title: Learning Distributions of Functions on a Continuous Time Domain
creator: Petersen, Jens
subject: ddc-004
subject: 004 Data processing Computer science
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-530
subject: 530 Physics
subject: ddc-570
subject: 570 Life sciences
subject: ddc-610
subject: 610 Medical sciences Medicine
description: This work presents several contributions on the topic of learning representations of function spaces, as well as on learning the dynamics of glioma growth as a particular instance thereof. We begin with two preparatory efforts, showing how expert knowledge can be leveraged efficiently in an interactive segmentation context, and presenting a proof of concept for inferring non-deterministic glioma growth patterns purely from data. The remainder of our work builds upon the framework of Neural Processes. We show how these models represent function spaces and discover that they can implicitly decompose the space into different frequency components, not unlike a Fourier transform. In this context we derive an upper bound on the maximum signal frequency Neural Processes can represent and show how to  control the learned representations to only contain certain frequencies. We continue with an improvement of a more recent addition to the Neural Process family called ConvCNP, which we combine with a Gaussian Process to make it non-deterministic and to improve generalization. Finally, we show how to perform segmentation in the Neural Process framework by extending a typical segmentation  architecture with spatio-temporal attention. The resulting model can interpolate complex spatial variations of segmentations over time and, applied to glioma growth, it is able to represent multiple temporally consistent growth trajectories, exhibiting realistic and diverse spatial  growth patterns.
date: 2020
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/29234/1/Jens_Petersen-Learning_Distributions_of_Functions_on_a_Continuous_Time_Domain.pdf
identifier: DOI:10.11588/heidok.00029234
identifier: urn:nbn:de:bsz:16-heidok-292346
identifier:   Petersen, Jens  (2020) Learning Distributions of Functions on a Continuous Time Domain.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/29234/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng