  Recently, deep learning based methods have demonstrated promising results on
the graph matching problem, by relying on the descriptive capability of deep
features extracted on graph nodes. However, one main limitation with existing
deep graph matching (DGM) methods lies in their ignorance of explicit
constraint of graph structures, which may lead the model to be trapped into
local minimum in training. In this paper, we propose to explicitly formulate
pairwise graph structures as a \textbf{quadratic constraint} incorporated into
the DGM framework. The quadratic constraint minimizes the pairwise structural
discrepancy between graphs, which can reduce the ambiguities brought by only
using the extracted CNN features.
  Moreover, we present a differentiable implementation to the quadratic
constrained-optimization such that it is compatible with the unconstrained deep
learning optimizer. To give more precise and proper supervision, a
well-designed false matching loss against class imbalance is proposed, which
can better penalize the false negatives and false positives with less
overfitting. Exhaustive experiments demonstrate that our method competitive
performance on real-world datasets.
