After introducing several results relating to the modification of the
homotopy of gradient functions based on extrema in the base image and
building on earlier results in morphological scale-space, we introduce
a scale-space monotonicity theorem for regions of an image defined by
watersheds of a gradient function modified to retain only the local m
inima or maxima of its smoothed parent image, We then illustrate the t
heorem with an example of the scale-space extraction of texture featur
es from the nuclei of cervical cells.