Given a 3D array of data, with an implicitly defined coordinate system, i.e., voxel coordinates, and given a set of points in this coordinate system (not necessarily integer), I want to interpolate the data at these given points, which is also known as unstructured interpolation.

In PyTorch, torch.nn.functional.grid_sample is the easiest way to do this. However, exploiting the power of this function for our task is not straightforward.

For a given 2D/3D array of data values of shape 1CHW(D) and a set of points points of shape ND, run the following code to interpolate the data at the given points:

output = unstructured_interpolation(values, points)

The returned tensor will be of shape NC.