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

arXiv: https://arxiv.org/abs/2310.07669 · HTML: https://mlsanity.com/paper/2310.07669/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Learning Rich Features from RGB-D Images for Object Detection and Segmentation](https://mlsanity.com/paper/1407.5736/) (2014)
- [Bi-directional Cross-Modality Feature Propagation with Separation-and-Aggregation Gate for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2007.09183/) (2020)
- [Morphological Network: How Far Can We Go with Morphological Neurons?](https://mlsanity.com/paper/1901.00109/) (2019)
- [Deep Morphological Neural Networks](https://mlsanity.com/paper/1909.01532/) (2019)
- [Global-Local Propagation Network for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2101.10801/) (2021)
- [MorphoActivation: Generalizing ReLU activation function by mathematical morphology](https://mlsanity.com/paper/2207.06413/) (2022)
- [MorphPool: Efficient Non-linear Pooling & Unpooling in CNNs](https://mlsanity.com/paper/2211.14037/) (2022)
- [Advances in the training, pruning and enforcement of shape constraints of Morphological Neural Networks using Tropical Algebra](https://mlsanity.com/paper/2011.07643/) (2020)

## Abstract (arXiv)

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.