5. Explain why do we downsample images, and what role does decimation play in reducing image resolution effectively?
Answer:
Why Do We Downsample Images?
Downsampling, or reducing the resolution of an image, is essential in many applications such as:
- Image compression
- Multi-scale analysis (e.g., pyramids, MIP-maps)
- Efficient storage and transmission
- Speeding up algorithms (e.g., feature detection, object recognition)
- Progressive rendering and zooming
However, if done improperly, downsampling can introduce aliasing artifacts — distortions due to high-frequency information folding back into the low-frequency spectrum.
What is Decimation?
Decimation is the process used to downsample an image. It involves two major steps:
- Low-pass filtering the image to remove high-frequency content
- Subsampling (keeping every rthr^{th}rth sample)
This avoids aliasing by ensuring the signal being sampled no longer contains components higher than the Nyquist frequency.
