Like the 2D reduce operation, the 2D project operation can be implemented by consecutive 1D project operations on the rows and columns:
Because some pixels at level L-1 are located directly underneath a pixel at level L, while others straddle the boundary between two pixels at level L, the 1D project operation comes in two different flavors, depending on whether or not the row (or column) index of the pixel at level L-1 is even or odd:
For example, to do the project operation in the y-direction (in the even case) output[i,j] = 0.1*input[i,j/2-1] + 0.8*input[i,j/2] + 0.1*input[i,j/2+1].