# Segmentation-Based vs. Regression-Based Biomarker Estimation: A Case Study of Fetus Head Circumference Assessment from Ultrasound Images

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Fetus Head Circumference Estimation

^{2}CNN neural network to perform HC distance-field regression for head delineation in an end-to-end way, which does not need prior HC localization or postprocessing for outlier removal. All these methods rely on a segmentation of the fetus head as a prerequisite to estimating the HC.

#### 2.2. Segmentation-Free Approaches for Biomarker Estimation

## 3. Methodological Framework

#### 3.1. Head Circumference Estimation Based on Segmentation

#### 3.1.1. CNN Segmentation Model

#### 3.1.2. Post-Processing of Segmentation Results

#### 3.1.3. HC Computation Based on Segmentation Results

#### 3.2. Head Circumference Estimation Using Regression CNN

#### 3.2.1. Regression CNN Model

#### 3.2.2. Loss Functions

#### 3.3. Model Configuration

## 4. Experimental Settings

#### 4.1. Dataset and Pre-Processing

#### 4.2. Experiment Configuration

#### 4.3. Evaluation Metrics

## 5. Results and Discussion

#### 5.1. HC Estimation Based on Segmentation

#### 5.2. HC Estimation Based on Regression CNN

#### 5.3. Interpretability of Regression CNN Result

#### 5.3.1. Saliency Maps of Regression CNN Results on HC

#### 5.3.2. Saliency Maps on Outlier Analysis

#### 5.4. Comparison of Segmentation CNN vs. Regression CNN

#### 5.5. Memory Usage and Computational Efficiency

#### 5.6. Comparison of HC Estimation with State-of-the-Art

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HC | Head circumference |

US | Ultrasound |

CT | Computed tomography |

MR | Magnetic resonance |

CNN | Convolutional neural networks |

pp | post processing |

EF | Ellipse fitting |

MAE | Mean absolute error |

MSE | Mean square error |

HL | Huber loss |

DI | Dice index |

HD | Hausdorff distance |

ASSD | Average symmetric surface distance |

PMAE | Percentage mean absolute error |

LRP | Layer-wise relevance propagation |

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**Figure 1.**Ultrasound images of fetus head from the HC18 dataset [1] at different pregnancy stages. Red ellipses are head contours. Below the image, the corresponding head circumference (HC) is given. Images may have a different pixel size.

**Figure 2.**Overview of head circumference estimation process based on either segmentation-based method or regression-based method. HC: Head circumference, pp: Post-processing (the dotted box means is optional), and EF: Ellipse fitting.

**Figure 3.**Segmentation results on three large fetus head and vague US images with U-Net-B2 and LinkNet-B2.

**Figure 4.**Saliency maps of regression CNN models on three cases of bad prediction results. The red points mean positive contribution and the blue points mean a negative contribution.

**Figure 5.**Saliency maps of different regression CNNs explained by LRP method. The numbers in input images and saliency maps are the ground truth and predicted HC values respectively. The best predicted results are in bold. The red points in saliency maps are positive values, the blue points are negative values.

**Figure 6.**Learning curves of segmentation (U-Net-B2) vs. segmentation-free method (Reg-B3-L1) in the training and validation stage. The x-axis represents the training epochs; the y-axis is the loss.

**Figure 7.**Scatter plots of the two best segmentation models U-Net-B2 and LinkNet-B2, and regression models (L1 = MAE loss, L2 = MSE loss). The x-axis represents the ground truth HC and the y-axis the predicted HC (in mm).

**Figure 8.**Bland–Altman plots of the segmentation (pretrained on ResNet50) and regression EfficientNet (efn) models (L1 = MAE loss, L2 = MSE loss). The x-axis represents the average value of ground truth and predicted HC; the y-axis represents the difference between ground truth and predicted HC (in mm). The horizontal red solid lines represent the upper and lower limits of 95% consistency. The middle dotted green line represents the mean of the difference.

