title: A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system.
abstract: OBJECTIVE
  To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system.
  
  
  METHODS
  The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method.
  
  
  RESULTS
  On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions.
  
  
  CONCLUSIONS
  The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications.
authors.affiliation: Department of Bioengineering, University of California, Los Angeles, Los Angeles, California 90095.
authors.forename: Wenyang
authors.initials: W
authors.lastname: Liu
authors.affiliation: Department of Radiation Oncology, University of Texas Southwestern, Dallas, Texas 75390.
authors.forename: Yam
authors.initials: Y
authors.lastname: Cheung
authors.affiliation: Department of Radiation Oncology, University of Texas Southwestern, Dallas, Texas, 75390 and Department of Radiation Oncology, University of Maryland, College Park, Maryland 20742.
authors.forename: Amit
authors.initials: A
authors.lastname: Sawant
authors.affiliation: Department of Bioengineering, University of California, Los Angeles, Los Angeles, California 90095 and Department of Radiation Oncology, University of California, Los Angeles, Los Angeles, California 90095.
authors.forename: Dan
authors.initials: D
authors.lastname: Ruan
mesh_terms: D000005:Abdomen / Q000000981:diagnostic imaging; D000465:Algorithms; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016014:Linear Models; D009038:Motion; D010780:Photogrammetry / Q000379:methods*; D061089:Radiotherapy, Image-Guided / Q000379:methods; D016683:Supine Position; D013909:Thorax / Q000000981:diagnostic imaging; D013997:Time Factors