aditmeh/interpolation

implementing interpolation because I'm bored

Interpolation

Bilinear interpolation

I implemented bilinear interpolation to resize some image of a dog

Differentiable Interpolation

Math

Given a density grid $D$ of shape $H, W$ and an image, compute the density of a pixel $(x,y)$ in the image as $\text{softplus}(\text{interp}((x,y), D))$. Interpolation is linear here, so it is differentiable.

You optimize $D$ to reduce the MSE between the reconstructed original image and the original image

Results

The following is using a grid size of shape $H//5, W//5$, where $H,W$ is the size of the image

Ground truth:

Using no nonlinearity, just linear interpolation:

Linear interpolation with softplus nonlinearity:

Notice that the edges are sharper compared to the nonlinear version.