**Table 1.**Number of trainable parameters (#) of segmentation and regression CNN (convolutional neural network) models. M = million. Backbone names: VGG16 (B1), ResNet50 (B2), EfficientNetb2 (B3), DenseNet121 (B4), Xception (B5), MobileNet (B6), and InceptionV3 (B7). Reg = Regression.

Segmentation Models | # Parameters (M) | Regression Models | # Parameters (M) |
---|---|---|---|

Original U-Net | 31.06 | Reg-B1 | 15.15 |

U-Net-B1, B2, B3 | 23.75, 32.51, 14.23 | Reg-B2 | 23.63 |

DoubleU-Net | 29.29 | Reg-B3 | 76.73 |

U-Net++ B1, B2, B3 | 24.15, 34.34, 16.03 | Reg-B4 | 70.04 |

FPN-B1, B2, B3 | 17.59, 26.89, 10.77 | Reg-B5 | 20.91 |

LinkNet-B1, B2, B3 | 20.32, 28.73, 10.15 | Reg-B6 | 3.26 |

PSPNet-B1, B2, B3 | 21.55, 17.99, 9.41 | Reg-B7 | 21.82 |

**Table 2.**Segmentation accuracy of segmentation models and HC estimation accuracy with (w) and without (w/o) post-processing (pp). The results are given as mean and ±standard deviation. B1:VGG16, B2: ResNet50, B3: EfficientNetb2. DI = Dice index, HD = Hausdorff distance, ASSD = Average symmetric surface distance (mm), MAE = Mean absolute error (mm, pixel), PMAE = Percentage MAE. The best results are in bold.

Method | DI ↑ (%) | HD ↓ (mm) | ASSD ↓ (mm) | MAE ↓ (mm) w/o pp | MAE (mm) w pp | MAE (px) w/o pp | MAE (px) w pp | PMAE ↓ (%) w/o pp | PMAE (%) w pp |
---|---|---|---|---|---|---|---|---|---|

U-Net-original | 98.5 ± $1.3$ | 1.56 ± $2.67$ | 0.35 ± $0.29$ | 1.55 ± $4.41$ | 1.23 ± $1.49$ | 11.83 ± $38.75$ | 9.11 ± $10.70$ | 1.04 ± $4.13$ | 0.75 ± $1.04$ |

DoubleU-Net | 98.7 ± $1.4$ | 1.14 ± $0.86$ | 0.29 ± $0.26$ | 2.60 ± $1.89$ | 2.59 ± $1.88$ | 18.94 ± $11.53$ | 18.76 ± $10.97$ | 1.58 ± $1.19$ | 1.56 ± $1.17$ |

U-Net-B1 | 98.6 ± $1.3$ | 1.16 ± $1.24$ | 0.31 ± $0.26$ | 1.31 ± $2.07$ | 1.21 ± $1.29$ | 9.99 ± $18.73$ | 8.98 ± $8.48$ | 0.85 ± $1.98$ | 0.74 ± $0.75$ |

U-Net-B2 | 98.8 ± $0.9$ | 1.09 ± $1.11$ | 0.27 ± $\mathbf{0.22}$ | 1.16 ± $\mathbf{1.78}$ | 1.08 ± $\mathbf{1.25}$ | 8.69 ± $14.41$ | 7.87 ± $\mathbf{7.51}$ | 0.74 ± $1.46$ | 0.65 ± $\mathbf{0.68}$ |

U-Net-B3 | 98.7 ± $1.1$ | 1.11 ± $1.03$ | 0.29 ± $0.24$ | 1.34 ± $1.97$ | 1.32 ± $1.67$ | 10.23 ± $16.98$ | 9.94 ± $13.58$ | 0.86 ± $1.62$ | 0.84 ± $1.32$ |

U-Net++ B1 | 98.5 ± $2.4$ | 1.29 ± $1.46$ | 0.31 ± $0.25$ | 2.03 ± $8.39$ | 1.3 ± $2.12$ | 16.95 ± $77.93$ | 9.92 ± $18.52$ | 1.51 ± $7.72$ | 0.87 ± $2.32$ |

