Learned Bias Correction for Surface-Area Estimation from CT-like Voxel Data

Abstract Measuring the surface area of an object from a CT scan is harder than it looks because the scan consists of a grid of small cubes (voxels), while the true surface passes between them. Counting the exposed faces of the voxels overestimates the surface area by approximately 50% at every resolution. Marching Cubes, which fits a triangular mesh to the data, provides a closer estimate, but its error depends on the object's curvature and the noise in the scan.In this study, we generated 2,400 synthetic shapes from seven families, each with a known true surface area to better than 0.01%. These shapes were converted into 14,400 CT-like volumes at resolutions of 32³ and 64³ voxels, with three different noise levels.We then trained three models to predict corrections to the surface area estimated by Marching Cubes: Random Forest: Uses ten simple shape measurements. 3D Convolutional Neural Network (CNN): Learns features directly from volumetric data. PointNet: Learns features from point-cloud representations.Testing on previously unseen shapes showed that Marching Cubes produced average errors of 4.78% at 32³ resolution and 3.52% at 64³ resolution. The best correction models reduced these errors to 0.68% using the 3D CNN at 32³ resolution and 0.18% using the Random Forest at 64³ resolution.The corrected methods also maintained errors below 2% on two shape families that were completely excluded from training. Overall, the simple Random Forest performed comparably to the CNN. The CNN was more effective only for objects smaller than 16 voxels. However, none of the methods could reliably recover structures thinner than approximately two voxels.