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Elastic Statistical Shape Analysis with Landmark Constraints

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2018, Doctor of Philosophy, Ohio State University, Statistics.
Due to mathematical and computational advances, the study of shape data is of great interest in numerous fields, including biology, medicine, computer vision, and biometrics. Shape can be de fined as a property of an object which remains after removing variability associated with shape-preserving transformations, including translation, scale, rotation, and, in some cases, re-parameterization. This type of data presents mathematical challenges, as objects may have identical shape despite appearing differently in Euclidean space. The complex structure of shape data requires tools from fi elds such as differential geometry, algebra, and functional analysis. One challenge in analyzing shape data is the choice of shape representation used for subsequent comparison and statistical modeling. Two of the primary choices in existing literature are landmark-based and function-based. Landmarks are a finite collection of labeled points pre-speci fied by the researcher. Once shape-preserving transformations are accounted for, landmark sets can be analyzed using multivariate statistical techniques. More recently, there has been a push to develop infi nite-dimensional shape representations, which treat an object's outline using a continuous function. This thesis explores the interplay between elastic shape representations (a special type of function-based representation) and landmark sets. A primary contribution is the development of a joint landmark-elastic shape representation, which allows researchers to represent shape by a function, while also incorporating landmark constraints provided by subject-matter experts. We demonstrate improvement in shape comparison, and present some available statistical tools using this representation. In many cases, we show improved performance in tasks such as clustering and classi fication. Under the aforementioned landmark-constrained elastic shape representation, this thesis also introduces a weighted metric. This allows one to emphasize features which are deemed important, which in turn affects optimal pairwise registration of shapes. If weights cannot be easily speci fied, this metric can allow for inference of these weights through optimization over a particular statistical task. Lastly, this thesis presents a model for inference of landmark locations, if they are unknown to the researcher. Annotating curves with landmarks is subject to uncertainty, and can be time-consuming for larger datasets. We present a hierarchical model for automatic detection of landmark locations, as well as the number of landmarks. Computational Bayesian techniques provide efficient posterior inference and uncertainty quanti fication. All methods discussed are applied to simulated curves, as well as data provided from various disciplines, including biology, medical imaging, and forensic analysis.
Sebastian Kurtek (Advisor)
Oksana Chkrebtii (Committee Member)
Steven MacEachern (Committee Member)
210 p.

Recommended Citations

Citations

  • Strait, J. (2018). Elastic Statistical Shape Analysis with Landmark Constraints [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1530966023478484

    APA Style (7th edition)

  • Strait, Justin. Elastic Statistical Shape Analysis with Landmark Constraints. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1530966023478484.

    MLA Style (8th edition)

  • Strait, Justin. "Elastic Statistical Shape Analysis with Landmark Constraints." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1530966023478484

    Chicago Manual of Style (17th edition)