Geometric morphometrics has traditionally relied on named anatomical landmarks for the statistical analysis of shape, but that is changing. With the now-widespread availability of 3D surface and volumetric scanning technology, performing shape analysis using high-resolution 3D data is a very active area of research. The method described by Pomidor, Makedonska, and Slice (2016), Generalized Procrustes Surface Analysis (GPSA), is one of many new techniques to analyze the shape of objects using 3D surfaces instead of landmarks, but is still based on a generalized Procrustes framework. Frequently, surface-based shape analysis methods are limited by the topological properties of the objects being analyzed. In geometric morphometric data sets, one is often working with data sets where connectivity and number of boundary components may differ, and objects may or may not be closed. By continuing development as a generalization of multivariate shape analysis, it is possible to largely circumvent this problem. While methodologically sound, GPSA has several areas that could be improved. It is predicated on a basic version of the Iterative Closest Point (ICP) algorithm (a family of methods for image superimposition) and a simple, but weak, set of correspondence rules. This reduces the accuracy of the estimated homology and methods that rely on this estimation. GPSA also operates only on the cloud of points making up a surface and, if one exists, does not make use of the accompanying surface mesh, which makes it highly dependent on the distribution of points in space. The inclusion of a mesh has become relatively standard practice and can be used to significantly improve the superimposition and analysis by allowing calculation of metrics that describe the local shape. The methods for prototype deformation and homologization, both of which are reliant on the estimated homology, only use the prototype-to-sample homology for stability reasons, biasing any resultant analysis towards the mean. Finally, the cost function used during superimposition (point-to-plane ICP) is not derived from the distance metric (Procrustes Surface Metric) used to analyze the objects after superimposition. The two are closely related, so the distance metric is reduced as the ICP cost function is minimized, but they are not identical and thus the distance metric is not optimally minimized by the superimposition. Here, the same generalized Procrustes algorithmic structure used in GPSA is kept, but with several modifications made to offer a more accurate, more efficient, more robust method for surface-based statistical shape analysis. These modifications begin with re-deriving the cost function from a reformulated shape distance metric. This metric is based on the area-weighted vertices of one surface mesh and corresponding points on another mesh, rather than pairs of points in two point clouds. Local shape descriptors and λ|μ smoothing are used to improve the approximated homology. Efficiency is addressed with a better memory management model and a different implementation of the space partitioning tree. A newly defined metric helps determine the quality of a match between two points. These match quality values are used in a resistant-fit extension based on Trimmed ICP to emulate the outlier-resistant behavior of the Generalized Resistant-Fit superimposition method for landmark-based morphometrics. The method is then evaluated using several data sets. Some of these are artificial data sets generated using the Stanford bunny, a surface scan commonly used for testing mesh-based algorithms, while the rest are real-world data sets. These include scans of phytoliths, which are relatively smooth, featureless silicate structures found in plants and a key tool for paleobotanists in reconstructing ancient environments. The scanned phyotliths come from Anomochloa, a genus of grass-like Brazilian plants. The scans of small primate skulls originally used to test GPSA are also used in order to provide a way to compare this improved method to both GPSA and to Generalized Procrustes Analysis (GPA), the standard tool for landmark-based morphometric analysis. No attempt is made to draw any conclusions regarding the biological interpretation of these results; rather, these tests are used to make inferences about the properties of the analysis method. Some of this evaluation is qualitative, such as appraising how sound the topology of the resulting meshes are or interpreting heat maps. The shape distances between the surfaces generated or superimposed during the analysis are used as the basis for quantitative comparison. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / 2019 / November 15, 2019. / Geometric morphometrics, Procrustes, Resistant-Fit, Shape analysis, Surface mesh / Includes bibliographical references. / Peter Beerli, Professor Directing Dissertation; Scott Steppan, University Representative; Nick Cogan, Committee Member; Anke Meyer-Baese, Committee Member; Sachin Shanbhag, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_752452 |
| Contributors | Pomidor, Benjamin J. (author), Beerli, Peter (professor directing dissertation), Steppan, Scott J. (university representative), Cogan, Nicholas G. (committee member), Meyer-Bäse, Anke (committee member), Shanbhag, Sachin (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Scientific Computing (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (117 pages), computer, application/pdf |
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