Equivalence of Two Expressions of Principal Line
This work provides incremental theoretical validation for geometry-based camera calibration methods, benefiting researchers in computer vision.
The paper proves the algebraic equivalence of two expressions for the principal line in camera calibration, one based on homography and the other using orthogonal vanishing points, and extends the second expression to include infinite vanishing points with simple mathematics.
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.