Reconstructive Geometry
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Date
2011
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Ullrich
Text.PhDThesis
Abstract
The thesis “Reconstructive Geometry” by TORSTEN ULLRICH presents a new collision
detection algorithm, a novel approach to generative modeling, and an innovative
shape recognition technique. All these contributions are centered around the questions
“howto combine acquisition data with generative model descriptions” and “how
to perform this combination efficiently”. Acquisition data – such as point clouds and
triangle meshes – are created e.g. by a 3D scanner or a photogrammetric process. They
can describe a shape’s geometry very well, but do not contain any semantic information.
With generative descriptions it’s the other way round: a procedure describes a
rather ideal object and its construction process. This thesis builds a bridge between
both types of geometry descriptions and combines them to a semantic unit. An innovative
shape recognition technique, presented in this thesis, determines whether a
digitized real-world object might have been created by a given generative description,
and if so, it identifies the high-level parameters that have been passed to the generative
script. Such a generative script is a simple JavaScript function. Using the generative
modeling compiler “Euclides” the function can be understood in a mathematical
sense; i.e. it can be differentiated with respect to its input parameters, it can be embedded
into an objective function, and it can be optimized using standard numerical
analysis. This approach offers a wide range of applications for generative modeling
techniques; parameters do not have to be set manually – they can be set automatically
according to a reasonable objective function. In case of shape recognition, the objective
function is distance-based and measures the similarity of two objects. The techniques
that are used to efficiently perform this task (space partitioning, hierarchical
structures, etc.) are the same in collision detection where the question, whether two
objects have distance zero, is answered. To sum up, distance functions and distance
calculations are a main part of this thesis along with their application in geometric
object descriptions, semantic enrichment, numerical analysis and many more.
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