Image Sampling

Image Scaling

Image sub-sampling

Image sub-sampling

Even worse for synthetic images

Sampling and the Nyquist rate
Aliasing can arise when you sample a continuous signal or image
occurs when your sampling rate is not high enough to capture the amount of detail in your image
Can give you the wrong signal/image—an alias
formally, the image contains structure at different scales
called “frequencies” in the Fourier domain
the sampling rate must be high enough to capture the highest frequency in the image
To avoid aliasing:
sampling rate ≥ 2 * max frequency in the image
said another way: ≥ two samples per cycle
This minimum sampling rate is called the Nyquist rate

2D example

Subsampling with Gaussian pre-filtering

Subsampling with Gaussian pre-filtering

Compare with...

Slide 11

Subsampling with Gaussian pre-filtering

Some times we want many resolutions

Gaussian pyramid construction

Image resampling
So far, we considered only power-of-two subsampling
What about arbitrary scale reduction?
How can we increase the size of the image?

Image resampling
So far, we considered only power-of-two subsampling
What about arbitrary scale reduction?
How can we increase the size of the image?

Image resampling
So what to do if we don’t know

Resampling filters
What does the 2D version of this hat function look like?

Bilinear interpolation
A simple method for resampling images