Traditionally, a convolutional filter is one where you take a matrix of numbers, multiply it with a subset of the data, and then sum it up. Then you move the filter left to right and top to bottom in a sweeping fashion to generate a smaller (or equal) grid.
But I wonder if there are filters that work in rotations meaning, consider a 2x2 filter containing these parameters.
a, b d, c
And consider a 4x4 input data. Normally, in the CNN world, after applying the filter to the input, I would get a 3x3 output, which is the result of the sweeping I described earlier.
Now say, instead of sweeping across, I would like to rotate the weight before I apply, and I do not do sweeping, I rotate the matrix for each of the 4 corners in the 4x4 input.
Meaning, I would apply to the top-left these values
a, b d, c
then to bottom-left these values which is the above rotated
b, c a, d
then to the bottom-right
c, d b, a
then to the top-right
d, a c, b
so I end with another 2x2 matrix after applying the above filter to the 4x4 input.
Does such filter have a name already?