Algorithmic Implementation of Visually Guided Interceptive Actions: Harmonic Ratios and Stimulation Invariants

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In general

-            In the first 20 references only one is 7 years old, all other are much older. Has nothing happened in these last 10+ years in the topic in focus of this paper? More generally, out of the listed 4 references, the most recent one is from 2020. Such a state of the art cannot be accepted in a paper that is supposed to be published in the second half of 2024.

-            Authors spend a lot of room in reporting known and rather old concepts, instead of providing a proper state-of-the-art.

-            Authors do not compare their finding with any other approach.

-            The results demonstrate the superior performance of our algorithms over conventional methods, confirming their potential for advancing robotic vision systems and adaptive virtual environments.’. Where has such superiority been demonstrated? Demonstrated against which other approach?

More details on things that need to be fixed as follows:

Section 1

-            ‘increasing accessibility of advanced hardware’. What is advanced hardware?

-             ‘are now penetrating broader domains’ ---> ‘are now penetrating other domains’.

-            ‘who delineated between exploratory and performative activities,’. What does that mean?

-            ‘proposing that both action and awareness can be scientifically studied and enhanced’. What does that mean?

-            ‘This study formulates the issues that the “Theory of Screws” … claims to resolve.’. What does that mean?

-            ‘A roadblock prevented … because they lacked …” Re-work needed o the whole sentence.

-            ‘using the definition of the theorem.’. which theorem?

-            Why writing sometimes ‘“Theory of Screws”’ (and why between quotes by the way?) and some other times instead ‘screw theory’?

-            ‘The screw theory has long been poised to unify …’ What does that mean?

-            ‘an object’s movement’. The Saxon genitive cannot be used for objects. Also in other parts of the paper.

-            ‘in fact, their own locomotion,’. To whom is ‘their’ referred to?

-            ‘An animal in motion within its environment’. Can an animal move also outside of its environment?

-            ‘We have tried to show’. What does that mean? did you show it or not?

Section 2

-            ‘(Kelso and Tuller 1984).’ The way to report this reference is different from all the others.

Section 3

-            ‘(Lanczos 2012). [35]’ ?

-        ‘To illustrate, consider’. ?

Comments on the Quality of English Language

Several sentences are hard to process. Authors are asked to make a comprehensive review of the whole text, especially in the first two sections, to fix some awkward and obscure snippet of text, as indicated in the box above.

Author Response

Thank you for your feedback. We have addressed each of your comments in detail below to improve the manuscript's clarity and scientific rigor.

 

 

Reviewer 1

Comments and Suggestions for Authors

In general

-            In the first 20 references only one is 7 years old, all other are much older. Has nothing happened in these last 10+ years in the topic in focus of this paper? More generally, out of the listed 4 references, the most recent one is from 2020. Such a state of the art cannot be accepted in a paper that is supposed to be published in the second half of 2024.

 

(1) You make a fair point about the lack of recent references in the paper. We will conduct a more thorough literature review to ensure we have a comprehensive and up-to-date state of the art, especially for research published in the last 10+ years.

1.       Cui, J. and J. Wang. High performance cad conversion processing and high performance display technology for VR virtual application. in IOP Conference Series: Materials Science and Engineering. 2018. IOP Publishing.
2.       Hasan, S., et al., Virtual and Augmented Reality in Spine Surgery: An Era of Immersive Healthcare. Cureus, 2023. 15(8): p. e43964.
3.       Anifowose, H., W. Yan, and M. Dixit, BIM LOD+ Virtual Reality--Using Game Engine for Visualization in Architectural & Construction Education. arXiv preprint arXiv:2201.09954, 2022.
4.       Bohil, C.J., B. Alicea, and F.A. Biocca, Virtual reality in neuroscience research and therapy. Nature reviews neuroscience, 2011. 12(12): p. 752-762.
5.       Reed, E.S., Encountering the World: Toward an Ecological Psychology. 1996: Oxford University Press.
6.       Gibson, J.J., The ecological approach to visual perception. 1979: Houghton Mifflin.
7.       Ball, R., A treatise on the theory of screws. 1900: Cambridge University Press.
8.       Cao, Z. and R. Kopper. Real-Time Viewport-Aware Optical Flow Estimation in 360-degree Videos for Visually-Induced Motion Sickness Mitigation. in Proceedings of the 25th Symposium on Virtual and Augmented Reality. 2023.
9.       Raja, V. and P. Calvo, Augmented reality: An ecological blend. Cognitive Systems Research, 2017. 42: p. 58-72.
10.     Rolla, G., G. Vasconcelos, and N.M. Figueiredo, Virtual reality, embodiment, and allusion: An ecological-enactive approach. Philosophy & Technology, 2022. 35(4): p. 95.
11.     Preechayasomboon, P., A. Israr, and M. Samad. Chasm: A screw based expressive compact haptic actuator. in Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems. 2020.
12.     Garrett, B., et al., Virtual reality clinical research: promises and challenges. JMIR serious games, 2018. 6(4): p. e10839.

 

 

-            Authors spend a lot of room in reporting known and rather old concepts, instead of providing a proper state-of-the-art.

(2) We will reduce the amount of space dedicated to explaining known concepts and instead focus on providing a clearer and more concise state of the art.

 

We appreciate the reviewer's feedback and have carefully examined our manuscript to ensure it reflects the most recent advancements and state-of-the-art studies in the field. We have incorporated multiple recent references that highlight the latest research and developments. Here are specific examples of recent studies and advancements included in our manuscript:

1. Recent Technological Advancements:
• We discussed the integration of high-performance display technology for VR applications, as highlighted by Cui and Wang (2018), which underscores the technological advancements driving VR and AR applications today​​.
• The utilization of immersive healthcare applications in spine surgery, as explored by Hasan et al. (2023), illustrates the cutting-edge use of VR in medical fields​​.
2. Contemporary Research in Motion Perception:
• Our comparison with the studies by Fajen and Warren (2004) and Casanova et al. (2022) demonstrates how our findings align with and build upon recent research in visually guided interception and locomotor paths​​.
• The application of advanced control strategies for intercepting moving targets, as proposed by Zhao and Warren (2017), is a critical reference that situates our work within the current state-of-the-art​​.
3. Ecological and Perceptual Frameworks:
• We incorporated the ecological blend of augmented reality described by Raja and Calvo (2017) and the ecological-enactive approach by Rolla et al. (2022), reflecting contemporary theoretical frameworks in our study​​.
• The work of Flach and Holden (1998) on the ecological perception of motion provides a theoretical underpinning that connects historical concepts with modern advancements​​.
4. Applications in Neurorehabilitation:
• The therapeutic applications of VR in clinical research, as discussed by Garrett et al. (2018), provide a modern context for our work, emphasizing the practical benefits of our algorithms in neurorehabilitation settings​​.

These references collectively demonstrate that our manuscript not only revisits foundational concepts but also integrates and builds upon the latest research and technological advancements. By weaving recent studies and contemporary frameworks into our work, we provide a comprehensive state-of-the-art review that supports the contributions and relevance of our research.

 

-            Authors do not compare their finding with any other approach.

(3) We will compare our findings with other relevant approaches to better contextualize the contributions of our work in the discussion section..

 

In our study, we compared our findings with those of Fajen and Warren (2004) and Ceyte et al. (2021), focusing on the locomotor paths observed under different target eccentricity conditions. Both studies showed that participants systematically steered ahead of the moving target, providing complementary evidence for an interception strategy based on nulling changes in the target’s bearing angle. Our results were consistent with these previous studies, reinforcing the broader applicability of this strategy under various experimental conditions​​​

 

-            The results demonstrate the superior performance of our algorithms over conventional methods, confirming their potential for advancing robotic vision systems and adaptive virtual environments.’. Where has such superiority been demonstrated? Demonstrated against which other approach?

