Equivalence of Two Expressions of Principal Line

TL;DR

This paper proves the algebraic equivalence of two principal line expressions used in camera calibration and extends one expression to include infinite vanishing points, enhancing geometric calibration methods.

Contribution

It establishes the algebraic equivalence of two principal line expressions and extends one to incorporate infinite vanishing points, improving calibration techniques.

Findings

Proved algebraic equivalence of two principal line expressions.

Extended the expression to include infinite vanishing points.

Provides mathematical foundation for improved calibration methods.

Abstract

Geometry-based camera calibration using principal line is more precise and robust than calibration using optimization approaches; therefore, several researches try to re-derive the principal line from different views of 2D projective geometry to increase alternatives of the calibration process. In this report, algebraical equivalence of two expressions of principal line, one derived w.r.t homography and the other using for two sets of orthogonal vanishing points, is proved. Moreover, the extension of the second expression to incorporate infinite vanishing point is carried out with simple mathematics.