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Accurate Reconstruction of Gas Turbine Blade Geometry Using 3D/2D Rigid Registration and CT View Optimization
Hristo Valtchanov, Nicolas Piché, Vladimir Brailovski, Justin Byers, Catherine Désrosiers, François Guibault
TL;DR
Dimensional inspection of gas-turbine blades with complex internal structures can be difficult using CT reconstruction. The paper instead registers multipart CAD models directly to X-ray projections, using greedy mutual-information alignment and view optimization. It reports subpixel accuracy, with experimental RMS errors of 0.36–0.42 pixels, while image noise, defects, and segmentation quality remain important uncertainty sources.
Problem
Gas-turbine blade inspection requires accurate measurement of complex internal structures, while CT reconstruction can be affected by image-quality limitations.
Method
The method greedily registers exterior and interior CAD components sequentially by maximizing mutual information between partial simulated and acquired X-ray projections.
Results
Subpixel accuracy was achieved, with noise-free simulation errors of 0.05–0.1 pixels and CT-comparison RMS errors of 0.36–0.42 pixels.
Takeaways & Limitations
Sequential rigid registration and greedy view selection support projection-based inspection, while adding views mainly reduces variability after the first few informative angles.
Takeaways & Limitations
Image noise, CT-derived segmentation quality, and elastic deformation constrain registration accuracy, and noise or defects can reduce precision.
Abstract
from arXiv · showhide
Non-destructive X-ray and computed tomography (CT) testing are essential for ensuring the dimensional accuracy of manufactured components with complex internal structures, such as the cooling channels in gas turbine blades, which directly affect thermal performance and service life. This study presents a multipart 3D-2D rigid registration approach for aligning CAD models with X-ray projections as an alternative to CT reconstruction for part inspection and measurement. A greedy registration algorithm sequentially aligns the blade's exterior before registering its internal components by maximizing the mutual information between simulated and acquired X-ray images. This stepwise approach reduces problem complexity and improves alignment accuracy. View angles are optimized using a greedy method that iteratively selects angles to minimize dimensional measurement errors. The results indicate that a small number of oblique views provides the best accuracy, although a broad range of angles yields acceptable results. The method achieves subpixel registration accuracy, with errors below one-fifth of the magnified detector-pixel pitch. Image noise and defects reduce registration precision, but direct registration in projection space mitigates these effects compared with CT reconstruction. Appropriate view selection can therefore preserve acceptable subpixel accuracy in the presence of image noise and defects.
1 Introduction
The study addresses multipart 3D-2D registration for industrial inspection, focusing on how image quality, noise, and projection-view geometry affect registration accuracy and robustness.
- 3D-2D Registration: 3D-2D registration aligns three-dimensional meshes or volumes with two-dimensional projection images for applications including industrial inspection and nondestructive testing.The paper focuses on registering multiple rigid CAD components with X-ray projections.
- Study Focus: The paper investigates projection-based registration as an industrial inspection and metrology approach using multiple rigid CAD components and X-ray projections.The work is situated within nondestructive testing and part inspection applications.
- Multipart Registration: Multipart registration must account for occlusion, clutter, missing visibility, and independently aligned segmented or articulated components.Prior approaches include deformable superquadrics, regularized iterative closest point, point-to-plane correspondence, and RANSAC-based registration.
- Image Quality and View Angles: Image quality, noise, and the number and angular separation of projection views strongly affect registration accuracy and robustness.Additional views can improve robustness without necessarily improving accuracy, while a small to moderate number of oblique views was often optimal.
2 Methods
The method sequentially registers CAD components to X-ray projections by maximizing mutual information, simulates radiograms with depth maps and attenuation, and optimizes views and registration numerically.
- Objectives: The study targets automated CAD-component pose estimation, view-angle selection, and subpixel accuracy relative to a 0.2-pixel manufacturing target.It evaluates registration against CT-based measurement and studies view-angle optimization with and without noise.
