  Signals from different modalities each have their own combination algebra
which affects their sampling processing. RGB is mostly linear; depth is a
geometric signal following the operations of mathematical morphology. If a
network obtaining RGB-D input has both kinds of operators available in its
layers, it should be able to give effective output with fewer parameters. In
this paper, morphological elements in conjunction with more familiar linear
modules are used to construct a mixed linear-morphological network called
HaarNet. This is the first large-scale linear-morphological hybrid, evaluated
on a set of sizeable real-world datasets. In the network, morphological Haar
sampling is applied to both feature channels in several layers, which splits
extreme values and high-frequency information such that both can be processed
to improve both modalities. Moreover, morphologically parameterised ReLU is
used, and morphologically-sound up-sampling is applied to obtain a
full-resolution output. Experiments show that HaarNet is competitive with a
state-of-the-art CNN, implying that morphological networks are a promising
research direction for geometry-based learning tasks.
