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Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data

The presence of non-linear shape variation in 3D data is known to influence the reliability of linear statistical shape models (SSM). This problem is regularly acknowledged, but disregarded, as it is assumed that linear models are able to adequately approximate such non-linearities. Model reliabilit...

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Main Author: Fehr, Fabio
Other Authors: Clark, Allan
Format: Thesis
Language:English
Published: Department of Statistical Sciences 2022
Subjects:
Advanced Analytics
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access_status_str Open Access
author Fehr, Fabio
author2 Clark, Allan
author_browse Clark, Allan
Fehr, Fabio
author_facet Clark, Allan
Fehr, Fabio
author_sort Fehr, Fabio
collection Thesis
description The presence of non-linear shape variation in 3D data is known to influence the reliability of linear statistical shape models (SSM). This problem is regularly acknowledged, but disregarded, as it is assumed that linear models are able to adequately approximate such non-linearities. Model reliability is crucial for medical imaging and computer vision tasks; however, prior to modelling, the non-linearity in the data is not often considered. The study provides a framework to identify the presence of non-linearity in using principal component analysis (PCA) and autoencoders (AE) shape modelling methods. The data identified to have linear and non-linear shape variations is used to compare two sophisticated techniques: linear Gaussian process morphable models (GPMM) and non-linear variational autoencoders (VAE). Their model performance is measured using generalisation, specificity and computational efficiency in training. The research showed that, given limited computational power, GPMMs managed to achieve improved relative generalisation performance compared to VAEs, in the presence of non-linear shape variation by at least a factor of six. However, the non-linear VAEs, despite the simplistic training scheme, presented improved specificity generative performance of at least 18% for both datasets.
format Thesis
id oai:open.uct.ac.za:11427/35725
institution University of Cape Town (South Africa)
language eng
last_indexed 2026-06-10T12:31:50.330Z
license_str Not specified — see source repository
provenance_str_mv Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository
publishDate 2022
publishDateRange 2022
publishDateSort 2022
publisher Department of Statistical Sciences
publisherStr Department of Statistical Sciences
record_format dspace
source_str UCTD — University of Cape Town Open Access Repository
spelling oai:open.uct.ac.za:11427/35725 Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data Fehr, Fabio Clark, Allan Mutsvangwa, Tinashe Advanced Analytics The presence of non-linear shape variation in 3D data is known to influence the reliability of linear statistical shape models (SSM). This problem is regularly acknowledged, but disregarded, as it is assumed that linear models are able to adequately approximate such non-linearities. Model reliability is crucial for medical imaging and computer vision tasks; however, prior to modelling, the non-linearity in the data is not often considered. The study provides a framework to identify the presence of non-linearity in using principal component analysis (PCA) and autoencoders (AE) shape modelling methods. The data identified to have linear and non-linear shape variations is used to compare two sophisticated techniques: linear Gaussian process morphable models (GPMM) and non-linear variational autoencoders (VAE). Their model performance is measured using generalisation, specificity and computational efficiency in training. The research showed that, given limited computational power, GPMMs managed to achieve improved relative generalisation performance compared to VAEs, in the presence of non-linear shape variation by at least a factor of six. However, the non-linear VAEs, despite the simplistic training scheme, presented improved specificity generative performance of at least 18% for both datasets. 2022-02-18T07:49:24Z 2022-02-18T07:49:24Z 2021 2022-02-10T14:59:17Z Master Thesis Masters MSc http://hdl.handle.net/11427/35725 eng application/pdf Department of Statistical Sciences Faculty of Science
spellingShingle Advanced Analytics
Fehr, Fabio
Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
thesis_degree_str Master's
title Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
title_full Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
title_fullStr Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
title_full_unstemmed Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
title_short Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
title_sort modelling non linearity in 3d shapes a comparative study of gaussian process morphable models and variational autoencoders for 3d shape data
topic Advanced Analytics
url http://hdl.handle.net/11427/35725
work_keys_str_mv AT fehrfabio modellingnonlinearityin3dshapesacomparativestudyofgaussianprocessmorphablemodelsandvariationalautoencodersfor3dshapedata

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