Does the conv in MeshVAE suffer from order problem?

[fishfishson]

Given 2 adjacent faces and denote the intersect edge as e. The adjacent edges of e will be {a, b, c, d}. The conv operation on adjacent edges can be w1*(a+c) + w2*(b+d) or w1*(b+d) + w2*(a+c). And the fully connected layer applied on edge features will also suffer the order problem (e.g. the max-pooling in PointNet). Do I understand your paper wrongly? If not, how do you deal with this problem?

[FreddieRao]

Given 2 adjacent faces and denote the intersect edge as e. The adjacent edges of e will be {a, b, c, d}. The conv operation on adjacent edges can be w1*(a+c) + w2*(b+d) or w1*(b+d) + w2*(a+c). And the fully connected layer applied on edge features will also suffer the order problem (e.g. the max-pooling in PointNet). Do I understand your paper wrongly? If not, how do you deal with this problem?

Thanks for your question! This is a good question. Firstly, as mentioned in the paper, all 3D mesh parts are registered from a unit cube, which means all mesh parts have the same connectivity. The order of edges of the input feature is fixed! Therefore, each row of feature map has a corresponding edge. Before entering in the FC layer, the feature map has a fixed order of edge, so the fc operation won't cause permutation issue. Secondly, as mentioned in our paper, in the convolution operation, the edges are ordered counter-clockwise. So, the conv operation on adjacent edges can only be w1*(a+c) + w2*(b+d). :) Feel free to ask more!