Due to noise and blur, regions in real images are seldom homogeneous in grey level and sharp along their borders. Preprocessing the image with an enhancement filter that reduces these effects will yield better segmentation results.
Figure 2: Symmetric Pairs of Pixels
The SNF filter compares each pixel to its 8-connected neighbors. (Note
that the 1-pixel image boundary is ignored in our implementation.) The
neighbors are inspected in symmetric pairs around the center, i.e.
N 
S, W 
E, NW 
SE, and NE 
SW; see
Figure 2 for diagram of a 
neighborhood
centered around a pixel, with the symmetric pairs colored the same.
Essentially, the one pixel in each pair closest to the center in grey
level is selected, but only if its intensity is within 
of
the center pixel, otherwise, the center pixel's value is used. If the
center pixel is equidistant from the pair, or is a local minima or
maxima, its value is selected instead. The collection of four selected
pixels are averaged together, and finally, the center pixel is
replaced by the mean of this average and the center pixel's current
grey level. This latter average is similar to that of a damped
gradient descent which yields a faster convergence.
The first phase of segmentation is a combination of three iterative
SNF filters. The first step runs for a small number of iterations
(e.g. four) with 
and is used to preserve edges. We
define 
to be the median of the standard deviations of all 
neighborhoods centered around each non-border pixel in the
image. See [5] for a parallel median algorithm. To flatten the
interior of regions, SNF is iterated with 
,
where 
is typically set to 
for this application. The
stopping criteria for this iterative filter occurs when the percentage
of ``fixed'' pixels reaches 100.0 %, this percentage has not changed
for three iterations, or when we reach 200 iterations, whichever comes
first. Finally, we sharpen the borders of regions with SNF using
, again stopping the iterative process when the pixels
have fixed, as defined above. The resulting image has near-homogeneous
regions with sharp transitions between bordering regions.