U-Net++ B2 | 98.7 ± $1.0$ | 1.24 ± $1.66$ | 0.29 ± $0.23$ | 1.74 ± $6.38$ | 1.15 ± $1.59$ | 12.65 ± $41.16$ | 8.63 ± $12.24$ | 1.16 ± $4.65$ | 0.72 ± $1.13$ |

U-Net++ B3 | 98.7 ± $1.2$ | 1.17 ± $1.28$ | 0.29 ± $0.25$ | 2.32 ± $11.80$ | 1.19 ± $1.44$ | 19.08 ± $108.01$ | 8.91 ± $11.01$ | 1.57 ± $9.02$ | 0.76 ± $1.21$ |

FPN-B1 | 98.6 ± $1.1$ | 1.28 ± $1.68$ | 0.32 ± $0.27$ | 1.44 ± $2.42$ | 1.29 ± $1.61$ | 11.17 ± $22.67$ | 9.70 ± $12.84$ | 0.99 ± $2.58$ | 0.80 ± $1.16$ |

FPN-B2 | 98.7 ± $0.9$ | 1.18 ± $1.18$ | 0.30 ± $0.23$ | 1.38 ± $2.16$ | 1.26 ± $1.33$ | 10.35 ± $17.99$ | 9.19 ± $8.58$ | 1.90 ± $9.68$ | 0.76 ± $0.87$ |

FPN-B3 | 98.7 ± 1 | 1.19 ± $1.52$ | 0.30 ± $0.25$ | 1.46 ± $1.92$ | 1.39 ± $1.5$ | 11.09 ± $16.01$ | 10.33 ± $10.52$ | 0.94 ± $1.58$ | 0.86 ± $1.06$ |

LinkNet-B1 | 98.6 ± $1.2$ | 1.31 ± $1.54$ | 0.33 ± $0.25$ | 1.46 ± $1.91$ | 1.32 ± $1.44$ | 11.32 ± $16.14$ | 9.91 ± $10.23$ | 0.98 ± $1.70$ | 0.83 ± $1.02$ |

LinkNet-B2 | 98.7 ± $1.1$ | 1.12 ± $0.99$ | 0.30 ± $0.23$ | 1.19 ± $\mathbf{1.56}$ | 1.15 ± $\mathbf{1.32}$ | 8.86 ± $\mathbf{11.83}$ | 8.45 ± $\mathbf{8.39}$ | 0.73 ± $\mathbf{1.08}$ | 0.69 ± $\mathbf{0.77}$ |

LinkNet-B3 | 98.6 ± 1 | 1.15 ± $1.04$ | 0.31 ± $0.26$ | 1.37 ± $1.94$ | 1.29 ± $1.51$ | 10.55 ± $15.97$ | 9.70 ± $9.84$ | 0.89 ± $1.62$ | 0.79 ± $0.84$ |

PSPNet-B1 | 98.6 ± $1.4$ | 2.01 ± $3.88$ | 0.38 ± $0.44$ | 3.07 ± $12.89$ | 1.32 ± $1.38$ | 22.38 ± $79.36$ | 9.84 ± $9.03$ | 2.21 ± $8.94$ | 0.81 ± $0.81$ |

PSPNet-B2 | 98.8 ± $0.9$ | 1.42 ± $2.31$ | 0.31 ± $0.28$ | 1.66 ± $3.62$ | 1.20 ± $1.34$ | 11.98 ± $22.70$ | 8.75 ± $7.98$ | 1.07 ± $2.47$ | 0.72 ± $0.68$ |

PSPNet-B3 | 98.7 ± $1.1$ | 1.12 ± $1.12$ | 0.32 ± $0.25$ | 1.38 ± $1.95$ | 1.29 ± $1.36$ | 10.59 ± $16.40$ | 9.64 ± $9.14$ | 0.93 ± $1.94$ | 0.81 ± $0.86$ |

**Table 3.**Average performance of 21 regression CNN models over five-fold cross validation. The results are mean and ±standard deviation. MAE = Mean absolute error, PMAE = Percentage MAE. B1 = VGG16, B2 = ResNet50, B3 = EfficientNetb2, B4 = DenseNet121, B5 = Xception, B6 = MobileNet, B7 = InceptionV3, L1 = MAE loss, L2 = MSE loss, and L3 = Huber loss.

