Locally Adaptable Mathematical Morphology Using Distance Transformations

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels. We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be e±ciently implemented as a variant of distance trans- formation algorithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation.