ComputerVision101_Week1_CubicInterpolation

university computervision week1 theory

Cubic Interpolation

Source:

• CV101_LectureNotes1b

Idea

Cubic interpolation fits a cubic polynomial between two neighboring samples.

For a segment x \in [k, k+1], the lecture writes:

$$\hat{f}(x)=a(x-k{)}^3+b(x-k{)}^2+c(x-k)+d$$

The coefficients are solved from four nearby samples:

• F(k-1)
• F(k)
• F(k+1)
• F(k+2)

Properties

• uses 4 samples
• continuous
• differentiable
• smoother than linear interpolation

Warning from the lecture

Higher-order polynomials can fluctuate too much between sample points, so you should not automatically increase the order.