Model | MAE (mm) | MAE (px) | PMAE (%) |
---|---|---|---|

Reg-B1-L1 | 3.04 ± $2.97$ | 22.41 ± $19.94$ | 1.94 ± $2.19$ |

Reg-B2-L1 | 3.24 ± $3.31$ | 24.11 ± $22.65$ | 2.14 ± $2.61$ |

Reg-B3-L1 | 1.83 ± $\mathbf{2.11}$ | 13.57 ± $\mathbf{13.53}$ | 1.17 ± $\mathbf{1.43}$ |

Reg-B4-L1 | 12.59 ± $12.49$ | 93.63 ± $83.53$ | 8.68 ± $11.25$ |

Reg-B5-L1 | 2.96 ± $2.79$ | 22.39 ± $19.34$ | 1.89 ± $1.97$ |

Reg-B6-L1 | 3.23 ± $3.29$ | 24.29 ± $22.11$ | 2.13 ± $2.50$ |

Reg-B7-L1 | 3.34 ± $3.49$ | 26.04 ± $27.89$ | 2.28 ± $2.99$ |

Reg-B1-L2 | 3.16 ± $3.28$ | 23.83 ± $23.13$ | 2.13 ± $2.69$ |

Reg-B2-L2 | 3.73 ± $3.48$ | 28.41 ± $26.99$ | 2.55 ± $3.15$ |

Reg-B3-L2 | 2.35 ± $\mathbf{2.74}$ | 17.32 ± $\mathbf{17.95}$ | 1.53 ± $\mathbf{2.02}$ |

Reg-B4-L2 | 5.69 ± $5.92$ | 43.54 ± $44.89$ | 3.87 ± $4.97$ |

Reg-B5-L2 | 3.12 ± $3.07$ | 23.77 ± $22.19$ | 1.99 ± $2.27$ |

Reg-B6-L2 | 4.68 ± $4.17$ | 35.39 ± $30.59$ | 3.10 ± $3.36$ |

Reg-B7-L2 | 4.33 ± $4.67$ | 32.29 ± $32.60$ | 2.87 ± $3.78$ |

Reg-B1-L3 | 3.37 ± $3.72$ | 25.75 ± $26.36$ | 2.33 ± $3.05$ |

Reg-B2-L3 | 3.12 ± $2.97$ | 24.03 ± $23.69$ | 2.11 ± $2.66$ |

Reg-B3-L3 | 2.78 ± $\mathbf{3.03}$ | 20.62 ± $\mathbf{20.22}$ | 1.79 ± $\mathbf{2.13}$ |

Reg-B4-L3 | 9.15 ± $9.07$ | 70.49 ± $67.38$ | 6.20 ± $7.39$ |

Reg-B5-L3 | 3.40 ± $3.09$ | 26.08 ± $21.34$ | 2.19 ± $2.28$ |

Reg-B6-L3 | 4.30 ± $4.44$ | 32.48 ± $32.45$ | 2.86 ± $3.67$ |

Reg-B7-L3 | 6.29 ± $13.86$ | 48.39 ± $111.02$ | 4.33 ± $11.25$ |

**Table 4.**Comparison of HC estimation for the two best segmentation and regression (segmentation-free) models. B2: Resnet50. B3: EfficientNet, L1 = MAE loss, and L2 = MSE loss. The results are mean and ±standard deviation. MAE = Mean absolute error, PMAE = Percentage MAE. The best results are in bold. (p value < 0.05).