- Multipart Registration Procedure: Registration proceeds from exterior to interior components, adding each registered component to partial simulated radiograms while excluding components not yet registered.Each component undergoes independent rigid translation and rotation estimated by maximizing mutual information over selected views.
- Simulated X-ray Projections: Depth maps are generated by casting rays through detector-pixel centers, combining solid and void path lengths, and converting the composite map into an attenuated simulated radiogram.The simulator uses ray casting or rasterization, and noise can be added to model real-world variability.
- Objective Function: Mutual information compares simulated and observed images through joint and marginal intensity distributions, with Shannon entropy used for normalization.The objective is evaluated across projection views during registration.
- Optimization Approach: Powell's conjugate-direction method was selected for the nonconvex objective, then modified using estimated directions, perturbation-based PCA or Hessian information, and parameter grouping.Reducing search directions decreases iterations while retaining the method's robustness, although convergence to the global optimum is not guaranteed.
- View-Angle Optimization: View angles are added and refined greedily, with repeated registrations and thickness-error evaluation based on ray intersections with inner and outer meshes.The Brent algorithm solves the single-angle refinement problem over [0,2π].
- Noise Model: Zero-mean Gaussian noise is independently added to pixels with standard deviation 0.025, followed by renormalization to intensities between 0 and 1.This noise level reproduces normalized mutual information values of 0.5–0.6 observed in actual CT images, depending on image quality.
3 Results
The method achieved subpixel agreement with CT-derived measurements and showed that oblique view separations improve registration accuracy, while noise and reconstruction defects affect precision.
- Greedy registration aligned the exterior and internal components sequentially while increasing mutual information as components were added.Figure 4 presents the sequential alignment process and its normalized mutual-information convergence history.
- 0.42 pixels for the PWA blade and 0.36 pixels for the PWC blade were the reported RMS registration errors against CT-derived measurements.These values were normalized by the magnified detector-pixel size and indicate subpixel agreement.
- RMS error peaked near angular separations of 0, π, and 2π, whereas oblique separations near π/2 and 3π/2 were most accurate.Outside these unfavorable orientations, the effect of angle was modest.
- Noise-free simulations were approximately one order of magnitude more precise than simulations with Gaussian noise.Figure 6 summarizes eight registrations per point with randomly directed pose perturbations and reports standard deviations as error bars.
- Projection-based registration remained stable despite poorly defined CT edges and cases requiring extensive manual intervention or infeasible CT reconstruction.The comparison concerned gas turbine blade data affected by high attenuation and scattering.
4 Discussion
The discussion attributes subpixel performance to sequential rigid registration and intensity-based mutual information, while identifying noise, segmentation, coordinate, mesh, measurement, and deformation uncertainties.
- Sequential greedy registration reduces the difficulty of later elastic registration by first solving the rigid component-alignment problem.Elastic registration has more degrees of freedom and a more complex objective landscape.
- Mutual information supports subpixel accuracy by using full intensity distributions and combining constraints from multiple views.These constraints can locate the optimum between detector pixels rather than relying only on extracted edges.
- Image noise, CT-derived segmentation quality, reference-coordinate accuracy, coarse mesh resolution, measurement-point placement, and unmodeled elastic deformation were identified as uncertainty sources.Occasional larger local discrepancies remained despite many close agreements with CT-derived reference values.
5 Conclusion
The study demonstrated sequential mutual-information registration with subpixel accuracy and found that greedy view selection improves reliability, while redundant views can be detrimental.
- 0.05–0.1 pixels in noise-free simulations and 0.36–0.42 pixels against CT-derived experimental measurements were the reported errors.The study describes both outcomes as subpixel accuracy.
- Greedy view-angle optimization improved reliability and helped limit the effect of image noise.Adding views generally reduced variability.
- Additional views provided little mean-accuracy improvement after the first few informative angles and could be detrimental when redundant.The conclusion supports view selection for projection-based inspection and initialization of future elastic registration.