title: FOCUSR: feature oriented correspondence using spectral regularization--a method for precise surface matching.
abstract: Existing methods for surface matching are limited by the tradeoff between precision and computational efficiency. Here, we present an improved algorithm for dense vertex-to-vertex correspondence that uses direct matching of features defined on a surface and improves it by using spectral correspondence as a regularization. This algorithm has the speed of both feature matching and spectral matching while exhibiting greatly improved precision (distance errors of 1.4 percent). The method, FOCUSR, incorporates implicitly such additional features to calculate the correspondence and relies on the smoothness of the lowest-frequency harmonics of a graph Laplacian to spatially regularize the features. In its simplest form, FOCUSR is an improved spectral correspondence method that nonrigidly deforms spectral embeddings. We provide here a full realization of spectral correspondence where virtually any feature can be used as an additional information using weights on graph edges, but also on graph nodes and as extra embedded coordinates. As an example, the full power of FOCUSR is demonstrated in a real-case scenario with the challenging task of brain surface matching across several individuals. Our results show that combining features and regularizing them in a spectral embedding greatly improves the matching precision (to a submillimeter level) while performing at much greater speed than existing methods.
authors.affiliation: Centre for Intelligent Machines, McGill University, 4239 Rue St-Denis, Montreal, QC H2J2K9, Canada.
authors.forename: Herve
authors.initials: H
authors.lastname: Lombaert
authors.forename: Leo
authors.initials: L
authors.lastname: Grady
authors.forename: Jonathan R
authors.initials: JR
authors.lastname: Polimeni
authors.forename: Farida
authors.initials: F
authors.lastname: Cheriet
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000033:anatomy & histology; D016208:Databases, Factual; D006736:Horses; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D012984:Software; D013499:Surface Properties