available then determine which of the two techniques produced the better results. Also consider why the results differed, i.e. how does the two Sobel mask compare with the LOG mask. Which LOG mask did you choose and why.

9. Segment the following bimodal histogram (4-bit image) using the global thresholding algorithm to determine T. Stop when delta T is less than 2.

10. Repeat 9, using the Otsu method. show the values for ETA, global variance, and between class variance.