Summary and Contributions: This works tackles the problem of localization by image retrieval, specifically the training for such a problem. They argue that most of previous work focuses on artificial hard image split to positive and negative classes, and propose to do it in a soft manner. Namely, they propose a formal framework for learning localization features instead of place recognition features; formulate a novel loss for such a purpose; obtain state of the art performance.
Strengths: + I really like the problem formulation, it is done in a really principled way and it properly motivates proposed solution + Newly proposed loss utilizing soft assignments seems to be very useful in this particular task/area, and the community would benefit from it + Very good experimental comparison against state-of-the-art approaches, on many datasets, and under different image conditions + Nice ablation study on the choice of soft assignment function, it showcase the benefit of using the proposed "influence" functions and the final proposed loss
Weaknesses: - Last contribution, ie, dataset cleaning, is a very minor contribution and shouldnt be the part of major ones. Unless there is some specific novel methodology applied to clean the dataset, I dont think this contributions should be listed here. - Loss is inspired by , authors should be more clear on how much different it is, and clearly state which are the improvements. I dont think that is too clear at the moment. - Table 2 is very hard to read, some color coding of the 1st and 2nd best results would be good. Additionally, saying "Our method performs best on all four test sets." is not supported in the RobotCar Seasons datasets (table 2 upper part), as looking at the mean results the proposed method is not the best in 2 out of 3 metrics used. Nevertheless, overall, this method is state-of-the-art approach, the wording could be better, that is all. Minor: l262: multi-similarity loss  ->  l266: Table 1 -> 2
Correctness: Yes, seems correct.
Clarity: I find the paper to be clear, well written, and easy to follow.
Relation to Prior Work: Additional comments on difference to very related work  could help the reader, as stated in weaknesses.
Additional Feedback: I like the work, and will propose to accept it. I think it benefits the area of place localization via image retrieval, gives a nice theoretical overview of the problem, and a novel solution that achieves state-of-the-art results. All issues I have are stated in weaknesses, and could be easily resolved at rebuttal time. I hope authors do that, in which case I will be overall happy to propose acceptance of the submission.
Summary and Contributions: The paper tackles visual localization. It is standard to train image representations for localization via metric learning by defining positive and negative pairs based on some threshold. This paper proposes to instead of using hard positive/negative labels use a softened labels, e.g. nearby images are 'very positive', far away 'very negative', medium distance images are '50-50'. These scores are then integrated into the loss of . Extensive comparisons show good benefits of the proposed method.
Strengths: 1) It makes sense not to have hard labelling of positives vs negative pairs, so making this soft is nice. 2) Overall results look good compared to many baselines / SOTA methods.
Weaknesses: 1) The training and evaluation protocols are somewhat non-standard and it's not clear why this is. E.g. L.193 talks about removing outliers and under/over-exposed images for training, L.208 about ignoring some images for evaluation. So essentially we can't compare the given numbers to any published results in the literature, despise using existing publicly available datasets for train and eval. Why not just use a standard procedure? E.g. train on the same data as others train on RobotCar? Or train on Pittsburgh? 2) A bit of a smaller point: It's not clear how fragile is the proposed method. For example, authors show figure 3 with tanh instead of sigmoid and this seems to significantly degrade results. It's a bit surprising as tanh and sigmoid are just scaled and shifted versions of each other. But I think sigmoid makes most intuitive sense to use so this might not be such an issue.
Correctness: All looks fine although I didn't check the proofs as they look intuitively correct (especially Proposition 3.3 which I think is fairly trivial)
Clarity: I think the paper is overly mathematical for what is actually proposed. It's simple (and that's not a negative): 1) instead of hard labels use soft labels, and you can use any function g+ and g- to define these soft labels depending on world distance, 2) insert this into loss of . I don't think we need all this maths and propositions and proofs to present this simple idea, it makes it a lot harder to follow than it should be. For example, L.135 talks about positiveness and negativeness and I find these terms very confusing - assuming g+ is box or sigmoid, the ideal network should yield f_i=a for x_i=x_a so the 'positiveness' score should actually be low (0) for the most positive example. Then it should be larger than 0 for some 'less positive' but near-enough examples (e.g. distance=5). Finally it should again be 0 for very far away points. I think it would make a lot more sense in terms of exposition to just state that g+ and g- are essentially the soft labels and build from there.
Relation to Prior Work: Yes
Additional Feedback: Results: - It's not quite true that L.267 "Our method performs best on all four test sets" - RobotCar Seasons Mean seems to show that Triplet works better for 2 out of 3 thresholds (and multiple other methods as well). - Table 2: a) it's way too hard to read on printed paper, b) please put best numbers in bold here as well as for table 1. - Table 1: it seems 'mean' is averaged over 4 subsets of RobotCar and Pittsburgh which is strange, it would be better to have 'RobotCar Mean' instead. Intro / related work / .. - I think there's a bit too much emphasis on 'arbitrarily chosen thresholds' that previous methods use. Are they really so arbitrary? In your production system you might want to define what success is, e.g. correct localization= up to 10m error (e.g. that's anyway how all evaluations are done!), so why is it arbitrary to use the 10m threshold at training to exactly optimize for what we want? Making training exactly aligned with evaluation sounds perfectly reasonable to me. Also for example "Visual Place Recognition with Repetitive Structures" Torii et al. states that the noise in GPS/StreetView is 7-15 m so a commonly used 25m threshold is not so arbitrarily chosen.. But I do agree that it's too harsh to say 9.99m is positive and 1.01m is negative so the proposed idea makes sense. - I'm not sure about the distinction in L.71 between (ii) and (iii). Why is e.g.  trained for place recognition and the proposed method is trained for localization? They both train with metric learning based on GPS distances. In fact, as explained in the paper, the hard labels with margin loss can be seen as a special case of what is proposed here, which should mean they fall into the same class of methods. --- Post rebuttal: I didn't need convincing, I think it is a solid paper. I think points in my review are still valid, e.g. I think the exposition is overly mathematical to the point that it hurts understanding, but it also comes down to personal preferences.
