Shape Analysis in the Presence of Measurement Error

• Activity Number: 605
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jiejun Du*+ and Ian L. Dryden and Xianzheng Huang
• Companies: University of South Carolina and University of South Carolina and University of South Carolina
• Keywords: Measurement Error ; Procrustes Matching ; Complex normal ; Quaternions

Abstract

In statistical shape analysis, the available landmark data are often prone to measurement error. This source of error is conventionally ignored when we calculate a non- Euclidean distance between two shapes or match one object to another. In this study, we consider measurement error models for two or three dimensional shape data.

For two dimensional data, the Procrustes matching can be formulated with a complex linear regression model, where the errors follow a complex normal distribution. For three dimensional data the matching problem can be expressed using quaternions, and hence the quaternion normal can be used.

First we show that the naive ordinary least squares estimator is biased when the measurement error is ignored. Then we consider structural measurement error models for shape data and derive improved estimators for the parameters in the model. The methodology is illustrated with an application in forensic face identification. A large database of over 3000 faces in three dimensions is available, and landmarks have been placed on each face by different observers. We quantify and model the measurement error in the study, and investigate the practical implications.