image processing - Kernel Convolution in Frequency Domain - Cyclic Padding

I don't know whether this is the right place to post this, but I suppose it is.

I know that frequency multiplication = circular convolution in time space for discrete signals (vectors).

I also know that "the convolution theorem yields the desired linear convolution result only if x(n) and h(n) are padded with zeros prior to the DFT such that their respective lengths are Nx+Nh-1, essentially zeroing out all circular artifacts."

and everything works with vectors.. but my goal is circular convolution with matrices as in this paper:

http://developer.download.nvidia.com/compute/cuda/2_2/sdk/website/projects/convolutionFFT2D/doc/convolutionFFT2D.pdf

If you watch the first two figures (figure 1 and 2) you'll see that the kernel is padded in a weird way I've never seen before, what's this?

Answer

Figures 1 and 2 are not showing any padding whatsoever. The larger matrix is the data (probably image) matrix, not a padded kernel matrix. The figures are simply showing how the circular aspect of the convolution works in 2 dimensions.