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Learning Distributions of Functions on a Continuous Time Domain

Petersen, Jens

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Abstract

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.

Item Type: Dissertation
Supervisor: Debus, Prof. Dr. Dr. Jürgen
Place of Publication: Heidelberg
Date of thesis defense: 9 December 2020
Date Deposited: 18 Dec 2020 07:33
Date: 2020
Faculties / Institutes: The Faculty of Physics and Astronomy > Dekanat der Fakultät für Physik und Astronomie
Subjects: 004 Data processing Computer science
500 Natural sciences and mathematics
530 Physics
570 Life sciences
610 Medical sciences Medicine
Controlled Keywords: Maschinelles Lernen, Maschinelles Sehen, Deep learning
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