International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
X, R, G, B,
X, R. G, 8 (24)
X= ; =[x,,x,,x,]= : h :
M s MM
X. 2,6, B,
In order to define the fundamental colour morphological
operators, new infimum and supremum should be defined first.
Using the vector ordering approach described in the previous
section, we define the infimum operator ^ in X as follows:
AX2 AX, X,A Xy] 7 mn(X, X, A X4) Q5)
In a similar way, we define the supremum operator V in X as
. follows:
vXz v(X, X,,A Xy) 2 mx(X,, X,,A X,j (26)
The application of these two operators to a particular window
W results in only one output vector that is included in the input
window W. Consequently, it is obvious that the proposed
operators are colour preserving since no new colour (vector),
which is not present in the window, is generated.
4.20 Definitions of Colour Morphological Operators
As stated in Section 4.1, we model a colour image as a vector
field. For the definition of morphological operators in the vector
field we need to point out the structuring element G. In this
paper, we define a small single colour image as the structuring
element for our colour morphological operators in which its size
is the MXN window W related to a pixel p and its colour is
either the colour of the pixel p or another colour of interest
given by the user. We use the colour as the referent vector to
calculate the variance sj.
Definition 4 Let C is a colour image, W is a window
corresponding to pixel p having data matrix X, and G is a
structuring element with the same size as W and the same
vers eG ; G ;
colour as p. The colour dilation o , erosion. €c , closing
zc , and opening Oc of C by G is the colour image given by:
óS(C)z (vX,Npeci (27)
(Cy AX. Vpec (28)
Xé(C) = e€ (0€ (C) (29)
oC (C) s o6 (eO (CY (30)
From the Definition 4, the colour dilation of colour image C by
the structuring element G keeps the steps as follows:
a. First, we construct a window J/ at pixel p consisting of the
neighbourhood of p as the structuring element.
b. Then, we order all observations in data matrix X
corresponding to W using the vector ordering approach.
c. Step (b) results in a rank order of colours in W. we find the
infimum (supremum) in these colours.
d. The colour of the dilation (erosion) at the pixel p is the
infimum chosen in above step.
5. COLOUR EDGE DETECTION
Edge detection is one of the basic techniques for many image
processing tasks, such as image segmentation, image
compression, feature extraction and so on. Various edge
detection techniques have been proposed (Pratt, 1991).
Generally, edges are defined as a discontinuity in some image
attributes, for example, the brightness for grayscale images. For
colour images, the situation is different. Several definitions of
colour edges have been proposed (Pratt, 1991). First, a colour
edge can be said to exist if and only if the luminance field
contains an edge. This definition ignores discontinuities in hue
and saturation that occur in regions of constant luminance. The
second way to define a colour edge is to check if an edge exists
in any of its constituent‘ primary components. The third
definition is based on forming the sum of gradients of the
primary values or some linear or nonlinear colour component.
A colour edge is said to exist if the gradient exceeds a
threshold. Grayscale erosion and dilation have been
successfully applied to extract the edges in grayscale imagery
based on the subtraction of images (Dougherty, 1991; Lee et al.,
1987). Unfortunately, these algorithms cannot be applied
directly to colour imagery by means of colour erosion and
dilation, since it does not make sense to subtract arithmetically
two colours in RGB colour space.
In this section, a new algorithm to detect colour edge is
introduced by using proposed colour morphological operators.
According to the definitions of colour edges given by Pratt
(1991), we define a loose colour edge is defined in the context
of vector field. Colour edges are defined as any significant
discontinuity in the vector field representing the colour image.
Based on these definitions, we further define a basic colour
edge detector as follows.
Definition 5 Let C is a colour image, the W is a window
corresponding to pixel p having data matrix X, and G is a
structuring element with the same size as W and the same
SG s n
colour as p. The colour edge detector EÖC of is the grayscale
image given by:
&ó£ (C) » lac € - ££(C) (31)
where
| represents an appropriate vector norm. It is worth
making some remarks about the meaning of this colour edge
detector, which point out that, in a uniform area of the image C,
where all colours will be close to each other; the output of the
detector will be small. However, its response on an edge will be
large since dilation of image C will be created from the colours
on the one side of the edge, which have ‘large’ vectors while
erosion of image C will be created from another side with
‘small’ vectors.
6. EXPERIMENTAL RESULTS
To test the feasibility and the performance of the developed
methodology, experiments have been conducted using real data
(1) pansharpened 61cm resolution QuickBird satellite imagery,
(2) pansharpened Im resolution Ikonos satellite imagery, and
(3) cm-level colour aerial images have been conducted. Three
of the tested images are shown in Fig. 3. Each colour image has
24 bits per pixel and 150x150 pixels in size.
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