Meaning of "Base" in Walsh Hadamard Tranform in Image Processing? Currently, I am studying a paper by K. He and J. Sun, “Computing nearest-neighbor ﬁelds via propagation-assisted KD-trees,” in Proc. IEEE Conf. Comput. Vis. Pattern Recog., 2012, pp. 111–118.

In the paper there is a sentence which i can quote as:


  ...  We use the ﬁrst 16 WHT bases for the Y channel2 and 4 for each
  chrominance channel (Cb/Cr) throughout this paper. ...


Although I have made a search on the internet, I couldn't get the meaning of base.

In MATLAB 2014b There is a function fwht(x,n) where n is the order of the transform. Can this order be the base that i am trying to find the meaning of?
I believe that here bases stands for "basis vectors". From the cited paper by  Y. Hel-Or and H. Hel-Or. Real time pattern matching using projection kernels, 2003, ICCV,  you can see the set of $8 \times 8$ vectors from  a separable Walsh-Hadamard basis:

[20] Y. Hel-Or and H. Hel-Or. Real time pattern matching using
projection kernels. In ICCV, pages 1430–1445, 2003.

It consists in a tensor product of two $8$ 1D Walsh-Hadamard transforms (one horizontal, one vertical).



The sixteen 2D vectors  in the left-top $4\times 4$ square are the one with the lowest sequencies (sequency is the  frequency analog for Walsh-Paley-Hadamard transforms), in terms of "maximum sequency":