Image Processing Reference
In-Depth Information
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Fig. 10.16. The images illustrate the direction tensor, represented as I 20 ( left )and I 11 ( right ),
for Fig. 10.15 and computed by using theorem 10.4. The hue encodes the direction, whereas
the brightness represents the magnitudes of complex numbers
the right the reference orientation is encoded as a color image. Using the HSB color
space, the hue is modulated by 2 ϕ , whereas the brightness and the saturation are set
to the maximum at all points. The colored dots define curves along which the struc-
ture tensor measurements will be extracted and discussed in detail further below. The
color coded reference image has axes marked by angles separated in 5 as seen from
the center.
The images in Fig. 10.16 illustrate the structure tensor computed for all local
images. The color image on the left represents the complex-valued I 20 . The hue of
an image point is modulated by the arg( I 20 ) of its local neighborhood, whereas its
brightness is given by
. The saturation of all points is set to the maximum. The
computations are implemented according to theorem 10.4 wher e the deri vative Gaus-
|
I 20 |
sian filter had σ p =0 . 8 and the integrative Gaussian filter, σ p + σ w =2 . 5. The
hue of a point should be the same as the reference color given at the same point of the
color image in Fig. 10.16. Visually, it appears that the colors are in good conformity
with those of the reference image. The image on the right shows I 11 , which, being
nonnegative and real-valued, modulates the gray values. It is possible to verify that
the direction measurements adhere to the theoretical values, even in the noisy part of
the test image, where the signal-to-noise ratio, (SNR), was 2log 2 ( 0 . 3
2 . 4 dB.
The brightness of the points at the noisy part are lower in both images for two rea-
sons. First, the
)
≈−
0 . 7
should be weak or ideally zero because the unique direction is
disturbed, and second, because the linear derivation and integration operations have
effectively a bandpass character and the noise components are suppressed by the lin-
ear process. In the clean part of the signal, the brightness of the corresponding points
in the left and the right images is the same. We will discuss these conclusions more
quantitatively next.
|
I 20 |
 
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