Microsaccades, Drifts, Hopf Bundle and Neurogeometry
Round 1
Reviewer 1 Report
This is a really interesting paper, in which a classical and celebrated topic in differential geometry, i.e. the Hopf fibration, is applied to the investigation of visual information, providing an interpretation of the Donder's and Listing's laws in terms of sections of the Hopf bundle. The paper presents a rigorous approach both in the description of the visual processes involved in static and dynamic vision, and in the presentation of geometrical tools. I recommed the publication of the paper in the present form, suggesting the correction of the following misprints:
Line 11: microsaccades
Line 134: B^3 instead of B^2
Line 420: punctured instead of punctures
Line 430: induced instead of induces
Line 471-4: correct the image of the inverse map s (Listing section) in the centered formula. This should be S^+_L\subset S^3
Line 538+4: in [0,T]] delete one bracket ]
Line 544-1: delete the last bracket )
Line 581: T_k instead of T-k
Line 693: We also conjecture
Line 698: I thank... who read
Author Response
I thank the referee for careful reading of the manuscript and the list of misprints. I correct all indicated misprints with exception of line 583. Here I have kept the last bracket, which makes the formula more understandable.
Reviewer 2 Report
Please regard the attached document.
Comments for author File: 
Comments.pdf
Author Response
I thank the referee for comments and indication of misprints. I correct all of them and I check that the formula at the line 389 is correct.
I took the Figure 5 from Google. When I wrote “Action of Marr fiters, Elena” , many images of Elena appeared and also some reference to theory of edge detection by Marr – Hilldreth.(D. Marr, E. Hildreth, “Theory of Edge detection”, Proc. R. Soc. Lond., B. 207, 187-217,. 1980).
But the next time I could not reproduce this result.
The review of this theory and the result of the application of the Marr- Hildreth algothim may be found in the paper by Haldo Sponton, Cardelino “A Review of Classic Edge Detectors” Published 7 June 2015 in Semantic Scholar.
