In the current vast image segmentation literature, there seems to be considerable redundancy among algorithms,
while there is a serious lack
of methods that would allow their theoretical comparison to establish their similarity, equivalence, or distinctness.
In this paper, we make an attempt to fill this gap.
To accomplish this goal, we argue that:
(1) every digital segmentation algorithm *A* should have a
well defined continuous counterpart *M _{A}*, referred to as its model,
which constitutes an asymptotic of

The main goal of this article is to
explore a line of investigation for
formally pairing the digital segmentation algorithms
with their asymptotic models, justifying such relations with mathematical proofs,
and using the results to compare the segmentation algorithms in this general theoretical framework.
As a first step towards this general goal, we *prove* here that the gradient based thresholding
model *M _{gr}* is the asymptotic for the fuzzy connectedness
Udupa and Samarasekera segmentation algorithm used with gradient based affinity

**SPIE Conference Proc. version.**

MIPG Technical Report
**# 335 version.**

**Last modified March 15, 2011.**