Recursive erosion, dilation, opening, and closing transforms

A new group of recursive morphological transforms on the discrete space Z(2) are discussed. The set of transforms include the recursive erosion transform (RET), the recursive dilation transform (RDT), the recursive opening transform (ROT), and the recursive closing transform (RCT), The transforms are able to compute in constant time per pixel erosions, dilations, openings, and closings with all sized structuring elements simultaneously. They offer a solution to some vision tasks that need to perform a morphological operation but where the size of the structuring element has to be determined after a morphological examination of the content of the image. The computational complexities of the transforms show that the recursive erosion and dilation transform can be done in N+2 operations per pixel, where N is the number of pixels in the base structuring element. The recursive opening and closing transform can be done in 14N operations per pixel based on experimental results.