SMI 2022 - Statistical methods for complex objects

Thursday, May 26, 2022 • 2:00–3:15 pm (CT) Light Hall, Room 202

Organizer: Zhengwu Zhang, University of North Carolina at Chapel Hill 

Chair: Jefffrey S. Morris, University of Pennsylvania


Object oriented data analysis of peatlands using satellite imagery

Ian L. Dryden, Florida International University

Emily Mitchell, University of Nottingham

Chris Fallaize, University of Nottingham

David Large, University of Nottingham

Roxane Andersen, Environmental Research Institute / University of the Highlands and Islands

Andrew Bradley, University of Nottingham

Object Oriented Data Analysis (OODA) provides a framework that involves asking questions and making choices on (i) the data objects, (ii) the conceptual object space in which the objects lie, (iii) the feature space for the practical data analysis, and (iv) the methods and models that are used for analysis. We apply OODA to the important problem of peatland monitoring. For the past 25 years global peatland restoration has been actively promoted in the hope that the degradation of peatlands can be reversed, halting carbon and water losses and bringing back key biodiversity attributes. We use OODA to develop methodology to monitor peatlands using InSAR satellite radar images which generate a surface motion time series at each location. The characteristics of the time series (e.g timing and amplitude of seasonal peaks and overall trend) are indicative of the condition. We use OODA to focus on the underlying continuous functional representation obtained from smoothing at different scales to extract the trend and seasonal variation, and then warping using the Fisher-Rao metric gives a measure of the peak timing differences. In order to take account of spatial smoothness in peatland we use Bayesian classification with a Potts model prior. The final output is a probabilistic map for each class of peatland (wet, dry, degraded), which has been demonstrated to correspond closely with peatland condition on the ground for an area of blanket bog in the Scottish Flow Country.


Statistical analysis of shape networks

Anuj Srivastava, Florida State University

Xiaoyang Guo, Florida State University

Aditi Basu Bal, Florida State University

Tom Needham, Florida State University

Imaging data from many applications leads to geometrical structures resembling complex pathways or curvilinear networks. We will call them "shape networks." A prominent example of a shape network is the Brain Arterial Network (BAN) in the human brain, which is a complex arrangement of individual arteries, branching patterns, and interconnectivities. Another example is a road network. Shapes or structures of these objects play an essential role in characterizing and understanding the functionality of larger systems. One would like tools for statistically analyzing shape networks—i.e., quantifying shape differences, summarizing shapes, comparing populations, and studying the effects of covariates on these shapes. This talk represents and statistically analyzes shape networks as "elastic shape graphs." Each elastic shape graph consists of nodes, or points in 3D, connected by some 3D curves, or edges, with arbitrary shapes. We develop a mathematical representation, a Riemannian metric, and other geometrical tools, such as computations of geodesics, means, covariances, and PCA, for helping analyze elastic shape graphs. We apply this framework to analyzing shapes of BANs taken from 92 subjects. Specifically, we generate shape summaries of BANs, perform shape PCA, and study the effects of age and gender on their shapes. We conclude that age has a clear, quantifiable effect on BAN shapes. Specifically, we find an increased variance in BAN shapes as age increases.


Significance in scale space for Hi-C analysis

J. S. Marron, University of North Carolina at Chapel Hill

Rui Liu, University of North Carolina at Chapel Hill

Hyejung Won, University of North Carolina at Chapel Hill

Zhengywu Zhang, University of North Carolina at Chapel Hill

Hi-C measurements are used to study chromosome structure and location within cell nuclei.  They are collected as very large, sparse and noisy images. "Significance in scale space" approaches are taken to address normalization issue and to assess the statistical significance of potential structures of interest in the images, as well as compare across images.

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