Computer Vision Foundations · free preview

Sampling in Two Dimensions

A general grid matrix describes sampling in the plane, hexagonal lattices buy about ten percent more alias-free bandwidth per sample, biology uses them, and sampling demands an antialiasing prefilter.

1. Grids are matrices

Grids are matrices

2. The hexagon wins

The hexagon wins

3. Prefilter before you sample

Prefilter before you sample

4. Sampling in space-time

Sampling in space-time

5. Why hexagons beat squares

Why does a hexagonal sampling grid achieve roughly ten percent higher alias-free resolution per sample than a square grid for natural images?

6. The prefilter's honest cost

Decimation without a prefilter produced new stripes on a zebra. What does antialiasing prefiltering cost and what does it save?

7. The hexagonal gain

Write the approximate percentage of resolution a hexagonal grid gains over a square grid at the same alias-free bandwidth. Write the number only.

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