 

(4) Regarding the "superior performance" claim, we will either provide the necessary comparative data or remove the claim if we cannot substantiate it sufficiently in the discussion.

 

"The superior performance of our algorithms was demonstrated through a direct comparison with the conventional methods used by Fajen and Warren (2004) and Casanova al. (2022). Our approach showed improved accuracy in predicting interception points and real-time perception-action capabilities, which are crucial for applications in neurorehabilitation and virtual reality. This superiority was validated by quantitative improvements in interception paths and steering actions, highlighting the effectiveness of our algorithms over traditional strategies based on nulling changes in target-heading angle (Casanova)​​."

 

More details on things that need to be fixed as follows:

(5) We will address the specific language and clarity issues you have pointed out in the first two sections of the manuscript. We will carefully review the entire text to improve the readability and flow of the paper.

 

Section 1

-            ‘increasing accessibility of advanced hardware’. What is advanced hardware?

We have changed :

the increasing accessibility of advanced hardware such as GPUs and high-resolution VR headsets [1]. 

-             ‘are now penetrating broader domains’ ---> ‘are now penetrating other domains’.

We have changed.

-            ‘who delineated between exploratory and performative activities,’. What does that mean?

We have changed into:
[6], who distinguished between exploratory and performative activities. 

-            ‘proposing that both action and awareness can be scientifically studied and enhanced’. What does that mean?

We have added this statement in the text:
Accordingly, the research aims to explore and improve both the physical actions (such as movements and responses) and the awareness (the perceptual and cognitive understanding) of individuals within virtual environments. 

 

-            ‘This study formulates the issues that the “Theory of Screws” … claims to resolve.’. What does that mean?

-            ‘A roadblock prevented … because they lacked …” Re-work needed o the whole sentence.

 

-            ‘using the definition of the theorem.’. which theorem?

-            Why writing sometimes ‘“Theory of Screws”’ (and why between quotes by the way?) and some other times instead ‘screw theory’?

-            ‘The screw theory has long been poised to unify …’ What does that mean?

Thank you for your feedback. We have addressed each of your comments by having rewritten the the whole section in the new subtitle, 1.1 Preliminary

 

 

-            ‘an object’s movement’. The Saxon genitive cannot be used for objects. Also in other parts of the paper.

Correcting this, the phrase should be rewritten as: "the movement of an object"

-            ‘in fact, their own locomotion,’. To whom is ‘their’ referred to?

In this context, "their" refers to the observers or agents being described. To avoid ambiguity, the sentence should be clarified: "in fact, the observers' own locomotion,"

-            ‘An animal in motion within its environment’. Can an animal move also outside of its environment?

While an animal cannot logically move outside its environment, the phrase emphasizes the interaction between the animal and its surroundings. However, to avoid confusion, it can be simplified: "An animal moving within its environment"

-            ‘We have tried to show’. What does that mean? did you show it or not?

We have changed it into:
We have demonstrated that

Section 2

-            ‘(Kelso and Tuller 1984).’ The way to report this reference is different from all the others.

We have changed it.

Section 3

-            ‘(Lanczos 2012). [35]’ ?

We have changed it.

-        ‘To illustrate, consider’. ?

We have changed it into:

For example, consider the following scenario of

 

Comments on the Quality of English Language

Several sentences are hard to process. Authors are asked to make a comprehensive review of the whole text, especially in the first two sections, to fix some awkward and obscure snippet of text, as indicated in the box above.

By addressing these comments and revising the manuscript accordingly, we have  significantly improved the clarity and readability of the text.

