Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: This paper studies the problem of learning the feature representation for predicting the 3D shape of objects, from a single image or a point cloud. The proposed approach performs PCA on the SDF field. And then the transformed feature map is learned and used as input to task-specific decoders for 3D shape prediction. The authors claims that this approach trains faster and is easier to scale, while showing competitive performance compared to state-of-the-art methods.

I am leaning towards Weak Reject. The paper is generally easy to read, but with some details missing. And I found the discussion of the results to be insufficient. I think it can be an above-threshold paper if questions are addressed during rebuttal.

Being able to easily scale to higher resolutions is claimed to be one of the main advantages, but I am not convinced that this is useful under this setting. If I understand this correctly, the number of eigenvectors k is fixed, and projecting the SDF field to this space would remove the higher frequency components of the shape. So wouldn't the number of eigenvectors be the bottleneck in representational precision, not the resolution of the output space?

What is the chosen k (number of eigenvectors)? It says k was "chosen to capture 99.5% of the variance within the dataset", but I could not find how exactly it was chosen and what value of k was used (I apologize if I missed).

Also, I think the PCA is category-specific (page 4, section 4.1). Is k dependent on the category or is it the same across all categories? Some of the other methods (if not all) used for comparison are not category-specific, so if this is true, I think the comparison may not be entirely fair and it should be made clearer.

I think the writing could be polished as well, some minor typos:

Page 2:  3rd and 4th paragraphs: continous
Page 2: anlaysis, enlightning
Page3: under eigenSDF: reprsentation
Page 4: section 4.1: refered, signficant
Page 5: “seciton”
Page 7: tranform

Page 3, Section 3.2: Is N the number of training examples and M the resolution?
Figure 2 not referred in the main text.





review_title: Official Blind Review #2

final_score: rating: 6: Weak Accept
review_content: Thank the authors for the response. I am still in favor of the idea -- applying simple, old-school method into a new problem, and I also agree with R1 and R2 that the paper is currently lack of details and experimental results. I will keep my score, but would not fight for the acceptance if R1 and R2 insist.
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Summary
This paper presents a new method for 3D shape reconstruction, based on SDF (Signed Distance Function) and PCA. The basic idea is to conduct PCA on all the shapes with SDF as feature, and encode a shape by the eigenvectors from PCA. The authors present experiments on 3D reconstruction from 2D view and point clouds, which demonstrate the effectiveness of the proposed method. I lean to vote for accepting this paper since the idea is simple but novel, and it achieves good performance.
Strengths
- The idea itself is simple and novel. The basic idea of this approach is simple -- keep most information / variance by using PCA, and it is also very novel, since I have not seen papers using PCA to encode 3D shapes.
- The idea is effective. As the authors demonstrated in section 4, this approach works well, and it outperforms all other methods by a large margin according to Chamfer distance. This is impressive since such a simple method can improve the performance this much.
Weaknesses
- More analysis could be provided about how do the authors choose SDF. Choosing SDF here is obviously a reasonable choice, but is it the best? More analysis could be provided, or more experiments could be included.
Possible Improvements
As mentioned above, more analysis about why choosing SDF or more experiments about comparing SDF to other representations under this PCA approach could be provided.
review_title: Official Blind Review #3

final_score: rating: 3: Weak Reject
review_content: The paper introduces a 3D object reconstruction/completion algorithm that utilizes a simple decoder from features generated using PCA of SDF. The approach was tested in a few experiments on public benchmarks and achieves competitive results. 

The overall presentation of the paper is decent, and the network structure of the proposed approach is reasonable. It's interesting to see that using a simple PCA can help improve performance using a simple network structure. The experimental results make sense, and it's nice to see the performance is reasonable as well.

I have a few questions regarding the paper:
- Without looking at the code, I don't think I fully understand the formulation of the network structure just by reading the text. For example, what is the dashed line mean in Fig. 1? What's the meaning of the dot over "E" in Sec 3.2, is it "derivatives"? If so, why not use this symbol in Eq. (2) as well? In general, I find it's a bit hard to follow when only 2-3 paragraphs are used for describing the proposed approach. It'll be good if the authors can elaborate on the approach in a more thorough manner. 
- Regarding experimental results, it's nice to see that eigenSDF is better than linearSDF, demonstrating that the approach is quite effective. However it is not always the best in several metrics (as indicated in experimental result tables). I wonder if authors can provide more analysis or discussions on why this could happen, either the metric may not make too much sense in their setting, or if there is potential room for improvement. A few failure case visualizations could also be helpful in understanding the issues of the proposed approach.
- Moreover, do authors have thoughts on eigenSDF vs deepSDF (cited in the paper, published in CVPR 2019)? It'll be interesting to compare those as well, as deepSDF has proven useful in a few papers already. 
review_title: Official Blind Review #1

Meta-review: This paper proposes to use PCS to replace the conventional decoder for 3D shape reconstruction. It shows competitive performance to the state of the art methods. While reviewer #3 is overall positive about this work, both reviewer #1 and #2 rated weak rejection. Reviewer #1 concerns that important details are missing, and the discussion of results is insufficient. Reviewer #3 has questions on the clarity of the presentation and comparison with SOTA methods. The authors provided response to the questions, but did not change the rating of the reviewers. The ACs agree that this work has merits. However, given the various concerns raised by the reviewers, this paper can not be accepted at its current state.
Decision: Reject