I need an explanation about Bilinear Interpolation. I use KNN and find $4$ points which I need to use bilinear interpolation to find unknown position.
I was unable to understand explanations in other sites. I need to write equations for $x$ and $y$ using bilinear interpolation. How can i do this ?
Please fully describe.
Bilinear interpolation is just the extension of linear interpolation for interpolating functions of two variables.
A bilinear function write $$z=A+B x+C y +D x y$$ You can easily check that, if $x$ is fixed, $z$ is linear with respect to $y$ and vice-versa.
So, if you have four data points $(x_i,y_i,z_i)$, you have to solve four linear equations for four unknowns $A,B,C,D$; when you have them, just apply the formula for the point you want to interpolate at.