Image Processing Reference
In-Depth Information
z
Dilation
R 2
z - f (x) = 0
Erosion
R 1
x
R w (weight function, structual element)
Fig. 3.1. An example of morphological operations for a 1D curve.
Applications of the morphological operation to practical image process
have increased during the last ten years. In the computer aided diagnosis of
medical 3D images, for example, this procedure is applied to the segmentation
of organs from chest and abdominal CT images and to the nodule detection
in lungs. Design of an appropriate weight or a structural element is the most
important factor in such practical applications.
Remark 3.7. Let us show an example of the morphological operation. An
input is a 1D image (waveform), and a mask is a circle of the radius r (Fig. 3.1).
In this example, R w = the region below the curve.
Figure erosion = the trace of the center of circles (weight) such that all the
circles stay below the curve.
Figure dilation = the trace of the center of circles (weight) such that the
entire circle stays above the curve or the circle touches the curve at least
at one point.
3.3 Difference filter
3.3.1 Significance
When we see an unknown image (a 2D image) for the first time, we focus on
the following areas:
(i) an area with subtle variation in density,
(ii) abrupt change in density values,
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