Correcting the Eccentricity Error of Projected Spherical Objects in Perspective Cameras

Round 1

Reviewer 1 Report

while this well-written paper focuses on a very interesting and practical research question, the title of the paper is very lengthy and general, the authors are recommended to revise the tile based on the contribution of the paper. For example "Feasibility study of Eccentricity Error Modeling in Perspective Cameras"

Author Response

The authors would like to thank the reviewer for their valuable comment.

The title has reduced to the following to address your comment:

"Correcting the Eccentricity Error of Projected Spherical Objects in Perspective Cameras"

Reviewer 2 Report

Dear Authors,

the paper is well set up and well presented.

Some comments about the paper:

1. C is the center of the projected sphere. In figure 1a could be shown the sphere, too.
2. Sometimes there are some typos (e.g. some occurrences of “spere” instead of “sphere”!).
3. Maybe it is a flaw of mine; you told about closed-form solutions (lines 73-85), but you also mention a “best-fit ellipse” when you speak about its axes length: doesn't the ellipse have a closed-form too, given all those geometric data?
4. It is not so clear when you speak about simulated point clouds and acquired point clouds.
5. Something more is needed about the Styrofoam spherical target, e.g: how much “spherical” is it? how much “near” to 50mm its radius is?

Author Response

The authors would like to thank the reviewer for their valuable comment.

The following are responses to the reviewer's comments:

1- We tried a few options to add the original sphere to the image as well ; however, the original sphere always interesects with the Dandelin spheres. Therefore, it was not included for clarity.

2- Thank you very much for pointing out the typos. All have been addressed through out the manuscript.

3- The closed-form solution, presented here is to correct the center eccentricity for ellipses corresponding to real-world spheres, projected onto images. The formulation requires the best fit ellipse in the image to be estimated.

As for best fit ellipses, there are a few direct (closed-form) algebraic methods, such as that of Fitzgibbon et. al (1999). Other more accurate geometric methods, such as Ahn et. al (2003), and Maalek and Lichti (2021), are typically non-linear minimization problems. For interested readers, a comprehensive evaluation of different ellipse fitting methods and their capabilities is documented in "Maalek, R.; Lichti, D.D. New confocal hyperbola-based ellipse fitting with applications to estimating parameters of mechanical pipes from point clouds. Pattern Recognit. 2021, 107948, doi:10.1016/j.patcog.2021.107948.".

4- All point clouds presented in this study were simulated. "Acquired point clouds" was not mentioned through out the body of the manuscript.

5- Thank you very much for your comment. The measurement precision was added to the manuscript (Line 124).

Reviewer 3 Report

The paper presents a geometric method for correcting the eccentricity error of projected spherical objects in perspective cameras and a robust sphere fitting method to meet the experimental needs of the former. The proposed method has important significance in high precision metrology. The work is interesting and worthy of publication if some points are addressed:

1. Correcting the eccentricity error of projected spherical objects is the main innovation of the manuscript. However, the analysis of related work is missing in the introduction.
2. It is well known that it is a difficult work to obtain a dense point cloud of a sphere with no obvious features with multiple images. The authors should make it clear how to obtain the dense point cloud.
3. In page 7, the following sentence is garbled: " For the sphere detection quality, the precision, recall, accuracy and F-measure metrics were used, which are calculated as follows: …"
4. The citation of some references is not rigorous enough, e.g., the registration with sphere is not mentioned in the reference 4. In addition, references 16 and 17 are repeated.

Author Response

Thank you for your comments. They are addressed as follows:

1- All related work has been provided in the introduction.

2- SfM and the Dense Reconstruction using COLMAP is utilized in this study. This has been already presented in Line 134 of the manuscript.

3- The sentence has been changed to the following for clarity:

"To evaluate the quality of automatic detection of points following spherical patterns (sphere detection quality), the established metrics, namely, precision, recall, accuracy and F-measure, were used, which are calculated as follows [21]"

4- Thank you for your comment. The repetitive references were removed.