CS1674: Homework 3 - Written

1. How is correlation different than convolution?
2. Is it more efficient to filter an image with two 1D filters as opposed to a 2D filter? Why?
3. How does a median filter preserve edges?
4. How does one use filters to describe an image, i.e. to compute an image representation? Please describe the process.
5. In what situations would a texture-based representations allow you to distinguish between different types of images? For example, can you distinguish panthers from leopards? What about leopards from tigers? What about leopards from cheetahs? Please describe whether using textures does or does not make sense in each of these situations, and why.
6. In what way does using filtering help achieve quality as a pre-processing step when scaling down images?
7. Suppose we form a texture description using a filter bank of Gaussian filters at two scales and six orientations like the one displayed below. Is the resulting representation sensitive to orientation, or is it invariant to orientation? In other words, if I rotate an image by an arbitrary degree, and I compute the responses to the filters, would those responses be the same as if I hadn't rotated the image? Explain why. [Acknowledgement: This question is adapted from Kristen Grauman.]