# Dealing with Unreliable Annotations: A Noise-Robust Network for Semantic Segmentation through A Transformer-Improved Encoder and Convolution Decoder

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## Abstract

**:**

## 1. Introduction

- 1.
- Inspired by the previous success of CNN and ViT, a ViT-based modified encoder and CNN-based decoder UNet-style segmentation network is proposed.
- 2.
- To simulate real clinical scenarios, noise is manually added to the ground truth to create noisy labels, constructing a CT spine segmentation dataset with noisy labels for evaluation purposes.
- 3.
- A simple and efficient adaptive denoising learning (ADL) is proposed for segmentation network to achieve a noise-robust segmentation framework.
- 4.
- The proposed segmentation network with ADL attains competitive performance against other baseline methods across various evaluation metrics under the same data conditions with both accurate and noisy label sets.

## 2. Methods

#### 2.1. Vision Transformer Layer

- (i)
- The process of tokenization converts the input image x of dimensions $H\times W$ into a sequence of flattened 2D patches denoted ${\{{x}_{i}^{p}\in {\mathbb{R}}^{{P}^{2}\xb7C}\}}_{i=1,\cdots ,N}$. Each patch measures $P\times P$, and $N=\frac{H\times W}{{P}^{2}}$ accounts for the total number of image patches, thereby defining the input sequence length.
- (ii)
- These patches are subsequently mapped onto vectors ${x}^{p}$ in a latent D-dimensional embedding space using a trainable linear projection. To capture the spatial information inherent in the patches, learnable position embeddings are added to the patch embeddings, as follows:$${z}^{0}=[{x}_{1}^{p}E;{x}_{2}^{p}E;\cdots ;{x}_{N}^{p}E]+{E}_{\mathrm{pos}}$$In this expression, $E\in {\mathbb{R}}^{({P}^{2}\xb7C)\times D}$ represents the patch embedding projection, ${E}_{\mathrm{pos}}\in {\mathbb{R}}^{N\times D}$ is the position embedding, and ${z}^{0}$ provides the feature map input to the first ViT layer.
- (iii)
- Comprising L layers, each incorporating an MSA and a MLP, the transformer encoder’s output from the ${l}^{th}$ layer is illustrated as$${z}_{l}^{{}^{\prime}}=\mathrm{MSA}\left(\mathrm{LN}\left({z}_{l-1}\right)\right)+{z}_{l-1}$$$${z}_{l}=\mathrm{MLP}\left(\mathrm{LN}\left({z}_{l}^{{}^{\prime}}\right)\right)+{z}_{l}^{{}^{\prime}}$$
- (iv)
- The MLP is a fully connected feedforward neural network that consists of multiple layers of nodes. In the proposed NR-UNet, the MLP refines the features extracted by the MSA mechanism. The MLP involves two linear layers interspersed with a GELU activation function [35], defined as$$\mathrm{MLP}\left({z}_{l}^{{}^{\prime}}\right)={\mathrm{Linear}}_{2}\left(\mathrm{GELU}\left({\mathrm{Linear}}_{1}\left({z}_{l}^{{}^{\prime}}\right)\right)\right)$$In this equation, ${\mathrm{Linear}}_{1}$ and ${\mathrm{Linear}}_{2}$ denote the first and second linear layers. The subsequent MSA is composed of multiple self-attention heads that operate in parallel to capture different aspects of the input tokens. Each self-attention head calculates attention scores employing Query (Q), Key (K), and Value (V) matrices, which are derived from the input tokens via linear transformations:The matrices Query (Q), Key (K), and Value (V) are derived from the input tokens ${z}_{l}^{{}^{\prime}}$ through linear transformations:$$Q={z}_{l}^{{}^{\prime}}{W}_{Q},K={z}_{l}^{{}^{\prime}}{W}_{K},V={z}_{l}^{{}^{\prime}}{W}_{V}$$
- (v)
- The attention scores are computed by taking the dot product of the Q and K matrices, subsequently scaling and normalizing through softmax:$$\mathrm{Attention}(Q,K,V)=\mathrm{softmax}\left(\right)open="("\; close=")">\frac{Q{K}^{\top}}{\sqrt{{d}_{k}}}$$
- (vi)
- The individual outputs of the self-attention heads are concatenated and linearly transformed to generate the final output of the MSA:$$\mathrm{MSA}\left({z}_{l}^{{}^{\prime}}\right)=\mathrm{Concat}({\mathrm{Head}}_{1},\cdots ,{\mathrm{Head}}_{H}){W}_{O}$$

