Combined reconstruction and edge detection in dimensioning

The result of tomographic examination is a series of two-dimensional (2D) or three-dimensional (3D) images, on which a diagnosis is based. Automatic evaluations of these images are rather common in nondestructive testing, in medical analysis this may partially be the case in the future. Typically the two tasks, image reconstruction and image evaluation, are treated separately. This paper describes an approach where the two steps are combined in just one method. By joint optimization of the two steps, the results are much superior to the separate treatment of the two tasks, as the comparisons in Louis (2008 SIAM J. Imaging Sci. 1 188–208) show. By constructing corresponding reconstruction filters, the algorithms are of filtered backprojection type, hence the computing time essentially remains the same as for the reconstruction of the density itself. We consider the reconstruction problem in x-ray tomography for the fan-beam geometry with flat detectors and edge detection. This method is then extended to filtered backprojection with Feldkamp-type kernels for the 3D cone-beam case. We calculate special reconstruction kernels which work also in the case of very noisy real data, and we present numerical examples from the measured data.