I recently read that before downsampling an image, it should be blurred using a Gaussian Kernel. This way, the downsampled image is better than just picking a single pixel out of a NxN block or averaging over the block. After searching in this site as well as google, I didn't get any exact answer.
But there were questions on how to select $\sigma$ for blurring. Reading the answers on those posts, I learned that downsampling has to be done in accordance with sampling theorem. Downsampling without blurring causes aliasing effects.
- Can someone please explain why image has to be blurred before downsampling? I mean what is the exact relation to sampling theorem. What happens when an image is downsampled without blurring? I mean what are these aliasing effects? How can I notice them in the downsampled image?
- Why is Gaussian blurring better than Averaging over a block?
If you can give some examples of the images, I would be a lot grateful. Ans, I would appreciate all kind of answers, partial, intuitive, rigorous, anything.