Straight

Straight tells the story of radial lens distortion and of the theorem that undoes it exactly, published in Sensors in 2016. Four short chapters, to be handled more than read. 1. Seeing the curvature. Take the place of the glass: one slider bends a composition of straight lines, barrel one way, pincushion the other, and straightening it again shows the mirror polynomial that did the work. 2. Measuring the curvature. Stretch Brown's plumb lines and calibrate a lens by eye, then let least squares do the same thing and compare. The eye gets there in a handful of seconds; the machine wins at the fourth decimal. 3. The exact mirror. Watch the inverse series collapse, or diverge. Its coefficients hide the Fuss-Catalan numbers, the ones that count ternary trees, and the chapter says why. 4. The bridge and the tool. Convert between Metashape, OpenCV, millimetres and pixels, and read the nine mirror coefficients with the residual that certifies them. The tool and its Python module are gifts: the module is printed in full, with no dependency, and it self-tests on the paper's reference data. Four languages, no account, no advertising, no data collection, and no network permission at all: it works in airplane mode, and you can check that yourself. Based on P. Drap and J. Lefevre, "An Exact Formula for Calculating Inverse Radial Lens Distortions", Sensors 2016, 16(6), 807, doi 10.3390/s16060807. Epigraph quoted from F. Devernay and O. Faugeras, 2001. IMAGE4D, image4d.fr