# Parameter-Efficient 3D Segmentation of Liver and Liver tumors: Depthwise factorization Scales Better Than Dense Convolution with Spatial Dimensionality

arXiv: https://arxiv.org/abs/2609.33077 · HTML: https://mlsanity.com/paper/2609.33077/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 30 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [nnU-Net: Self-adapting Framework for U-Net-Based Medical Image Segmentation](https://mlsanity.com/paper/1809.10486/) (2018)
- [UNeXt: MLP-based Rapid Medical Image Segmentation Network](https://mlsanity.com/paper/2203.04967/) (2022)
- [Shift: A Zero FLOP, Zero Parameter Alternative to Spatial Convolutions](https://mlsanity.com/paper/1711.08141/) (2017)
- [Automatic Liver and Lesion Segmentation in CT Using Cascaded Fully Convolutional Neural Networks and 3D Conditional Random Fields](https://mlsanity.com/paper/1610.02177/) (2016)
- [All You Need is a Few Shifts: Designing Efficient Convolutional Neural Networks for Image Classification](https://mlsanity.com/paper/1903.05285/) (2019)
- [CMUNeXt: An Efficient Medical Image Segmentation Network based on Large Kernel and Skip Fusion](https://mlsanity.com/paper/2308.01239/) (2023)
- [One Network to Segment Them All: A General, Lightweight System for Accurate 3D Medical Image Segmentation](https://mlsanity.com/paper/1911.01764/) (2019)
- [Constructing Fast Network through Deconstruction of Convolution](https://mlsanity.com/paper/1806.07370/) (2018)
- [S2-MLPv2: Improved Spatial-Shift MLP Architecture for Vision](https://mlsanity.com/paper/2108.01072/) (2021)
- [1M parameters are enough? A lightweight CNN-based model for medical image segmentation](https://mlsanity.com/paper/2306.16103/) (2023)
- [LATUP-Net: A Lightweight 3D Attention U-Net with Parallel Convolutions for Brain Tumor Segmentation](https://mlsanity.com/paper/2404.05911/) (2024)
- [LSU-Net: Lightweight Automatic Organs Segmentation Network For Medical Images](https://mlsanity.com/paper/2502.00042/) (2025)

## Abstract (arXiv)

Three-dimensional dense convolutional networks are the strongest performers on volumetric medical image segmentation, but their parameter counts scale poorly: moving a dense k x k convolution to k x k x k multiplies its weights by k. We observe that depthwise separable factorization does not share this penalty. Because the cubic kernel term applies only to the depthwise stage while the pointwise projection, which dominates the parameter count, is unchanged, the same architecture grows by 5 % from 2D to 3D where a dense convolutional U-Net grows by 200 %. We exploit this asymmetry to build a 3D U-Net with 536,990 parameters, 24x fewer than an identical dense 3D U-Net. On MSD Task03 Liver (the Medical Segmentation Decathlon liver task, derived from LiTS), evaluated per case under five-fold cross-validation over all 131 public volumes, the model reaches a tumor Dice of 0.577 (95% CI [0.518, 0.633]) and a liver Dice of 0.947 (95% CI [0.941, 0.952]). Its liver Dice exceeds previously reported performance. Its tumor Dice exceeds their low-resolution configuration (0.4701) by 0.107 and their 2D configuration (0.5394), at approximately one twenty-fourth of the parameters and roughly half the in-plane resolution. Trained under identical conditions on a common held-out split, it exceeds a dense 3D U-Net on liver by +0.031 Dice (paired p = 0.006) and on tumor by +0.041 (95 % CI [+0.005, +0.081], paired p = 0.056), suggesting the factorization also acts as a regularizer in the small-data regime characteristic of medical imaging. We further show, on both LiTS and a 2D endoscopy benchmark, that a large fraction of the network's learnable spatial filters can be replaced by fixed shifts at no cost in accuracy, but that replacing all of them is measurably worse, the placement of spatial capacity matters more than its total amount.