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Deep DIC: Deep Learning-Based Digital Image Correlation for End-to-End Displacement and Strain Measurement
Ru Yang, Yang Li, Danielle Zeng, Ping Guo
TL;DR
Traditional DIC can become unreliable when deformation is large and speckle patterns deteriorate, while prior deep-learning approaches had not reliably demonstrated full-field strain prediction. Deep DIC uses separate CNNs for displacement and direct strain prediction, and the paper reports comparable or better performance than traditional DIC, including robust strain prediction in challenging conditions.
Problem
Prior deep-learning DIC methods had not reliably demonstrated full-field strain prediction, and traditional DIC becomes problematic under large deformation and deteriorated speckle patterns.
Method
Deep DIC uses an end-to-end approach with separate CNNs that predict displacement and strain fields directly from image inputs.
Results
Deep DIC is reported to provide comparable or better predictions than traditional DIC, with more robust strain prediction at large deformation.
Takeaways & Limitations
Direct strain prediction is presented as a route to addressing the limitations of deriving strain from predicted displacement fields.
Takeaways & Limitations
Earlier deep-learning DIC work did not achieve strain prediction and did not outperform traditional DIC in displacement prediction.
Abstract
from arXiv · showhide
Digital image correlation (DIC) has become an industry standard to retrieve accurate displacement and strain measurement in tensile testing and other material characterization. Though traditional DIC offers a high precision estimation of deformation for general tensile testing cases, the prediction becomes unstable at large deformation or when the speckle patterns start to tear. In addition, traditional DIC requires a long computation time and often produces a low spatial resolution output affected by filtering and speckle pattern quality. To address these challenges, we propose a new deep learning-based DIC approach--Deep DIC, in which two convolutional neural networks, DisplacementNet and StrainNet, are designed to work together for end-to-end prediction of displacements and strains. DisplacementNet predicts the displacement field and adaptively tracks a region of interest. StrainNet predicts the strain field directly from the image input without relying on the displacement prediction, which significantly improves the strain prediction accuracy. A new dataset generation method is developed to synthesize a realistic and comprehensive dataset, including the generation of speckle patterns and the deformation of the speckle image with synthetic displacement fields. Though trained on synthetic datasets only, Deep DIC gives highly consistent and comparable predictions of displacement and strain with those obtained from commercial DIC software for real experiments, while it outperforms commercial software with very robust strain prediction even at large and localized deformation and varied pattern qualities. In addition, Deep DIC is capable of real-time prediction of deformation with a calculation time down to milliseconds.
1. Introduction
Traditional DIC provides full-field deformation measurements but faces trade-offs among continuity, precision, efficiency, and robustness under severe deformation. Deep DIC addresses these challenges with end-to-end CNN-based displacement and direct strain prediction.
- Traditional DIC extracts full-field displacement and strain from image pairs, supporting noncontact measurement in material testing.
- Subset-based methods can be parallelized, but discontinuities between subsets may produce noisy strain fields.
- Global methods enforce displacement compatibility for heterogeneous deformation, but have lower prediction precision and computational efficiency than subset-based methods.
- Large tensile strains can tear speckle patterns, causing commercial DIC software to fail to predict strain or output displacement in severely distorted regions.
- Deep DIC directly predicts displacement and strain fields from image inputs using two CNNs, with StrainNet avoiding spatial derivatives of displacement.
- The approach targets robust large-deformation strain prediction, comparable or better accuracy for smaller deformations, and reduced computation time.
2. Methods
Deep DIC uses separate CNNs to predict displacement and strain fields directly from image pairs, with adaptive ROI tracking for large deformation. It is trained on synthetic data generated from varied speckle patterns and analytically defined deformation fields.
- Deep DIC workflow: DisplacementNet and StrainNet independently predict displacement and strain fields from raw image inputs within an adaptively tracked ROI.The ROI is updated from accumulated displacement at four corner points and repeated across image pairs.
- Deep DIC architecture: DisplacementNet outputs two displacement-component images, while StrainNet outputs three plane-strain-component images from the same image-pair input.The reported components are u and v for displacement and εxx, εyy, and εxy for strain.
- Deep DIC architecture: The two CNNs use modified encoder-decoder architectures designed to recover high-resolution displacement and strain fields.Encoder-decoder operations condense and restore feature maps, while added feature-map concatenations preserve details.
- Synthetic dataset generation: The models are trained entirely on synthetic datasets containing reference and deformed images with predefined displacement and calculated strain ground truths.Synthetic training reduces data-generation cost and provides control over dataset quality.
- Synthetic dataset generation: Synthetic samples combine varied speckle patterns with analytically defined motion and deformation fields, then warp the patterns to produce deformed images.Strain ground truth is calculated from spatial derivatives of the defined displacement field.