Metrics | MAE (mm) | MAE (px) | PMAE (%) |
---|---|---|---|

Methods | Segmentation-based methods | ||

U-Net-B2 | 1.08 ± 1.25 | 7.87 ± 7.51 | 0.65 ± 0.68 |

LinkNet-B2 | 1.15 ± 1.32 | 8.45 ± 8.39 | 0.69 ± 0.77 |

Segmentation-free methods | |||

Reg-B3-L1 | 1.83 ± 2.11 | 13.57 ± 13.53 | 1.17 ± 1.43 |

Reg-B3-L2 | 2.35 ± 2.74 | 17.32 ± 17.95 | 1.53 ± 2.02 |

**Table 5.**Training and predicting time and memory cost of segmentation vs. segmentation-free models on test set (200 images). B1 = VGG16, B2 = ResNet50, B3 = EfficientNetb2, B4 = DenseNet121, B5 = Xception, B6 = MobileNet, B7 = InceptionV3, L1 = MAE loss, Mem-M = theoretical memory of model, Mem-P = memory in prediction stage, and GB = gigabyte.

Methods | Train (s/Epoch) | Predict (s/Test Set) | Mem-M (GB) | Mem-P (GB) |
---|---|---|---|---|

Segmentation-based methods | ||||

U-Net-B2 | 29 | 68.26 | 3.06 | 1.84 |

DoubleU-Net | 70 | 114.21 | 7.21 | 2.40 |

U-Net++-B2 | 68 | 172.45 | 7.26 | 2.34 |

FPN-B2 | 44 | 101.30 | 5.47 | 2.04 |

LinkNet-B2 | 30 | 80.36 | 3.82 | 1.90 |

PSPNet-B2 | 88 | 225.38 | 11.06 | 4.04 |

Segmentation-free method | ||||

Reg-B1-L1 | 17 | 30.86 | 0.96 | 1.36 |

Reg-B2-L1 | 20 | 48.28 | 2.31 | 1.73 |

Reg-B3-L1 | 38 | 36.95 | 2.29 | 2.68 |

Reg-B4-L1 | 21 | 65.55 | 3.01 | 1.69 |

Reg-B5-L1 | 35 | 51.78 | 2.15 | 1.67 |

Reg-B6-L1 | 14 | 18.71 | 1.03 | 1.14 |

Reg-B7-L1 | 17 | 22.55 | 1.09 | 1.60 |

**Table 6.**Comparison of HC estimation with state-of-the-art on the HC18 dataset. B2 = ResNet50, B3 = EfficientNetb2, L1 = MAE loss, DI = Dice index, and N/A = Not applicable.

Metrics | MAE (mm) | DI (%) |
---|---|---|

Methods | Segmentation-based methods | |

Budd et al. [16] | 1.81 ± $1.65$ | 98.20 ± $0.80$ |

Sobhaninia et al. [18] | 2.12 ± $1.87$ | 96.84 ± $2.89$ |

Fiorentino et al. [19] | 1.90 ± $1.76$ | 97.75 ± $1.32$ |

Moccia et al. [20] | 1.95 ± $1.92$ | 97.90 ± $1.11$ |

U-Net-B2 (Proposed) | 1.08 ± $\mathbf{1.25}$ | 98.80 ± $\mathbf{0.9}$ |

Segmentation-free methods | ||

Reg-B3-L1 (Proposed) | 1.83 ± $\mathbf{2.11}$ | N/A |

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**MDPI and ACS Style**

Zhang, J.; Petitjean, C.; Ainouz, S.
Segmentation-Based vs. Regression-Based Biomarker Estimation: A Case Study of Fetus Head Circumference Assessment from Ultrasound Images. *J. Imaging* **2022**, *8*, 23.
https://doi.org/10.3390/jimaging8020023

**AMA Style**

Zhang J, Petitjean C, Ainouz S.
Segmentation-Based vs. Regression-Based Biomarker Estimation: A Case Study of Fetus Head Circumference Assessment from Ultrasound Images. *Journal of Imaging*. 2022; 8(2):23.
https://doi.org/10.3390/jimaging8020023

**Chicago/Turabian Style**

Zhang, Jing, Caroline Petitjean, and Samia Ainouz.
2022. "Segmentation-Based vs. Regression-Based Biomarker Estimation: A Case Study of Fetus Head Circumference Assessment from Ultrasound Images" *Journal of Imaging* 8, no. 2: 23.
https://doi.org/10.3390/jimaging8020023