title: Computing Diffeomorphic Paths for Large Motion Interpolation.
abstract: In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphismsDiff(Ω) is difficult, and it can be attributed mainly to the infinite dimensionality ofDiff(Ω). Our proposed framework, to some degree, bypasses this difficulty using the quotient map ofDiff(Ω) to the quotient spaceDiff(M)/Diff(M)μobtained by quotienting out the subgroup of volume-preserving diffeomorphismsDiff(M)μ. This quotient space was recently identified as the unit sphere in a Hilbert space in mathematics literature, a space with well-known geometric properties. Our framework leverages this recent result by computing the diffeomorphic path in two stages. First, we project the given diffeomorphism pair onto this sphere and then compute the geodesic path between these projected points. Second, we lift the geodesic on the sphere back to the space of diffeomerphisms, by solving a quadratic programming problem with bilinear constraints using the augmented Lagrangian technique with penalty terms. In this way, we can estimate the path of diffeomorphisms, first, staying in the space of diffeomorphisms, and second, preserving shapes/volumes in the deformed images along the path as much as possible. We have applied our framework to interpolate intermediate frames of frame-sub-sampled video sequences. In the reported experiments, our approach compares favorably with the popular Large Deformation Diffeomorphic Metric Mapping framework (LDDMM).
authors.affiliation: Department of Electrical and Computer Engineering, University of Florida.
authors.forename: Dohyung
authors.initials: D
authors.lastname: Seo
authors.affiliation: Department of Computer and Information Sciences and Engineering, University of Florida.
authors.forename: Ho
authors.initials: H
authors.lastname: Jeffrey
authors.affiliation: Department of Computer and Information Sciences and Engineering, University of Florida.
authors.forename: Baba C
authors.initials: BC
authors.lastname: Vemuri