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\noindent Object: Revision of   Fully Invariant Image Comparison,
authors Jean-Michel Morel and Guoshen Yu.
\medskip

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$December
19, 2008

\medskip Dear Editor in Chief,

\bigskip I am writing to you concerning the above referenced manuscript, which we have submitted to SIIMS.
We thank the reviewers for their constructive comments and for their minor
required changes. Below, we provide detailed responses to their specific
comments.



\bigskip

\medskip
 Best regards,

\medskip  Jean-Michel Morel and Guoshen Yu

\small
\section*{Referee 1}
\begin{itemize}
\item {\bf Referee:} The contribution of the paper, while worthy of publication, is somewhat marginal and is likely to have little practical impact. Even though the proposed method has been shown by the authors to be marginally more accurate than existing SIFT-based methods, it is unlikely to be widely used because its increased complexity (both in terms of implementation and in terms of computation) does not justify the relatively small improvement in terms of matching results. Also, the low-level mathematical and implementation details described in the paper are of interest to a relatively small audience. For this reason, I suggest that the manuscript be shortened from its current 54 pages. Specifically, some of the background material in Section 3 does not appear to be essential to the paper, and neither are the lengthy excerpts from other papers in Section 4 (p. 11). The technical derivations and presentation of low-level details should be condensed throughout with a view to making this paper more widely accessible.

\item {\it Author answer:  The manuscript as been shortened as much as possible. We have removed 17 pages. We  kept the mathematical proofs, but several have been simplified and considerably shortened. All excerpts have been removed. }

- The experimental evaluation is reasonably convincing, but a more extensive evaluation using datasets made available by Krystian Mikolajczyk (http://www.robots.ox.ac.uk/~vgg/research/affine/) would be better. However, given that this paper is a submission to a mathematical journal and not to IJCV or PAMI, the current results may be sufficient. Also, it would help if the authors gave actual running times of their method compared to the other methods.

\item {\it Author answer: We know this dataset and have added a performance evaluation on it. As for the  running time,  we thought it best if we put on line the algorithm, so that users can directly try it. We have also added running time comparison in terms of SIFT and installed an online demo.}

\textbf{GUOSHEN:  On donne l'adresse?}

\textbf{Jean-Michel: comme on a mis l'adresse dans l'article, je
pense c'est pas vraiment la peine de donner aux rapporteurs
l'adresse. Par contre ca sera bien je pense de donner l'addresse a
Sapiro comme tu disais dans le mail.}

\end{itemize}

\section{Referee 2 }
 \begin{itemize}
 \item
However, the paper is simply far longer than needed to present this material, and the presentation style is very loose and conversational, so that it frustrates the reader. I believe that the length of the paper should be cut in half, and the presentation style tightened to eliminate unnecessary commentary.

\item {\it Author answer:   The paper has been shortened by 17 pages.}

\item Examples of sections that can be eliminated are 3.1 and 3.3 which just present previous methods that are not part of the approach being presented. The quotes at the beginning of section 4 are completely unnecessary. I see no purpose to Figure 9. The experiment description should be greatly shortened and the number of figures cut at least in half.

\item {\bf GUOSHEN : Qu'est-ce qu'on fait? C'est vrai que d'expliquer Hessian affine, SIFT ou MSER alourdit un peu le papier. Mais d'un autre cot\'{e} c'est vraiment idiot de montrer plein de comparaisons avec ces m\'{e}thodes sans les expliquer un peu, non? Dis moi ton avis s'il te plait.}

\textbf{Jean-Michel: je suis bien accord qu'il est necessaire de
introduire SIFT, MSER et Harris-Affine. Ta reponse sur ce point
m'apparait parfait.}

\item {\it Author answer:  3. and 3.1 have been shortened but not eliminated because the point to discuss their invariance and prepare the comparisons. The quotes have been removed. The figures have been  halved. }

\item
Not only should material be eliminated, but the many informal comments should be greatly reduced. For example, in the introduction, there is no need to list 4 questions and then answer them, when just presenting the points in a concise manner would be much easier and faster to read. Similarly, the introduction mentions "transition tilts" even though the term is only defined much later in the paper. Figure 1 should be replaced with something like Figure 8, which demonstrates the effectiveness of the approach in a dramatic fashion and is much easier to understand.

\item {\it Author answer:  The 4 questions have been removed. Fig. 1 has been kept but with a comment added to explain the intuition of the  transition  tilt.}

\item
Given the many presentation issues, I advise the authors to consult with others for feedback on presentation and possibly hire a professional editor. The material is important, but the paper will not be taken seriously in its current form.

\item {\it Author answer: Thanks for the positive comment. The editing has been done.}

\end{itemize}
\section{Third referee}
\begin{itemize}
\item Title. The title is adequate, but I suggest to include in it the word A-SIFT for diffusion purposes (e.g.
“A-SIFT: a new framework for fully affine invariant image comparison”).

\item {\it  Author answer: We took this title.}

\item Manuscript organization. Sections organization is adequate. The informal introduction, followed by
more formal details, helps readability.

\item  {\it  Author answer:  Thanks,  we reduced it anyway. }

\item Proofs. Include all proofs for the sake of completeness. For instance, Theorem 1 is proved in [45], which
is a university preprint. Proofs can all be moved to an appendix, to reduce the main core burden.


\item  {\it  Author answer: Theorem 1 is in course of publication in another paper. It is  accessible as preprint and we have added the  reference of the journal where it is going to appear.  }

\item Conclusion. Please present a brief summary or conclusion at the end of the paper.

 \item  {\it  Author answer:   We did it.}

 \item Bibliography. The bibliographic review is exhaustive and complete. Please check that all references are
correct. For example, there is a mistake in references [9] and [49].
\item  {\it  Author answer:   Done.}

\item Detailed comments (not reproduced)

\item {\it Author answer: thank you very much for the detailed comments. You have read the paper very carefully and found typos and blunders in the  proofs that we had completely missed after many readings.  All of your detailed comments have been implemented without a single exception.}
\end{itemize}

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