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Conjoining Gestalt Rules for Abstraction of Architectural Drawings

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Conjoining Gestalt Rules for Abstraction of Architectural Drawings Conjoining Gestalt Rules for Abstraction of Architectural Drawings Liangliang Nan 1 Andrei Sharf Ke Xie1 Tien-Tsin Wong3 Oliver Deus sen" Daniel Cohen-Or5 Baoquan Chen1 1 SlAT 2 Ben Gurion Univ. 3 CUHK 4 Konstanz Univ. 5 Tel Aviv Univ. Figure 1: Simplification a/a cOlllplex cityscape line-drawing obtained [(sing o/./ /" Gestalt-based abstraction. Abstract those of architectural models. Our approach to abstracting shape directly aims to clarify shape and preserve meaningful structures We present a method for structural summari zation and abstraction using Gestalt principles. of complex spatial arrangements found in architectural draw in gs. Thc wdl-knllwn Gcstalt principles hy Wcrthciml:r rI 92:1 ], rdkct The method is based on the well -known Gestalt rules, which sum­ strategies of the human vi sual system to group objects into forms mari ze how form s, pattern s, and semantics are perceived by humans and create internal representations for them. Wheneve r groups of I"rOI11 hits and pi ccl:s 0 1" gl:o l11 l: tri c inl"ormati on. Although defining visual element have one or several characteristics in common, they a computational model for each rul e alone has been extensively s­ get grouped and form a new larger vi sual object - a gestalt. Psychol­ tudied, modeling a conjoint of Gestalt rules remains a challenge. ogists have tried to simulate and model these principles, by find in g In thi s work, we develop a computational framework which mod­ computational means to predict wh at human perceive as gestalts in els Gestalt rules and more importantly, their complex interaction­ images. s. We apply conjoining ru.les to line drawings, to detect groups of objects and repetitions that conform to Gestalt principles. We sum­ The notion of Gestalt is very well -k nown and widely used in var­ mari ze and abstract such groups in ways that maintain structural ious fi elds. In particular, it ex pl ains the tendency of the human semantics by displaying only a reduced number of repeated ele­ vi sual recognition to form whole shapes and forms just from bits ments, or by replacing them with si mpler shapes. We show an ap­ and pieces of geometric information. Naturall y, Gestalt principles plication of our method to line drawings of architectural models of have been used in computer vision, primarily in context with object various styl es, and the potenti al of extending the technique to other recognition and scene understanding. In computer graphics, Gestalt computer-generated illustrations, and three-dimensional models. principles have been applied to a variety of applications, like scene completion [Orori et a!. 2003], image and scene abstraction [Wang et a!. 2004; Mehra et a!. 2009], stroke synthesis [Barla el a!. 2006; Ijiri et a!. 2008] and emerging images generation [Mitra et a!. 2009]. Tn general, these works rely on discrete Gestalt principles, but none addresses the complex interactions emerging from the multitude of Gestalt principles operating simultaneously. A diffi cult problem while dealin g wit.h gestalts is th e conj oin ed ef­ fect of two or more Gestalt principles operating at the same time 1 Introduction on the same site. Modeling gestalts in such cases is especiall y challenging due to the complexity and ambiguity of the scene. Re­ Artistic im agery, architectural renderings, cartography and games cently, attempts to di scover how grouping principles interact were often ex pl oit abstracti on to clari fy, exaggerate, simplify or empha­ made in psychology and computer vision [Oesolneux et a!. 2002; size the visual content. Abstraction is a strategy for communicating Feldman 2003; Cao et a!. 2007; Kubovy and van den Berg 2008]. in fo rmat ion effectively. It all ows artists to hi ghli ght specifi c visu­ These works model limited gestalt interactions, by finding com­ al inform ation and thereby direct the viewer to important aspects putationalmeans which are physiologically pl ausible. Kubovyand of the structure and organization of the scene. In thi s paper, we van den Berg [2008] explore the quantification of perceptual group­ present. an approach to the abstracti on of 20 shapes, in particul ar ings formed conjointly by two grouping principles: similarity and prox imity. Nevertheless, providing general computational means for modeling the interaction of multiple Gestalt principles remains a diffi cult chall enge. In thi s paper, we take a first step in developing a computati onal model fo r conjoining Gestalt rul es. We model a subset of Gestalt rules and their mutual interaction for abstracting architectural line drawings. We choose to focus on architectural drawings since typ­ ically their visual elements are of rather low complexity and their spatial arrangement is strongly biased to the main axes (due to en­ gineering considerati ons). Hence, architectural drawings consist of prevalent