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}.

Traditional point cloud registration methods require large overlap between scans, which imposes strict constraints on data acquisition. To facilitate registration, users have to carefully position scanners to ensure sufficient overlap. In this work, we propose to use high-level structural information (i.e., plane/line features and their inter-relationship) for registration, which is capable of registering point clouds with small overlap, allowing more freedom in data acquisition. We design a novel plane/linebased descriptor dedicated to establishing structure level correspondences between point clouds. Based on this descriptor, we propose a simple but effective registration algorithm. We also provide a dataset of real-world scenes containing a larger number of scans with a wide range of overlap. Experiments and comparisons with state-of-the-art methods on various datasets reveal that our method is superior to existing techniques. Though the proposed algorithm outperforms state-of-the-art methods on the most challenging dataset, the point cloud registration problem is still far from being solved, leaving significant room for improvement and future work.