Abstract
In this paper we extended the 3D Skeletonization method based on Euler number count & cluster count to 4D. As the Euler sum in 4D is always 0, we solved this by embedding 4D objects in a 5D space to calculate the 5D Euler number. The 5D Euler number changes due to 3 events: 1D tunnels, 2D tunnels and 3D tunnels. As the latter does not occur in 4D objects, together with a foreground and a background cluster count, the number of equations is equal to the number of unknown variables, and a breakpoint change can be detected. However, this also indicates that making a skeleton in this way is limited to the 4th dimension.
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Jonker, P.P., Vermeij, O. (1996). On skeletonization in 4D images. In: Perner, P., Wang, P., Rosenfeld, A. (eds) Advances in Structural and Syntactical Pattern Recognition. SSPR 1996. Lecture Notes in Computer Science, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61577-6_9
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DOI: https://doi.org/10.1007/3-540-61577-6_9
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