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ifp University of Stuttgart Institute for Photogrammetry Combined Grammar for the Modeling of Building Interiors INDOOR3D – Cape Town Susanne Becker, Michael Peter, Dieter Fritsch - (ifp) Damian Philipp, Patrick Baier, Christoph Dibak - (IPVS) Com’N’Sense

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University of Stuttgart ifp 3D Indoor Models 2 © © © © © © cjwalsh.ie © © © www. cg.cis.upenn.edu

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University of Stuttgart ifp 3D Indoor Models 3 © BIM world 3D GIS world high geometric and semantic detail modeled manually © isa2009/keynote.html © © Budroni & Böhm, 2009 mostly pure geometry models with limited geometric detail focus on automatic derivation from observation data

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University of Stuttgart ifp 3D Indoor Models 4 3D GIS world © isa2009/keynote.html © BIM world high geometric and semantic detail modeled manually © © Budroni & Böhm, 2009 mostly pure geometry models with limited geometric detail focus on automatic derivation from observation data Problems when erroneous or incomplete sensor data Powerful means: formal grammars Goal: fully automatic approach for grammar-supported indoor modeling based on observation data from low-cost sensors

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University of Stuttgart ifp Formal Grammar 5 Powerful means for representing complex geometric structures using a set of formal rules Compact representation of geometries and construction processes Generative component: automated reconstruction of geometries A formal grammar defines a formal language as a set of sequences of symbols symbols alphabet rules syntax Notation: G(V,T,P,F) non-terminals V terminals T production rules P id: lc rc : cond → succ : prob axiom F (non-terminal defining the start point)

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University of Stuttgart ifp Shape Grammar 1972 Stiny & Gips Enriched L-Systems Split Grammar 2003 Wonka et al. Müller, 2001 CGA Shape Grammar 2006 Müller et al. Facade Grammar 2009 Becker Indoor Grammar 2010 Gröger & Plümer Formal Grammars for modeling geometric structures 6 Lindenmayer- Systems Prusinkiewicz & Lindenmayer, 1990

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University of Stuttgart ifp Formal Grammars Lindenmayer-Systems Parallel rewriting systems over strings Rewriting rules produce sequences of symbols Sequences of symbols are interpreted and transferred to explicit geometry Simple initial object is successively overwritten by more complicated structures 7 (Prusinkiewicz & Lindenmayer, 1990) 7 : F - - F - - F p : F F + F - - F + F Example 2: rule application axiom production rule © Example 1:

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University of Stuttgart ifp Formal Grammars Lindenmayer-Systems Application of L-Systems in urban modeling 8 (Müller, 2001) Problems with modeling of buildings: no growth process but iterative partitioning of space geometric conditions (parallelism, rectangularity,...) difficult to integrate long and intricate production rules

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University of Stuttgart ifp Formal Grammars for modeling geometric structures 9 Lindenmayer- Systems Prusinkiewicz & Lindenmayer, 1990 Shape Grammar 1972 Stiny & Gips Enriched L-Systems Split Grammar 2003 Wonka et al. Müller, 2001 CGA Shape Grammar 2006 Müller et al. Facade Grammar 2009 Becker Indoor Grammar 2010 Gröger & Plümer

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University of Stuttgart ifp Formal Grammars Shape Grammar 10 (Stiny und Gips, 1972) Problem: complex rule applications Example: axiom production rule rule application (1)(2)(3) works not on symbols but on shapes: alphabet consists of a set of shapes rules directly work on these shapes

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University of Stuttgart ifp Formal Grammars Split-Grammar 11 (Wonka et al., 2003) Specified for the generation of building structures Production rules are limited to split rules G(T,V,R,I) Shapes are treated as symbolic objects Example: regular, grid-like structures production rules rule applications START FFFF KS W W W W WIN

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University of Stuttgart ifp Formal Grammars CGA Shape Grammar 12 (Müller et al., 2006) Continued development of split grammar Highly detailed building models in a pre-defined architectural style Example: virtual Pompeji Problem: highly complex production rules depending on the level of detail manual definition of rules

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University of Stuttgart ifp Formal Grammars for modeling geometric structures 13 Lindenmayer- Systems Prusinkiewicz & Lindenmayer, 1990 Shape Grammar 1972 Stiny & Gips Enriched L-Systems Split Grammar 2003 Wonka et al. Müller, 2001 CGA Shape Grammar 2006 Müller et al. Facade Grammar 2009 Becker Indoor Grammar 2010 Gröger & Plümer

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University of Stuttgart ifp 14 Cell Decomposition Extraction and modeling of facade geometries from terrestrial LiDAR data Knowledge Inference Detection of repetitive features and structures Inference of rules Knowledge Propagation Top-down prediction for completion Generation of synthetic facades data driven knowledge based Formal Grammars Facade Grammar (Becker, 2009) Facade Grammar

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University of Stuttgart ifp Formal Grammars Indoor Grammar 15 (Gröger & Plümer, 2010) Generation of geometrically and topologically consistent 3D indoor models G(N,T,S,P) split rules are applied on 3D boxes and 2D rectangles topology is explicitly modeled through constraints Example: (a) (b) (c) (d) (e)(f) (g)