Summary and Contributions: The paper is dealing with image-based localization handled as instance search. The goal is to learn good image embeddings that work well for search. Typically, the locations of the training data are used to make discrete groups of positive and negative images. The authors depart from that. They exploit the continuous nature of the training data coordinates and propose a continuous measure for positiveness and negativeness.
Strengths: - This is a novel approach, that is simple and easy to understand. - The authors fix a drawback of previous approaches. It is natural to exploit the continuity of the training labels. - The method is technically sound and comes with theoretical justifications. Other than that, it is intuitively understandable. - There is an extensive experimental validation comparing with prior losses. All are evaluated by the authors under the same conditions. The proposes method achieves top results. -
Weaknesses: - Many images that are nearby to the anchor will not share the same viewpoint. Therefore, they are not visually positives. This is handled in  by disambiguate using the image similarity according to the current descriptor. I am missing the discussion of this case in the paper. Can the authors comment? Is the approach of  not needed in their method? Can it still be complementary? - The paper does not include any variations or ablations of the proposed approach, but only restricts to comparisons with other approaches. I am missing some understanding of what are the key ingredients and what is the sensitivity of the method. For instance: -- it is said "Although any choice of strictly increasing and decreasing functions are eligible for influence functions, a careful choice is necessary for the desired outcome in practice.". How much does one have to tune the shape of the function? If it is very sensitive to that, then, tuning this instead of the distance thresholds in other approaches might even be less convenient. -- The number of nearby and far examples are kept fixed. What is the sensitivity to that? How many tuples does one batch include? Does it make sense to consider examples of all other tuples as far examples for the current tuple?
Correctness: I did not spot any flaws, but did not check all the derivations and proofs thoroughly.
Clarity: The paper is a pleasure to read.
Relation to Prior Work: The method is well positioned wrt prior work, and well motivated using the drawbacks of previous methods.
Additional Feedback: questions to the authors are listed in weaknesses. --- After reading the other reviews and the rebuttal, I still believe the paper is worth to be published. The authors should include the experimental results of Figure 1 from the rebuttal (sensitivity of the approach to hyper-parameters and influence functions) in the final supplementary material, but in a more readable way.
Summary and Contributions: This paper tackles the problem of visual geo-localization using metric learning. Given a set of images, features are learned so as to respect the ordering between their respective geographic distance. This is usually done using classical metric learning loss functions (contrastive, triplet, etc). In the paper, it is argued that defining a set of positive and negative images for a given query based on their geographic distance leads to an ill-posed problem. As such, they propose to relax the hard assignment label. They cast this into a multiple objective problem where all retrievable images have a positive and a negative score, weighted by monotonic functions of their geographic distance to the query. The multi-objective problem is reduced using a sum-log-exp aggregation. Experiments are performed on visual localization datasets.
Strengths: The formulation using a multi-objective problem is really nice and leads to a different interpretation of the metric learning problem. The paper is well written and well structured.
Weaknesses: Although the multiple objective is very nice, when aggregating using the sum-log-exp, it boils down to something very similar to multi-similarity. A clear analysis of the difference with MS should have been done. Also, what is the point of Proposition 3.3? Why would the case tau_1 -> tau_2 matter? Given that the training set is always finite in the studied problem, there will always be some small margin between tau_1 and tau_2. Or you want 2 images at exactly the same distance to be in different classes? Section 3.2 seems really off to motivate the choice of soft-assignement. Similarly, l.131 complains that the order is not preserved. This is not a problem of hard assignment but a problem of having reduced an ordinal regression problem into a binary classification problem. Learning to rank exists with methods able to preserve the ordering, which by the way the proposed method does not.
Correctness: The formal developments are correct, although some conclusions are deceptive (like the fact that hard assignment does not preserve ordering). Experiments are correct.
Clarity: The paper is well written, although the long string of references hinder readability. It is not enjoyable to have to skip to the reference section to discover what papers correspond to the ten numbers in brackets at the end of every other sentence Also, since the proofs are so small, they could have fitted the main paper.
Relation to Prior Work: The related work is sort of small in term of development. In particular,  is the paper that most likely answers the problems presented in later sections. It should have been more thoroughly explained and how the current work solves a problem that  does not. Similarly, as the method looks very similar to MS, a more detailed comparison should have been done.
Additional Feedback: There are 2 things that to my mind would greatly improve the paper: 1. Better use the setup presented in the beginning of section 4, or remove it. As it is in the current paper, it is difficult to see the motivation for a multi-objective problem and how it solves the problems raised in section 3.2. 2. Make a better comparison with both  and MS since these are the 2 most related paper. What precise problems do they both have and how the proposed weighting scheme solves them. Final comments: I would like to thank the authors for providing a strong rebuttal, which together with the discussion with other reviewers made me update my review towards acceptance. I nonetheless still feel that the theoretical section is misleading in the sense that the proposed methods does not offer more guarantees than the literature. In particular, the proposed method does not guarantee that the solution is in the feasible set of problem 3.2 or that the corresponding feasible set has a margin >0. Maybe this could be clarified in the final version. The relation with multi-similarity is also very important and I hope to see it in the final version.