Generative Methods for Data Completion in Shape Driven Systems

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In many application domains, such as building planning, construction, or documentation, 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 objects 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 generate a whole class of similarly structured objects. In this thesis, I review shape-based methods for generative creation of models, 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 measurement errors. The first method parses the hierarchical structure of a building façade, given an ortho photo and a grammar that describes architectural constraints. 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.