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 the pronounced instability of these parameters. As a remedy, we show that by introducing intermediate strips into the 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.