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Computational Depth Measurement in Thermographic Video: Overcoming Spatial Overfitting via Spatio-Temporal Decoupling

Zain Ul Abidin, Habeeban Memon, Junaid Ahmed

arXiv:2608.29223v1cs.AIcs.CV

TL;DR

Hidden CFRP delamination depth matters for structural assessment, but regular calibration layouts can make regression models memorize spatial geometry rather than thermal-depth relationships. The paper separates defect localization from temporal depth measurement and evaluates physics-informed regression under specimen-level cross-validation. Regularized XGBoost achieves MAE 0.056 mm and RMSE 0.085 mm, while RF, GBM, and Adv-MLP degrade under geometric shifts.

  • Problem

    Regular calibration layouts can correlate spatial position with depth, allowing models to use geometry as a hidden depth label instead of learning thermal physics.

  • Method

    The framework localizes defects spatially, averages each region into a one-dimensional temporal response, and uses physics-informed features without pixel coordinates for depth regression.

  • Results

    MAE 0.056 mm and RMSE 0.085 mm are achieved by regularized XGBoost under specimen-level cross-validation, while RF and GBM fail on the changed circular layout.

  • Takeaways & Limitations

    Spatio-temporal decoupling and regularization reduce spatial memorization in thermographic-video depth regression across geometric shifts.

Abstract

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Accurate through-thickness measurement of subsurface delamination depth in Carbon Fiber Reinforced Polymer (CFRP) is important for structural assessment because defect location determines affected load-bearing layers. Optical pulsed thermography (OPT) provides a two-dimensional thermal video rather than volumetric measurements, so depth must be inferred from temporal heat-diffusion responses. A challenge is spatial dataset bias: when calibration defects follow regular grids, regression models may memorize their geometry instead of learning physical relationship between thermal decay and depth. This work introduces a spatio-temporal decoupling architecture that separates spatial defect localization from temporal depth measurement. Defect regions are first localized using segmentation methods, after which thermal responses are spatially averaged and converted into sixteen physics-informed temporal, energy, statistical, and geometric features. These features expose the one-dimensional heat-conduction relationship while withholding pixel coordinates from the depth model. Four regression models are evaluated using specimen-level cross-validation: Random Forest (RF), Gradient Boosting Machine (GBM), Advanced Multi-Layer Perceptron (Adv-MLP), and XGBoost. Unregularized trees and over-parameterized Adv-MLP exhibit calibration collapse under geometric shifts, with errors exceeding 0.5 mm. In contrast, regularized XGBoost with L1/L2 penalties and column sampling maintains cross-specimen calibration, achieving a mean absolute error (MAE) of 0.056 mm and root mean square error (RMSE) of 0.085 mm. Predicted depths are merged with masks to generate Delaunay-triangulated three-dimensional defect models in three to five seconds per specimen. Results show that mathematical regularization and spatio-temporal decoupling reduce spatial memorization in thermal-video depth regression.

I. INTRODUCTION

Thermographic depth measurement is needed because hidden CFRP delaminations affect different load-bearing layers, but spatially regular calibration layouts can let models memorize geometry instead of learning thermal-depth relationships. The proposed response is to separate defect localization from temporal depth regression and use physics-informed features without pixel coordinates.

  • Motivation: Through-thickness depth estimates are necessary because hidden delaminations at different laminate depths affect different load-transfer paths.Binary defect detection alone is therefore insufficient for structural assessment.
  • Thermographic basis: OPT records transient surface cooling in a thermal tensor, while one-dimensional heat conduction relates defect depth to peak contrast time.Thermal diffusivity and a geometric factor define the physical relationship.
  • Challenge: Analytical depth estimation remains sensitive to specimen-dependent thermal properties, geometry, and heating conditions.
  • Spatial dataset bias: Regular calibration layouts correlate spatial position with depth, allowing unregularized trees and over-parameterized neural networks to memorize geometry as a hidden label.Such models can lose calibration when the geometric proxy changes.
  • Proposed response: The framework averages localized defect pixels into one-dimensional temporal responses and supplies sixteen physics-informed features to the depth model instead of image coordinates.Spatial information is retained for mapping predicted depth back onto detected boundaries and three-dimensional reconstruction.

II. SPATIO-TEMPORAL DECOUPLING MEASUREMENT METHODOLOGY

The methodology uses a pretrained segmentation front end to identify defect regions, then applies the same downstream measurement procedure across specimen geometries while withholding component position from regression.

