{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T21:56:05Z","timestamp":1780437365519,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,21]],"date-time":"2017-03-21T00:00:00Z","timestamp":1490054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>This paper presents a novel method for the prediction of building floor plans based on sparse observations in the absence of measurements. We derive the most likely hypothesis using a maximum a posteriori probability approach. Background knowledge consisting of probability density functions of room shape and location parameters is learned from training data. Relations between rooms and room substructures are represented by linear and bilinear constraints. We perform reasoning on different levels providing a problem solution that is optimal with regard to the given information. In a first step, the problem is modeled as a constraint satisfaction problem. Constraint Logic Programming derives a solution which is topologically correct but suboptimal with regard to the geometric parameters. The search space is reduced using architectural constraints and browsed by intelligent search strategies which use domain knowledge. In a second step, graphical models are used for updating the initial hypothesis and refining its continuous parameters. We make use of Gaussian mixtures for model parameters in order to represent background knowledge and to get access to established methods for efficient and exact stochastic reasoning. We demonstrate our approach on different illustrative examples. Initially, we assume that floor plans are rectangular and that rooms are rectangles and discuss more general shapes afterwards. In a similar spirit, we predict door locations providing further important components of 3D indoor models.<\/jats:p>","DOI":"10.3390\/ijgi6030090","type":"journal-article","created":{"date-parts":[[2017,3,21]],"date-time":"2017-03-21T12:22:22Z","timestamp":1490098942000},"page":"90","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Estimation of 3D Indoor Models with Constraint Propagation and Stochastic Reasoning in the Absence of Indoor Measurements"],"prefix":"10.3390","volume":"6","author":[{"given":"Sandra","family":"Loch-Dehbi","sequence":"first","affiliation":[{"name":"Department of Geoinformation, Institute of Geodesy and Geoinformation, University of Bonn, Meckenheimer Allee 172, 53115 Bonn, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Youness","family":"Dehbi","sequence":"additional","affiliation":[{"name":"Department of Geoinformation, Institute of Geodesy and Geoinformation, University of Bonn, Meckenheimer Allee 172, 53115 Bonn, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lutz","family":"Pl\u00fcmer","sequence":"additional","affiliation":[{"name":"Department of Geoinformation, Institute of Geodesy and Geoinformation, University of Bonn, Meckenheimer Allee 172, 53115 Bonn, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,21]]},"reference":[{"key":"ref_1","unstructured":"Gr\u00f6ger, G., Kolbe, T.H., Nagel, C., and H\u00e4fele, K.H. 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