Loch-Dehbi, Sandra: Algebraic, logical and stochastic reasoning for the automatic prediction of 3d building structures. - Bonn, 2021. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-60873
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-60873,
author = {{Sandra Loch-Dehbi}},
title = {Algebraic, logical and stochastic reasoning for the automatic prediction of 3d building structures},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = jan,

note = {3D building models are nowadays an important prerequisite for many applications such as rescue management or navigation tasks. However, most approaches for the automatic reconstruction of buildings rely on high-resolution data that cannot always be provided due to occlusions or high cost of the acquisition of data. Instead, reasoning methods have to cope with sparse and possibly incomplete data. This thesis presents a novel reasoning approach for the prediction of building substructures in the absence of dense measurements. The developed reasoner benefits from a strong profound prior knowledge of functional dependencies and probability density distributions in a model-driven top-down approach that is legitimated by strong regularities and symmetries in man-made objects. It thereby holds the view that it is easier to verify or falsify predicted hypotheses than to reconstruct buildings bottom-up from measurements and automatically generates a small number of qualified hypotheses based only on sparse observations such as footprints. However, the mathematical model for buildings is a priori characterized by multimodal probability density functions as well as non-linear relations with both discrete and continuous parameters that in general leads to approximate stochastic inference instead of exact inference. One substantial design decision in order to use well established exact algorithms of parameter estimation is the representation of distributions by Gaussian mixtures. For efficient reasoning in hybrid models, the key idea of this thesis is to divide the problem into a combinatorial (discrete) and stochastic (continuous) part and to combine constraint logic programming with Bayesian networks. Constraint programming reduces the search space by constraint propagation and intelligent search strategies and determines the discrete parameters first. Afterwards this intermediate result is refined by stochastic inference to evaluate and determine the continuous parameters and finding the most likely hypotheses out of an a priori large hypothesis space. The method has been demonstrated to predict façade structures on the one hand. As the seemless outdoor/indoor modeling gets more and more attention the developed approach was adapted to the prediction of indoor models on the other hand. As models are a prerequisite of model-based reasoning, tools are needed that facilitate the development of redundancy-free and consistent prototyped models providing prior knowledge during model prediction. At the same time, it is useful to make implicit constraints explicit for supporting the interpretation of measurements for building reconstruction. Recognizing that the task of checking redundancy and consistency is equivalent to proving that one constraint follows from a set of premises this thesis complements the reasoning with methods of automatic theorem proving. In order to handle the increasing complexity of symbolic reasoning in the 3D space a novel approach is presented that combines algebraic and logical reasoning based on an appropriate representation of the envisaged constraint-based model using multivariate polynomials and first-order predicate logic. Algebraic reasoning is based on Wu's method of pseudodivision and characteristic sets and identifies redundancy, inconsistency and implicit knowledge. Rule-based reasoning based on logical facts and rules supports the reasoning process using known implications. The aspect of uncertainty that is inevitable in the context of geoinformation systems (GIS) is handled in the developed reasoning methods by the incorporation of probability density functions, graphical models and uncertain projective geometry.},
url = {https://hdl.handle.net/20.500.11811/8897}

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