Project Details
Funding Scheme : General Research Fund
Project Number : 17200218
Project Title(English) : A derivative-free optimization (DFO) approach to architectural symmetry detection from 3D point clouds  
Project Title(Chinese) : 三維點雲中建築對稱性識別的一類無導數優化(DFO)方法 
Principal Investigator(English) : Dr Xue, Fan 
Principal Investigator(Chinese) :  
Department : Department of Real Estate and Construction
Institution : The University of Hong Kong
Co - Investigator(s) :
Mr Chiaradia, Alain Joseph Franck
Prof Lu, Wilson
Panel : Engineering
Subject Area : Civil Engineering, Surveying, Building & Construction
Exercise Year : 2018 / 19
Fund Approved : 522,846
Project Status : On-going
Completion Date : 18-7-2021
Abstract as per original application
Symmetry is fundamental in nature, science, engineering, and art. Perception and recognition of symmetries influence not only our understanding of the world but also our design processes. Symmetry is also ubiquitous and continuous in architecture, appearing in all places over the world and at all times throughout history, for example, the Great Wall of China, the Parthenon of Greece, the Taj Mahal of India, ‘The Gherkin’ in London, and the Sydney Opera House in Australia. The ubiquity of symmetry in architecture is far from accidental, rather it is the result of considerations relating to function, economics, mechanics, manufacturing, and aesthetics. Recent advances in sensing technology, such as laser scanning and photogrammetry, provide increasingly available 3D point clouds of architectures and cities. Detection of architectural symmetries from 3D point clouds is not only an intriguing inquiry in its own right, but also an effective and essential step in creating accurate and informative digital building/city models for various applications such as architectural design, computer vision, construction management, heritage conservation, and smart and resilient city development. However, as it is too time-consuming, tedious, and costly to manually recognize and segment architectural symmetries from 3D point clouds, the challenge is to devise an automated detection of architectural symmetries. To meet this challenge, the proposed research project aims to apply modern derivative-free optimization (DFO) algorithms, which have been successfully used to solve many science and engineering problems, to automated architectural symmetry detection from 3D point clouds. Extending the mathematical definition of symmetry, this research proposes a general formulation of detecting symmetry in architecture. The major innovation here is an elegant means of detecting all types of architectural symmetries, including reflection, translation, rotation, uniform scaling, or combinations thereof, as a unified nonlinear optimization problem which is solvable by modern DFO methods. Our recent pilot study, involving a dense cloud of over one million points from a neoclassical building, has confirmed the technological feasibility of this proposed DFO approach. The project offers both academic insights and practical benefits. The findings will extend knowledge of how modern mathematical methods can be used to discover symmetry in architecture or related areas. The outcomes may lead to a breakthrough in theoretical explanation of the challenges in architectural symmetry detection. Practically, the research will offer a useful methodological tool for the creation of accurate and informative building/city models from inexpensive point clouds for industries related to architecture, construction, engineering, automobiles, and robotics.
對稱性普遍存在於世界各地各時期的建築中,例如長城、帕特農神廟、泰姬陵、倫敦“小黃瓜”及悉尼歌劇院。無處不在的對稱性并非意外使然,而是綜合功能性、經濟性、結構、可生產性及美觀性的全面考量的結果。目前,測量建築物及城市的三維點雲已變得日益準確、全面及廉價。三維點雲中的對稱性識別不僅是一種知識獲取,更是創建智慧城市所必須的建築和城市信息模型的必要步驟。然而,人工識別費時費力且成本高昂;因此,需要研究自動化對稱性識別技術。 本項目將運用最新的無導數優化(DFO)算法,自動化三維點雲中的建築對稱性識別過程。在本項目中,不論是鏡像、平移、旋轉、等比縮放或是它們的各種組合,都會被統一地形式化為一類非綫性優化問題。進而采用無導數優化算法來求解此類問題。本項目兼具學術及實踐意義。預期結果料將拓展運用當代數學方法發現建築及相關領域的對稱性的研究,亦可識別建築對稱性識別的理論難點。在實踐影響力方面,本研究將為建築和城市信息模型提供一套有效的方法論工具。
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