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• Changing grid from triangular into hex improves boundary reconstruction accuracy. • Marching squares algorithm is 5 times more accurate than a simple square grid. • Average error values may be used as correction coefficients. This paper presents methods to calculate the length overestimation errors which are being made when approximating a discrete line by edges of triangular tessellation and marching squares algorithm. The maximum error and its average value are 15.47 % and 10.27 % for the triangular tessellation, while for the marching squares approach they are 8.24 % and 5.49 %, respectively. Mathematical calculations were compared with experimental results obtained by the Electron Backscatter Diffraction technique showing their usefulness as correction coefficients to obtain more accurate boundary length estimates. [ABSTRACT FROM AUTHOR]