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A proof of image Euler Number formula

A proof of image Euler Number formula
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摘要 Euler Number is one of the most important characteristics in topology. In twodimension digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved in this paper. It is a new idea to locally compute Euler Number of 2D image. Euler Number is one of the most important characteristics in topology. In twodimension digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved in this paper. It is a new idea to locally compute Euler Number of 2D image.
作者 LIN Xiaozhu SHA Yun JI Junwei WANG Yanmin
机构地区 Information Engineering School
出处 《Science in China(Series F)》 2006年第3期364-371,共8页 中国科学（F辑英文版）
关键词 TOPOLOGY Euler Number binary image 4-connected 8-connected. topology, Euler Number, binary image, 4-connected, 8-connected.
分类号 TN911.73 [电子电信—通信与信息系统]
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参考文献15

  • 1[1]Sonka M,Hlavac V,Boyle R.Image Processing,Analysis,and Machine Vision.2nd ed.Beijing:PPTPH and Thomson Learning,2002.256-259
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  • 8[8]Kong T Y,Rosenfeld A.If we use 4-or 8-connectedness for both the objects and the background,the Euler characteristic is not locally computable.Pattern Recogn Lett,1990,11:231-232
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Science in China(Series F)
2006年 第3期

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