Editor Comments
Editor: 1
Comments to the Author:
The paper needs minor revisions (see comments of reviewers #1 and #3).
Also, note that as a short paper it needs to be shortened to 15 pages.
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Reviewer Comments
Reviewer: 1
Recommendation: Author Should Prepare A Minor Revision
Comments:
The authors have satisfactorily responded to all my questions and made the necessary changes to the manuscript.
However, another question occurred to me in reading the revised manuscript. Specifically, Theorem 8 states "Assume that there is a perfect isometric instance of T within the scene point pattern S." But what about a case in which there are two or more perfect isometric instances of T within S? This can happen if there are two perfect "copies" of T within S. Additionally, it can happen even in the absence of multiple "copies" if there are symmetries that make the matching non-unique. For instance, suppose T consists of the 4 vertices of a square, and S contains exactly one perfect square; then there are four valid isometric instances of T within S (corresponding to rotating the square by 0, 90, 180 and 270 degrees). In such degenerate cases where there are "ties" (multiple, equally good solutions), the marginal estimates furnished by belief propagation do not point unambiguously to *coherent* solutions.
These degenerate cases are nearly impossible in typical real-world point matching problems, and can be safely ignored in practice (or prevented by adding small amounts of noise to break any unforeseen symmetries), but it would be good for the authors to add a sentence or two discussing these cases.
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1. Which category describes this manuscript?: Research/Technology
2. How relevant is this manuscript to the readers of this periodical? If you answer Not very relevant or Irrelevant please explain your rating under Public Comments below.: Very Relevant
1. Please evaluate the significance of the manuscripts research contribution.: Good
2. Please explain how this manuscript advances this field of research and/or contributes something new to the literature. : See my review of the original manuscript.
3. Is the manuscript technically sound? In the Public Comments section, please provide detailed explanations to support your assessment: Appears to be - but didn't check completely
4. How thorough is the experimental validation (where appropriate)? Please discuss any shortcomings in the Public Comments section.: Compelling experiments; clearly state of the art
1. Are the title, abstract, and keywords appropriate? If not, please comment in the Public Comments section.: Yes
2. Does the manuscript contain sufficient and appropriate references? Please comment and include additional suggested references in the Public Comments section.: References are sufficient and appropriate
3. Does the introduction state the objectives of the manuscript in terms that encourage the reader to read on? If not, please explain your answer in the Public Comments section.: Yes
4. How would you rate the organization of the manuscript? Is it focused? Please elaborate with suggestions for reorganization in the Public Comments section.: Satisfactory
5. Please rate the readability of the manuscript. Explain your rating under Public Comments below. : Readable - but requires some effort to understand
6. How is the length of the manuscript? If changes are suggested, please make explicit recommendations in the Public Comments section.: About right
Please rate the manuscript overall. Explain your choice.: Good
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Reviewer: 2
Recommendation: Accept With No Changes
Comments:
The authors addressed the main concerns from the reviews, the revised version of the manuscript appears to be good. In particular the proof of convergence of LBP on their
clique graph is now more readable, stressing the results of Ihler et. al based on the finite dynamic range of the potentials, and giveing a clearer explanation of the mapping from a clique-cycle to a pairwise cycle-MRF. It looks ready for publication as far as I can tell.
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1. Which category describes this manuscript?: Research/Technology
2. How relevant is this manuscript to the readers of this periodical? If you answer Not very relevant or Irrelevant please explain your rating under Public Comments below.: Very Relevant
1. Please evaluate the significance of the manuscripts research contribution.: Good
2. Please explain how this manuscript advances this field of research and/or contributes something new to the literature. : This paper addresses the problem of point-pattern matching by formulating it as a graphical model and applying loopy max-product. It extends an earlier paper [1] by creating a globally rigid graph with a
smaller max clique size. The new graph is however not chordal, so instead of applying the junction tree algorithm the authors use loopy max-product. By considering groups of variables the resulting graph
is a single loop, and the authors refer to an earlier result of max-product convergence and correctness in single-loops to show that they also obtain the MAP solution.
