# CFSSeg: Closed-Form Solution for Class-Incremental Semantic Segmentation of 2D Images and 3D Point Clouds

arXiv: https://arxiv.org/abs/2412.10834 · HTML: https://mlsanity.com/paper/2412.10834/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 69 references that are in the map.
- First posted on arXiv 14 Dec 2024.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Per-Pixel Classification is Not All You Need for Semantic Segmentation](https://mlsanity.com/paper/2107.06278/) (2021)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [Modeling the Background for Incremental Learning in Semantic Segmentation](https://mlsanity.com/paper/2002.00718/) (2020)
- [Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining](https://mlsanity.com/paper/2402.03302/) (2024)
- [PLOP: Learning without Forgetting for Continual Semantic Segmentation](https://mlsanity.com/paper/2011.11390/) (2020)
- [Incremental Learning Techniques for Semantic Segmentation](https://mlsanity.com/paper/1907.13372/) (2019)
- [Continual Semantic Segmentation via Repulsion-Attraction of Sparse and Disentangled Latent Representations](https://mlsanity.com/paper/2103.06342/) (2021)
- [RECALL: Replay-based Continual Learning in Semantic Segmentation](https://mlsanity.com/paper/2108.03673/) (2021)
- [Representation Compensation Networks for Continual Semantic Segmentation](https://mlsanity.com/paper/2203.05402/) (2022)
- [SSUL: Semantic Segmentation with Unknown Label for Exemplar-based Class-Incremental Learning](https://mlsanity.com/paper/2106.11562/) (2021)
- [Collaborative Unsupervised Domain Adaptation for Medical Image Diagnosis](https://mlsanity.com/paper/2007.07222/) (2020)

## Built on by (most cited first, 2 of 2)

- [Towards Efficient and Exact Forgetting Services in Pre-Trained-Model-based Continual Learning](https://mlsanity.com/paper/2505.12239/) (2025)
- [DeepAFL: Deep Analytic Federated Learning](https://mlsanity.com/paper/2603.00579/) (2026)

## Abstract (arXiv)

2D images and 3D point clouds are foundational data types for multimedia applications, including real-time video analysis, augmented reality (AR), and 3D scene understanding. Class-incremental semantic segmentation (CSS) requires incrementally learning new semantic categories while retaining prior knowledge. Existing methods typically rely on computationally expensive training based on stochastic gradient descent, employing complex regularization or exemplar replay. However, stochastic gradient descent-based approaches inevitably update the model's weights for past knowledge, leading to catastrophic forgetting, a problem exacerbated by pixel/point-level granularity. To address these challenges, we propose CFSSeg, a novel exemplar-free approach that leverages a closed-form solution, offering a practical and theoretically grounded solution for continual semantic segmentation tasks. This eliminates the need for iterative gradient-based optimization and storage of past data, requiring only a single pass through new samples per step. It not only enhances computational efficiency but also provides a practical solution for dynamic, privacy-sensitive multimedia environments. Extensive experiments on 2D and 3D benchmark datasets such as Pascal VOC2012, S3DIS, and ScanNet demonstrate CFSSeg's superior performance.