## CS1674: Homework 2 - Written

Due: 9/12/2016, 11:59pm

This assignment is worth 15 points.

1. What is the effect of the sigma parameter of a Gaussian, on the appearance of the image that has been convolved with a Gaussian?
2. Explain how sharpening an image with filters works, in English (not in math). Intuitively, what steps are we performing?
3. Say I am at a pixel (r, c), where r is the row index and c is the column index. How can you find the difference between pixels to the right of me and pixels to the left of me, i.e. between pixels (r, c-1) and (r, c+1), using a filter? What about the difference between pixels below/above me, i.e. (r+1, c) and (r-1, c)?
4. How can you highlight edges in an image using filters?
5. Say you have an image of a tree, and an image of a sky. You compute the dI/dx and dI/dy image gradients for all pixels, using the answer to Question 3 above. Which image would have a larger number of high-magnitude gradients? Why?
6. How can you find patterns in an image (e.g. let's say you're looking for a plus sign in images) in an image using a filter? Would a 3x3 filter work for any image, i.e. where the plus signs appear at different sizes and orientations? Explain why it would/wouldn't.
7. Say you want to illustrate both the finer and coarser details in an image, separately. Describe a process that allows you to produce 3 "detail" images (i.e. images that only show the sharp detail of the image), the first one being very fine, the second a little coarser, and the third even more coarse.

Note: Think of the last two problems as brainstorming exercises. You can even just tell me what you know that you think might be relevant to the question, and not give me an actual answer to the question. As long as you give me any answer, you'll get credit for these last two.