||Binary mathematical morphology can be computed by thresholding a distance transform, provided that the distance transform is a metric. The structuring element (SE) is defined by the shape of the disc as well as the threshold. If the distance transform varies with the spatial coordinates of the image, so will the shape and size of the SE and we get spatially-variant morphology.
In a paper published at ICPR 2008 we proved that the polar distance transform is a metric and thus can be used in morphology. I will show some applications and results from this.
Towards the end of the seminar there will be a discussion on other possible distance transforms to use and other possible applications.