Geometric and statistical models for multi-object shape analysis
Public Deposited- Creator
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Liu, Zhiyuan
- Affiliation: College of Arts and Sciences, Department of Computer Science
- Abstract
- Shape analysis of multi-object complexes is important in many applications because it reveals additional information of interest over single-object shape analysis. For example, in medical applications where multiple structures in the human body often deform together, joint shape analysis of those interrelated structures facilitates robust and efficient algorithms. Specifically, shape correlation of functionally related structures allows us to understand the common underlying biological factors (e.g., disease). Also, beyond the within-object shape relations, between-object shape relations provide additional understanding of multi-object complexes. Despite the need of multi-object shape analysis, this field has been challenged by many issues. For instance, shape variation is often coupled with pose and size variation between objects. Moreover, within-object shape variation is often coupled with between-object shape variation. These issues have prevented us from sufficiently understanding multi-object complexes. To address the issues, this dissertation proposes geometric and statistical methods for joint analysis of multi-object complexes. In particular, I base my research on skeletal representations (i.e., s-reps) that are designed to provide intrinsic shape features with good correspondences. This dissertation improves the previous method fitting an s-rep to an object such that the fitted s-reps have desirable geometric and statistical properties. This improvement allows me to analyze intrinsic shape correlation between objects. To this end, this dissertation extends the existing statistical method to effectively extract joint shape variation, leading to a method called Non-EUclidean Joint and Individual Variation Explained (NEUJIVE). NEUJIVE shows notable robustness in analyzing multi-block non-Euclidean data with different variability. Last, to decouple within- and between-object shape variation, I develop non-branching linking structures for statistical analysis of between-object shape features. To capture geometric features that are insensitive to pose variation of multi-object complexes, this dissertation extends fitted local frames on s-reps to affine frames. The fitted local affine frames show special advantage because they free multi-object shape analysis from pre-alignment. The driving problem of the proposed methods involves classifying and testing hypotheses on the shape of the hippocampus-caudate pairs between an autism group and a non-autism group. Also, this dissertation discusses other potential applications that can benefit from the proposed methods.
- Date of publication
- 2022
- Keyword
- DOI
- Resource type
- Rights statement
- In Copyright - Educational Use Permitted
- Advisor
- Pizer, Stephen
- Marron, James
- Degree
- Doctor of Philosophy
- Degree granting institution
- University of North Carolina at Chapel Hill Graduate School
- Graduation year
- 2022
- Language
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