  Graphic sketch representations are effective for representing sketches.
Existing methods take the patches cropped from sketches as the graph nodes, and
construct the edges based on sketch's drawing order or Euclidean distances on
the canvas. However, the drawing order of a sketch may not be unique, while the
patches from semantically related parts of a sketch may be far away from each
other on the canvas. In this paper, we propose an order-invariant,
semantics-aware method for graphic sketch representations. The cropped sketch
patches are linked according to their global semantics or local geometric
shapes, namely the synonymous proximity, by computing the cosine similarity
between the captured patch embeddings. Such constructed edges are learnable to
adapt to the variation of sketch drawings, which enable the message passing
among synonymous patches. Aggregating the messages from synonymous patches by
graph convolutional networks plays a role of denoising, which is beneficial to
produce robust patch embeddings and accurate sketch representations.
Furthermore, we enforce a clustering constraint over the embeddings jointly
with the network learning. The synonymous patches are self-organized as compact
clusters, and their embeddings are guided to move towards their assigned
cluster centroids. It raises the accuracy of the computed synonymous proximity.
Experimental results show that our method significantly improves the
performance on both controllable sketch synthesis and sketch healing.
