Learning grammar rules of building parts from precise models and noisy observations

Abstract

The automatic interpretation of dense three-dimensional (3D) point clouds is still an open research problem. The quality and usability of the derived models depend to a large degree on the availability of highly structured models which represent semantics explicitly and provide a priori knowledge to the interpretation process. The usage of formal grammars for modelling man-made objects has gained increasing interest in the last few years. In order to cope with the variety and complexity of buildings, a large number of fairly sophisticated grammar rules are needed. As yet, such rules mostly have to be designed by human experts. This article describes a novel approach to machine learning of attribute grammar rules based on the Inductive Logic Programming paradigm. Apart from syntactic differences, logic programs and attribute grammars are basically the same language. Attribute grammars extend context-free grammars by attributes and semantic rules and provide a much larger expressive power. Our approach to derive attribute grammars is able to deal with two kinds of input data. On the one hand, we show how attribute grammars can be derived from precise descriptions in the form of examples provided by a human user as the teacher. On the other hand, we present the acquisition of models from noisy observations such as 3D point clouds. This includes the learning of geometric and topological constraints by taking measurement errors into account. The feasibility of our approach is proven exemplarily by stairs, and a generic framework for learning other building parts is discussed. Stairs aggregate an arbitrary number of steps in a manner which is specified by topological and geometric constraints and can be modelled in a recursive way. Due to this recursion, they pose a special challenge to machine learning. In order to learn the concept of stairs, only a small number of examples were required. Our approach represents and addresses the quality of the given observations and the derived constraints explicitly, using concepts from uncertain projective geometry for learning geometric relations and the Wakeby distribution together with decision trees for topological relations.