Structure-aware Building Mesh Simplification

Abstract

In recent years, there is an ever-increasing demand — both by industry and academia — for 3D spatial information and especially, for 3D building models. One of the ways to acquire such models derives from the combination of massive point clouds with reconstruction techniques, such as Ball Pivoting and Poisson Reconstruction. The result of these techniques is the representation of individual buildings or entire urban scenes in the form of surface meshes — data structures consisting of vertices, edges and faces. Despite their usefulness for visualization purposes, the high complexity of these meshes, along with various geometric and topological flaws, stands as an obstacle to their usage in further applications, such as simulations and urban planning. To address the issue of complexity, the production of lightweight building meshes can be achieved through mesh simplification, which reduces the amount of faces used in the original representations. Moreover, simplification methods focus on conforming the resulting mesh to the original one, in order to minimize the differences between the two of them. As a consequence, simple and accurate building models are possible to be acquired, whose geometric and topological validity is yet questionable. In this thesis, we introduce a novel approach for the simplification of building models, which results into a more compact representation, free of topological defects. The main characteristic of our method is structure awareness — namely, the recovery and preservation, for the input mesh, of both its primitives and the interrelationships between them (their configuration in 3D space). This awareness asserts that the resulting mesh closely follows the original and at the same time, dictates the geometric operations needed for its construction in the first place — thus providing accuracy, along with computational efficiency. Our proposed methodology is divided into three main stages: (a) primitive detection via mesh segmentation, (b) storage of primitive interrelationships in a structure graph and (c) simplification. In particular, simplification is accomplished here by approximating the primitive borders with a building scaffold, out of which a set of candidate faces is defined. The selection of faces from the candidate set to form the simplified mesh is achieved through the formulation of a linear binary programming problem, along with certain hard constraints to ensure that this mesh is both manifold and watertight. Experimentation reveals that our simplification method is able to produce simpler representations for both closed and open building meshes, which highly conform to the initial structure and are ready to be used for spatial analysis. Additionally, a fairly good approximation of a given mesh is possible to be obtained within reasonable execution times, regardless of the initial noise level or topological invalidity. Finally, a comparative analysis shows that the accuracy of our method stands in parallel with that of other available simplification techniques.