Abstract
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%.
Highlights
3D least-squares matching algorithm was proven to be reduced by 27%
The pixels are illustrated as red squares with red circles in the centers
The paper presents an optimized algorithm to compute 3D least-squares matching in voxel data sequences including geometric and radiometric parameters
Summary
Volume data analysis in a voxel space representation is a logical extension of 2D image data processing. The pixels are illustrated as red squares with red circles in the centers. In this example, the transformation includes translation, rotation, scale and shear and the corresponding parameters are obtained by the LSM algorithm. The most important parameters are the shifts, which typically show an accuracy of 0.02 to 0.05 pixels in this kind of application
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