Estimation of systematic errors of discrete line approximation by triangular tessellation and marching squares...

Area of Science:

• Computational geometry
• Image processing
• Materials science

Background:

• Discrete line representation is crucial in digital imaging and geometric analysis.
• Approximating continuous lines with discrete methods can introduce significant length errors.
• Accurate boundary length estimation is vital for quantitative analysis in various scientific fields.

Purpose of the Study:

• To develop and present methods for calculating length overestimation errors.
• To compare the accuracy of triangular tessellation and marching squares algorithms for line approximation.
• To validate computational results with experimental data for improved boundary length estimation.

Main Methods:

• Mathematical formulation of length overestimation errors for discrete lines.
• Implementation and analysis of triangular tessellation and marching squares algorithms.
• Experimental validation using Electron Backscatter Diffraction (EBD) technique.

Main Results:

• Triangular tessellation exhibited maximum and average errors of 15.47% and 10.27%.
• Marching squares algorithm showed lower errors, with maximum and average values of 8.24% and 5.49%.
• Calculated correction coefficients derived from mathematical models align with EBD experimental results.

Conclusions:

• The marching squares algorithm provides a more accurate method for approximating discrete line lengths compared to triangular tessellation.
• The developed methods and correction coefficients enhance the accuracy of boundary length estimations.
• This research offers a pathway to more precise quantitative analysis in fields relying on digital geometric representations.