similarities, proximities and regul arities among their el- 2 • • • • • • • • • • 0 0 • • • • • 0 0 0 0 0 0 0 0 0 0 • • • • • 0 0 • • • • • (a) (b) (c) Figure 2: Conjoining gestalts (frOIl! KClIlizsa [1 980]). Overlapping (a): white dots are elemellts oj the grid (regularity) and sim ultaneously belong to a curve (continuity). Conflicting (b): colltinllit)' principle OJ IlliO closed curves (b-Ieft) cO Ilf/iets wilh the symlllell y princip le (b-righl). Masking (c): the basis oj the triangle becomes invisible as it is embedded ill a grollp oj regularly paraliellines. ements, forming complex grouping conligurati ons that can be de­ ies focused main ly on qualitative and empirical studies, more recent scribed by Gestalt principles and their interaction. These rules de­ psychological works study quantitative aspects of Gesta lt principles fin e vari ous perceptual scene groupings, naturall y lending them­ and their conjoining. Desolneux et al. [2002] and Cao et al. [2007] selves to simplilicati on and ahstraction of architectural drawings. formulate probabilistic quantities for di stinctive Gesta lt rules and utilize them for detecting collinearity, regul arity and p roximity in Interacting gestalts rules cast a difli cult problem sin ce they oper­ images. In hi s work, Feldman [2003] suggests a hi era rchical rep­ ate simultaneously on common sites. They can compete, confl ict, resentati on for modeling proximity and collinearity grouping prin­ overlap, and mask with each other yielding complex vi sual phe­ ciples. He applies a minimal model theory for selecting the best nomena. Up to now, psychologists are stili studying how exactl y grouping interpretation, pre ferring a maximally explained group. multiple Gestalt principles interact. It is not in our scope to study Kubovy and van den Berg [2008] present a probabilistic model for the human visual system under these complex phenomena. Our measuring proximity and similarity grouping quantities. Similar to goal is to quantitatively model and apply conjoining rules with re­ us, they analyze and model the conjoint effect o f grouping princi­ spect to a specific type of data. Specifically, we propose a co m­ ples operati ng simultaneously. Nevertheless, their work focuses on putational f ramcwork to fa cilitate the integrati on of fi ve principal interacti on of only two principles performing on simple dot lattice Gestalt rul es, namely similarity, proximity, contintlity, closure, and confi gurations, while our goal is to provide a generic fra mework fo r regularity, and then apply it to the abstracti on of architectural line resolving conjoining gestalts in the context of architectural abstrac­ drawings. Due to the grouping nature of Gestalt rules, we fo rmulate tion. Claessens and Wagemans [2008] present a B ayesian model abstraction as a grouping optimizati on problem. The additive nature for contour detecti on using proximity and collinearity grouping. In of Gestalt principles interactions (i.e., gestalts combine additively contrast to ours, their method handles simplified inte racti ons be­ as showed in [Elder and Goldberg 2002; Feldman 2003; Kubovy tween two gestalts that perform as independent variables on dot and van den Berg 2008)) is modeled by a multi-label normali zed lattices. In recent work by Cole et al. [2008; 2009], the authors graph cut formulation. study the correlation between shape conveying hand d rawn lines and speei fi e 3D shape reatures. Their work quanti fi cs the strength We apply conjoining Gestalt grouping rules, inspired by the com­ of different line drawings at depi cting shape. putati onal model of Kubovy and van den Berg [2008]. We devel­ op a global energy function that relates grouping strength , number Abstraction and S implification of 20 Content. Gestalt effect is of di sjoint groups and inter-part characteri sti cs to Gestalt princi­ hi ghl y re lated to abstracti on and simplifi cati on. By understanding ples. The minimal energy de fin es a global segmentati on into di s­ how a collecti on of detail s aggregates, we can replace this collec­ joint groups while accounting for metrics that measure grouping in tion with a simpler, coarser or abstract representati on, while pre­ terms of Gestalt rules. The set of e lements grouped is then abstract­ serving the o riginal semantics. In computer graphics and vi sion, ed by means of repl acin g them with simplilied or abstract represen­ Gestalt prin ciples have been studi ed in the contex t of simpli fica ti on tatives. Our method computes a progressive series of abstracti ons and abstraction in several works. We focus here on works which from the fi nest, most detailed drawin g, up to the coarsest most ab­ address simpli fication usin g perceptual principles. stracted one (see Fi gure I). Our framework naturall y lends itselr to effi cient abstracti on of ar­ In an earl y work, DeCarl o and Santell a [2002] compute image ab­ chitectural line drawings confo rming to perceptual grouping con­ stracti on by preserving meaningful structures using an eye tracker cepts.
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