# Bilinear Interpolation

Heard Jack Zhang from NVIDIA say this term while he was working on ESS.

Resources

notes from Cyrill Stachniss.

##### Bilinear Interpolation

This is intuitive. To calculate the new intensity value, compute a weighted average of the 4 neighbouring pixel intensity values.

\begin{align} b(x,y) = &a_{00} (1- \Delta x)(1- \Delta y) + a_{01}(1-\Delta x)\Delta y \\ &+ a_{10} \Delta x (1 - \Delta y) + a_{11} \Delta x \Delta y \end{align}

- Where $a_{00},…a_{11}$ are the 4 neighbouring pixel intensity values

Normalized

Notice that things seem to be normalized between 0 and 1 here. I don’t know how I am supposed to do this in practice.

Cyrill Stachniss likes to write this more compact form

$z=∑_{i≤1}∑_{j≤1}c_{ij}Δx_{i}Δy_{j}$

However, be careful since $c_{ij}$ doesn’t correspond to $a_{ij}$.

c_{01} &= a_{01} - a_{00} \\ c_{10} &= a_{10} - a_{00} \\ c_{11} &= a_{11} - a_{10} - a_{01} + a_{00} \\ \end{align}$$ ![[attachments/Screenshot 2023-10-08 at 1.38.46 PM.png]]How am I supposed to determine

`c_{ij}`

?You need to compare the original equation term by term.