Browsing by Author "Lieutier, A."
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Item Simplification of 2D Polygonal Partitions via Point‐line Projective Duality, and Application to Urban Reconstruction(© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2022) Vuillamy, J.; Lieutier, A.; Lafarge, F.; Alliez, P.; Hauser, Helwig and Alliez, PierreWe address the problem of simplifying two‐dimensional polygonal partitions that exhibit strong regularities. Such partitions are relevant for reconstructing urban scenes in a concise way. Preserving long linear structures spanning several partition cells motivates a point‐line projective duality approach in which points represent line intersections, and lines possibly carry multiple points. We propose a simplification algorithm that seeks a balance between the fidelity to the input partition, the enforcement of canonical relationships between lines (orthogonality or parallelism) and a low complexity output. Our methodology alternates continuous optimization by Riemannian gradient descent with combinatorial reduction, resulting in a progressive simplification scheme. Our experiments show that preserving canonical relationships helps gracefully degrade partitions of urban scenes, and yields more concise and regularity‐preserving meshes than common mesh‐based simplification approaches.