# Hyper-Convolution Networks for Biomedical Image Segmentation

arXiv: https://arxiv.org/abs/2105.10559 · HTML: https://mlsanity.com/paper/2105.10559/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 42 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [Large Kernel Matters -- Improve Semantic Segmentation by Global Convolutional Network](https://mlsanity.com/paper/1703.02719/) (2017)
- [Asymmetric Non-local Neural Networks for Semantic Segmentation](https://mlsanity.com/paper/1908.07678/) (2019)
- [ParseNet: Looking Wider to See Better](https://mlsanity.com/paper/1506.04579/) (2015)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [MixConv: Mixed Depthwise Convolutional Kernels](https://mlsanity.com/paper/1907.09595/) (2019)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [HyperSeg: Patch-wise Hypernetwork for Real-time Semantic Segmentation](https://mlsanity.com/paper/2012.11582/) (2020)
- [Hypernetwork functional image representation](https://mlsanity.com/paper/1902.10404/) (2019)
- [Compact Generalized Non-local Network](https://mlsanity.com/paper/1810.13125/) (2018)
- [Effective Use of Dilated Convolutions for Segmenting Small Object Instances in Remote Sensing Imagery](https://mlsanity.com/paper/1709.00179/) (2017)

## Built on by (most cited first, 10 of 10)

- [Spatially Covariant Lesion Segmentation](https://mlsanity.com/paper/2301.07895/) (2023)
- [Combiner and HyperCombiner Networks: Rules to Combine Multimodality MR Images for Prostate Cancer Localisation](https://mlsanity.com/paper/2307.08279/) (2023)
- [As large as it gets: Learning infinitely large Filters via Neural Implicit Functions in the Fourier Domain](https://mlsanity.com/paper/2307.10001/) (2023)
- [HyperSpace: Hypernetworks for spacing-adaptive image segmentation](https://mlsanity.com/paper/2407.03681/) (2024)
- [Hypernet-Ensemble Learning of Segmentation Probability for Medical Image Segmentation with Ambiguous Labels](https://mlsanity.com/paper/2112.06693/) (2021)
- [Hyper-Convolutions via Implicit Kernels for Medical Imaging](https://mlsanity.com/paper/2202.02701/) (2022)
- [Object Pursuit: Building a Space of Objects via Discriminative Weight Generation](https://mlsanity.com/paper/2112.07954/) (2021)
- [HyDA: Hypernetworks for Test Time Domain Adaptation in Medical Imaging Analysis](https://mlsanity.com/paper/2503.04979/) (2025)
- [RBF Weighted Hyper-Involution for RGB-D Object Detection](https://mlsanity.com/paper/2310.00342/) (2023)
- [Modality-Projection Universal Model for Comprehensive Full-Body Medical Imaging Segmentation](https://mlsanity.com/paper/2412.19026/) (2024)

## Abstract (arXiv)

The convolution operation is a central building block of neural network architectures widely used in computer vision. The size of the convolution kernels determines both the expressiveness of convolutional neural networks (CNN), as well as the number of learnable parameters. Increasing the network capacity to capture rich pixel relationships requires increasing the number of learnable parameters, often leading to overfitting and/or lack of robustness. In this paper, we propose a powerful novel building block, the hyper-convolution, which implicitly represents the convolution kernel as a function of kernel coordinates. Hyper-convolutions enable decoupling the kernel size, and hence its receptive field, from the number of learnable parameters. In our experiments, focused on challenging biomedical image segmentation tasks, we demonstrate that replacing regular convolutions with hyper-convolutions leads to more efficient architectures that achieve improved accuracy. Our analysis also shows that learned hyper-convolutions are naturally regularized, which can offer better generalization performance. We believe that hyper-convolutions can be a powerful building block in future neural network architectures for computer vision tasks. We provide all of our code here: https://github.com/tym002/Hyper-Convolution