Polygon Matching and Indexing Under Affine Transformations
Edgar Ch\'avez, Ana C. Ch\'avez-C\'aliz, Jorge L., L\'opez-L\'opez

TL;DR
This paper presents efficient algorithms for polygon matching and indexing under affine and similarity transformations, enabling rapid retrieval of matching polygons in large collections even with unknown transformations.
Contribution
It introduces algorithms that perform polygon matching under affine transformations in time independent of collection size, including special cases like triangles and noisy conditions.
Findings
Matching polygons under affine transformations can be done in logarithmic time for known transformations.
Algorithms can find all matching polygons with unknown affine transformations in linear time.
Special bounds are provided for triangle matching in noisy conditions.
Abstract
Given a collection of -sided polygons in the plane and a query polygon we give algorithms to find all such that with an unknown similarity transformation in time independent of the size of the collection. If is a known affine transformation, we show how to find all such that in time. For a pair of polygons we can find all the pairs such that and for an unknown affine transformation in time. For the case of triangles we also give bounds for the problem of matching triangles with variable vertices, which is equivalent to affine matching triangles in noisy conditions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Algorithms and Data Compression · Data Management and Algorithms
