Locally adaptable mathematical morphology

We investigate how common binary mathematical morphology op-erators can be adapted so that the size of the structuring element (SE) can vary across the image. We show that when the SE are balls of a metric, locally adaptable erosion and dilation can be ef-ficiently implemented as a variant of distance transformation algo-rithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation. 1