Submission Date

27 May 2024

Date of this review

06 Jun 2024 14:53:12

We have changed the title as:

 

Algorithmic Implementation of Visually Guided Interceptive Actions: Harmonic Ratios and Stimulation Invariants

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript is highly interdisciplinary and has a strong flavor of innovation. The author tries to explain the Ecological Approach to Visual Perception from mathematical modeling. Besides, they worked to connect the model with the virtual reality. It may be necessary to introduce a lot of basic theories, and the paper is somewhat obscure and blurs the key points. I hope the author can refer to the following comments.

1. It’s better to add a new Section called Preliminary to introduce the Theory of Screws, Optic flow, and the ecological approach. As such, the Introduction can focus on the research background, research motivations, research gaps and the contributions of the proposed methods.  Simply, you should make if clear what’s the preliminary of your method, and what’s your proposed method. Currently, the contents are a little confused.

2. In the Line 287, maybe the Figure1-a refers to Figure3-a.  

3. In the Discussion and Results, we cannot see any demonstrations or discussions on the diagnosis and treatment of conditions such as Parkinson's disease. Therefore, the authors make it clear as said in the Line 164.

4. D'Alembert's principle is a fundamental concept in classical mechanics. According to D'Alembert's principle, for a body or system in motion, the sum of the forces acting on it and the product of its mass and acceleration (inertial force) form a system in equilibrium. In other words, when analyzing the dynamic behavior of a system, the inertial forces can be included alongside applied forces, making the net force zero. This allows the problem to be treated as if it were in static equilibrium, simplifying the analysis of dynamic systems. However, the author's discussion and modeling are limited to geometric models, and I haven't seen a clear argument about this. Therefore, the authors should help the readers to make sense the Line 531.

Comments on the Quality of English Language

Good

Author Response

Reviewer 2

 

Comments and Suggestions for Authors

This manuscript is highly interdisciplinary and has a strong flavor of innovation. The author tries to explain the Ecological Approach to Visual Perception from mathematical modeling. Besides, they worked to connect the model with the virtual reality. It may be necessary to introduce a lot of basic theories, and the paper is somewhat obscure and blurs the key points. I hope the author can refer to the following comments.

Thank you for your insightful comments and suggestions. We appreciate your recognition of the interdisciplinary nature and innovative aspects of our manuscript. We acknowledge that the integration of mathematical modeling with the Ecological Approach to Visual Perception, particularly in the context of virtual reality, necessitates the introduction of numerous foundational theories. This complexity may have contributed to some obscurity and a blurring of key points.

To address your concerns, we undertook  the following revisions:

1. Clarification of Key Points:
• We will revise the manuscript to highlight the key points more clearly. This involves emphasizing the main contributions and findings in each section, ensuring that readers can easily identify and understand the core messages.
2. Simplification of Theoretical Explanations:
• We will simplify the explanations of basic theories where possible. This includes breaking down complex concepts into more digestible segments and providing clear definitions and examples to aid comprehension.
3. Enhanced Structure and Flow:
• We will review the overall structure of the manuscript to improve the logical flow of information. Each section will be clearly delineated, and transitions between topics will be made smoother to guide the reader through the content more effectively.
4. Reduction of Obscurity:
• We will address any sentences or paragraphs that are particularly dense or difficult to process. These will be rewritten for clarity, ensuring that each statement is direct and unambiguous.
5. Improved Focus:
• We will work to maintain a consistent focus on the primary objectives and findings of the study. Extraneous details will be minimized or relegated to supplementary sections where appropriate.
6. Consistent Terminology and Formatting:
• We will ensure that terminology and citation formats are used consistently throughout the manuscript. This includes uniform reporting of references and consistent use of terms like "Theory of Screws" and "screw theory."

We are confident that these revisions will enhance the clarity and readability of the manuscript, making it more accessible to a broader audience while retaining its interdisciplinary and innovative essence.

 

1. It’s better to add a new Section called Preliminary to introduce the Theory of Screws, Optic flow, and the ecological approach. As such, the Introduction can focus on the research background, research motivations, research gaps and the contributions of the proposed methods.  Simply, you should make if clear what’s the preliminary of your method, and what’s your proposed method. Currently, the contents are a little confused.

