A Semi-Supervised Sparsity-Aware Loss Function for Crack Segmentation

Detecting and identifying cracks is critical for infrastructure health monitoring. In surface images, cracks often appear as thin structures with background-like intensity due to low contrast and noise from road elements. Although deep learning has greatly advanced image segmentation techniques, pixel-level loss functions are insufficient for maintaining the connection and topology of thin curvilinear structures such as cracks, which causes sparsity. In this paper, a semi-supervised sparsity-aware loss function for crack segmentation is proposed to address this problem, which incorporates an unsupervised sparsity-aware loss with supervised losses ${\mathcal{L}_{{\text{BCE}}}}{\text{ and }}{\mathcal{L}_{{\text{Dice}}}}$. First, we propose an unsupervised Sparsity-Aware loss function, ${\mathcal{L}_{{\text{SA}}}}$ to penalize the model's intention to create more regions. Then, we combine the ${\mathcal{L}_{{\text{BCE}}}}{\text{ with }}{\mathcal{L}_{{\text{SA}}}}$ to reduce fragmented segmentation. Eventually, in order to resolve the imbalance in pixel-level crack segmentation, we integrate it with ${\mathcal{L}_{{\text{Dice}}}}$ to obtain the proposed Semi-Supervised Sparsity-Aware loss ${\mathcal{L}_{{\text{SSSA}}}}$. We demonstrate the proposed method with crack segmentation models on three public datasets: Crack500, DeepCrack, and Gaps384. Compared to the most widely used ${\mathcal{L}_{{\text{BCE - Dice}}}}$ loss in public datasets, our proposed ${\mathcal{L}_{{\text{SSSA}}}}$ improved recall, F<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-score, and IoU by as much as 4.1%, 2.2%, and 3.2%, respectively.