# Investigating Shift Equivalence of Convolutional Neural Networks in Industrial Defect Segmentation

arXiv: https://arxiv.org/abs/2309.16902 · HTML: https://mlsanity.com/paper/2309.16902/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 47 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [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)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1910.03151/) (2019)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [DUNet: A deformable network for retinal vessel segmentation](https://mlsanity.com/paper/1811.01206/) (2018)
- [Delving Deeper into Anti-aliasing in ConvNets](https://mlsanity.com/paper/2008.09604/) (2020)
- [Truly shift-invariant convolutional neural networks](https://mlsanity.com/paper/2011.14214/) (2020)
- [SAM Fails to Segment Anything? -- SAM-Adapter: Adapting SAM in Underperformed Scenes: Camouflage, Shadow, Medical Image Segmentation, and More](https://mlsanity.com/paper/2304.09148/) (2023)
- [MIAD: A Maintenance Inspection Dataset for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2211.13968/) (2022)
- [Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networks](https://mlsanity.com/paper/2210.08001/) (2022)
- [Print Defect Mapping with Semantic Segmentation](https://mlsanity.com/paper/2001.10111/) (2020)
- [Investigating Shift-Variance of Convolutional Neural Networks in Ultrasound Image Segmentation](https://mlsanity.com/paper/2107.10431/) (2021)

## Built on by (most cited first, 6 of 6)

- [Bayesian Prompt Flow Learning for Zero-Shot Anomaly Detection](https://mlsanity.com/paper/2503.10080/) (2025)
- [DictAS: A Framework for Class-Generalizable Few-Shot Anomaly Segmentation via Dictionary Lookup](https://mlsanity.com/paper/2508.13560/) (2025)
- [MRAD: Zero-Shot Anomaly Detection with Memory-Driven Retrieval](https://mlsanity.com/paper/2602.00522/) (2026)
- [AG-VAS: Anchor-Guided Zero-Shot Visual Anomaly Segmentation with Large Multimodal Models](https://mlsanity.com/paper/2603.01305/) (2026)
- [DeltaDeno: Zero-Shot Anomaly Generation via Delta-Denoising Attribution](https://mlsanity.com/paper/2511.16920/) (2025)
- [Hyper-FSAD: Training-Free and Language-Free Few-Shot Anomaly Detection via Sparse Hyper Matching](https://mlsanity.com/paper/2605.10628/) (2026)

## Abstract (arXiv)

In industrial defect segmentation tasks, while pixel accuracy and Intersection over Union (IoU) are commonly employed metrics to assess segmentation performance, the output consistency (also referred to equivalence) of the model is often overlooked. Even a small shift in the input image can yield significant fluctuations in the segmentation results. Existing methodologies primarily focus on data augmentation or anti-aliasing to enhance the network's robustness against translational transformations, but their shift equivalence performs poorly on the test set or is susceptible to nonlinear activation functions. Additionally, the variations in boundaries resulting from the translation of input images are consistently disregarded, thus imposing further limitations on the shift equivalence. In response to this particular challenge, a novel pair of down/upsampling layers called component attention polyphase sampling (CAPS) is proposed as a replacement for the conventional sampling layers in CNNs. To mitigate the effect of image boundary variations on the equivalence, an adaptive windowing module is designed in CAPS to adaptively filter out the border pixels of the image. Furthermore, a component attention module is proposed to fuse all downsampled features to improve the segmentation performance. The experimental results on the micro surface defect (MSD) dataset and four real-world industrial defect datasets demonstrate that the proposed method exhibits higher equivalence and segmentation performance compared to other state-of-the-art methods.Our code will be available at https://github.com/xiaozhen228/CAPS.