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

Area of Science:

• * Materials Science and Engineering
• * Computational Physics
• * Image Processing

Background:

• * Accurate measurement of subvoxel-precise displacements is crucial for deformation analyses in time-series computed tomography (CT) data.
• * In-situ X-ray micro-tomography generates extensive datasets requiring efficient processing for deformation studies.

Purpose of the Study:

• * To develop and validate an optimized algorithm for 3D least-squares matching.
• * To reduce computation time and memory requirements for analyzing CT voxel data.

Main Methods:

• * Implemented a gradient-based 3D least-squares matching algorithm using an iterative Gauss-Markov process.
• * Developed a direct normal equation computation approach to minimize computational steps.
• * Validated the optimized algorithm through theoretical comparisons and practical tests on CT data.

Main Results:

• * Theoretical analysis indicated a 28% reduction in multiplications and a 17% reduction in additions.
• * Practical tests demonstrated a 27% decrease in computation time for the 3D least-squares matching algorithm.
• * The optimized algorithm efficiently determines geometric and radiometric transformation parameters.

Conclusions:

• * The proposed direct normal equation computation significantly enhances the efficiency of 3D least-squares matching.
• * The optimized algorithm provides a faster and more memory-efficient solution for deformation analysis in CT data.
• * This advancement is vital for processing large datasets in in-situ X-ray micro-tomography studies.