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.