Mapped Hexahedral Meshing

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Home < Mapped Hexahedral Meshing


  • Develop a tool for mapped meshing that will warp a template mesh onto a surface for a new subject
  • Determine the limits that the warping algorithm will succeed and fail
  • Apply these techniques to a sample of data to determine the reliability of the algorithm with respect to mesh quality


  • Previous work on this project was performed at the 2007 AHM - Mapped Mesh 4 Block
  • Warped meshing framework has been developed using VTK and ITK using a finite element approach
    • VTK
      • Support the reading and writing of meshes (vtkUnstructuredGrid) and surfaces (vtkPolyData)
      • Distance measures between the deforming mesh and the subject surface
      • Initial registration - Iterative Closest Point or Procrustes
    • ITK
      • Finite element framework used to warped the template mesh onto the subject surface
  • Registration made hierarchical to speed up the registration process
    • Requires multiple template meshes to exist
    • This is readily supported using the interactive meshing tools by changing the average edge length
    • Subsequent meshes are initialized using a thin plate splines
  • Parameters allowed to vary at each level of the registration
    • Iterations
    • Young's Modulus
  • Convergence based on distance between the warped template and the subject surface
    • User specified convergence threshold in mm
    • Convergence can be based on average or maximum distance
  • Boundary conditions can be applied
    • Center of the mesh - Holds the eight nodes closest to the center of the mesh fixed
    • External - Applies boundary conditions to the mesh as they fall within a user specified tolerance of the subject surface
  • Initial testing done by warping a cube mesh onto a sphere
    • Evaluation:
      • Distance between warped mesh and subject surface
      • Mesh quality


Key Investigators:

  • Iowa: Nicole Grosland, Vincent Magnotta, Ritesh Bafna



Initial position of the cube template mesh and the sphere surface prior to registration using the itk::FEM mapped meshing algorithm
Mesh quality evaluation of the warped cube
a)Position of the template cube mesh and surface after ICP registration. b) Resulting warped cube after itk::FEM mapped meshing. c) Distance map between the warped cube and the sphere surface
Initial attempt to apply mapped meshing algorithm to the proximal phalanx