From Sinograms to Surfaces: A Direct Approach to the Segmentation of Tomographic Data

Abstract

Abstract. Under ideal circumstances the problem of tomographic reconstruction is well-posed, and measured data are sufficient to obtain accurate estimates of volume densities. In such cases segmentation and surface estimation from the reconstructed volume are justified. In other situations the reconstructed volumes are not suitable for subsequent segmentation. This can happen in the case of incomplete sinograms, noise in the measurement process, or misregistration of the views. This paper presents a direct approach to the segmentation of incomplete and noisy tomographic data. The strategy is to impose a fairly simple model on the data, and treat segmentation as a problem of estimating the interface between two substances of somewhat homogeneous density. The segmentation is achieved by simultaneously deforming a surface model and updating density parameters in order to achieve a best fit between the projected model and the input sinograms. The deformation is implemented with level-set surface models, calculated at the resolution of the input data. Several computational innovations make the approach feasible with state-of-the-art computers. The usefulness of the approach is demonstrated by reconstructing the shape of spiny dendrites from electron microscope tomographic data.

Shape from projections via differentiable forward projector for computed tomography

“…Our proposed method is related to tomographic segmentation, where segments are directly computed from projections. This includes (Elangovan and Whitaker, 2001;Whitaker and Elangovan, 2002;Alvino and Yezzi, 2004) that are based on the Mumford-Shah model (Mumford and Shah, 1989) where boundaries are represented using level-sets (Osher and Fedkiw, 2004). Recently, the parametric level-set method (Aghasi et al, 2011) has been used for tomographic segmentation in (Kadu et al, 2018;Eliasof et al, 2020) where level-sets are represented as an aggregation of radial basis functions.…”

Computing segmentations directly from x-ray projection data via parametric deformable curves

“…This leads to curve deformation algorithms similar to ours, cf. [2] and [7], but only in combination with the level-set curve representation. A related 3D algorithm also based on level-sets is presented in [8].…”

Level-set reconstruction algorithm for ultrafast limited-angle X-ray computed tomography of two-phase flows

“…A similar approach has been proposed by Elangovan & Whitaker [14], however without the ART-specific weighting of the projections.…”