Surface Reconstruction via L1-Minimization

Authors:
Veselin Dobrev;Jean-Luc Guermond;Bojan Popov
Affiliations:
Department of Mathematics, Texas A&M University, College Station, USA TX-77843;Department of Mathematics, Texas A&M University, College Station, USA TX-77843;Department of Mathematics, Texas A&M University, College Station, USA TX-77843
Venue:
Numerical Analysis and Its Applications
Year:
2009

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Abstract

A surface reconstruction technique based on the L 1- minimization of the variation of the gradient is introduced. This leads to a non-smooth convex programming problem. Well-posedness and convergence of the method is established and an interior point based algorithm is introduced. The L 1-surface reconstruction algorithm is illustrated on various test cases including natural and urban terrain data.