TY - JOUR
T1 - Statistics on manifolds and landmarks based image analysis
T2 - A nonparametric theory with applications
AU - Bhattacharya, Rabi
AU - Patrangenaru, Vic
N1 - Funding Information:
Many thanks go to our colleagues of the SAMSI Working Group (2010–2011) on sampling from stratified spaces, especially to Steve Marron and the group co-leaders Ezra Miller and Stephan Huckemann, and to Xiuwen Liu and Leif Ellingson for related joint work. We are also grateful to Susan Holmes for giving us access to her talks on phylogenetic trees in the Working Group of Trees at SAMSI in Fall 2010. The authors gratefully acknowledge support from NSF grants DMS-0806011 , 1107053 and DMS-0805977 , 1106935 .
PY - 2014/2
Y1 - 2014/2
N2 - This paper provides an exposition of some recent developments in nonparametric inference on manifolds, along with a brief account of an emerging theory on data analysis on stratified spaces. Much of the theory is developed around the notion of Fréceht means with applications, for the most part, to landmark based shape spaces. A number of applications are illustrated with real data in such areas as paleomagnetism, morphometrics and medical diagnostics. Connections to scene recognition and machine vision are also explored.
AB - This paper provides an exposition of some recent developments in nonparametric inference on manifolds, along with a brief account of an emerging theory on data analysis on stratified spaces. Much of the theory is developed around the notion of Fréceht means with applications, for the most part, to landmark based shape spaces. A number of applications are illustrated with real data in such areas as paleomagnetism, morphometrics and medical diagnostics. Connections to scene recognition and machine vision are also explored.
KW - Fre'chet mean
KW - Nonparametric inference on manifolds Kendall's shape spaces
KW - Projective shape spaces
KW - Reflection similarity shape
KW - Stratified spaces
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U2 - 10.1016/j.jspi.2013.08.001
DO - 10.1016/j.jspi.2013.08.001
M3 - Article
AN - SCOPUS:84887606917
SN - 0378-3758
VL - 145
SP - 1
EP - 22
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -