Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/66930
Title: Approximations of the diffeomorphic metric and their applications in shape learning.
Authors: Yang, X. 
Goh, A.
Qiu, A.
Issue Date: 2011
Source: Yang, X.,Goh, A.,Qiu, A. (2011). Approximations of the diffeomorphic metric and their applications in shape learning.. Information processing in medical imaging : proceedings of the ... conference 22 : 257-270. ScholarBank@NUS Repository.
Abstract: In neuroimaging studies based on anatomical shapes, it is well-known that the dimensionality of the shape information is much higher than the number of subjects available. A major challenge in shape analysis is to develop a dimensionality reduction approach that is able to efficiently characterize anatomical variations in a low-dimensional space. For this, there is a need to characterize shape variations among individuals for N given subjects. Therefore, one would need to calculate (2(N)) mappings between any two shapes and obtain their distance matrix. In this paper, we propose a method that reduces the computational burden to N mappings. This is made possible by making use of the first- and second-order approximations of the metric distance between two brain structural shapes in a diffeomorphic metric space. We directly derive these approximations based on the so-called conservation law of momentum, i.e., the diffeomorphic transformation acting on anatomical shapes along the geodesic is completely determined by its velocity at the origin of a fixed template. This allows for estimating morphological variation of two shapes through the first- and second-order approximations of the initial velocity in the tangent space of the diffeomorphisms at the template. We also introduce an alternative representation of these approximations through the initial momentum, i.e., a linear transformation of the initial velocity, and provide a simple computational algorithm for the matrix of the diffeomorphic metric. We employ this algorithm to compute the distance matrix of hippocampal shapes among an aging population used in a dimensionality reduction analysis, namely, ISOMAP. Our results demonstrate that the first- and second-order approximations are sufficient to characterize shape variations when compared to the diffeomorphic metric constructed through (2(N)) mappings in ISOMAP analysis.
Source Title: Information processing in medical imaging : proceedings of the ... conference
URI: http://scholarbank.nus.edu.sg/handle/10635/66930
ISSN: 10112499
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

31
checked on Dec 7, 2017

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.