Reconstruction of consistent shape from inconsistent data: Optimization of $$2{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}$$ D sketches

Abstract

Although the 3D orientations of edges and surfaces are theoretically sufficient for reconstructing the 3D object shape, this does not mean that the 3D object shape can actually be reconstructed. Specifying the edge and surface orientations is often overspecification, and inconsistency may result if image data contain errors. We propose a scheme of optimization to construct a consistent polyhedron shape from inconsistent data. Our optimization is achieved by solving a set of linear equations; no searchers and iterations are necessary. This technique is first applied to the problem of shape-from-motion and then to the 3D recovery based on the rectangularity hypothesis and the parallelism hypothesis. We also present a strategy of heuristic reasoning on rectangularity and parallelism.