Abstract: This paper reveals the essential connection between mathematical morphology and pulse coupled neural network （PCNN) which has the biological background.Granulometry is analyzed in detail as an example to show this essential connection and we come to the conclusion that the PCNN granulometry algorithm we proposed in this paper is entirely equal to the granulometry algorithm based on mathematical morphology with certain structuring elements.In the meantime,our research shows that the parallel pulse transmission characteristic of PCNN in image processing is equal to the erosion computation of mathematical morphology.Therefore,this paper bridges the gap between mathematical morphology and PCNN.