Although centerlines (aka ‘skeletons’ or ‘medial axes’) are among the most efficient ways to represent items in digital images, and obtaining these from 2D shapes is relatively straight forward, extracting centerlines from 3D objects has remained a challenge—particularly if they are not smooth or uniform. Therefore, we have developed a novel 3D centerline extraction method for discrete binary objects using a ‘divide and conquer’ approach, in which any 3D object is sliced into a series of 2D images (in the X, Y and Z directions), a geometric (Voronoi) algorithm is applied to each planar image to extract the 2D centerlines, and the information is recombined (using an intersection technique) to obtain the centerline of the original 3D object. Validation of this approach was performed using a ground truth benchmark, standard 3D database objects, and more complex anatomical structures (segmented from medical imaging data). The algorithm consistently performed well for objects of moderate complexity, but occasionally left discontinuities in the extracted 3D skeletons of the most complex objects. Therefore, in order to deal with such cases, an optional 3D interpolation step—based on Delaunay triangles and a spherical search to establish the nearest neighboring points in 3D space—was developed to allow continuous centerlines to be extracted from even the most complex anatomical structures tested. As a result, we anticipate that this approach could have wide-ranging applications, including data reduction for large microscopy and other 3D imaging datasets, automatic quantification of medical imaging data along anatomical structures, and others.
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This work was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant, Brain Canada Platform Support Grant, Winnipeg Health Sciences Centre Foundation Operating Grant, and University of Manitoba Startup Grant to CRF, as well as a Manitoba Graduate Fellowship to SY. We would also like to thank Drs. Melanie Martin, Jennifer Kornelsen and Sherif Sherif for helpful input and discussions regarding the project, and Dr. Nasir Uddin, Teresa Figley, Anwar Shatil and Kevin Solar for commenting on earlier versions of the manuscript.
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Younas, S., Figley, C.R. Development, Implementation and Validation of an Automatic Centerline Extraction Algorithm for Complex 3D Objects. J. Med. Biol. Eng. 39, 184–204 (2019). https://doi.org/10.1007/s40846-018-0402-1
- Medial axis
- 2D images
- 3D object
- Voronoi Diagram
- Delaunay triangle
- White matter