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Dissertation (Min Ho Cho).pdf (18.77 MB)

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Aggregated Pairwise Classification and Other Applicationsfor Elastic Statistical Shapes

Cho, Min Ho
http://rave.ohiolink.edu/etdc/view?acc_num=osu1595426726818697

Abstract Details

2020, Doctor of Philosophy, Ohio State University, Statistics.
Statistical shape analysis has progressed significantly over the last few decades, especially with the increasing availability of large datasets and with computational advances. Shape has been widely used as a primary feature for detection, tracking and recognition of objects in images and videos. Analyzing shapes of curves (outlines of objects in 2D images) or surfaces (outlines of objects in 3D images) has been of great interest in diverse applicationsranging from medical imaging to computer vision and beyond. Shape analysis makes use of ideas from geometry and statistics. Specifically, much work has been devoted to the development of appropriate representations and metrics for shape data based on conceptsfrom Riemannian geometry. Statistical shape data have three main properties: (1) shape is invariant to shape-preserving transformations: translation, scaling, rotation, and re-parameterization, (2) shapes are inherently infinite dimensional with strong dependence among the position of nearby points, and (3) shape spaces are not Euclidean, but rather are fundamentally curved. Thus, one generally cannot directly apply standard statistical tools developed for multivariate data to shape data. To accommodate these features of the data, we work with a special representation of shape, called the square-root velocity function (SRVF), to provide a useful formal description of the shape. In addition, we use the elastic metric which enables efficient statistical analysis on the corresponding shape space under the SRVF representation. The main focus of this dissertation is classification of shapes. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem – with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Thus, we first linearize the shape space by passing to tangent spaces of the manifold of shapes at different projection points, and then use principal components within these tangent spaces to reduce dimensionality. We propose a novel method using multiple projection points which effectively separate shapes forpairwise classification. We aggregate these pairwise classifiers for the multiclass problem. We consider classification procedures based on linear and quadratic discriminant analysis (LDA and QDA) in the lower dimensional linearized spaces. We use two different final decision rules for classification based on aggregated likelihoods from the LDA or QDA models: one-shot and recursion. We illustrate the impact of the projection point and choice of subspace on the misclassification rate through extensive simulation studies and empirical real data examples. We further apply our methods to other types of data including data on spheres, landmark shape data, and nonelastic shape data. We also compare our methods to other classification approaches including distance-based methods (nearest neighbor and nearest mean classifiers), classwise models, and alternative approaches for dimension reduction. Next, we develop an effective graphical tool that plays off the histogram for shapes and functions, two types of data which are known to pose challenges for visualization. We use various choices of score to order shapes, such as the first tangent principal component coefficient, residual of fitted shapes to a particular tPC space, and geometric features (average curvature and area for closed curves). The shapes are then binned on the basis of this score. They are displayed, with the raw data appearing on the top of the plot and fitted shapes on the bottom. For functional data, we can visualize the amplitude component on the top and the phase component on the bottom. If a covariate is available, we can incorporate it in the graphical display. These visualization techniques are proving to be useful exploratory tools to guide a formal analysis. Third, we propose a method of canonical correlation analysis (CCA) for probability density functions (PDFs) and shapes. Based on the elastic shape analysis framework, we use separate tangent spaces defined at the mean of two groups and use an eigen basis estimated from the covariance to reduce the dimension. This tangent CCA approach using a low dimensional representation has the advantage of easier computation and interpretation, compared to other functional CCA approaches. These tools are especially useful in discovering associations between PDFs of intensities for quantifying tumor heterogeneity and tumor shapes, in a medical imaging application. These associations then help characterize the disease via non-invasive imaging.
Sebastian Kurtek (Advisor)
Steven MacEachern (Advisor)
Yoonkyung Lee (Committee Member)
Yunzhang Zhu (Committee Member)
Statistics

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Citations

  • Cho, M. H. (2020). Aggregated Pairwise Classification and Other Applicationsfor Elastic Statistical Shapes [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1595426726818697

    APA Style (7th edition)

  • Cho, Min Ho. Aggregated Pairwise Classification and Other Applicationsfor Elastic Statistical Shapes. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1595426726818697.

    MLA Style (8th edition)

  • Cho, Min Ho. "Aggregated Pairwise Classification and Other Applicationsfor Elastic Statistical Shapes." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1595426726818697

    Chicago Manual of Style (17th edition)

osu1595426726818697
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This open access ETD is published by The Ohio State University and OhioLINK.