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@PHDTHESIS{Lim:817902,
author = {Lim, Isaak},
othercontributors = {Kobbelt, Leif and Mitra, Niloy J.},
title = {{L}earned embeddings for geometric data},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2021-04188},
pages = {1 Online-Ressource : Illustrationen, Diagramme},
year = {2021},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2021},
abstract = {Solving high-level tasks on 3D shapes such as
classification, segmentation, vertex-to-vertex maps or
computing the perceived style similarity between shapes
requires methods that are able to extract the necessary
information from geometric data and describe the appropriate
properties. Constructing functions that do this by hand is
challenging because it is unclear how and which information
to extract for a task. Furthermore, it is difficult to
determine how to use the extracted information to provide
answers to the questions about shapes that are being asked
(e.g. what category a shape belongs to). To this end, we
propose to learn functions that map geometric data to an
embedding space. The outputs of those maps are compressed
encodings of the input geometric data that can be optimized
to contain all necessary task-dependent information. These
encodings can then be compared directly (e.g. via the
Euclidean distance) or byother fairly simple functions to
provide answers to the questions being asked. Neural
networks can be used to implement such maps and comparison
functions. This has the benefit that they offer flexibility
and expressiveness. Furthermore, information extraction and
comparison can be automated by designing appropriate
objective functions that are used to optimize the parameters
of the neural networks on geometric data collections with
task-related meta information provided by humans. We
therefore have to answer two questions. Firstly, given the
often irregular nature of representations of 3D shapes, how
can geometric data be represented asinput to neural networks
and how should such networks be constructed? Secondly, how
can we design the resulting embedding space provided by
neural networks insuch a manner that we are able to achieve
good results on high-level tasks on 3Dshapes? In this thesis
we provide answers to these two questions. Concretely,
depending on the availability of the data sources and the
task specific requirements we compute encodings from
geometric data representations in the form of images, point
clouds and triangle meshes. Once we have a suitable way to
encode the input, we explore different ways in which to
design the learned embedding spaceby careful construction of
appropriate objective functions that extend beyond straight
forward cross-entropy minimization based approaches on
categorical distributions. We show that these approaches are
able to achieve good results inboth discriminative as well
as generative tasks.},
cin = {122310 / 120000},
ddc = {004},
cid = {$I:(DE-82)122310_20140620$ / $I:(DE-82)120000_20140620$},
pnm = {3D Reconstruction and Modeling across Different Levels of
Abstraction (340884)},
pid = {G:(EU-Grant)340884},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2021-04188},
url = {https://publications.rwth-aachen.de/record/817902},
}
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