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Title: Large deformation diffeomorphic metric curve mapping
Authors: Glaunès, J.
Qiu, A. 
Miller, M.I.
Younes, L.
Keywords: Curve matching
Large deformation
Vector-valued measure
Issue Date: Dec-2008
Citation: Glaunès, J., Qiu, A., Miller, M.I., Younes, L. (2008-12). Large deformation diffeomorphic metric curve mapping. International Journal of Computer Vision 80 (3) : 317-336. ScholarBank@NUS Repository.
Abstract: We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space ℝd . Curves are first represented as vector-valued measures, which incorporate both location and the first order geometric structure of the curves. Then, a Hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves. We describe a discretized version of this, in which discrete sequences of points along the curve are represented by vector-valued functionals. This gives a convenient and practical way to define a matching functional for curves. We derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in ℝ2 and ℝ3. Behaviors of the curve mapping are discussed using 2D curves. The applications to shape classification is shown and experiments with 3D curves extracted from brain cortical surfaces are presented. © 2008 Springer Science+Business Media, LLC.
Source Title: International Journal of Computer Vision
ISSN: 09205691
DOI: 10.1007/s11263-008-0141-9
Appears in Collections:Staff Publications

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