  • Architecture: The workflow separates spatial defect-boundary extraction from temporal regression modeling.The overall architecture is presented as a structured two-stage measurement pipeline.
  • Stage 1: Spatial Defect Localization: A pretrained DeepLabV3+ model localizes defects from a cyclically aligned three-channel thermographic fusion.The fusion combines raw intensity, PCT spatial components, and TSR temporal coefficient images.
  • Stage 1: Spatial Defect Localization: The segmentation network produces a binary mask, and connected-component labeling identifies individual defect regions.
  • Geometry-independent processing: The same downstream procedure handles square and circular specimens without supplying component (x, y) position as a regression feature.Predicted masks were reported across all six specimens with reliable detection across both geometries.

B. Stage 2: Spatial-to-Temporal Decoupling

The method averages thermal responses within localized defect regions, replacing pixel-level spatial signals with one-dimensional temporal measurements and sixteen physics-informed features for depth regression.

  • Averaging within each region reduces local thermal fluctuations and suppresses the geometric arrangement that can create spatial bias.Under approximately independent pixel noise, the noise standard deviation decreases approximately with 1/√|Ωk|.
  • Spatial averaging transforms each detected defect from a two-dimensional signal into a one-dimensional temporal measurement.The regression model no longer receives calibration-grid position, while spatial coordinates are retained for later visualization and reconstruction.
  • Depth levels remain distinguishable after spatial averaging through changes in peak timing and thermal amplitude.The measured curves include SQ 01 depths from 0.2 to 1.0 mm and CI 01 inserts at 2.0 and 2.2 mm.
  • The sixteen features combine temporal, energy, statistical, and geometric descriptors to constrain regression around the one-dimensional heat-conduction relationship.Temporal features include peak time and drel = √tpk; geometric descriptors characterize defect extent rather than absolute image position.
  • The architecture separates spatial localization from temporal measurement, using detected masks to support downstream thermal-response extraction.The figure sequence shows defect masks followed by mean thermal responses and a feature table for depth regression.

D. Algorithmic Diagnostics and Regularized Regression

The study compares four regression strategies diagnostically and uses regularized XGBoost to constrain dependence on idiosyncratic features and accidental training-set structure.

  • RF, GBM, Adv-MLP, and XGBoost are compared to diagnose robustness under geometric distribution shift rather than merely minimize training error.RF and GBM are unregularized tree controls, Adv-MLP tests neural-network capacity, and XGBoost tests explicit regularization.
  • The Adv-MLP uses three hidden layers with batch normalization, dropout, Adam optimization, Huber loss, and early stopping, but high capacity does not ensure representation robustness.It serves as a control separating robustness of the loss function from robustness of the representation.
  • XGBoost is the regularized model used for final depth measurement, with L1/L2 penalties and column sampling.These constraints discourage reliance on a small set of idiosyncratic feature dimensions and reduce capacity to reproduce accidental training-set structure.
  • The correlation diagnostic shows that temporal variables have the strongest relationship with depth, whereas geometric variables are weaker indicators of through-thickness position.The result is consistent with depth being encoded primarily in temporal diffusion response rather than lateral extent or shape.
  • Spatial decoupling removes the main geometric shortcut before regression, while regularization controls the remaining model capacity.The two constraints operate at different levels within the measurement pipeline.

E. Feature Diagnostic

The feature diagnostic indicates that temporal variables carry the strongest relationship with depth, while geometric variables primarily describe lateral defect properties.

  • Temporal variables, particularly tpk and drel, show the strongest relationship with depth in the Pearson correlation matrix.This agrees with the heat-conduction relationship linking depth to temporal diffusion response.
  • Geometric variables are weaker indicators of through-thickness position and instead describe defect area and aspect ratio.

F. Automated 3D Reconstruction for Structural Analysis

The framework converts localized thermal defects into predicted depths and then reconstructs three-dimensional surface meshes. This preserves spatial registration while completing reconstruction in 3–5 seconds per specimen.

  • Surface generation: Predicted depths are combined with calibrated pixel coordinates to form top and bottom point clouds for each defect.The bottom surface adds the 0.0075 mm insert-thickness gap.
  • Mesh construction: Delaunay triangulation converts the point clouds into three-dimensional defect surface meshes, with mean surface distance equal to absolute regression error.The predicted depth determines the mesh elevation, while segmentation supplies spatial localization.
  • Pipeline: The pipeline segments thermal data, averages each defect region into a temporal response, extracts sixteen features, and predicts depth with regression models.Each defect is processed independently before reconstruction.

A. Datasets and Specimen-Level Cross-Validation

The study uses six CFRP specimens spanning square and circular defect layouts, then evaluates models with specimen-level cross-validation. This design tests whether calibration survives changes in specimen geometry and defect arrangement.