3. Is the manuscript technically sound? In the Public Comments section, please provide detailed explanations to support your assessment: Yes
4. How thorough is the experimental validation (where appropriate)? Please discuss any shortcomings in the Public Comments section.: Compelling experiments; clearly state of the art
1. Are the title, abstract, and keywords appropriate? If not, please comment in the Public Comments section.: Yes
2. Does the manuscript contain sufficient and appropriate references? Please comment and include additional suggested references in the Public Comments section.: References are sufficient and appropriate
3. Does the introduction state the objectives of the manuscript in terms that encourage the reader to read on? If not, please explain your answer in the Public Comments section.: Yes
4. How would you rate the organization of the manuscript? Is it focused? Please elaborate with suggestions for reorganization in the Public Comments section.: Satisfactory
5. Please rate the readability of the manuscript. Explain your rating under Public Comments below. : Easy to read
6. How is the length of the manuscript? If changes are suggested, please make explicit recommendations in the Public Comments section.: About right
Please rate the manuscript overall. Explain your choice.: Good
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Reviewer: 3
Recommendation: Author Should Prepare A Minor Revision
Comments:
In the response to my review the authors claim that for isometric
matching, where all pairwise-distances need to be preserved, a 2-tree
is not sufficient for matching in the plane. This is incorrect. It
is only true if the clique potentials only look at pairwise distances.
But clique potentials in a 2-tree can look at the joint configuration
of 3 nodes at a time. The clique potentials can not only look at
pairwise distances but also the "orientation" of a triangle.
Let C=(a,b,c) be a 3-clique in the model. Let (a',b',c') be three
points in the plane. We can define Phi_C(a',b',c') = 0 if the
pairwise distances within (a',b',c') agree with the pairwise distances
within (a,b,c) AND the determinant of [b-a; c-a] and [b'-a'; c'-a']
have the same sign. Phi_C = infinity otherwise (of course in practice it
shouldn't be infinity, to allow for small deformations). The distance
constraints ensures that Phi is zero for rigid motions+reflections.
The determinant constraint eliminates reflections.
Thus a 2-tree on 3 node can be made rigid. Now we can prove by induction
that a 2-tree on n nodes can be made rigid.
A 2-tree on n nodes is obtained by adding a node c to a 2-tree on n-1
nodes and connecting it to two nodes a and b. If we know the
location of a and b, fixing the distances |c-a| and |c-b| gives 2
possible locations for c. If we fix the determinant [b-c; c-a] there
is a single location.
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1. Which category describes this manuscript?: Research/Technology
2. How relevant is this manuscript to the readers of this periodical? If you answer Not very relevant or Irrelevant please explain your rating under Public Comments below.: Relevant
1. Please evaluate the significance of the manuscripts research contribution.: Good
2. Please explain how this manuscript advances this field of research and/or contributes something new to the literature. : The paper describes an approach for matching point sets using belief propagation. The method is designed for matching nearly isometric point sets, and in this case it improves on a previous method based on belief propagation.
3. Is the manuscript technically sound? In the Public Comments section, please provide detailed explanations to support your assessment: Partially
4. How thorough is the experimental validation (where appropriate)? Please discuss any shortcomings in the Public Comments section.: Lacking in some respects; some cases of interest not tested
1. Are the title, abstract, and keywords appropriate? If not, please comment in the Public Comments section.: Yes
2. Does the manuscript contain sufficient and appropriate references? Please comment and include additional suggested references in the Public Comments section.: References are sufficient and appropriate
3. Does the introduction state the objectives of the manuscript in terms that encourage the reader to read on? If not, please explain your answer in the Public Comments section.: Yes
4. How would you rate the organization of the manuscript? Is it focused? Please elaborate with suggestions for reorganization in the Public Comments section.: Satisfactory
5. Please rate the readability of the manuscript. Explain your rating under Public Comments below. : Easy to read
6. How is the length of the manuscript? If changes are suggested, please make explicit recommendations in the Public Comments section.: About right
Please rate the manuscript overall. Explain your choice.: Good