GExPC: An Explainable Evolutionary Approach for Crack Segmentation with Probabilistic Circuits

Crack segmentation is a fundamental task in structural inspection and has traditionally relied on resource-intensive, black-box Deep Learning (DL) models. To address this, we introduce GExPC, an explainable approach combining Probabilistic Neural Circuits (PCNets) with Grammatical Evolution (GE) to automatically discover compact, task-adapted architectures. Evaluated across six benchmarks, GExPC uses fewer than 100 learnable parameters yet achieves competitive performance—particularly in recall and shape preservation—against state-of-the-art DL models requiring millions of parameters. Our results demonstrate that evolutionary search over PC structures provides a highly efficient, interpretable alternative to standard DL for vision-based structural inspection.