Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design

Intrinsic parameter estimation by self-calibration is commonly used in Unmanned Aerial Vehicle (UAV) - based photogrammetry with Structure from Motion (SfM). However, obtaining stable estimates of these parameters from image-based SfM - which relies solely on images, without auxiliary data such as ground control points (GCPs) - remains challenging. Aerial imagery acquired with the constant-pitch (CP) flight pattern often exhibits non-linear deformations, highly unstable intrinsic parameters, and even alignment failures. We hypothesize that CP flights form a “critical configuration” that renders certain intrinsic parameters indeterminate. Through numerical experiments, we confirm that a CP flight configuration does not provide sufficient constraints to estimate focal length (f) and the principal point coordinate (cy) in image-based SfM. Real-world CP datasets further demonstrate pronounced instability of these parameters. As a remedy, we show that by introducing intermediate short strips into CP flight plan-what we call a CP-Plus flight - can effectively mitigate the indeterminacy of f and cy in simulations and markedly improve their stability in all tested cases. This approach enables more effective image-only SfM workflows without auxiliary data, simplifies data acquisition and improves three-dimensional reconstruction accuracy.