We introduce a novel approach for the polygonization of Multi-view Stereo (MVS) meshes of buildings, which results in compact and topologically valid models. The main characteristic of our method is structure awareness, i.e., the recovery and preservation of the initial mesh primitives and their adjacencies. Our proposed methodology consists of three main stages: (a) primitive detection via mesh segmentation, (b) encoding of primitive adjacencies into a graph, and (c) polygonization. Polygonization is based on the approximation of the original mesh with a candidate set of planar polygonal faces. On this candidate set, we apply a binary labelling formulation to select and assemble an optimal set of faces under hard constraints that ensure that the final model is both manifold and watertight. Experiments on various building models demonstrate that our simplification method can produce simpler representations for both closed and open building meshes. Furthermore, these representations highly conform to the initial structure and are ready to be used for spatial analysis. The source code of this work is freely available at https://github.com/VasileiosBouzas/MeshPolygonization.

We give a detailed proof of Siu’s theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in $\mathbb{C}^{n}, n \geq3$ , is not subelliptic.

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The purpose of this paper is to classify the Möbius homogeneous hypersurfaces with two distinct principal curvatures in$S$^{$n$+1}under the Möbius transformation group. Additionally, we give a classification of the Möbius homogeneous hypersurfaces in$S$^{4}.

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