Three-Dimensional Investigation of the Metric Properties of Parabolic Double Projection Involving Catadioptric Camera

TL;DR

This paper analytically investigates the metric properties of paraboloidal double projection in catadioptric cameras, focusing on true length determination, distortion analysis, and calibration, which are vital for camera accuracy and comparison.

Contribution

It provides the first detailed analytical study of the metric properties of paraboloidal double projection in catadioptric systems, addressing a gap in previous research.

Findings

Derived formulas for true lengths of projected lines

Analyzed distortion characteristics of the projection

Enhanced camera calibration techniques

Abstract

This paper presents an analytical study for the metric properties of the paraboloidal double projection, i.e. central and orthogonal projections used in the catadioptric camera system. Metric properties have not sufficiently studied in previous treatments of such system. These properties incorporate the determination of the true lengths of projected lines and areas bounded by projected lines. The advantageous main gain of determining metric elements of the paraboloidal double projection is studying distortion analysis and camera calibration, which is considered an essential tool in testing camera accuracy. Also, this may be considered as a significant utility in studying comparison analysis between different cameras projection systems.