Polar-vision¹: A Novel Collinearity Equation of Perspective Projection in Polar Coordinate System

Abstract. Progress has been made in the community of photogrammetry and 3d computer vision in addressing the mathematical challenge posed by the collinearity equation. We introduce a new method for establishing the coordinate reference for 2d pixels and 3d landmarks using 'angular coordinates'. The mathematical relationships required for converting 3d landmarks, expressed in angular coordinates, to the camera framework are presented. The landmarks are then projected using perspective projection to obtain 2d pixels represented in angular coordinates. This framework is formally nominated as the 'Polar-vision¹', which has been developed and integrated into the commercial software G3D-Cluster. Its application to pinhole camera image processing has demonstrated superior efficiency and admission rates of tie points, as well as reconstruction detail capabilities, compared to OpenMVG, achieving approximately a 1.4× improvement. The project 'Key Technologies and Tool System for Realistic 3D Modeling through Integration of Multi-Source Information in the Space-Air-Ground Domain' was awarded First Prize at the 2023 Surveying Science and Technology Awards, with Polar-vision¹ as one of the innovative points.