For a start, standard segmentation algorithms are investi-
gated. Some examples are watershed [3], zero crossing [4],
and region growing [5], that deliver region tokens directly.
Region growing can be performed with multiple input images
so that the segmentation can be based on several bands
of satellite imagery. The performance is improved further
by combining these methods with pure edge detection
algorithms, e.g. Canny [5], Burns, Gradient Edge, etc. It
turns out that these methods are quite suitable for the
segmentation task and deliver good results.
A region growing algorithm with adaptive thresholding was
employed to obtain figure 2. Let £ be a fixed threshold value
indicating where a region stops to grow. Adaptive threshold-
ing modifies the threshold tadaptive dynamically according to
the mean m and standard deviation c of the region as it
is being grown. The modification equation is based on an
algorithm by Levine and Shaheen [6] and is given by:
tadaptive = t - (1 — min(0.8, 29 (1)
the adaptive threshold £5455:. Will never be larger
than the value £ but can be much smaller. This method
prevents "bleeding" across slow image gradients (see [6],[2]).
Ultimately, "pure" spectral signatures of the region tokens
have to be calculated. Region tokens consist of boundary
pixels and interior pixels. Interior pixels provide pure inten-
sity values for the acquisation of the signatures, whereas
boundary pixels (4- or 8-adjacent to pixels outside the region
token) are most likely mixed pixels, which falsify the spectral
signatures. The problem of mixed pixels is a severe one if
the average size of region tokens is not much larger than
the pixel size, thus, having only few interior pixels with pure
signatures. In this case, there will be a very high percentage
of mixed pixels. lt is therefore necessary to apply spatial
subpixel analysis.
The mean pixel value of regions is determined from the in-
terior pixels. In case of regions with few interior pixels, the
boundary pixels are used to compute the mean pixel value.
Additionally, a reliability index r for each region is made avail-
able.
APvre
T= Amized? (2)
where AP“"° is the area of pure pixels and A”*°* the area of
mixed pixels. Before spatial subpixel analysis is applied, r is
equivalent to the ratio between interior pixels and boundary
pixels. r is modified dynamically as mixed pixels are subpixel
analysed.
3 SPATIAL SUBPIXEL ANALYSIS
There are several approaches to deal with the mixed pixel
problem (see [7],[8],[9],[10],[11]). In this contribution,
“edgels” are applied to obtain spatial subpixel information
for digital images of scenes built up of homogenous regions
delimited by edgel chains.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Edgels are tokens defined by the following features:
e point location at subpixel accuracy,
e gradient magnitude (Several kernels, e.g. Roberts,
Prewitt, Sobel with dimension 3 x 3 or 5 x 5 are pos-
sible for computing the gradient.),
e gradient angle, indicating the direction of the gradient.
Edgel detection is based on the following criteria:
e high gradient magnitude, above a specified threshold,
e locally maximal gradient magnitude in the gradient di-
rection.
Edge detection is performed at each pixel. If an edgel is found
(i.e. the gradient magnitude is above a specified threshold),
the location is determined to subpixel accuracy along the
gradient direction.
Edgels adjacent according to some metric are then linked
to "edgel chains" (i. e. open polygons, see also figure 3).
Parameters such as the angle between an edgel gradient and
the link to an adjacent edgel, the angle between gradients,
as well as the link length of adjacent edgels are used in the
chaining algorithm.
Once the edgel chains are determined, every triple of con-
secutive edgels in a chain (the edgels i — 1,4,i + 1 for
i— 2,---n —1, n is the number of edgels in a chain) are
used to produce a least mean square error line segment fitted
to these edgle triples. The error distance is measured by the
normal distance from the edgels to the line. The endpoints
of the line fit are the maximum extents of the projections of
the edgels onto the line. The midpoint of these line segments
is used to obtain the coordinates of a pixel. If this pixel is
a boundary pixel of a region, it is subject to spatial subpixel
analysis (see figure 4).
The mixed pixel value
p= fıpı + f2p2 (3)
is considered a linear combination of different signatures of
two adjacent regions as separated by the edgel chain (or line
segment). f; and f» are the area portions of the mixed pixel.
The line segment as described above delivers the parameters
to determine fi, f». lt is reasonable to use mean pixel values,
m1, ma, of the two regions adjacent to the mixed pixel for
computing the values p;. If the values m; have high reliability,
i.e. the reliability index r is high, the mean intensity values
cannot be corrected. If both m; are of low reliability then the
mixed pixel is marked for further processing. However, if one
mi is of low reliability, then a correction of the mean intensity
values can be achieved. Let m the mean pixel value of the
region with higher reliability. p; is then replaced by mi. po
is calculated according to the above mentioned relationship
3:
pa = ccm (4)
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