# Spatially Covariant Lesion Segmentation

arXiv: https://arxiv.org/abs/2301.07895 · HTML: https://mlsanity.com/paper/2301.07895/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [An Intriguing Failing of Convolutional Neural Networks and the CoordConv Solution](https://mlsanity.com/paper/1807.03247/) (2018)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [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)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [Standardized Assessment of Automatic Segmentation of White Matter Hyperintensities and Results of the WMH Segmentation Challenge](https://mlsanity.com/paper/1904.00682/) (2019)
- [Deep Feature Interpolation for Image Content Changes](https://mlsanity.com/paper/1611.05507/) (2016)
- [Machine Learning for Neuroimaging with Scikit-Learn](https://mlsanity.com/paper/1412.3919/) (2014)
- [GIFT: Learning Transformation-Invariant Dense Visual Descriptors via Group CNNs](https://mlsanity.com/paper/1911.05932/) (2019)
- [CTformer: Convolution-free Token2Token Dilated Vision Transformer for Low-dose CT Denoising](https://mlsanity.com/paper/2202.13517/) (2022)
- [Quadratic Autoencoder (Q-AE) for Low-dose CT Denoising](https://mlsanity.com/paper/1901.05593/) (2019)
- [Equivariant Transformer Networks](https://mlsanity.com/paper/1901.11399/) (2019)
- [Revisiting Spatial Invariance with Low-Rank Local Connectivity](https://mlsanity.com/paper/2002.02959/) (2020)
- [Multi-branch Convolutional Neural Network for Multiple Sclerosis Lesion Segmentation](https://mlsanity.com/paper/1811.02942/) (2018)
- [Fidelity Imposed Network Edit (FINE) for Solving Ill-Posed Image Reconstruction](https://mlsanity.com/paper/1905.07284/) (2019)
- [Ensemble learning with 3D convolutional neural networks for connectome-based prediction](https://mlsanity.com/paper/1809.06219/) (2018)
- [Hyper-Convolution Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/2105.10559/) (2021)
- [RSANet: Recurrent Slice-wise Attention Network for Multiple Sclerosis Lesion Segmentation](https://mlsanity.com/paper/2002.12470/) (2020)
- [Efficient Folded Attention for 3D Medical Image Reconstruction and Segmentation](https://mlsanity.com/paper/2009.05576/) (2020)

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

- [Spatially Covariant Image Registration with Text Prompts](https://mlsanity.com/paper/2311.15607/) (2023)
- [MemWarp: Discontinuity-Preserving Cardiac Registration with Memorized Anatomical Filters](https://mlsanity.com/paper/2407.08093/) (2024)
- [CoactSeg: Learning from Heterogeneous Data for New Multiple Sclerosis Lesion Segmentation](https://mlsanity.com/paper/2307.04513/) (2023)
- [Slicer Networks](https://mlsanity.com/paper/2401.09833/) (2024)
- [DeDA: Deep Directed Accumulator](https://mlsanity.com/paper/2303.08434/) (2023)
- [Encoder-Only Image Registration](https://mlsanity.com/paper/2509.00451/) (2025)
- [VoxelOpt: Voxel-Adaptive Message Passing for Discrete Optimization in Deformable Abdominal CT Registration](https://mlsanity.com/paper/2506.19975/) (2025)
- [Gaussian Primitive Optimized Deformable Retinal Image Registration](https://mlsanity.com/paper/2508.16852/) (2025)
- [DAGrid: Directed Accumulator Grid](https://mlsanity.com/paper/2306.02589/) (2023)
- [RimSet: Quantitatively Identifying and Characterizing Chronic Active Multiple Sclerosis Lesion on Quantitative Susceptibility Maps](https://mlsanity.com/paper/2312.16835/) (2023)

## Abstract (arXiv)

Compared to natural images, medical images usually show stronger visual patterns and therefore this adds flexibility and elasticity to resource-limited clinical applications by injecting proper priors into neural networks. In this paper, we propose spatially covariant pixel-aligned classifier (SCP) to improve the computational efficiency and meantime maintain or increase accuracy for lesion segmentation. SCP relaxes the spatial invariance constraint imposed by convolutional operations and optimizes an underlying implicit function that maps image coordinates to network weights, the parameters of which are obtained along with the backbone network training and later used for generating network weights to capture spatially covariant contextual information. We demonstrate the effectiveness and efficiency of the proposed SCP using two lesion segmentation tasks from different imaging modalities: white matter hyperintensity segmentation in magnetic resonance imaging and liver tumor segmentation in contrast-enhanced abdominal computerized tomography. The network using SCP has achieved 23.8%, 64.9% and 74.7% reduction in GPU memory usage, FLOPs, and network size with similar or better accuracy for lesion segmentation.