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University of Stuttgart ifp Formal Grammars for modeling geometric structures 16 Lindenmayer- Systems Prusinkiewicz & Lindenmayer, 1990 Shape Grammar 1972 Stiny & Gips Enriched L-Systems Split Grammar 2003 Wonka et al. Müller, 2001 CGA Shape Grammar 2006 Müller et al. Facade Grammar 2009 Becker Indoor Grammar 2010 Gröger & Plümer now ifp, IPVS Combined Indoor Grammar

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University of Stuttgart ifp Combined Indoor Grammar Design Decisions Building characteristics Public buildings are traversed by a system of hallways. The system of hallways divides each floor into hallway-spaces and non-hallway-spaces. Non-hallway-spaces can be further divided into smaller room units mostly arranged in a linear sequence parallel to the adjacent hallway. 17 Grammar concept Hallway system (linear structures) L-system Room configurations (spatial partitioning) split-grammar floorplan of ifp

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University of Stuttgart ifp Combined Indoor Grammar L-System for Modeling Hallways 18 G hallways = (V, ω,P) V : set of attributed symbols (modules), ω : axiom (initial hallway segment) P : production rules related to the enriched L-system for modeling streets (Parish & Müller, 2001) Idea: organize the setting of attributes, probabilities and the constraints induced by the geometric environment through external functions

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University of Stuttgart ifp Combined Indoor Grammar Split-Grammar for Modeling Rooms 19 G rooms = (N,T,S,R) N = {Space} T = {…, space i, space j, …} S = Space R = {Split, Merge, Instantiation} x y z x y d

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University of Stuttgart ifp Combined Indoor Grammar Split-Grammar for Modeling Rooms 20 Rule probabilities a priori probability: P(R i ) relative frequency of occurrence context aware probability: P(R j |R i ) conditional probability for modeling neighborhood relationships between rooms RiRi … RkRk RjRj … Implementation through Markov Chain nodes: rules edges: neighborhood relationships or transitions probability for a transition from R i to R j is given by

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University of Stuttgart ifp Instantiation of Individual Grammars 21 a aaa abc c a b d G indoor = (G hallways, G rooms ) G hallways G rooms specialized rule system ?

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University of Stuttgart ifp Instantiation of Individual Grammars 22 Grammar-based representation of a real floor plan hallway system using an individual instance of the L-system G hallways floorplan of ifp

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University of Stuttgart ifp floorplan of ifp Instantiation of Individual Grammars 23 Grammar-based representation of a real floor plan hallway system using an individual instance of the L-system G hallways room configurations in non-hallway spaces using an individual instance of the split Grammar G rooms floorplan of ifp Space 2 a Space 1 b c m j k i h g floorplan of ifp Space 1 Space 2 ;

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University of Stuttgart ifp specialized rule system ? Instantiation of Individual Grammars 24 a aaa abc c a b d G indoor = (G hallways, G rooms ) G hallways G rooms specialized rule system !

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University of Stuttgart ifp high low Instantiation of Individual Grammars Inverse Procedural Modeling Set up of rules and attributes requires observation data 25 observation data grammar instance quality completeness, accuracy high low 1, 2, 3, 4, 5, d1, d2, d3, d4, d5 1, 2 d1, d2, d3 1, 2, 3, 4, 5, d1, d2, d3, d4, d5 Inverse procedural modeling © Peter et al., 2011 © Peter, 2013

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University of Stuttgart ifp Grammar Application Procedural Modeling An instance of an individual indoor grammar contains knowledge about characteristic indoor geometries and room arrangements geometric properties: e.g. room size topological properties: e.g. connectivity of rooms semantic aspects: e.g. functional grouping of rooms Use the grammar to generate reliable hypotheses about possible indoor geometries in unknown areas 26 1, 2, 3, 4, 5, d1, d2, d3, d4, d5 observation data observation data grammar instance grammar instance Inverse procedural modeling Procedural modeling hypotheses © Peter et al., 2013

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University of Stuttgart ifp Grammar Application Results Application scenario: Generate hypotheses about indoor geometries for the 2 nd floor of university building using erroneous and incomplete trace data and grammar support 27 © Input data: Traces: 250 odometry traces covering the hallways of the 2 nd floor Grammar: high-level grammar automatically derived from a floor plan of the 1 st floor 3D building shell: LOD2 building model provided by city surveying office

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University of Stuttgart ifp Grammar Application Results Procedural modeling process derive initial hallway segments (axiom) apply L-system to the axiom apply split grammar to non- hallway spaces Comparison to ground trouth (131 rooms) purely data-driven: 29 rooms split grammar applied to the data-driven hallways: 92 rooms split grammar applied to completed hallways through L-system: 116 rooms average room width error: ~2m 28

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University of Stuttgart ifp Conclusions and Outlook 29 Combined indoor grammar to support the reconstruction of building interiors from real sensor data concepts of L-system and split grammar different geometric and topological characteristics of hallways and rooms Individual grammars can be derived automatically from observation data Grammar can be integrated in continuous update and enhancement loop Future work link indoor grammar to facade grammar (step over to real 3D) transfer the concept of split grammar from spaces to faces (model wall openings) © Peter, 2013© Becker, 2011

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ifp University of Stuttgart Institute for Photogrammetry Thank you for your attention

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