image processing style (2D kernel) convolutions?

[Jeff Epler]

Well, it seems that you could convolve each row of the input image with
each row of the kernel, with the rows offset from each other.  Then sum
the 3 convolved rows to get the output row

I know this isn't the right notation, and doesn't deal with r-1 or r+1
being out of range..
    for r in range(input_height):
        output[r] = (convolve(input[r-1], filter[0]) 
                  + convolve(input[r], filter[1])
                  + convolve(input[r+1], filter[2])

Jeff