CS1674: Homework 2 - Written

1. [3 pts] Is it more efficient to filter an image with two 1D filters as opposed to a 2D filter? Why?
2. [3 pts] Explain how sharpening an image with filters works, in English (not in math). Intuitively, what steps are we performing?
3. [3 pts] 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. [3 pts] 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?
5. [3 pts] 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.