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

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please consider the following recommendations:

1. While the term “critical configuration” is central to the paper, its definition and theoretical underpinnings are only briefly introduced. Please include a diagram illustrating what constitutes a critical configuration in camera motion.
2. The paper focuses on the indeterminacy of f and cy, not cx or distortion parameters. Please provide a brief justification or results indicating why cx and distortion parameters were excluded from the detailed analysis.
3. The study is highly focused on CP and CP-Plus flights, but please consider the readers working with other configurations. So, please add a short discussion on how these findings may translate to other flight configurations.
4. While statistical variability is shown, the practical implications, e.g., vertical accuracy improvements, could be more concrete. Please include a summary table comparing reconstruction accuracy, e.g. vertical RMSE or mean vertical error, between CP and CP-Plus flights across GSDs to better highlight the benefits.
5. Some terms in the paper, e.g., “image-based SfM,” “images-based SfM,” “self-calibration”) appear inconsistently. Please standardise terminology in the manuscript to avoid confusion.
6. The numerical experiments in Blender and Metashape are well-structured but difficult to replicate. If applicable, please consider include supplementary materials or a GitHub repository with Blender scene files, scripts, or Metashape XML templates. This would significantly improve reproducibility and reader engagement.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

Overall, I found your work well designed. The research question is clearly stated at the beginning, the methodology is explained and the analyses are well presented and supported by the data.

Some minor comments and suggestions:

-Why choose a pitch angle of 20°? There are similar works available in the literature that analyse the impact of introducing different camera angles in the UAV photogrammetric flight (an overview and some considerations on this topic might be of interest)

-The approach of using Aerobo markers is interesting. Please provide more details on these instruments and their precision

-Conclusion could be integrated with future perspectives and next steps for this kind of approach

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper primarily investigates the indeterminacy of camera intrinsic parameters in image-based Structure-from-Motion(SfM) using aerial photos from Constant-Pitch flights. Stabilizing SfM calibration can effectively enhanced dense point cloud generation and lead to more accurate 3D reconstruction.

The main contribution of this paper are:

1) Design the numerical and real-data experiments to analyze indeterminacy of camera intrinsic parameters(f and cy) from constant-pitch(CP)flights.

2) Proposing the integration of intermediate short strips for eliminate this indeterminacy.

However, there is still room for improvement, as detailed below:

1) It is recommended to add the equations used in SfM calibration and to analyze, from a theoretical perspective, why CP flights may lead to instability in the determination of camera intrinsic parameters.

2) Provide a theoretical analysis and explanation for the following statement:” As shown in Figure 6, the RMS reprojection error for cameras in the intermediate short strips is significantly larger than those in the main flight strips(from line 269 to line 270)”.

3) The proposed approach for eliminating this indeterminacy in this paper could be made more specific and reasonable. For example, the paper could analyze how the number and spatial distribution of intermediate short strips affect the stability of camera intrinsic parameters. Furthermore, if intermediate short strips are added to a constant-pitch (CP) random flight, will the camera intrinsic parameters in Structure-from-Motion remain stable?

4) The concept of the CP-Plus flight proposed in this paper has already been used as a standard approach in photogrammetry for improving the accuracy of aerial triangulation. Aerial triangulation, which includes camera self-calibration, is similar to the Structure-from-Motion (SfM) method used in this paper

Author Response

Please see that attachment.

Author Response File: Author Response.pdf