TY - GEN
T1 - Intrinsic regression models for manifold-valued data
AU - Shi, Xiaoyan
AU - Styner, Martin
AU - Lieberman, Jeffrey
AU - Ibrahim, Joseph G.
AU - Lin, Weili
AU - Zhu, Hongtu
N1 - Funding Information:
This work was supported in part by NSF grants SES-06-43663 and BCS-08-26844 and NIH grants UL1-RR025747- 01, R01MH08663 and R21AG033387 to Dr. Zhu, NIH grants R01NS055754 and R01EB5-34816 to Dr. Lin, Lilly Research Laboratories, the UNC NDRC HD 03110, Eli Lilly grant F1D-MC-X252, and NIH Roadmap Grant U54 EB005149-01, NAMIC to Dr. Styner.
PY - 2009
Y1 - 2009
N2 - In medical imaging analysis and computer vision, there is a growing interest in analyzing various manifold-valued data including 3D rotations, planar shapes, oriented or directed directions, the Grassmann manifold, deformation field, symmetric positive definite (SPD) matrices and medial shape representations (m-rep) of subcortical structures. Particularly, the scientific interests of most population studies focus on establishing the associations between a set of covariates (e.g., diagnostic status, age, and gender) and manifold-valued data for characterizing brain structure and shape differences, thus requiring a regression modeling framework for manifold-valued data. The aim of this paper is to develop an intrinsic regression model for the analysis of manifold-valued data as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in Euclidean space. Because manifold-valued data do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between manifold-valued data and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of manifold data. We develop an estimation procedure to calculate an intrinsic least square estimator and establish its limiting distribution. We develop score statistics to test linear hypotheses on unknown parameters. We apply our methods to the detection of the difference in the morphological changes of the left and right hippocampi between schizophrenia patients and healthy controls using medial shape description.
AB - In medical imaging analysis and computer vision, there is a growing interest in analyzing various manifold-valued data including 3D rotations, planar shapes, oriented or directed directions, the Grassmann manifold, deformation field, symmetric positive definite (SPD) matrices and medial shape representations (m-rep) of subcortical structures. Particularly, the scientific interests of most population studies focus on establishing the associations between a set of covariates (e.g., diagnostic status, age, and gender) and manifold-valued data for characterizing brain structure and shape differences, thus requiring a regression modeling framework for manifold-valued data. The aim of this paper is to develop an intrinsic regression model for the analysis of manifold-valued data as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in Euclidean space. Because manifold-valued data do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between manifold-valued data and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of manifold data. We develop an estimation procedure to calculate an intrinsic least square estimator and establish its limiting distribution. We develop score statistics to test linear hypotheses on unknown parameters. We apply our methods to the detection of the difference in the morphological changes of the left and right hippocampi between schizophrenia patients and healthy controls using medial shape description.
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U2 - 10.1007/978-3-642-04271-3_24
DO - 10.1007/978-3-642-04271-3_24
M3 - Conference contribution
C2 - 20426112
AN - SCOPUS:84883846347
SN - 3642042708
SN - 9783642042706
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 192
EP - 199
BT - Medical Image Computing and Computer-Assisted Intervention - MICCAI2009 - 12th International Conference, Proceedings
T2 - 12th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2009
Y2 - 20 September 2009 through 24 September 2009
ER -