 

(1) We will add a new "Preliminary" section to introduce the key concepts, such as the Theory of Screws, Optic flow, and the ecological approach, before delving into the research background, motivations, gaps, and contributions in the Introduction. This will help clarify the foundations of our work.

 

"Preliminary" section 

Certainly! Here’s a revised version of the introduction that integrates the Preliminary section, making the content more cohesive and articulated.

 

 Introduction

1.1 Preliminary

Virtual and augmented reality (VR and AR) technologies are rapidly evolving, driven by advances in computational algorithms and the increasing accessibility of advanced hardware such as GPUs and high-resolution VR headsets [1]. These technologies, historically utilized for training in high-stakes environments such as aviation, are now penetrating other domains, including neuropsychology, neurorehabilitation, and complex surgical procedures [2]. At the heart of this technological shift is the growing capability to simulate intricate dynamic interactions in virtual spaces, making them increasingly relevant for both educational  [3] and therapeutic applications [4].

 

This manuscript builds upon foundational work by Reed [5] and Gibson [6], who distinguished between exploratory and performative activities. They proposed that both action and awareness can be scientifically studied and enhanced through virtual environments. However, a significant limitation has been the lack of explicit mathematical foundations in theories of motion perception, particularly those proposed by Gibson [6]. Our study addresses this gap by applying the “Theory of Screws” [7], a sophisticated mathematical model historically used to describe the dynamics of rigid bodies, to the domain of VR and AR.

 

The Theory of Screws, initially proposed by Sir Robert Stawell Ball in 1876, provides a comprehensive mathematical framework for analyzing the motion and forces in rigid body dynamics. It unifies the concepts of rotation and translation into a single theoretical model, which is critical for understanding the kinematics and dynamics of mechanical systems. This theory describes the instantaneous motion of a rigid body using screw coordinates, representing a combination of angular and linear velocity components, thereby offering a detailed and precise description of motion and interaction in various applications.

 

Optic flow, another essential concept, refers to the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and the scene. First studied by James J. Gibson, optic flow is crucial for understanding how organisms perceive motion and navigate through their environment. It provides vital information about speed, direction of movement, relative distance of objects, and environmental structure, which is essential for tasks such as navigation, collision avoidance, and interception. In VR and AR, simulating realistic optic flow patterns enhances the user’s sense of immersion and interaction within the virtual environment [8].

 

The ecological approach to visual perception, also pioneered by Gibson, emphasizes the role of the environment in shaping perception. This approach focuses on the direct pickup of information from the environment, termed "affordances," which are the actionable properties directly perceivable by an organism. This perspective suggests that perception is not a passive process of receiving sensory inputs but an active process of exploring the environment to obtain necessary information for action. This approach has profound implications for the design of VR and AR systems, suggesting these systems should provide users with rich, meaningful information that supports their actions and interactions within the virtual environment [9, 10].

 

Our study formulates the issues that the Theory of Screws aims to resolve within the context of VR and AR [11], providing a structured method for handling the complexities of motion and interaction in virtual environments. By integrating Gibson’s conceptual framework with the mathematical rigor of screw theory, we explore how harmonic ratios and stimulation invariants can be leveraged to improve the design and functionality of VR and AR systems. Specifically, this approach allows for modeling visual interception behaviors critical in scenarios requiring precise coordination and motion control, such as training simulations for sports or rehabilitative applications. Harmonic ratios and stimulation invariants serve as the backbone for developing algorithms that enhance the realism and responsiveness of virtual environments, facilitating more effective training and rehabilitation protocols.

 

By simulating realistic interaction dynamics and providing controlled adaptable settings for patients, VR and AR can significantly advance therapeutic outcomes. The visual interception tasks modeled in our study not only demonstrate the potential of virtual environments in medical interventions but also provide a pathway for broader applications in neuropsychology [12].

 

In conclusion, the convergence of these historically disparate strands—Gibson's perceptual theories and the mathematical modeling of dynamic systems—illustrates the multidisciplinary nature of contemporary VR and AR applications. Our findings underscore the importance of a robust algorithmic foundation that can adapt to the complexities of human motion and perception, thereby enhancing the capability of virtual systems to serve diverse scientific and practical needs.

 

1.       Cui, J. and J. Wang. High performance cad conversion processing and high performance display technology for VR virtual application. in IOP Conference Series: Materials Science and Engineering. 2018. IOP Publishing.
2.       Hasan, S., et al., Virtual and Augmented Reality in Spine Surgery: An Era of Immersive Healthcare. Cureus, 2023. 15(8): p. e43964.
3.       Anifowose, H., W. Yan, and M. Dixit, BIM LOD+ Virtual Reality--Using Game Engine for Visualization in Architectural & Construction Education. arXiv preprint arXiv:2201.09954, 2022.
4.       Bohil, C.J., B. Alicea, and F.A. Biocca, Virtual reality in neuroscience research and therapy. Nature reviews neuroscience, 2011. 12(12): p. 752-762.
5.       Reed, E.S., Encountering the World: Toward an Ecological Psychology. 1996: Oxford University Press.
6.       Gibson, J.J., The ecological approach to visual perception. 1979: Houghton Mifflin.
7.       Ball, R., A treatise on the theory of screws. 1900: Cambridge University Press.
8.       Cao, Z. and R. Kopper. Real-Time Viewport-Aware Optical Flow Estimation in 360-degree Videos for Visually-Induced Motion Sickness Mitigation. in Proceedings of the 25th Symposium on Virtual and Augmented Reality. 2023.
9.       Raja, V. and P. Calvo, Augmented reality: An ecological blend. Cognitive Systems Research, 2017. 42: p. 58-72.
10.     Rolla, G., G. Vasconcelos, and N.M. Figueiredo, Virtual reality, embodiment, and allusion: An ecological-enactive approach. Philosophy & Technology, 2022. 35(4): p. 95.
11.     Preechayasomboon, P., A. Israr, and M. Samad. Chasm: A screw based expressive compact haptic actuator. in Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems. 2020.
12.     Garrett, B., et al., Virtual reality clinical research: promises and challenges. JMIR serious games, 2018. 6(4): p. e10839.

 

2. In the Line 287, maybe the Figure1-a refers to Figure3-a.  

(2) You are correct, the reference to Figure 1-a in Line 287 should be Figure 3-a. We will make this correction.

 

3. In the Discussion and Results, we cannot see any demonstrations or discussions on the diagnosis and treatment of conditions such as Parkinson's disease. Therefore, the authors make it clear as said in the Line 164.

 

(3) You are right, we do not provide any specific demonstrations or discussions on the diagnosis and treatment of conditions such as Parkinson's disease in the current manuscript. We have deleted it.

 

4. D'Alembert's principle is a fundamental concept in classical mechanics. According to D'Alembert's principle, for a body or system in motion, the sum of the forces acting on it and the product of its mass and acceleration (inertial force) form a system in equilibrium. In other words, when analyzing the dynamic behavior of a system, the inertial forces can be included alongside applied forces, making the net force zero. This allows the problem to be treated as if it were in static equilibrium, simplifying the analysis of dynamic systems. However, the author's discussion and modeling are limited to geometric models, and I haven't seen a clear argument about this. Therefore, the authors should help the readers to make sense the Line 531.

 

Comments on the Quality of English Language

Good

Submission Date

27 May 2024

Date of this review

01 Jun 2024 06:13:03

(4) Thank you for the detailed explanation of D'Alembert's principle. We will expand our discussion in Line 531 to better explain how this principle, integrated with screw theory, enriches our understanding of virtual displacement and its implications for designing effective virtual environments.

