Image Processing Reference
In-Depth Information
Fig. 10.24. Iso-magnitudes of three Gabor filters corresponding to an image that consists of a
sinusoid (planar) wave, having the direction and the absolute frequency indicated by the pair
of small circles.
In Fig. 10.25, we show on the left the quantity
I
20
computed according to Eq.
(10.87) where the Gabor decomposition had three filters differing only in tune-on
directions with increments of
π
3
. The hue encodes arg(
I
20
), whereas the brightness
encodes
. The absolute frequency represented by the radius of the ring where
the tune-on frequencies of the filters are placed is 0
.
62
π
. The standard deviation of
the directional Gaussians was set to
σ
η
=
|
I
20
|
π
6
in the log-polar mapped frequency do-
main discussed in Sect. 9.6. The hue appears to change continuously in the angular
direction, and the response is concentrated to a strict annulus, indicating a reasonable
approximation of the direction as well as the certainty in a narrow band of frequen-
cies. On the right we show
I
11
supporting the same visual conclusion. However, this
visual evaluation is too coarse to quantify the quality of the approximation.
To this end, on the left graph of Fig. 10.26 we show a plot of arg(
I
20
) along the
ring passing through the points 1-4 marked in Fig. 10.15. The direction estimations
follow the true direction, the piecewise linear graph, reasonably well, although the
estimation accuracy is not as good as in Fig. 10.17. Likewise, the total error graphs
on the right representing
and
I
11
do not perform nearly as well as compared
to Fig. 10.17. This is because on the clean part of the image
|
I
20
|
I
11
, and both
should be constant and large compared to the noisy part. However, this is only ap-
proximately true, as the oscillations show. The same result is confirmed in the mea-
surements across the lines joining the point 5 and point 6 to the center (Fig. 10.27).
The image on the left shows the direction estimations in double angle representation
|
I
20
|≈
