We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the sourcedetector pair, which creates the issue of unknown geometry. This work considers two approaches for geometry estimation. Our first approach is a calibration object correlation method in which we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The second approach is projection trajectory simulation, where we use a set of known intersection points and a sequential Monte Carlo method for estimating the posterior density of the parameters. We show numerically that a large set of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with Cauchy priors for synthetic and real sawmill data for detection of knots with a very low number of measurements and uncertain measurement geometry.

In industrial applications it is common to scan objects on a moving conveyor belt. If slice-wise 2D computed tomography (CT) measurements of the moving object are obtained we call it a sequential scanning geometry. In this case, each slice on its own does not carry sufficient information to reconstruct a useful tomographic image. Thus, here we propose the use of a Dimension reduced Kalman Filter to accumulate information between slices and allow for sufficiently accurate reconstructions for further assessment of the object. Additionally, we propose to use an unsupervised clustering approach known as Density Peak Advanced, to perform a segmentation and spot density anomalies in the internal structure of the reconstructed objects. We evaluate the method in a proof of concept study for the application of wood log scanning for the industrial sawing process, where the goal is to spot anomalies within the wood log to allow for optimal sawing patterns. Reconstruction and segmentation quality is evaluated from experimental measurement data for various scenarios of severely undersampled X-measurements. Results show clearly that an improvement of reconstruction quality can be obtained by employing the Dimension reduced Kalman Filter allowing to robustly obtain the segmented logs.

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We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source-detector pair, which creates the issue of unknown geometry. This work considers two approaches for geometry estimation. Our first approach is a calibration object correlation method in which we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The second approach is projection trajectory simulation, where we use a set of known intersection points and a sequential Monte Carlo method for estimating the posterior density of the parameters. We show numerically that a large set of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with Cauchy priors for synthetic and real sawmill data for detection of knots with a very low number of measurements and uncertain measurement geometry.