Page 283 - Digital Analysis of Remotely Sensed Imagery

Image Enhancement 245

point is located relative to the outer boundary. Intensity (also called
value) is the distance from the apex of the cone.
The transformation of pixel values in the RGB space into values
in the HIS space requires the establishment of a new reference sys-
tem. In this system hue is defined as proportional to the degree of
rotation about the achromatic point. Saturation is defined as the
length of a vector from the achromatic point to the point (R, G, B).
Intensity is the vector length from the origin. After the establishment
of this system, RGB can be translated to HIS using the following algo-
rithms (Carper et al., 1990):

⎧ 1
+
+
⎪ I = 3 ( B G R)
⎪
−
⎪ ⎡ RG⎤
⎨ H = tan −1 ⎢ ⎥ (6.26)
⎪ ⎣ 3 I ⎦
⎪
⎪ S = 05 3 I + ( R G) 2 2
−
2
.
⎩
Quantification of color through the RGB to HIS transformation
provides direct control over accurate portray and representation
of colors. This useful means of image enhancement is good at fus-
ing data from multiple sensors. For instance, images of different
resolutions (e.g., 1-m panchromatic band and 4-m multispectral
bands) can be fused through RGB to HIS transformation in a pro-
cedure known as “pan sharpening” to take advantage of the fine
spatial resolution imagery. It is also possible to differentially con-
trast enhance the saturation and intensity components before they
are transformed back to RGB.

6.7 Image Filtering in Frequency Domain
PCA, Kauth-Thomas, and RGB transformations share one common-
ality in that they are all carried out in the spatial domain. Apart from
this domain, image filtering can also be implemented in the frequency
domain using the common method of Fourier transformation that
operates on a single band (e.g., grayscale image). The fundamental
premise underlying this transformation is that each row of image f(x)
can be approximated by a series of sinusoidal waves, each having its
own amplitude, frequency, and coefficient (Fig. 6.26). The transformed
image can be described by the frequency of each wave form fitted to
the image and the proportion of information associated with each
frequency component (Mather, 2004). For satellite imagery, this
generalization needs to be extended in two ways. First, the image is
discrete instead of continuous, thus the transformation is termed
discrete Fourier transformation (DFT). A highly efficient version of
the DFT called fast Fourier transformation (FFT) has been developed