To segment an image using any fuzzy connectedness, FC, segmentation algorithm,
every object needs to be initiated with at least one seed. In this paper, we study
what kind of possible FC segmentations can be found in a seed-free environment.
In particular, we show that the possible absolute fuzzy connectedness segmentations
form a natural hierarchy
within the space of all image partitions. We will analyze these partitions in detail,
describing exactly the best possible
image segmentations having precisely *k* elements.
We will also describe an *efficient* algorithm for
finding all these segmentations
as well as the full image connectivity map, which
measures the connectivity
strength between every two image elements.

Work in progress. See MIPG Technical Report #336.

**Last modified April 9, 2007.**