Architectural Symmetry Detection from 3D Urban Point Clouds: A Derivative-Free Optimization (DFO) Approach

Abstract

Symmetry is a fundamental phenomenon in not only nature and science but also cities and architectures. Architectural symmetry detection (ASD) from 3D urban point clouds is an essential step in understanding the architectures as well as creating a semantic city/building information model (CIM/BIM) to enable various applications for a smart and resilient future. However, manual segmentation and recognition of 3D urban point clouds are too time-consuming, tedious, and costly, and automatic ASD is very challenging. This paper presents a derivative-free optimization (DFO) approach for automatic ASD from 3D urban point clouds. In this paper, we formulate the problem of ASD as a nonlinear optimization problem by extending the mathematical definition of geometric symmetry with architectural styles. We develop a ‘divide-and-detect’ process to detect the symmetry hierarchy based on the formulation and apply the state-of-the-art DFO algorithms. A pilot study was conducted on a case of the rooftop of a neoclassical building. The proposed approach detected the global reflection from 1.4 million points in 23.5 s, and the whole symmetry hierarchy of reflections in about ten minutes. The detected symmetry hierarchy was applied to a regularity-based rooftop modeling method. The contribution of this paper is twofold. First, this paper exposes the problem of ASD to many mathematical methods through an innovative problem formulation. Secondly, the proposed DFO approach is accurate, efficient, and capable of processing large-scale 3D urban point clouds for semantic CIMs/BIMs.