STOCHASTIC REASONING FOR UAV SUPPORTED RECONSTRUCTION OF 3D BUILDING MODELS

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

Estimation of 3D Indoor Models with Constraint Propagation and Stochastic Reasoning in the Absence of Indoor Measurements

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

PARAMETER ESTIMATION AND MODEL SELECTION FOR INDOOR ENVIRONMENTS BASED ON SPARSE OBSERVATIONS

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

PREDICTION OF BUILDING FLOORPLANS USING LOGICAL AND STOCHASTIC REASONING BASED ON SPARSE OBSERVATIONS

This paper introduces a novel method for the automatic derivation of building floorplans and indoor models. Our approach is based on a logical and stochastic reasoning using sparse observations such as building room areas. No further sensor observations like 3D point clouds are needed. Our method benefits from an extensive prior knowledge of functional dependencies and probability density functions of shape and location parameters of rooms depending on their functional use. The determination of posterior beliefs is performed using Bayesian Networks. Stochastic reasoning is complex since the problem is characterized by a mixture of discrete and continuous parameters that are in turn correlated by non-linear constraints. To cope with this kind of complexity, the proposed reasoner combines statistical methods with constraint propagation. It generates a limited number of hypotheses in a model-based top-down approach. It predicts floorplans based on a-priori localised windows. The use of Gaussian mixture models, constraint solvers and stochastic models helps to cope with the a-priori infinite space of the possible floorplan instantiations

Geometric reasoning for uncertain observations of man-made structures

Observations of man-made structures in terms of digital images, laser scans or sketches are inherently uncertain due to the acquisition process. Thus reverse engineering has to be applied to obtain topologically consistent and geometrically correct model instances by feature aggregation. The corresponding spatial reasoning process usually implies the detection of adjacencies, the generation and testing of hypotheses, and finally the enforcement of the detected relations. We present a complete and general work-flow for geometric reasoning that takes the uncertainty of the observations and of the derived low-level features into account. Thereby we exploit algebraic projective geometry to ease the formulation of geometric constraints. As this comes at the expense of an over-parametrization, we introduce an adjustment model which stringently incorporates uncertainty and copes with singular covariance matrices. The size of the resulting normal equation system depends only on the number of established constraints which paves the way to efficient solutions. We demonstrate the usefulness and the feasibility of the approach with results for the automatic analysis of a sketch and for a building reconstruction based on an airborne laser scan