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 groun...

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Main Authors: Truc Thanh Ho, Riku Sato, Ariyo Kanno, Tsuyoshi Imai, Koichi Yamamoto, Takaya Higuchi
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Remote Sensing
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Online Access:https://www.mdpi.com/2072-4292/17/12/2030
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author Truc Thanh Ho
Riku Sato
Ariyo Kanno
Tsuyoshi Imai
Koichi Yamamoto
Takaya Higuchi
author_facet Truc Thanh Ho
Riku Sato
Ariyo Kanno
Tsuyoshi Imai
Koichi Yamamoto
Takaya Higuchi
author_sort Truc Thanh Ho
collection DOAJ
description 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.
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spelling doaj-art-da27b4e793744d7194fd81c2c08c88342025-08-20T03:27:25ZengMDPI AGRemote Sensing2072-42922025-06-011712203010.3390/rs17122030Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight DesignTruc Thanh Ho0Riku Sato1Ariyo Kanno2Tsuyoshi Imai3Koichi Yamamoto4Takaya Higuchi5Graduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Yamaguchi 755-8611, JapanGraduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Yamaguchi 755-8611, JapanGraduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Yamaguchi 755-8611, JapanGraduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Yamaguchi 755-8611, JapanGraduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Yamaguchi 755-8611, JapanGraduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Yamaguchi 755-8611, JapanIntrinsic 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.https://www.mdpi.com/2072-4292/17/12/2030UAV-based photogrammetrystructure from motion (SfM)indeterminacyintrinsic parameterscritical configuration
spellingShingle Truc Thanh Ho
Riku Sato
Ariyo Kanno
Tsuyoshi Imai
Koichi Yamamoto
Takaya Higuchi
Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design
Remote Sensing
UAV-based photogrammetry
structure from motion (SfM)
indeterminacy
intrinsic parameters
critical configuration
title Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design
title_full Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design
title_fullStr Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design
title_full_unstemmed Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design
title_short Indeterminacy of Camera Intrinsic Parameters in Structure from Motion Using Images from Constant-Pitch Flight Design
title_sort indeterminacy of camera intrinsic parameters in structure from motion using images from constant pitch flight design
topic UAV-based photogrammetry
structure from motion (SfM)
indeterminacy
intrinsic parameters
critical configuration
url https://www.mdpi.com/2072-4292/17/12/2030
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