Speckle pattern generation
The dataset generator creates unique speckle images with controlled pattern-quality variations to improve Deep DIC robustness and adaptivity.
- Pattern construction: Each speckle pattern is generated by stacking ellipses with random sizes and gray-scale values.Each 512 × 512 frame contains 2,800 to 4,500 ellipses, and patterns are not reused across samples.
- Pattern-quality variation: The dataset deliberately includes sparse, large-speckle, noisy, and low-contrast patterns to vary speckle quality.The stated proportions are 5% sparse, 30% large-speckle, 5% extra-noise, and 5% low-contrast samples.
- Pattern-quality variation: The generated pattern-quality examples are documented in Figure 5 and the generation procedure is summarized in Table 1.These references organize the visual examples and parameterized generation algorithm.
Displacement and strain field generation
The synthetic displacement field combines rigid-body motion, uniform deformation, and localized Gaussian deformations, while its analytically derived strain field supplies StrainNet ground truth.
- Random rigid-body translation, rotation, stretch/compression, shear, and localized Gaussian deformations define each 2D displacement field.
- The displacement components u and v are defined over reference-image pixel coordinates x and y.
- Randomized parameters control translation, rotation, stretch/compression, shear, Gaussian amplitudes, centers, and standard deviations.
- Random cropping shifts the effective rotation center and allows Gaussian deformation peaks to lie outside the image frame.
- The generated displacement field trains DisplacementNet, while spatial derivatives under an infinitesimal-strain assumption generate StrainNet ground truth.
- Smooth Gaussian displacement functions ensure compatibility of the corresponding strain fields.
Image deformation
Deformed training images are synthesized by warping speckle images with prescribed displacement fields, then cropping, adding noise, and downsampling them.
- Prescribed displacements are applied to pixels, and scattered deformed-grid samples are interpolated back onto a uniform grid.
- Zero-mean Gaussian noise with intensity 0.001 is added separately to reference and warped images to mimic capture noise.
- Images are downsampled to 128 × 128 to blur sharp edges, and generated fields with reference/deformed speckle images are illustrated in Figure 6.
Appendix A.
The networks use PyTorch-based CNN implementations with separate mean-square-error objectives, Adam optimization, and validation-based convergence tracking.
- Implementation and training: DisplacementNet and StrainNet are implemented on PyTorch, with Torchvision building the CNN structure and Pillow handling image loading, cropping, and resizing.
- Implementation and training: DisplacementNet minimizes displacement-field MSE multiplied by 10, while StrainNet minimizes strain-field MSE multiplied by 100.
- Implementation and training: Adam optimization uses adaptive learning rates to accelerate convergence, with β1 = 0.9 and β2 = 0.999.
- Evaluation: Performance is evaluated on synthetic and experimental data through direct comparisons with VIC-2D and GOM Correlate, including displacement and strain fields.
Direct strain prediction from StrainNet
StrainNet predicts strain directly from image pairs rather than differentiating predicted displacement, avoiding derivative-amplified noise and improving strain accuracy. Across test examples, Deep DIC outperforms VIC-2D, including under complex and large deformation, but StrainNet assumes infinitesimal strain and supports only its trained strain measure directly.
- Direct prediction: StrainNet directly predicts strain from image pairs, independent of displacement predictions, unlike spatial-derivative strain recovery.
- Motivation: Traditional spatial filtering reduces strain resolution and requires a tuning parameter without an established selection guideline.
- Direct prediction: Displacement discontinuities amplify high-frequency noise during differentiation, so accurate displacement can still yield erroneous strain fields.
- Direct prediction: A displacement error of 0.016 pixels produced calculated-strain maximum and average errors of 5.93% and 0.24%, versus 0.11% and 0.018% for StrainNet.
- Direct prediction: Direct prediction also improves spatial resolution and handles rigid-body rotation by implicitly removing rotational influence from strain calculation.
- Scope and limitations: StrainNet is trained under an infinitesimal-strain assumption and cannot directly output other strain measures without separately defined networks.
- Comparison with VIC-2D: On test examples, Deep DIC predicts all displacement and strain components more accurately than VIC-2D, with VIC-2D errors 2–7 folds larger on one example.
- Comparison with VIC-2D: For the test set, maximum and average strain errors are 0.085% and 0.041%, and Deep DIC performs better than commercial DIC software.
Noise floor level
Deep DIC was evaluated on stationary speckle images to measure displacement and strain noise floors against VIC-2D. Its displacement noise was slightly better, while its strain noise was comparable but marginally higher.
