Venue: ICLR 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: The paper introduces a new approach to leveraging graph neural networks for image tasks. While prior work has been based on constructing graphs using a super-pixel map using methods like SLIC, that generate super-pixels of all roughly the same size, the proposed method generates a scale-adaptive partition. It also introduces a new pooling operator on this graph structure, and demonstrates that, together, these lead to improved performance when used with GNNs.

- Overall, the method is novel and innovative, and well executed. The experimental evaluation is reasonably compelling (even if on relatively small datasets).

- This paper adds to the body of literature exploring the use of GNNs as an alternative to CNNs for image tasks. The fact that past attempts have relied on a graph structure built at a specific scale likely handicap them when competing with CNNs, which are much better able to retain notion of space and scale across successive convolution and pooling operations.

- The idea of converting a tagged/thresholded wavelet coefficients into a quad-tree structure is interesting, and indeed natural in retrospect.

- I wonder though whether alternative approaches to building a multi-scale superpixel partition would perhaps not perform better. This isn't a negative for this paper (indeed, it could spur such research in the future), but perhaps something that's based on hierarchical clustering (on top of SLIC) might work better. One drawback of the wavelet approach is that the boundaries of the superpixels have to be regular and axis and aligned with the downsampling phase (have authors considered variants that are based on overcomplete wavelet transforms?).

- There is an interesting effect in Fashion-MNIST where a larger number of superpixels leads to lower accuracy. This doesn't seem to have been discussed in the text.

- Minor comment: For Fig 3, it would be good to have a brief legend or description in the caption itself. The caption currently points to Sec 3.3 (which is a little inconvenient when parsing the figure).

review_title: Good paper

final_score: rating: 5: Marginally below acceptance threshold
review_content: This paper introduces a wavelet-based superpixel algorithm and a spatially heterogeneous pooling. More specifically, they introduce an algorithm to compress images in the pixel domain and it leads non-uniformly distributed and multiscale superpixels. Furthermore, they introduced a spatially heterogeneous pooling method tailored to the superpixel algorithm. Finally, they demonstrate the effectiveness of their method on MNIST, Fashion-MNIST, and CIFAR-10 datasets. 
pros:
1. The proposed method is simple and elegant. It is theoretical well-founded and easily implemented.
2. The paper provides good initial results, showing that to some degree their method is generalizable.
cons:
1. In step 2 of wavemesh, the authors need to include the computational cost.
2. In Table1, the results of the proposed method are not significant. More experiments are needed to demonstrate the gain of the proposed method.
3. The authors should try other evaluation measurements, only acc is not enough.
4. I believe more generalization and deeper analysis would be beneficial. 

review_title: introduces a wavelet-based superpixel algorithm 

final_score: rating: 2: Strong rejection
review_content: This paper present WaveMesh, a wavelet-based superpixeling algorithm and WavePool, a spatially heterogeneous pooling scheme.

Strengths:

"A wavelet transform image coding technique with a quadtree structure" (Banham and Sullivan 1992) and "Geometric methods for wavelet-based image compression" (Wakin et al. 2003) indicate that a wavelet-coefficient based quadtree decomposition of images is an efficient image-compression technique. This suggests that the goal of this paper is reasonable and the method can likely be motivated.

Weakness:

The authors provide little theoretical justification for the use of wavelets as they are used in this paper.

Moreover, the pooling method in this paper appears to be the same as that in "Image Segmentation Based on Multiscale Fast Spectral Clustering". In addition, the pooling method seems to be applicable to any quadtree-based method. A superpixel quadtree can be defined in many ways, and quadtrees are the basis of other superpixel methods like the "A Hierarchical Data Structure for Picture Processing" (Tanimoto and Pavlidis 1975), analyzed in "Evaluation Framework of Superpixel Methods with a Global Regularity Measure."

There are two primary weaknesses: First, SLIC is a poor baseline and many other superpixel methods have been developed since 2010 - "Superpixel Segmentation using Linear Spectral Clustering" or "Robust superpixels using color and contour features along linear path" or even the recent "Simple and fast image superpixels generation with color and boundary probability".
Second, almost all of the gains of this method appear to come from the pooling method: In Tables 2 and 3, WaveMesh alone consistently underperforms SLIC.

Third, these results appear to depend on the classification model. While the variance is low, alternative hyperparameters for the SplineCNN (or a different model) may have resulted in different performance. Given that this paper did not use any of the existing superpixel evaluation metrics, it is difficult to compare it to prior work. While of course the two papers cannot be compared directly as they are both currently under ICLR review, "Probabilistic Numeric Convolutional Neural Networks," has similar performance on the 75 Superpixel MNIST dataset, using a third as many superpixels.

Due to these weaknesses, this paper has neither the experimental analysis nor the theoretical grounding to be appropriate for ICLR at this time.
review_title: Learning from multiscale wavelet superpixels using GNN with spatially heterogeneous pooling

final_score: rating: 5: Marginally below acceptance threshold
review_content: Quality: The motivation of this paper is great, and the proposed WaveMesh is interesting. In general, it is a high-quality work. It will be better to supplement more experiments.

Clarity: The expression is clear, and especially, the figures are very exquisite, and helpful for understanding.

Originality: The proposed image-specific superpixeling algorithm WaveMesh is novel and try to circumvent the limitation of SLIC. However, the insufficient experiments affect its persuasiveness.

Significance: The WaveMesh could filter the unimportant information and focus on the important information which is a significant research. It may be applied to more image-based task, such as image segmentation. Consequently, I think this work has a certain significance, but it needs more experiments to evaluate.

Pros:
1. It is a novel idea that non-uniformly downsamples the images and gets a multiscale superpixel representation.
2. The figures are concise and precise, and they provide an intuitive understanding about the WaveMesh and WavePool.

Cons:
1. The experiment is not sufficient. Take MNIST as example, this work only compares the WaveMesh and SLIC when the number of nodes is ~57 which is not convincing enough to conclude that the WaveMesh is effective. What is the acc about SLIC when the number of nodes is ~238. Besides, it seems that SLIC+SplineCNN achieves the best acc when the number of nodes is small. The experiments on Fashion-MNIST and CIFAR-10 have the same problem.
2. WaveMesh is a superpixeling algorithm that is not coupled with classification algorithm, but all the experiments are performed on SplineCNN. What is the performance of WaveMesh with other GNN algorithms?
3. How to evaluate the effectiveness of the image-dependent threshold T?

review_title: This paper proposes a multiscale superpixel algorithm that tries to circumvent the limitation of SLIC. It is novel but the experiments are not so convincing. 

Meta-review: This paper received mixed reviews.  One reviewer is positive, while the remaining three reviewers are either negative or feel that the paper is below the threshold for acceptance.

The ideas presented in the paper are interesting and novel - this was acknowledged by three of the reviewers, even those who did not recommend acceptance.  The AC also recognizes the technical novelty presented.  However, as all the reviewers pointed out to varying degrees, the experimentation is problematic and the AC in agreement with this.  In particular, the heavy focus on improvement on top of SLIC makes it the applicability of the proposed approach highly limited and also not so convincing.

Recommendation for the paper is to reject and resubmit with improved experimentation.
Decision: Reject