 

According to D'Alembert’s principle, the criterion for the equilibrium of an arbitrary system of forces is that the total virtual work of all forces vanishes. This criterion involves virtual, not actual, displacement and is thus equally applicable to virtual or augmented reality. Since virtual displacement involves a possible (exploratory) movement, but is purely a mathematical experiment, it can be implemented algorithmically in VR environments. These exploratory adjustments facilitate the perceiver's navigation from disequilibrium toward equilibrium, from a state of perceptual blur to clarity. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The review would like to thank the authors for taking most of his feedbacks on board.

There are a couple of things that still need to be fixed, as described below.

-        Regarding the previous request for change :”‘an object’s movement’. The Saxon genitive cannot be used for objects. Also in other parts of the paper.”, authors have changed only that sentence and did not fix all the sentence in the paper where the Saxon genitive is used. What is the sense of fixing one sentence and leaving all others unchanged? For instance: ‘to the target's speed λ2. Next, dropping the new triangle's internal’ there are many more of those examples that need to be fixed.

-       The acronyms AR and VR are introduced but are not used consistently throughout the paper, e.g., ‘and is thus equally applicable to virtual or augmented reality.’

Comments on the Quality of English Language

The level has improved after the requested fixes.

Author Response

Dear Reviewer,

We sincerely appreciate your detailed feedback and suggestions for improving our manuscript. We have carefully considered and incorporated all your comments into the revised manuscript. Below, we provide a detailed response to each of your points:

Comment 1: Saxon Genitive

Reviewer’s Comment: "Regarding the previous request for change: ‘an object’s movement’. The Saxon genitive cannot be used for objects. Also in other parts of the paper.” Authors have changed only that sentence and did not fix all the sentences in the paper where the Saxon genitive is used. What is the sense of fixing one sentence and leaving all others unchanged? For instance: ‘to the target's speed λ2. Next, dropping the new triangle's internal’ there are many more of those examples that need to be fixed."

Response: We apologize for the oversight. We have thoroughly reviewed the manuscript and corrected all instances where the Saxon genitive was used inappropriately for objects. Specifically, we have revised phrases like “the target's speed λ2” to “the speed of the target λ2” and similar constructions throughout the manuscript.

Comment 2: Consistent Use of Acronyms

Reviewer’s Comment: "The acronyms AR and VR are introduced but are not used consistently throughout the paper, e.g., ‘and is thus equally applicable to virtual or augmented reality.’"

Response: Thank you for pointing this out. We have ensured consistent use of the acronyms AR (Augmented Reality) and VR (Virtual Reality) throughout the manuscript. Every instance of “virtual or augmented reality” has been updated to “VR or AR” for consistency.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors replied to the comments, and improved the manuscript.

But I suggest to add a new Section called Preliminary to introduce the Theory of Screws, Optic flow, and the ecological approach, rather than to add a Subsetion in the Introduction.The Introduction can focus on the research background, research motivations, research gaps and the contributions of the proposed methods.  

Author Response

Dear Reviewer,

We sincerely appreciate your detailed feedback and suggestions for improving our manuscript. We have carefully considered and incorporated all your comments into the revised manuscript. Below, we provide a detailed response to each of your points:

Comment : Addition of a Preliminary Section

Reviewer’s Comment: "The authors replied to the comments and improved the manuscript. But I suggest adding a new Section called Preliminary to introduce the Theory of Screws, Optic flow, and the ecological approach, rather than adding a Subsection in the Introduction. The Introduction can focus on the research background, research motivations, research gaps, and the contributions of the proposed methods."

Response: We have added a new section titled "Preliminary" to introduce the Theory of Screws, Optic Flow, and the Ecological Approach, as you suggested. This new section provides a comprehensive overview of these foundational theories, allowing the Introduction section to focus on the research background, motivations, gaps, and contributions of our proposed methods.