Extrinsic Analysis on Manifolds is Computationally Faster than Intrinsic Analysis, with Application to Quality Control by Machine Vision

Rabi N Bhattacharya, Leif Ellingson, Xiuwen Liu, Vic Patrangenaru, Michael Crane

Research output: Contribution to journalArticle

Abstract

In our technological era, non-Euclidean data abound, especially because of advances in digital imaging. Patrangenaru (‘Asymptotic statistics on manifolds’, PhD Dissertation, 1998) introduced extrinsic and intrinsic means on manifolds, as location parameters for non-Euclidean data. A large sample nonparametric theory of inference on manifolds was developed by Bhattacharya and Patrangenaru (J. Stat. Plann. Inferr., 108, 23–35, 2002; Ann. Statist., 31, 1–29, 2003; Ann. Statist., 33, 1211–1245, 2005). A flurry of papers in computer vision, statistical learning, pattern recognition, medical imaging, and other computational intensive applied areas using these concepts followed. While pursuing such location parameters in various instances of data analysis on manifolds, scientists are using intrinsic means, almost without exception. In this paper, we point out that there is no unique intrinsic analysis because the latter depends on the choice of the Riemannian metric on the manifold, and in d
Original languageEnglish
Pages (from-to)14 pages
JournalApplied Stochastic Models in Business and Industry
DOIs
StatePublished - Jul 25 2011

Fingerprint Dive into the research topics of 'Extrinsic Analysis on Manifolds is Computationally Faster than Intrinsic Analysis, with Application to Quality Control by Machine Vision'. Together they form a unique fingerprint.

  • Cite this