Image Processing Reference
In-Depth Information
FIGURE 10.1: Rough approximation set
single value. The similar color sphere is the region in RGB color space such that all the
colors falling in that region can be classied as one color. The concept of histon aids in
visualization of the spatial correlation of similar color valued segments in the image.
For every intensity value on the base histogram, the number of pixels encapsulated in the
similar color sphere is evaluated and the count is then added to the value of the histogram at
that particular intensity value. This computation is carried out for all the intensity values
that lead to the formation of histon.
Consider a color imageI, of size M N, consisting of three primary components, redR,
greenG, and blueB. The histogram of the image for each of theR,G, andBcomponents
can be computed as follows:
M
X
N
X
h
i
(g) =
(I (m;n;i) g)
m=1
n=1
for 0 g L 1 and i = fR;G;Bg
(10.6)
where (:) is the Dirac impulse function andLis the total number of intensity levels in
each of the color components. The value of each bin is the number of image pixels having
intensityg.
Consider a P Q neighborhood around a pixel I (m;n) and let I (p;q) be a pixel in the
neighborhood. The Euclidean distance between I (m;n) and I (p;q) is given by
s
X
(I (m;n;i) I (p;q;i))
2
d (I (m;n) ;I (p;q)) =
(10.7)
i
2
R;G;B
and the total distance of all the pixels in the neighborhood and the pixel I (m;n) is then
given by
d
T
(m;n) =
X
p
2
P
X
d (I (m;n) ;I (p;q))
(10.8)
q
2
Q
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