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A Discrete Version of Green's Theorem

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1 Author(s)
Tang, Gregory Y. ; MEMBER, IEEE, Department of Electrical Engineering, State University of New York at Buffalo, Buffalo, NY; Department of Information Engineering, National Taiwan University, Taipei, Taiwan, Republic of China.

We formulate a discrete version of Green's theorem such that a summation of a two-dimensional function over a discrete region can be evaluated by the use of a summation over its discrete boundary. In many cases, the discrete Green theorem can result in computational gain. Applications of the discrete Green theorem to several typical image processing problems are demonstrated. We also apply it to analyze shapes of particle aggregates of Fe2O3. Experimental results of the shape study are presented.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-4 ,  Issue: 3 )