A derivative-free optimization-based approach for detecting architectural symmetries from 3D point clouds

Abstract Symmetry is ubiquitous in architecture, across both time and place. Automated architectural symmetry detection (ASD) from a data source is not only an intriguing inquiry in its own right, but also a step towards creation of semantically rich building and city information models with applications in architectural design, construction management, heritage conservation, and smart city development. While recent advances in sensing technologies provide inexpensive yet high-quality architectural 3D point clouds, existing methods of ASD from these data sources suffer several weaknesses including noise sensitivity, inaccuracy, and high computational loads. This paper aims to develop a novel derivative-free optimization (DFO)-based approach for effective ASD. It does so by firstly transforming ASD into a nonlinear optimization problem involving architectural regularity and topology. An in-house ODAS (Optimization-based Detection of Architectural Symmetries) approach is then developed to solve the formulated problem using a set of state-of-the-art DFO algorithms. Efficiency, accuracy, and robustness of ODAS are gauged from the experimental results on nine sets of real-life architectural 3D point clouds, with the computational time for ASD from 1.4 million points only 3.7 s and increasing in a sheer logarithmic order against the number of points. The contributions of this paper are threefold. Firstly, formulating ASD as a nonlinear optimization problem constitutes a methodological innovation. Secondly, the provision of up-to-date, open source DFO algorithms allows benchmarking in the future development of free, fast, accurate, and robust approaches for ASD. Thirdly, the ODAS approach can be directly used to develop building and city information models for various value-added applications.

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