ComputerVision101_Week1_Interpolation

university computervision week1 theory

Interpolation

Source:

• HC1a Images and Interpolation
• https://rvdboomgaard.github.io/ComputerVision_LectureNotes/LectureNotes/IP/index.html

Core idea

After discretization, we only know image values on a grid:

$$F(i,j)$$

But sometimes we want the value at a location that is not exactly on the grid:

$$f(x,y)$$

with non-integer $x$ or $y$.

Interpolation means:

$$\text{estimate values between known samples}$$

Why we need it

Interpolation is used whenever we:

• resize an image
• rotate an image
• warp an image
• sample at non-integer coordinates

What the lecture assumes

The lecture says interpolation makes sense when the image is well sampled.

That means the discrete samples still contain enough information about the original signal.

The Remarkable notes phrase interpolation as an informed guess:

• we already lost information when going from continuous to discrete
• interpolation does not recover the true original function exactly
• it estimates reasonable values between samples

Your confusion: “why does nearest neighbor make a staircase?”

Because nearest neighbor says:

$$\hat{f}(x)=\text{copy the closest sample}$$

So for a whole interval of $x$ values, the output stays exactly the same.

That produces flat horizontal pieces, which look like stairs.

Main methods from the lecture

• ComputerVision101_Week1_NearestNeighborInterpolation
• ComputerVision101_Week1_LinearInterpolation
• ComputerVision101_Week1_BilinearInterpolation