Medical Imaging Application: Nonparametric Statistics on 3D Size-and-Reflection Shape Manifold

• Activity Number: 649
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Daniel Osborne*+ and Victor Patrangenaru and Xiuwen Liu and Hillary W. Thompson
• Companies: Florida State University and Florida State University and Florida State University and Louisiana State University
• Keywords: Size-and-reflection shape ; statistical methods in medical imaging ; statistics on manifolds ; extrinsic means ; nonparametric bootstrap ; confidence region

Abstract

For medical imaging problems, nonparametric statistics on size-and-reflection shape space of k-ads in general position in 2D or 3D, is performed for purposes of diagnostics, discrimination, and/or identification. Here we focus on various steps of a larger collaborative project between researchers from Louisiana State and Florida State, on planning reconstructive neurosurgery for severe injuries of the skull. The pre-processing step consists of the extraction the boundary of the bone structure from the CT slices while the post-processing step consists of 3D reconstruction of the virtual skull from these bone extractions. Next, we present preliminary results for the Schoenberg sample mean size-and-reflection shape of groups of anatomic landmarks in general position in 3D for the human skull based on these virtual reconstructions. The bootstrap distribution of the Schoenberg's sample mean size-and-reflection shape for a selected group of k-ads ( landmarks and pseudo-landmarks ) was computed for 500 bootstrap resamples of the original 20 skulls represented by the 3 by k configurations, when k = 9, k = 17. Finally, we report a confidence region for the Schoenberg mean configuration.