# Interpretable Small Training Set Image Segmentation Network Originated from Multi-Grid Variational Model

arXiv: https://arxiv.org/abs/2306.14097 · HTML: https://mlsanity.com/paper/2306.14097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 62 references that are in the map.
- First posted on arXiv 25 Jun 2023.

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

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Med3D: Transfer Learning for 3D Medical Image Analysis](https://mlsanity.com/paper/1904.00625/) (2019)
- [REFUGE Challenge: A Unified Framework for Evaluating Automated Methods for Glaucoma Assessment from Fundus Photographs](https://mlsanity.com/paper/1910.03667/) (2019)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Weakly- and Semi-Supervised Learning of a DCNN for Semantic Image Segmentation](https://mlsanity.com/paper/1502.02734/) (2015)
- [Recurrent Residual Convolutional Neural Network based on U-Net (R2U-Net) for Medical Image Segmentation](https://mlsanity.com/paper/1802.06955/) (2018)
- [Semi-Supervised Medical Image Segmentation via Cross Teaching between CNN and Transformer](https://mlsanity.com/paper/2112.04894/) (2021)
- [SimCVD: Simple Contrastive Voxel-Wise Representation Distillation for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2108.06227/) (2021)
- [Efficient piecewise training of deep structured models for semantic segmentation](https://mlsanity.com/paper/1504.01013/) (2015)
- [DeepAtlas: Joint Semi-Supervised Learning of Image Registration and Segmentation](https://mlsanity.com/paper/1904.08465/) (2019)
- [Semantic Image Segmentation via Deep Parsing Network](https://mlsanity.com/paper/1509.02634/) (2015)
- [MgNet: A Unified Framework of Multigrid and Convolutional Neural Network](https://mlsanity.com/paper/1901.10415/) (2019)
- [FCN-Transformer Feature Fusion for Polyp Segmentation](https://mlsanity.com/paper/2208.08352/) (2022)
- [Automatic 3D Cardiovascular MR Segmentation with Densely-Connected Volumetric ConvNets](https://mlsanity.com/paper/1708.00573/) (2017)
- [Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation](https://mlsanity.com/paper/2002.03989/) (2020)
- [Deep Learning Markov Random Field for Semantic Segmentation](https://mlsanity.com/paper/1606.07230/) (2016)
- [Medical Image Segmentation with 3D Convolutional Neural Networks: A Survey](https://mlsanity.com/paper/2108.08467/) (2021)
- [An efficient iterative thresholding method for image segmentation](https://mlsanity.com/paper/1608.01431/) (2016)
- [Exploring Context with Deep Structured models for Semantic Segmentation](https://mlsanity.com/paper/1603.03183/) (2016)
- [Image Segmentation with Adaptive Spatial Priors from Joint Registration](https://mlsanity.com/paper/2203.15548/) (2022)

## Built on by (most cited first, 1 of 1)

- [Slender Object Scene Segmentation in Remote Sensing Image Based on Learnable Morphological Skeleton with Segment Anything Model](https://mlsanity.com/paper/2411.08592/) (2024)

## Abstract (arXiv)

The main objective of image segmentation is to divide an image into homogeneous regions for further analysis. This is a significant and crucial task in many applications such as medical imaging. Deep learning (DL) methods have been proposed and widely used for image segmentation. However, these methods usually require a large amount of manually segmented data as training data and suffer from poor interpretability (known as the black box problem). The classical Mumford-Shah (MS) model is effective for segmentation and provides a piece-wise smooth approximation of the original image. In this paper, we replace the hand-crafted regularity term in the MS model with a data adaptive generalized learnable regularity term and use a multi-grid framework to unroll the MS model and obtain a variational model-based segmentation network with better generalizability and interpretability. This approach allows for the incorporation of learnable prior information into the network structure design. Moreover, the multi-grid framework enables multi-scale feature extraction and offers a mathematical explanation for the effectiveness of the U-shaped network structure in producing good image segmentation results. Due to the proposed network originates from a variational model, it can also handle small training sizes. Our experiments on the REFUGE dataset, the White Blood Cell image dataset, and 3D thigh muscle magnetic resonance (MR) images demonstrate that even with smaller training datasets, our method yields better segmentation results compared to related state of the art segmentation methods.