A Discrete Version of Green's Theorem

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.