title: Shape-aware surface reconstruction from sparse 3D point-clouds.
abstract: The reconstruction of an object's shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. However, medical applications often provide contextual information about the 3D point data that allow to incorporate prior knowledge about the shape that is to be reconstructed. To this end, we propose the use of a statistical shape model (SSM) as a prior for surface reconstruction. The SSM is represented by a point distribution model (PDM), which is associated with a surface mesh. Using the shape distribution that is modelled by the PDM, we formulate the problem of surface reconstruction from a probabilistic perspective based on a Gaussian Mixture Model (GMM). In order to do so, the given points are interpreted as samples of the GMM. By using mixture components with anisotropic covariances that are "oriented" according to the surface normals at the PDM points, a surface-based fitting is accomplished. Estimating the parameters of the GMM in a maximum a posteriori manner yields the reconstruction of the surface from the given data points. We compare our method to the extensively used Iterative Closest Points method on several different anatomical datasets/SSMs (brain, femur, tibia, hip, liver) and demonstrate superior accuracy and robustness on sparse data.
authors.affiliation: Centre Hospitalier de Luxembourg, Luxembourg, Luxembourg; Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg. Electronic address: f.bernardpi@gmail.com.
authors.forename: Florian
authors.initials: F
authors.lastname: Bernard
authors.affiliation: Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg.
authors.forename: Luis
authors.initials: L
authors.lastname: Salamanca
authors.affiliation: Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg.
authors.forename: Johan
authors.initials: J
authors.lastname: Thunberg
authors.affiliation: Zuse Institute Berlin (ZIB), Berlin, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Tack
authors.affiliation: Zuse Institute Berlin (ZIB), Berlin, Germany.
authors.forename: Dennis
authors.initials: D
authors.lastname: Jentsch
authors.affiliation: Zuse Institute Berlin (ZIB), Berlin, Germany; 1000shapes GmbH, Berlin, Germany.
authors.forename: Hans
authors.initials: H
authors.lastname: Lamecker
authors.affiliation: Zuse Institute Berlin (ZIB), Berlin, Germany; 1000shapes GmbH, Berlin, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Zachow
authors.affiliation: Centre Hospitalier de Luxembourg, Luxembourg, Luxembourg.
authors.forename: Frank
authors.initials: F
authors.lastname: Hertel
authors.affiliation: Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg.
authors.forename: Jorge
authors.initials: J
authors.lastname: Goncalves
authors.affiliation: Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, Luxembourg; Trier University of Applied Sciences, Trier, Germany.
authors.forename: Peter
authors.initials: P
authors.lastname: Gemmar
mesh_terms: D000465:Algorithms; D001921:Brain / Q000000981:diagnostic imaging; D005269:Femur / Q000000981:diagnostic imaging; D006615:Hip / Q000000981:diagnostic imaging; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008099:Liver / Q000000981:diagnostic imaging; D015233:Models, Statistical; D016011:Normal Distribution; D013977:Tibia / Q000000981:diagnostic imaging
keywords: Expected conditional maximisation; Gaussian mixture model; Point distribution model; Sparse shape reconstruction; Statistical shape model