Higher-Order Ratio Cycles for Fast and Globally Optimal Shape Matching

2D-3D shape matching on wolf (2D outline is shown in the bottom left) with various methods Guitar outline and road network to create GPS art Figure 1. Left: We show results on 2D-3D shape matching computed with Lähner et al. [41], Roetzer et al. [61] and our approach. Competing methods either have fast computation times, or high-quality matchings, but not both at the same time. Instead, our method combines both desirable properties and even further improves accuracy as we effectively avoid bias towards shorter matchings (see zoomedin parts). Right: Our algorithm can be used to find object-shaped tracks in road networks, known as GPS-art, such as the shape of a guitar in the road network of Nashville (represented as a graph, compute time 1s).