HaarNet: Large-scale Linear-Morphological Hybrid Network for RGB-D Semantic Segmentation

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.

MorphPool: Efficient Non-linear Pooling & Unpooling in CNNs

Pooling is essentially an operation from the field of Mathematical Morphology, with max pooling as a limited special case. The more general setting of MorphPooling greatly extends the tool set for building neural networks. In addition to pooling operations, encoder-decoder networks used for pixel-level predictions also require unpooling. It is common to combine unpooling with convolution or deconvolution for up-sampling. However, using its morphological properties, unpooling can be generalised and improved. Extensive experimentation on two tasks and three large-scale datasets shows that morphological pooling and unpooling lead to improved predictive performance at much reduced parameter counts.