# NeRD: Neural Representation of Distribution for Medical Image Segmentation

arXiv: https://arxiv.org/abs/2103.04020 · HTML: https://mlsanity.com/paper/2103.04020/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 6 Mar 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [How Much Position Information Do Convolutional Neural Networks Encode?](https://mlsanity.com/paper/2001.08248/) (2020)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Standardized Assessment of Automatic Segmentation of White Matter Hyperintensities and Results of the WMH Segmentation Challenge](https://mlsanity.com/paper/1904.00682/) (2019)
- [Image Generators with Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2011.13775/) (2020)
- [Deep Feature Interpolation for Image Content Changes](https://mlsanity.com/paper/1611.05507/) (2016)
- [Cube Padding for Weakly-Supervised Saliency Prediction in 360deg Videos](https://mlsanity.com/paper/1806.01320/) (2018)
- [Learning to Segment Every Thing](https://mlsanity.com/paper/1711.10370/) (2017)
- [Mind the Pad -- CNNs can Develop Blind Spots](https://mlsanity.com/paper/2010.02178/) (2020)
- [Image Question Answering using Convolutional Neural Network with Dynamic Parameter Prediction](https://mlsanity.com/paper/1511.05756/) (2015)
- [Fidelity Imposed Network Edit (FINE) for Solving Ill-Posed Image Reconstruction](https://mlsanity.com/paper/1905.07284/) (2019)
- [Efficient Folded Attention for 3D Medical Image Reconstruction and Segmentation](https://mlsanity.com/paper/2009.05576/) (2020)
- [Geometric Loss for Deep Multiple Sclerosis lesion Segmentation](https://mlsanity.com/paper/2009.13755/) (2020)
- [Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2004.12573/) (2020)

## Built on by (most cited first, 5 of 5)

- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [UltraSR: Spatial Encoding is a Missing Key for Implicit Image Function-based Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2103.12716/) (2021)
- [Reinforcement Learning with Neural Radiance Fields](https://mlsanity.com/paper/2206.01634/) (2022)
- [Implicit Neural Representation Learning for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2112.10541/) (2021)
- [Estimating Neural Orientation Distribution Fields on High Resolution Diffusion MRI Scans](https://mlsanity.com/paper/2409.09387/) (2024)

## Abstract (arXiv)

We introduce Neural Representation of Distribution (NeRD) technique, a module for convolutional neural networks (CNNs) that can estimate the feature distribution by optimizing an underlying function mapping image coordinates to the feature distribution. Using NeRD, we propose an end-to-end deep learning model for medical image segmentation that can compensate the negative impact of feature distribution shifting issue caused by commonly used network operations such as padding and pooling. An implicit function is used to represent the parameter space of the feature distribution by querying the image coordinate. With NeRD, the impact of issues such as over-segmenting and missing have been reduced, and experimental results on the challenging white matter lesion segmentation and left atrial segmentation verify the effectiveness of the proposed method. The code is available via https://github.com/tinymilky/NeRD.