  • Datasets: Six CFRP specimens from two databases provide different geometries, defect arrangements, spatial resolutions, and depth ranges for diagnostic testing.The datasets are intentionally evaluated across differing spatial organizations rather than merged into a homogeneous dataset.
  • Datasets: Dataset 1 contains three specimens with 25 square inserts arranged in a 5 × 5 grid at depths from 0.2 to 1.0 mm.The specimens include flat, curved, and trapezoidal geometries.
  • Datasets: Dataset 2 contains circular inserts at two depth levels, 2.0 and 2.2 mm, without the rigid five-column arrangement of the square specimens.This layout is useful for diagnosing spatial bias.
  • Cross-validation: No individual defect is split across training and test sets in specimen-level cross-validation.This prevents evaluation on another region of the same specimen after learning specimen-specific spatial or thermal signatures.
  • Cross-validation: Fold 2 trains on the rigid-grid SQ 03 specimen and tests on columnless circular CI 02, creating the strongest diagnostic geometry shift.A geometry-dependent model should show a large calibration change in this split.

B. Evaluation Metrics

The evaluation reports MAE, RMSE, and R2, with MAE as the primary depth metric because it is expressed directly in millimeters. For circular specimens, R2 must be read alongside absolute-error metrics because the target range is narrow.

  • Metrics: Mean absolute error is the primary measurement metric because it is expressed directly in millimeters.The metric compares true and predicted depths through absolute differences.
  • Metrics: Root mean square error gives greater influence to large calibration errors.This complements MAE by emphasizing larger deviations.
  • Interpretation: R2 should be interpreted together with MAE and RMSE for circular specimens because their target range is narrow.A modest absolute error can produce a strongly negative R2 when true-label variance is small.

IV. RESULTS AND DISCUSSION

The cross-fold results test whether depth calibration survives changes in specimen geometry rather than merely matching a familiar layout. Regularized XGBoost maintains the strongest cross-specimen performance, while unregularized controls degrade under geometric shifts.

  • Evaluation logic: Matched-geometry accuracy is insufficient evidence of learned thermal physics; the decisive test is calibration after changing specimen geometry and defect arrangement.The evaluation is framed primarily as a generalization diagnostic.
  • Fold 1: Fold 1 is a favorable control in which training and test specimens preserve comparable square and circular families.RF and GBM achieve low errors on several test groups, while Adv-MLP still records an overall MAE of 0.1831 mm.
  • Fold 2: RF reaches an MAE of 0.5209 mm and GBM reaches 0.6834 mm on CI 02 in Fold 2, exceeding the 0.2 mm separation between circular depth levels.Their R2 values are −27.37 and −51.29, respectively, when the spatial proxy changes.
  • Fold 2: XGBoost reaches a CI 02 MAE of 0.0756 mm and an overall Fold 2 MAE of 0.0473 mm, with overall R2 of 0.992.The representation removes pixel-level coordinates, while L1/L2 penalties and column sampling constrain model capacity.
  • Fold 3: Fold 3 yields an overall XGBoost MAE of 0.0888 mm and R2 of 0.971, while Adv-MLP reaches 0.5620 mm overall.All models experience some degradation when training shifts from curved SQ 02 to flat SQ 01.
  • Aggregate results: 0.056 mm MAE and 0.085 mm RMSE are achieved by regularized XGBoost averaged across the three folds.The corresponding overall GBM error is approximately 0.123 mm, and the XGBoost advantage persists across geometric distribution shifts.
  • Visual results: Fig. 5 compares actual and predicted depths across folds, highlighting GBM calibration in Fold 1 and regularized XGBoost generalization in Folds 2 and 3.The visual comparison spans shifts from rigid square grids to columnless circular layouts.
  • Visual results: Fig. 6 shows true green and predicted red three-dimensional defect surfaces with accurate spatial registration and resolution of closely spaced layers.The reconstruction visualizes the depth predictions as registered structural geometries.

B. Three-Dimensional Computational Reconstruction

The framework converts predicted depths and segmentation masks into Delaunay-triangulated three-dimensional defect models, preserving detailed spatial and sub-millimeter depth structure. Regularized XGBoost supports this reconstruction, while the method remains constrained by its one-depth-per-defect assumption and practical segmentation and resolution limits.

  • 3–5 seconds per specimen: Delaunay triangulation converts predicted depths and segmentation masks into three-dimensional defect models.Top and bottom point clouds are generated before triangulation.
  • All 25 square defects across five depth layers are resolved with close alignment between predicted and true positions for SQ 03.The layers span 0.2, 0.4, 0.6, 0.8, and 1.0 mm.
  • 0.2 mm spacing between circular defect levels is distinctly visible for CI 03, indicating preserved sub-millimeter depth resolution.The separated levels are 2.0 and 2.2 mm.
  • Regularized XGBoost achieves an MAE of 0.056 mm and an RMSE of 0.085 mm under specimen-level cross-validation.The model uses L1/L2 penalties and column sampling.
  • The framework assumes one depth per localized defect and is not yet suited to sloped or multi-level impact damage.Small defects near the camera resolution limit and segmentation errors remain practical constraints.
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