ِA help to the understand

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Can anyone help me to understand this part of this document please which is attached !
http://www.csd.uwo.ca/~olga/Courses/Fall2014/CS9840/PossibleStudentPapers/pami2010.pdf[^]

page[5] Section"c" part "S[1]"

[S1] We used a square grid of pooling centres (see Figure 4),
with the overall footprint size of this grid being a parameter. The
vectors from the previous stage were summed together spatially
by bilinearly weighting them according to their distance from the
pooling centres as in the SIFT descriptor [19] so that the width of
the bilinear function is dictated by the output sample spacing. We
use sub-pixel interpolation throughout as this allows continuous
control over the size of the descriptor grid. Note that all these
summation operations are performed independently for each of
the k vector elements.

Regards!
Thanks in advance!