  The Guided Filter (GF) is well-known for its linear complexity. However, when
filtering an image with an n-channel guidance, GF needs to invert an n x n
matrix for each pixel. To the best of our knowledge existing matrix inverse
algorithms are inefficient on current hardwares. This shortcoming limits
applications of multichannel guidance in computation intensive system such as
multi-label system. We need a new GF-like filter that can perform fast
multichannel image guided filtering. Since the optimal linear complexity of GF
cannot be minimized further, the only way thus is to bring all potentialities
of current parallel computing hardwares into full play. In this paper we
propose a hardware-efficient Guided Filter (HGF), which solves the efficiency
problem of multichannel guided image filtering and yields competent results
when applying it to multi-label problems with synthesized polynomial
multichannel guidance. Specifically, in order to boost the filtering
performance, HGF takes a new matrix inverse algorithm which only involves two
hardware-efficient operations: element-wise arithmetic calculations and box
filtering. In order to break the linear model restriction, HGF synthesizes a
polynomial multichannel guidance to introduce nonlinearity. Benefiting from our
polynomial guidance and hardware-efficient matrix inverse algorithm, HGF not
only is more sensitive to the underlying structure of guidance but also
achieves the fastest computing speed. Due to these merits, HGF obtains
state-of-the-art results in terms of accuracy and efficiency in the computation
intensive multi-label
