Image Resampling | Sahithyan's Notes

Changing image size parameters requires resampling to create new pixel values: adding pixels when upsampling, replacing pixels when downsampling.

Resampled pixels must:

Preserve image features, including fine detail
Reduce noise
Not introduce artefacts

Scaling by a factor of 2

Enlarge by replicating each row and column
Reduce by removing every other row and column
Repeat progressively for larger scaling factors

Nearest neighbour method

Replaces each new pixel with the value of the closest pixel among its $N_4(p)$ neighbours, using any distance metric.

Preserves most fine detail
Still prone to checkerboard and aliasing effects

Interpolation

An alternative to direct scaling: reconstruct, or estimate, the continuous intensity function from discrete samples, then resample it at the required resolution.

Linear interpolation
Assumes the variation between samples is a straight line.
Cubic interpolation
Uses a higher-order polynomial, giving a smoother variation.

In 2-D, these become bilinear and bicubic interpolation.

Aliasing

Aliasing is more prominent in high-frequency components, where fine detail lives.

Nyquist theory requires sampling at least twice the highest signal frequency to capture all detail
Some blurring reduces aliasing, at the cost of high-frequency detail. Less noticeable in sub-sampling.

Multi-scale pyramids

A series of progressively lower-resolution images, storing different degrees of detail.

L_n = G_n - \widehat{G_{n+1}}

Here:

$G_n$ : image at level $n$
$\widehat{G_{n+1}}$ : level $n+1$ , upsampled back to level $n$ ‘s resolution
$L_n$ : difference stored at level $n$
Common in image indexing and search
Lower levels need less storage, since only the difference from the upsampled original needs to be kept
Used as the basis for progressively encoded image compression