Shape complexity: relative and emergent, with applications in deep learning

Date

2024-3-15

Author

Arslan, Mazlum Ferhat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

42
views

12
downloads

Cite This

Quantifying shape complexity is useful for a variety of applications including medical imaging and measuring the difficulty of samples in image datasets. However, the subject is underexplored, mostly due to its multifaceted nature. In this thesis, we start by proposing a benchmark dataset, subsets of which aim to account for the different aspects of the phenomenon. We compare a variety of shape complexity-related measures on the proposed dataset. Next, we propose a novel method that emphasizes the relative and emergent nature of shape complexity. The method operates in both continuous and discrete spaces of arbitrary dimensions. We demonstrate the properties of the method through extensive experiments and theoretical analysis. In the last part of the thesis, we turn to applications of the proposed measure. We obtain state-of-the-art results in domain generalization for prostate segmentation. As a separate application, we employ the proposed measure for curriculum learning on instance segmentation and image classification tasks on PASCAL VOC 2012 and CIFAR-10 datasets. We hypothesize the quantified shape complexity is an indicator of sample difficulties. Leveraging the estimated sample complexities, we devise curriculum strategies that lead to statistically significant performance increases on both tasks.

Subject Keywords

shape complexity, morphological differential equations, medical image segmentation, domain generalization, curriculum learning

URI

https://hdl.handle.net/11511/109434

Collections

Graduate School of Natural and Applied Sciences, Thesis