Document Type



Doctor of Philosophy (PhD)


Computer Science

First Advisor's Name

Wei Zeng

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

S. S. Iyengar

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Niki Pissinou

Third Advisor's Committee Title

Committee Member

Fourth Advisor's Name

Leonardo Bobadilla

Fourth Advisor's Committee Title

Committee Member

Fifth Advisor's Name

Yuanchang Sun

Fifth Advisor's Committee Title

Committee Member


brain mapping, brain registration, brain morphometry analysis, shape analysis, atlas graph, structural surface mapping, diffeomorphic mapping, AD classification, graph-consatrained surface parameterization, surface registration, feature graph, harmonic map, surface morphing

Date of Defense



Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing.

This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications.







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