Alogtime Algorithms for Tree Isomorphism, Comparison, and Canonization
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
NFP-based nesting algorithm for irregular shapes
Proceedings of the 2006 ACM symposium on Applied computing
Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity
Graphs and Combinatorics
Multiple polyline to polygon matching
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Jigsaw puzzles with pieces of unknown orientation
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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In this paper, we present a simple definition for, and a method to find, cavities and protrusions of a 2D polygon. Using these, we fit conformal polygons with each other, which is similar to a jigsaw puzzle and in a general case is NP-hard to solve. We first build a hierarchy of cavities and protrusions for each polygon and use this hierarchy to check for matches between these geometric features of two polygons. This data structure allows for early rejection of mismatches and thus speeds up the fitting process. We show using many examples, that most of the common configurations in exact polygon fitting can be handled by this algorithm in polynomial time. In case of exact, yet non-unique matches, this algorithm will solve the problem in exponential time.