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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.

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ABSTRACT:This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed. MOTIVATION AND CONTEXTIndoor models are of great interest in a wide range of applications. They are of high relevance for indoor navigation, evacuation planning, facility management or guide for the blind. While models of the exterior such as models in level of detail 3 (LoD3) according to CityGML (Gröger and Plümer, 2012) are by now state of the art, modelling of indoor environments is not yet widely available and the acquisition of the corresponding data remains expensive. While most approaches require measurements of high density such as 3D point clouds or images, we propose an approach which gets along with few observations in order to predict floorplans of high accuracy.The challenge is to estimate an indoor model based on few observations. More precisely, the task that we consider in this paper is to place a set of n rectangular rooms within a polygonal footprint, locating the doors and estimating the height of the rooms. The resulting model is characterized by discrete and continuous model parameters that are related by both linear and non-linear constraints. Our approach is characterized by sparse observations such as room areas, functional use, window locations and, possibly, room numbers that can be acquired from building management services. Indoor images or laser scans are not required. A maximum a-posteriori (MAP) estimation uses further statistical knowledge such as probability density functions and Gaussian mixtures for model parameters.In this paper, we assume that the topological model is provided by a preceding step using Constraint Logic Programming as presented by Loch-Dehbi et al. (2017). The topological model consists of the room neighbourhood information and the correspondence between rooms and windows. This article foc...

ABSTRACT:The acquisition of detailed information for buildings and their components becomes more and more important. However, an automatic reconstruction needs high-resolution measurements. Such features can be derived from images or 3D laserscans that are e.g. taken by unmanned aerial vehicles (UAV). Since this data is not always available or not measurable at the first for example due to occlusions we developed a reasoning approach that is based on sparse observations. It benefits from an extensive prior knowledge of probability density distributions and functional dependencies and allows for the incorporation of further structural characteristics such as symmetries. Bayesian networks are used to determine posterior beliefs. Stochastic reasoning is complex since the problem is characterized by a mixture of discrete and continuous parameters that are in turn correlated by nonlinear constraints. To cope with this kind of complexity, the implemented reasoner combines statistical methods with constraint propagation. It generates a limited number of hypotheses in a model-based top-down approach. It predicts substructures in building facades -such as windows -that can be used for specific UAV navigations for further measurements.