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Journal Articles Computer Graphics Forum Year : 2022

Simplification of 2D Polygonal Partitions via Point‐line Projective Duality, and Application to Urban Reconstruction

Abstract

We 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.
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Dates and versions

hal-03661872 , version 1 (08-05-2022)

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Julien Vuillamy, André Lieutier, Florent Lafarge, Pierre Alliez. Simplification of 2D Polygonal Partitions via Point‐line Projective Duality, and Application to Urban Reconstruction. Computer Graphics Forum, 2022, ⟨10.1111/cgf.14511⟩. ⟨hal-03661872⟩
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