From 2D projections to the 3D rotation matrix: an attempt for finding a machine learning approach for the efficient evaluation of mechanical joining elements in X-ray computed tomography volume data

Destructive and predominantly manual procedures are commonly used in the automotive industry for the testing of mechanical joints, such as rivets or screws. Combining X-ray computed tomography (CT) and machine learning (ML) bears the potential of a non-destructive and largely automated methodology. Assuming the desired result is a comprehensible and documentable evaluation, three basic steps need to be automatized: First, a joint must be detected and identified as such in a CT scan of the joined parts. Second, the detected region containing the joint is rotated to a predefined orientation. Third, key measures in cross-sections from the newly oriented joint are dimensioned and documented. This work deals only with the second step, the rotation. On the one hand, we present a methodology for creating a well-curated data set for the contextual machine learning application. On the other, we evaluate its performance on the well-known ResNet50. More concretely, we investigate if it is possible for a deep convolutional neural network (CNN) to learn the respective rotation matrix from three volume projections that are perpendicular to each other. Two scenarios are investigated: In one scenario we assume that future data that is presented to the network has similar rivet demographics to historic data. We therefore do not employ hold-out sets for the network evaluation. In the other scenario we assume the opposite and therefore evaluating the networks performance with hold-out sets. We show that from a machine learning point of view, a CNN like ResNet50 is well able to learn this relationship with acceptable accuracy. In most cases the validation loss dropped below 0.1 after only a couple of epochs. In one particular case, we even reached both mean and median errors lower than 0.2 for approximately 80% of the entire test set of 1600 examples using our methodology. From an application point of view, however, these low test set errors should be treated with caution since small deviations from the intended rotation matrix can cause volume warping and translation. In another case, in which we used a hold-out set, only a fraction of the median errors were below 0.2.