Paper: Contrastive Graph Autoencoder for Geometric Polygon Retrieval from Building Datasets (ICLR-2024)

Reviewer comment (Evaluation):
The author claimed the proposed method could retrieve polygons with holes better than existing methods, but did not provide quantitative metrics like persistent diagram whose 0-th dimension topological feature represents the number of component and 1-th dimension topological feature represents number of holes.

Author response:
Thanks for the suggestion. We update the manuscript by generating persistent diagrams for ten query geometries from the Melbourne dataset (as demonstrated in Appendix, Figure 10-11), showing the number of components (indicated by 0-th dimension topological features) and number of holes (indicated by 0-th dimension topological features). Note that the polygon geometries in Melbourne dataset (in total of 37139 samples) contains varying number of holes and are difficult to quantify as compared to other synthetic datasets (such as Glyph dataset and MNIST-cplx70k dataset in [Mai, Gengchen, et al.]).

Reviewer comment (Experiments):
The author claimed the proposed method is free of polygonal vertex counts which is a major benefit over the traditional methods and other graph autoencoders, but I cannot find any experiment results in the paper that can support such claim. Basically CGAE is close to GAE in terms of architecture so why CGAE can scale significantly better than GAE? I think the author should provide more evidences and arguments to this point since it is a critical contribution claimed by the author.

Author response:
Recall that our models are trained on the synthetic Glyph dataset and tested on real-world building footprints (OSM and Melbourne dataset). The number of vertex counts of the real-world building footprints vary compared to the synthetic dataset. 
The experimental results demonstrate how the current method is free of vertex count dependency are shown in the Appendix, Figures 10 - 11. Take as example query shapes 3 and 4 ( complex circular polygons with a single hole). The baseline GAE extracts polygons with over-simplified exteriors, which are not geometrically similar to the queries. CGAE, oppositely, can extract polygons with complex exteriors that are similar to the queries. In queries 5 - 7, GAE and CGAE fetch polygons for complex rectangular queries with or without holes. CGAE is capable of extracting rectangular counterparts for complex rectangular queries whereas GAE only identifies over-simplified rectangular polygons. We finally investigate CGAE’s capability of retrieving polygons for complex queries with multiple holes.
We update the manuscript by adding additional experiment results in Appendix, Figures 12 - 13. The two figures demonstrate the qualitative results of proposed CGAE and baseline GAE on simplified polygon geometries (with trivial vertices removed) by the topology-preserving Douglas-Peucker algorithm [Saalfeld, Alan.].
We also address the comment  “CGAE scales better than GAE”. We do *not* make any such claim - they are equivalent in how they scale, but CGAE is more robust and accurate.
Comparing Figures 6-7 (original sample from OSM dataset in [Yan, Xiongfeng, et al.]) to Figures 8-9 (rotated sample from OSM dataset in [Yan, Xiongfeng, et al.]), we observe how the baseline GAE is sensitive to rotations/reflections of buildings, failing to extract similar shapes when query shapes are rotated. The empirical quantitative results (in Table 1 Glyph-R, and Table 2 OSM-R) further support this claim.

Reviewer comment (Theory):
Why is CGAE robust to polygon rotations and reflections given that the proposed contrastive loss mainly focuses on local perturbation?

Author response:
We attribute the CGAE’s robustness to geometric transformations (i.e., rotations and reflections) to two aspects: 1. The Message-passing layers. Empirical results in the ablation study (Table 1, Glyph-R and Table 2, OSM-R) support that argument. GIN and EdgeConv (message-passing backbones) improves model performance on both datasets; and 2. Graph reconstruction based on both node-wise and edge-wise features (Eq. 5-7). In particular, compared to baseline GAE, the proposed CGAE reconstructs graph features from the perturbed node-wise and edge-wise features given by graph augmentations, forcing the graph autoencoder to reconstruct proper graph embedding from the perturbed latent embedding. This is supported by the quantitative results of ($L_N$ + $L_E$) in ablation study (Table 1-2) .

Reviewer comment (Writing):
Can you clarify this sentence:  

` CGAE generalizes effectively the geometric information learned from simple polygons to complex shapes, demonstrating a desirable model property, i.e., decoupling of shape detail (i.e., polygon vertex count) from classification accuracy.`  

I'm a bit confused about what classification means here.

Author response:
We rephrase the sentence into “CGAE generalizes effectively the geometric information learned from simple polygons to complex shapes, demonstrating a desirable model property, i.e., decoupling of shape detail (i.e., polygon trivial vertex count.”) from shape retrieval accuracy.

Reviewer comment (Theory):
What in the method is specific to polygons? Would the approach work for arbitrary graphs? Could it be improved by considering that the graphs are specifically non-intersecting polygon boundary loops?

Author response:
**Response sWPL-1** In our submission we focus on the retrieval of *simple* (as in, without self loops , intersections, and tangents) polygons *embedded* in 2D space, with linear segment edges. This provides a strong inferential bias to the retrieval method. The generalisation to arbitrary graphs ( e.g., social networks, etc) that only capture topology, but not geometry is not assured, and not the focus here. In such arbitrary graphs the planarity is not guaranteed. Here, the spatial embedding of the vertices is as important as the ring topology of the vertex connectivity. Hence we assume that any graphs where this method contributes should include, broadly speaking, geometry (shapes) as well as topology (the location of the vertices provides an inferential bias).

Reviewer comment (Theory):
In the domain of building footprints, is there a need to consider the precise topology of the input polygons? For example, if a straight boundary segment is subdivided into smaller segments by inserting vertices, the geometric shape remains the same, but the descriptor will presumably change. Is this behavior desired? While the authors introduce augmentation to be robust to geometric and topological noise, this specific type of variation appears to be beyond its scope.

Author response:
**Response sWPL-3** We design our system to mimic the perspective of human perception of shapes. This is what is here captured by “trivial vertex count independence” (i.e., colinear vertices taht do not add “information). See response **SxCs-2** and **sEzw-4**.

Reviewer comment (Experiments):
Why not simply encode raster footprints instead of non-regular vector representations? Given that building footprints are relatively simple, the advantages of vector representations for handling complex geometry may not provide meaningful benefits in this context.

Author response:
**Response sWPL-4** Rasterization, conceptually equivalent to aggregation of trivial vertices into buckets, does help in some cases (and is the traditional approach to handling vector shape data in ML thus far, with the exceptions noted in the literature review). Then the results will be critically dependent on augmentation, much more than here. Aggregation is also significantly dependent on the granularity of the raster imposed (and leads to artifacts, known in the geographical literature as the modifiable areal unit problem).