Paper:
Learning Spherical Convolution for Fast Features from 360°Imagery
While 360°cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make core feature extraction non-trivial. Convolutional neural networks (CNNs) trained on images from perspective cameras yield "flat" filters, yet 360°images cannot be projected to a single plane without significant distortion. A naive solution that repeatedly projects the viewing sphere to all tangent planes is accurate, but much too computationally intensive for real problems. We propose to learn a spherical convolutional network that translates a planar CNN to process 360°imagery directly in its equirectangular projection. Our approach learns to reproduce the flat filter outputs on 360°d ata, sensitive to the varying distortion effects across the viewing sphere. The key benefits are 1) efficient feature extraction for 360°images and video, and 2) the ability to leverage powerful pre-trained networks researchers have carefully honed (together with massive labeled image training sets) for perspective images. We validate our approach compared to several alternative methods in terms of both raw CNN output accuracy as well as applying a state-of-the-art "flat" object detector to 360°data. Our method yields the most accurate results while saving orders of magnitude in computation versus the existing exact reprojection solution.

Review:
This paper describes a method to transform networks learned on perspective images to take spherical images as input. This is an important problem as fisheye and 360-degree sensors become more and more ubiquitous but training data is relatively scarce. The method first transforms the network architecture to adapt the filter sizes and pooling operations to convolutions on a equirectangular representation/projection. Next the filters are learned to match the feature responses of the original network when considering the projections to the tangent plane of the respective feature response. The filters are pre-learned layer-by-layer and fine-tuned to output features as similar as possible to the original network projected to the tangent planes. Detection experiments on Pano2Vid and PASCAL demonstrate that the technique performs slightly below the optimal performance using per-pixel tangent projections (however significantly faster) while outperforming several baselines, including cube map projections.
The paper is well written and largely easy to read. While simple and sometimes quite ad hoc (Sec 3.2), I like the idea and am not aware of any closely related work (though I am not an expert in that domain). The technical novelty is quite limited though as it largely boils down to retraining a newly structured network on equirectangular images based on a pre-trained model. I think the experiments still warrant publication (though I would have believed that a pure computer vision venue would be more appropriate than NIPS due to the specific application), so overall I am slightly on the positive side.
Detailed comments (in order of the paper):
Introduction: The upper bound the method can achieved is defined by running a CNN on all possible tangent projections. This seems fair, but does not deal with very large and close objects which would be quite distorted on the tangent plane (and occur frequently in 360 degree videos / GoPro Videos / etc). I don't think this is a weakness but maybe a comment on this might be good.
Related work: I am missing a section discussing related work on CNNs operating on distorted inputs and invariance of CNNs against geometric transformations, eg., spatial transformer networks, warped convolutions, and other works which consider invariance.
l. 117: W -> W x W pixels
Eq. 2: I find ":=" odd here, maybe just "=" or approximate? Also, it is a bit sloppy to have x/y on the lhs and \phi/\psi on the rhs without formalizing their connection in that context (it is only textual before). Maybe ok though.
After this equation there is some text describing the overall approach, but I couldn't fully grasp it at this point. I would add more information here, for example that the goal is to build a network on the equirectangular image and match the outputs after each convolution to the corresponding outputs of the CNN computed on the tangent plane.
Fig. 2b: It is unclear to me how such a distortion pattern (top image) can arise. Why are the boundaries so non-smooth (double curved left image boundary for instance). I don't see how this could arise.
Fig. 2 caption: It would be good to say "each row of the equirectangular image (ie, \phi)" and in (b) what is inversely projected.
l. 131: It is never clearly described how these true outputs are computed from exhaustive planar reprojections. Depending on the receptive field size, is a separate network run on each possible tangent plane? More details would be appreciated.
Sec. 3.2: I found the whole description quite ad-hoc and heuristic. I don't have a concrete comment for improvement here though except that it should be mentioned early on that this can only lead to an approximate result when minimizing the loss in the end.
l. 171: It is unclear here if the loss is over all feature maps (must be) and over all layers (probably not?). Also, how are the weights initialized? This seems never mentioned.
l. 182: It is unclear why and how max-pooling is replaced by dilated convolutions. One operation has parameters while the others has not.
l. 191: It is not Eq. 2 that is used but a loss that considers the difference between the lhs and the rhs of that equation I assume? Why not stating this explicitly or better reuse the equation from the beginning of Sec 3.3.?
l. 209: What happens to the regions with no content? Are they excluded or 0-padded?
l. 222: Why is detection performance evaluated as classification accuracy. Shouldn't this be average precision or alike?
Experiments: Some more qualitative results would be nice to shed some light. Maybe some space can be made by squeezing the text partially.