Computational Optimization of the 3D Least-Squares Matching Algorithm by Direct Calculation of Normal Equations

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung



3D least-squares matching is an algorithm that allows to measure subvoxel-precise displacements between two data sets of computed tomography voxel data. The determination of precise displacement vector fields is an important tool for deformation analyses in in-situ X-ray micro-tomography time series. The goal of the work presented in this publication is the development and validation of an optimized algorithm for 3D least-squares matching saving computation time and memory. 3D least-squares matching is a gradient-based method to determine geometric (and optionally also radiometric) transformation parameters between consecutive cuboids in voxel data. These parameters are obtained by an iterative Gauss-Markov process. Herein, the most crucial point concerning computation time is the calculation of the normal equations using matrix multiplications. In the paper at hand, a direct normal equation computation approach is proposed, minimizing the number of computation steps. A theoretical comparison shows, that the number of multiplications is reduced by 28% and the number of additions by 17%. In a practical test, the computation time of the 3D least-squares matching algorithm was proven to be reduced by 27%.


Seiten (von - bis)760-777
FachzeitschriftTomography : a journal of imaging research
PublikationsstatusVeröffentlicht - 14 März 2022

Externe IDs

PubMed 35314640
Scopus 85126836620


Forschungsprofillinien der TU Dresden

Fächergruppen, Lehr- und Forschungsbereiche, Fachgebiete nach Destatis

ASJC Scopus Sachgebiete


  • 3D least-squares matching; cuboid tracking; 3D displacement field; voxel data; microtomography data