IEEE Transactions on Pattern Analysis and Machine Intelligence
Analysis of PSLQ, an integer relation finding algorithm
Mathematics of Computation
IEEE Transactions on Pattern Analysis and Machine Intelligence
PIMs and Invariant Parts for Shape Recognition
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Rotations, translations and symmetry detection for complexified curves
Computer Aided Geometric Design
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Automatic deduction in (dynamic) geometry: Loci computation
Computational Geometry: Theory and Applications
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We propose an algorithm for automated recognition of computationally constructed curves and discuss several aspects of the recognition problem. Recognizing loci means determining a single implicit polynomial equation and geometric invariants, characterizing an algebraic curve which is given by a discrete set of sample points. Starting with these discrete samples, arising for example from a geometric ruler and compass construction, an eigenvalue analysis of a matrix derived from the data leads to proposed curve parameters. Utilizing the construction itself, with its free and dependent geometric elements, further specifications of the type of constructed curves under genericity assumptions are made. This is done by a second eigenvalue analysis of parameters of several generically generated curves.