Event Details - Mathematics and Statistics Colloquium

The Department of Mathematics and Statistics would like to invite faculty and students to a special colloquium talk on Friday, February 24th at 3pm. The speaker is Dr. Chalani Prematilake from Texas Tech University and her talk is titled Comparing the Performances of Different Parameterizations used for Dimension Reduction in Approximating Shapes of Planar Contours. Please see below for more information about the colloquium talk.

Mathematics and Statistics Colloquium

SIUE features: Dr. Chalani Prematilake - Department of Mathematics and Statistics, Texas Tech University

Comparing the Performances of Different Parameterizations used for Dimension Reduction in Approximating Shapes of Planar Contours

Abstract:

As a result of rapid advancements of technology, high dimensional data can be easily found almost everywhere. One type of such data is the shape of a contour, where a contour may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold. It can thus be studied using statistical shape analysis.

Practically speaking, each observed contour, while theoretically infinite dimensional, must be discretized for computations. As such, the coordinates for each contour are obtained at k sampling times, resulting in the contour being represented as a k-dimensional complex vector. While choosing large values of k will result in closer approximations to the original contour, this will also result in higher computational costs in the subsequent analysis. The goal of this study is to determine reasonable values for k so as to keep the computational cost low, while maintaining accuracy. To do this, we consider three parameterizations for selecting sample points and determine lower bounds for k for obtaining a desired level of approximation error using two different criteria.

Because this process is computationally inefficient to perform on a large scale, we then develop models for predicting the lower bounds for k based on simple characteristics of the contours. Current procedure develops simple linear regression models to predict the lower bounds for k using three characteristics of the original contour, length of the contour, total absolute curvature, and the number of times the curvature changes its sign. Study discusses procedures for model validation as well as the effectiveness added to the models by smoothing.

Key Words: Statistical shape analysis, Statistics in manifolds, planar contours