- Experimental setup: 21 stationary speckle-image pairs were processed by both Deep DIC networks and VIC-2D, with ideal displacement and strain fields equal to zero and uniform.The experiment used a CMOS camera and telecentric lens under fixed imaging conditions.
- Displacement noise: 0.0094 pixels was DisplacementNet’s average noise floor, with a standard deviation of 0.065 pixels, slightly better than VIC-2D.The comparison is summarized in Table 5.
- Strain noise: 0.0073% strain was StrainNet’s average noise floor, with a standard deviation of 0.0045%, on par with the commercial solution.Unlike conventional strain evaluation derived from displacement, StrainNet’s independent strain prediction makes its noise floor directly measurable.
Validation of rigid body translation
Deep DIC was tested on rigid-body translation using real image sequences and compared with VIC-2D. Its displacement prediction differed noticeably because the synthetic training data lacked uniform translation examples.
- Experimental setup: 19 commanded motions of 35 μm each produced 20 captured images for evaluating rigid-body translation without sample stretching.The moving side was clamped, and the camera system matched the noise-floor experiment.
- Comparison: 0.275 pixels was the maximum difference between DisplacementNet and VIC-2D, occurring in the eighth frame.The predicted translational motion was obtained by averaging each predicted displacement field.
- Comparison: DisplacementNet produced non-uniform fields and noticeable differences from VIC-2D in this rigid-translation test.The result was less impressive than its tensile-testing performance.
- Limitation: The training distribution contained no uniform displacement field, so adding pure translation or rotation samples could improve rigid-body prediction.The paper attributes the limitation to how random displacement fields were defined.
Experimental result on a tensile test sample of bronze
On a bronze tensile test, Deep DIC produced displacement fields comparable to VIC-2D and strain fields that remained valid around large deformation and torn speckles. It also preserved image-scale resolution and ran substantially faster.
- Comparison: Interpolation made VIC-2D predictions appear smoother in some comparisons, but the paper states this did not indicate better prediction accuracy.VIC-2D’s subset and step sizes also reduced its output resolution relative to the input image.
- Displacement: DisplacementNet and VIC-2D showed closely matching displacement magnitudes and spatial distributions across the tensile sequence.VIC-2D exhibited quality fluctuations near a white speckle-image spot, whereas DisplacementNet was less affected by pattern variation.
- Strain: StrainNet produced reasonable strain results at edges and locations where VIC-2D became invalid as speckles broke under large deformation.The methods otherwise matched well in overall strain magnitude and spatial pattern, while StrainNet better captured localized concentration at T3.
- Computation: 12.5 milliseconds per frame was Deep DIC’s calculation time for 189 frames, versus about 27 seconds for VIC-2D.Deep DIC’s 2.35-second total included image loading and calculation of both displacement and strain fields.
Validation on ultra-large strain measurement
On an ultra-stretchable polymer test, StrainNet remained reliable beyond 100% strain and around torn speckles, where commercial DIC became unstable or invalid. Deep DIC also maintained faster, more stable computation and uses direct image-to-strain prediction.
- Full-field robustness: StrainNet produced reasonable full-field strain predictions where GOM Correlate showed invalid zones around specimen edges and cracks.The two methods had comparable strain distributions and magnitudes in the tested frame before this divergence.
- Ultra-large strain: StrainNet and GOM Correlate agreed through 80% strain, after which GOM Correlate frequently produced invalid values under localized deformation and torn speckles.StrainNet remained reliable for the group exceeding 100% cumulative strain.
- Method: Direct strain prediction from StrainNet avoids errors from discontinuous displacement fields, preserves high spatial resolution, and requires no post-filtering.StrainNet predicts strain independently from displacement and implicitly removes rigid-body motion effects from strain calculation.
- Overall outcome: Deep DIC was trained only on synthetic data yet performed well on simulated and experimental data, including large localized deformation and torn speckle patterns.Its dataset included varied speckle quality and deformation cases such as translation, rotation, stretch, compression, shear, and localization.
B. Visualization of the feature maps
The feature maps show that DisplacementNet and StrainNet extract increasingly different representations with depth. DisplacementNet develops localized features, whereas StrainNet distributes features more uniformly, consistent with their different computational needs.
- Both networks extract low-level features such as speckle boundaries in their first convolutional layer.The first layer contains 64 feature maps in each CNN.
- The second-layer feature maps remain topologically similar but exhibit substantial point-to-point variance.
- From the third layer onward, the learned representations of DisplacementNet and StrainNet become clearly different.
- DisplacementNet develops localized features, while StrainNet retains more uniformly distributed features.This indicates that the two CNNs extract information from different spatial regions and distributions.
- StrainNet requires more global information because strain calculation removes rigid-body translation and rotation, unlike local displacement correlation.