Generative Methods for Data Completion in Shape Driven Systems

In many application domains, such as building planning, construction, or docu-
mentation, it is of high importance to acquire a digital representation of the shape
of real world objects, e.g. for visualization or documentation purposes. Such ob-
jects are often part of a class or domain of similarly structured objects; and often
complex objects, such as houses, are composed by simpler objects, such as walls,
doors and windows. Especially man-made objects exhibit such structure, mostly
due to manufacturability and design reasons.
A rich digital representation of a complex object consists not only of its shape,
but also its structure, i.e. the composition hierarchy of simpler objects. A more
general way to represent such a composition hierarchy is a generative model, that
generates the structure upon evaluation; a parametric generative model can ge-
nerate a whole class of similarly structured objects.
In this thesis, I review shape-based methods for generative creation of mo-
dels, and present a novel system for generative forward modeling based on shape
grammars. Furthermore, I present two methods for solving the inverse problem:
acquiring a rich digital representation of real-world objects from measurements
and utilizing a generative model of prior domain knowledge. Using this prior
knowledge, it is now possible to complete missing features, or reduce measu-
rement errors. The first method parses the hierarchical structure of a building
façade, given an ortho photo and a grammar that describes architectural con-
straints. The second method yields a hypothesis of electrical wiring inside walls,
given optical measurements (point clouds and photographs), and a grammar that
describes the technical standards