Y. Dehbi

Statistical Relational Learning of Grammar Rules for 3D Building Reconstruction

The automatic interpretation of 3D point clouds for building reconstruction is a challenging task. The interpretation process requires highly structured models representing semantics. Formal grammars can describe structures as well as the parameters of buildings and their parts. We propose a novel approach for the automatic learning of weighted attributed context-free grammar rules for 3D building reconstruction, supporting the laborious manual design of rules. We separate structure from parameter learning. Specific Support Vector Machines (SVMs) are used to generate a weighted context-free grammar and predict structured outputs such as parse trees. The grammar is extended by parameters and constraints, which are learned based on a statistical relational learning method using Markov Logic Networks (MLNs). MLNs enforce the topological and geometric constraints. MLNs address uncertainty explicitly and provide probabilistic inference. They are able to deal with partial observations caused by occlusions. Uncertain projective geometry is used to deal with the uncertainty of the observations. Learning is based on a large building database covering different building styles and facade structures. In particular, a treebank that has been derived from the database is employed for structure learning.

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.

Identification and Modelling of Translational and Axial Symmetries and their Hierarchical Structures in Building Footprints by Formal Grammars

Buildings and other man-made objects, for many reasons such as economical or aesthetic, are often characterized by their symmetry. The latter predominates in the design of building footprints and building parts such as façades. Thus the identification and modeling of this valuable information facilitates the reconstruction of these buildings and their parts. This article presents a novel approach for the automatic identification and modelling of symmetries and their hierarchical structures in building footprints, providing an important prior for façade and roof reconstruction. The uncertainty of symmetries is explicitly addressed using supervised machine learning methods, in particular Support Vector Machines (SVMs). Unlike classical statistical methods, for SVMs assumptions on the a priori distribution of the data are not required. Both axial and translational symmetries are detected. The quality of the identified major and minor symmetry axes is assessed by a least squares based adjustment. Context-free formal grammar rules are used to model the hierarchical and repetitive structure of the underlying footprints. We present an algorithm which derives grammar rules based on the previously acquired symmetry information and using lexical analysis describing regular patterns and palindrome-like structures. This offers insights into the latent structures of building footprints and therefore describes the associated façade in a relational and compact