Math Modeling Seminar - Statistical Frameworks for Mapping 3D Shape Variation

Statistical Frameworks for Mapping 3D Shape Variation onto Genotypic and Phenotypic Variation

Dr. Lorin Crawford
RGSS Assistant Professor of Biostatistics
Center for Computational Molecular Biology
Center for Statistical Sciences
Brown University

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Abstract:
The recent curation of large-scale databases with 3D surface scans of shapes has motivated the development of tools that better detect global-patterns in morphological variation. Studies which focus on identifying differences between shapes have been limited to simple pairwise comparisons and rely on pre-specified landmarks (that are often known). In this talk, we present SINATRA: a statistical pipeline for analyzing collections of shapes without requiring any correspondences. Our method takes in two classes of shapes and highlights the physical features that best describe the variation between them.
The SINATRA pipeline implements four key steps. First, SINATRA summarizes the geometry of 3D shapes (represented as triangular meshes) by a collection of vectors (or curves) that encode changes in their topology. Second, a nonlinear Gaussian process model, with the topological summaries as input, classifies the shapes. Third, an effect size analog and corresponding association metric is computed for each topological feature used in the classification model. These quantities provide evidence that a given topological feature is associated with a particular class. Fourth, the pipeline iteratively maps the topological features back onto the original shapes (in rank order according to their association measures) via a reconstruction algorithm. This highlights the physical (spatial) locations that best explain the variation between the two groups.
We use a rigorous simulation framework to assess our approach, which themselves are a novel contribution to 3D image analysis. Lastly, as a case study, we use SINATRA to analyze mandibular molars from four different suborders of primates and demonstrate its ability recover known morphometric variation across phylogenies.

Speaker Bio:
Dr. Lorin Crawford is the RGSS Assistant Professor of Biostatistics, and a core faculty member of the Center for Statistical Sciences and Center for Computational Molecular Biology at Brown University. His scientific research interests involve the development of novel and efficient computational methodologies to address complex problems in statistical genetics, cancer pharmacology, and radiomics (e.g., cancer imaging). Dr. Crawford has an extensive background in modeling massive data sets of high-throughput molecular information as it pertains to functional genomics and cellular-based biological processes. His most recent work has earned him a place on Forbes 30 Under 30 list, The Root 100 Most Influential African Americans list, and recognition as an Alfred P. Sloan Research Fellow. Before joining Brown, Dr. Crawford received his PhD from the Department of Statistical Science at Duke University and received his Bachelor of Science degree in Mathematics from Clark Atlanta University.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.