Layered analysis of irregular facades via symmetry maximization

Abstract

Figure 1: Symmetry-driven structural analysis of an irregular facade (a) results in a hierarchical decomposition (b) into regular grids. Our analysis introduces layering (b), going beyond flat segmentation via splits (c) and allowing more compact and natural structural representations. The resulting hierarchical model of facades enables applications such as structural editing (d) and retargeting (e). AbstractWe present an algorithm for hierarchical and layered analysis of irregular facades, seeking a high-level understanding of facade structures. By introducing layering into the analysis, we no longer view a facade as a flat structure, but allow it to be structurally separated into depth layers, enabling more compact and natural interpretations of building facades. Computationally, we perform a symmetry-driven search for an optimal hierarchical decomposition defined by split and layering operations applied to an input facade. The objective is symmetry maximization, i.e., to maximize the sum of symmetry of the substructures resulting from recursive decomposition. To this end, we propose a novel integral symmetry measure, which behaves well at both ends of the symmetry spectrum by accounting for all partial symmetries in a discrete structure. Our analysis results in a structural representation, which can be utilized for structural editing and exploration of building facades. Links:DL PDF WEB VIDEO DATA CODE

Symmetrization of facade layouts

“…In specific cases, the grammars can be extracted from a facade image [13] . Structural analysis is another type of the facade layout modeling [2,5,14] . These approaches concentrate on the high-level semantic information.…”

“…These approaches concentrate on the high-level semantic information. The split operation [15] and layering operation [5] are chosen to generate the hierarchical segmentation of the existing facade layout. During this procedure, some consensuses of the facade, such as the symmetry and regularity, are used to formulate the constraints to guide the segmentation and synthesis [2] .…”

“…1 shows two such examples). In computer graphics, symmetry has become a key ingredient for facade modeling [2][3][4] , high level structural analysis [5] , and manipulation [6] . However, when digitizing existing symmetric facades (e.g., extraction of facade layouts), errors are unavoidably introduced during the digitization process.…”

Coupled segmentation and similarity detection for architectural models

“…Pauly et al [2008] conduct a pattern analysis on some architectural models. Lin et al[2013] focus on segmenting residential buildings in LIDAR urban data, Demir et al [2014] segment city meshes based on feature clustering for procedural modeling, and Zhang et al [2013] segment facades using symmetry maximization. Our approach can be used as a pre-segmentation step to generate appropriate inputs for some of such systems and for editing systems [Wu et al 2013;Nan et al 2010].…”

An evolutionary approach to the extraction of object construction trees from 3D point clouds

“…Weiss used genetic programming for the structural optimization of CAD specification trees in [59]. Analysis of facade is carried out in [63] by finding a hierarchical decomposition that maximizes some measure of symmetry. A genetic algorithm is used as an heuristic for finding the decomposition optimizing this measure.…”