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| A Proof of New Formula for 3D Images Euler Number |
| LIN Xiao-Zhu1,JI Jun-Wei1,HUANG Step-Hen2,YANG Jian-Hua2 |
1. School of Information Engineering,Beijing Institute of Petrochemical Technology,Beijing 102617
2.Department of Computer Science,University of Houston,Houston,TX77005,USA |
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Abstract The Euler number for digital images is one of the most important features of the digital topology parameter. The method for calculating the Euler number has been constantly explored to understand the nature of the Euler number for three-dimensional images better and to conveniently calculate the 3D image Euler number. Through the in-depth study of the connectivity of three-dimensional images, a new formula to locally calculate the Euler number for 3D images is proposed based on the two basic definitions of a 3D foreground run and a 3D neighbor number. Equivalence between the new formula and the global formula is proved by the induction method. A new way to locally calculate the Euler number for 3D images is provided which is unlike the description of the previous pixels and connectivity.
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Received: 10 October 2008
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2010, Vol. 23 
