Impact of geometric irregularity and error on 3D surface reconstruction in Digital Imaging Elasto-Tomography System

High-accuracy three-dimensional (3-D) breast-surface reconstruction is pivotal for vibration-based diagnostic modalities, such as the Digital Imaging Elasto-Tomography (DIET) breast cancer screening technology. Yet the coupled influence of geometric complexity and measurement noise in structured-light systems has not been quantified rigorously in this type of application. To address this gap, we establish a dual-track evaluation framework combining ground-truth numerical simulations with laser-scanned silicone phantom data to assess reconstruction fidelity under clinically relevant conditions.

Analytically defined hemispherical point clouds, both regular and irregular, were synthesised and corrupted with random and periodic noise of varying amplitudes, creating a benchmark data set with explicit, known ground truth. In parallel, anatomically realistic silicone breast phantoms without internal, high stiffness tumour-mimicking inclusions were imaged using a 39-beam, 520 nm structured-light system. Approximately 70 calibration poses were acquired per laser line, yielding sub-millimetre accuracy. All data were processed within a spherical-polar parameterisation and optimised by a Levenberg–Marquardt scheme. Reconstruction error was quantified via root-mean-square error (RMSE), inter-quartile range (IQR), outlier counts, and multiple visualisations (histograms, spatial error maps, and boxplots).

Results reveal a clear performance hierarchy. Under noise-free conditions the simulated hemisphere shows the lowest RMSE, whereas sparse sampling in the phantoms causes local surface depressions. Systematic (periodic) noise dominates the error budget, increasing RMSE by an order of magnitude and producing persistent ring- or band-shaped artefacts across all reconstructions. Random noise mainly introduces local high-frequency roughness. Concave deformations generate a stable toroidal residual whose contribution to global RMSE remains below 10 % in the absence of noise. When geometric irregularities and noise coexist, the resulting errors greatly exceed those due to shape alone, underscoring noise suppression as the primary determinant of best attainable accuracy in this application.

The proposed simulation-and-phantom framework delivers the first comprehensive error map for structured-light breast reconstruction in a DIET system and indicates future algorithms must integrate curvature-adaptive modelling with explicit compensation for periodic perturbations to remain robust across the wide spectrum of breast sizes and shapes encountered in clinical practice.