Binary morphology: working in the sampled domain

A description is given of the relationship between morphologically filtering and then sampling vs. sampling, and then morphologically filtering in the sampled domain. The authors also describe the relationship between morphologically filtering vs. sampling, morphologically filtering in the sampled domain, and then reconstructing. Unlike the standard communication sampling theory where for appropriately low-pass filtered images there is commutivity between sampling and filtering, this is not the case for appropriately morphologically simplified images. The relationship which does exist shows that the commutivity holds to within one sampling interval distance in the unsampled domain and to within two sampling intervals in the sampled domain