#### 2.2. ViT Encoder to CNN Decoder

#### 2.3. Noisy Labels

- a
- Starting with a dataset containing perfect annotations, we randomly select a subset of annotations to be altered, and the ratio of noisy labels to the whole dataset is denoted as $\beta \in [0,1]$.
- b
- For the selected annotations, we apply image-processing operations such as erosion, dilation, and elastic transformation to generate noisy labels. These operations mimic the types of noise that could be present in real-world clinical scenarios, where annotations might be imperfect due to various factors. Erosion and dilation are fundamental morphological operations. Let A be the binary annotation mask and B be a structuring element. The erosion (⊖) and dilation (⊕) operations can be defined as$$(A\ominus B)(x,y)=\underset{(i,j)\in B}{min}A(x-i,y-j)$$$$(A\oplus B)(x,y)=\underset{(i,j)\in B}{max}A(x+i,y+j)$$Elastic transformation is a nonlinear deformation technique that can simulate the local warping of shapes. Given an image $I(x,y)$ and two displacement fields $\mathsf{\Delta}x(x,y)$ and $\mathsf{\Delta}y(x,y)$, which are generated by Gaussian smoothing of random fields, an elastic transformation can be defined as$${I}_{\mathrm{transformed}}(x,y)=I(x+\alpha \mathsf{\Delta}x(x,y),y+\alpha \mathsf{\Delta}y(x,y))$$
- c
- The altered annotations are then used to replace their corresponding original annotations in the dataset, creating a new dataset with a mix of perfect and noisy labels. By simulating noisy labels in this manner, we create a dataset that can challenge experiments, enabling us to assess the noise-robustness of our proposed method and compare its performance against existing high-performing techniques.

#### 2.4. Adaptive Denoising Learning Strategy

## 3. Experiments and Results

#### 3.1. Dataset

#### 3.2. Experimental Setup

#### 3.3. Metrics

#### 3.4. Experiments in a Noise-Free Setup

#### 3.5. Experiments in a Noisy Setup

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The example images of CT spine images and corresponding segmentation ground truth and noisy labels generated by erosion, dilation, and elastic transform.

**Figure 2.**The framework of the proposed NR-UNet. (

**a**) The U-shaped encoder–decoder segmentation network through transformer-improved encoder and convolution decoder. ViT-based blocks and CNN-based blocks are green and yellow, respectively. (

**b**) The green CNN-based block consists of two successive CNN layers. (

**c**) The yellow ViT-based block consists of two successive ViT layers.

**Figure 3.**The adaptive denoising learning strategy during training. Predictions get generated through conventional training. Labels with higher prediction losses are more likely to be considered as noisy. ADL detects and removes a specific number of labels deemed as noisy during training. Precise (in blue) and imprecise (in green) labels get classified and, if imprecise, discarded.

**Figure 4.**The example images of input CT spine images; prediction of each network against ground truth.

**Figure 6.**History of training loss (in blue) and validation loss (in red) against the number of epochs for (

**a**) the CNN encoder–decoder, and for (

**b**) the ViT-improved encoder and CNN decoder.

**Figure 7.**The example images of input CT spine images; prediction of NR-UNet against ground truth under various data situations.

