Abstract: A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field. A trajectory within the tubular structure is computed based on the centerline.

Abstract: A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field. A trajectory within the tubular structure is computed based on the centerline.

Abstract: A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field.

Abstract: A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field.

Abstract: A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field.

Abstract: A computer implemented method for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure. A gradient field of a distance transformation is computed for the edge-detected dataset. A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field.

Abstract: A computer implemented method (350) for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure (360). A gradient field of a distance transformation is computed for the edge-detected dataset (380). A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field (390).

Abstract: A computer implemented method (350) for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure (360). a gradient field of a distance transformation is computed for the edge-detected dataset (380). a voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field (390).

Abstract: In an algorithm for deriving radiation images, where view independent radiation calculations are precomputed so that they do not need to be repeated for every view of the same environment. To find the form factors for radiosity techniques, a hemi-cube is constructed around the surface with grid cells defined for all faces on the hemi-cube. All other surfaces in the environment are projected onto the hemi-cube to facilitate the form factor calculations. A novel ray-tracing technique is disclosed where a light buffer in the form of a cube is constructed around each radiation source and grid cells are defined on the faces of the cube. Surfaces in the environment are projected onto the cube and the depths from the source are stored for each grid cell to facilitate shadow testing. Light reflected off of the viewed surface from another surface may be modeled by determining mirror positions of the viewer and the image plane.