HAC-NET: A soft displacement estimation network for digital image correlation

Digital image correlation (DIC) plays an important role in full-field deformation analysis. However, existing methods suffer from insufficient accuracy because hard matching mechanisms fail to fully exploit the matching information in correlation volumes. Additionally, the limited receptive field of conventional convolutional neural networks (CNNs) and the inadequate feature fusion in mainstream coarse-to-fine architectures make it difficult to achieve high-precision continuous measurement of small-displacement deformations. To address these issues, this paper proposes a Hierarchical Attention-guided Coarse-to-fine displacement estimation Network (HAC-NET). A Swin Transformer backbone is employed to enlarge the receptive field. A Bidirectional Cross-Feature Transformer (BCFT) module is designed to enable global feature interaction between the reference and deformed images. A Soft-Matching Adaptive Patch Matching (SMAPM) module is further constructed to resolve the discretization problem of hard matching and achieve high-precision sub-pixel displacement estimation. In addition, convex upsampling combined with a multi-stage fusion strategy is employed to address boundary blurring and inter-stage error accumulation. Experimental results demonstrate that HAC-NET reduces the endpoint error (EPE) to 0.0150 and 0.0205 pixels on the Speckle and Hermite datasets, respectively, representing improvements of 75.8% and 44.9% over state-of-the-art methods. On a Multi-deformation dataset (Mfd-Dataset) constructed to cover diverse real-world engineering deformation scenarios, the EPE reaches 0.0225 pixels. In real-world uniaxial tensile experiments, the predicted displacement fields show strong agreement with those obtained by a traditional high-precision subset-based algorithm. These results verify the advantages of the proposed method in terms of both high accuracy and generalization capability under small-displacement deformation scenarios.