Network $\left(\mathit{\beta}=0\right)$ | Dice | IoU | Acc | Pre | Rec | Spe | Par${10}^{6}$ |
---|---|---|---|---|---|---|---|

FPN [39] | 0.9373 | 0.8821 | 0.9944 | 0.9191 | 0.9563 | 0.9961 | 17.59 |

Residual UNet [13] | 0.9416 | 0.8897 | 0.9949 | 0.9481 | 0.9353 | 0.9976 | 9.90 |

VNet [10] | 0.9446 | 0.8950 | 0.9950 | 0.9202 | 0.9703 | 0.9961 | 14.74 |

LinkNet [38] | 0.9524 | 0.9091 | 0.9959 | 0.9662 | 0.9390 | 0.9985 | 20.32 |

UNet [1] | 0.9580 | 0.9193 | 0.9963 | 0.9619 | 0.9541 | 0.9983 | 8.64 |

Dense UNet [13] | 0.9612 | 0.9252 | 0.9966 | 0.9600 | 0.9624 | 0.9982 | 15.47 |

MultiRes UNet [19] | 0.9644 | 0.9312 | 0.9969 | 0.9633 | 0.9655 | 0.9983 | 7.76 |

UNet++ [2] | 0.9659 | 0.9340 | 0.9970 | 0.9676 | 0.9642 | 0.9985 | 8.86 |

RARUNet [17] | 0.9674 | 0.9369 | 0.9972 | 0.9721 | 0.9629 | 0.9987 | 11.79 |

QAPNet [3] | 0.9690 | 0.9399 | 0.9973 | 0.9715 | 0.9666 | 0.9987 | 15.14 |

NR-UNet | 0.9703 | 0.9424 | 0.9974 | 0.9740 | 0.9667 | 0.9988
| 182.90 |

**Table 2.**Ablation studies of adaptive denoising learning via various segmentation networks under different proportions of noisy labels.

Proportion ($\mathit{\beta}$) | Network | ADL | Dice | IoU |
---|---|---|---|---|

75% | Residual UNet | ✗ | 0.7962 | 0.6614 |

✓ | 0.8210 | 0.6964 | ||

75% | UNet | ✗ | 0.8004 | 0.6672 |

✓ | 0.8337 | 0.7148 | ||

75% | NR-UNet | ✗ | 0.8196 | 0.6943 |

✓ | 0.8466 | 0.7340 | ||

50% | Residual UNet | ✗ | 0.8179 | 0.6919 |

✓ | 0.8453 | 0.7321 | ||

50% | UNet | ✗ | 0.8188 | 0.6932 |

✓ | 0.8564 | 0.7489 | ||

50% | NR-UNet | ✗ | 0.8362 | 0.7185 |

✓ | 0.8832 | 0.7908 | ||

25% | Residual UNet | ✗ | 0.9002 | 0.8185 |

✓ | 0.9213 | 0.8541 | ||

25% | UNet | ✗ | 0.9084 | 0.8322 |

✓ | 0.9303 | 0.8697 | ||

25% | Dense UNet | ✗ | 0.9096 | 0.8342 |

✓ | 0.9284 | 0.8664 | ||

25% | NR-UNet | ✗ | 0.9101 | 0.8350 |

✓ | 0.9532 | 0.9106 |

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**MDPI and ACS Style**

Wang, Z.; Voiculescu, I.
Dealing with Unreliable Annotations: A Noise-Robust Network for Semantic Segmentation through A Transformer-Improved Encoder and Convolution Decoder. *Appl. Sci.* **2023**, *13*, 7966.
https://doi.org/10.3390/app13137966

**AMA Style**

Wang Z, Voiculescu I.
Dealing with Unreliable Annotations: A Noise-Robust Network for Semantic Segmentation through A Transformer-Improved Encoder and Convolution Decoder. *Applied Sciences*. 2023; 13(13):7966.
https://doi.org/10.3390/app13137966

**Chicago/Turabian Style**

Wang, Ziyang, and Irina Voiculescu.
2023. "Dealing with Unreliable Annotations: A Noise-Robust Network for Semantic Segmentation through A Transformer-Improved Encoder and Convolution Decoder" *Applied Sciences* 13, no. 13: 7966.
https://doi.org/10.3390/app13137966