Learning Constrained Structured Spaces with Application to Multi-Graph Matching
Multi-graph matching is a prominent structured prediction task, in which the predicted label is constrained to the space of cycle-consistent matchings. While direct loss minimization is an effective method for learning predictors over structured label spaces, it cannot be applied efficiently to the problem at hand, since executing a specialized solver across sets of matching predictions is computationally prohibitive. Moreover, there’s no supervision on the ground-truth matchings over cycle-consistent prediction sets. Our key insight is to strictly enforce the matching constraints in pairwise matching predictions and softly enforce the cycle-consistency constraints by casting them as weighted loss terms, such that the severity of inconsistency with global predictions is tuned by a penalty parameter. Inspired by the classic penalty method, we prove that our method theoretically recovers the optimal multi-graph matching constrained solution. Our method's advantages are brought to light in experimental results on the popular keypoint matching task on the Pascal VOC and the Willow ObjectClass datasets.
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Task | Dataset | Model | Metric Name | Metric Value | Global Rank | Benchmark |
---|---|---|---|---|---|---|
Graph Matching | PASCAL VOC | Direct-2HGM | F1 score | 0.601 | # 8 | |
Graph Matching | PASCAL VOC | Direct-MGM | F1 score | 0.575 | # 11 | |
Graph Matching | PASCAL VOC | Direct-2GM | F1 score | 0.597 | # 10 | |
Graph Matching | Willow Object Class | Direct-MGM | matching accuracy | 0.987 | # 4 | |
Graph Matching | Willow Object Class | Direct-2HGM | matching accuracy | 0.981 | # 6 |