already generated salient points. The rank of a window is an
integer value denoting the gray shade rank of the central
pixel as compared with other pixels of the window. It is
assumed that conjugate features should demonstrate a rather
similar rank values. Our experiment with different data sets
show that the rank values can contribute effectively to the
determination of the conjugate features.
3.3 Matching of Corresponding Key Points Based on
Fuzzy Logic
Although in the classical image matching approaches
radiometric and geometric conditions are effective tools for
the determination of the conjugate points, in practice,
however, the main problem with these methods is their
inability to reliably and realistically fuse these conditions for
decision making. There are several schemes for the fusion of
different conditions (Strother ef al., 1994).
Fuzzy reasoning is one of these methods by which the
parameters that influence the decision making process can be
realistically fused using a human like reasoning strategy.
This is achieved by defining the so called linguistic variables,
linguistic labels and membership functions. The fuzzy
reasoning process is then realized using the fuzzy if-then
rules that enable the linguistic statements to be treated
mathematically (Nyongesa and Rosin, 2000). Our proposed
linguistic variables (Table 1) are: (a) y-difference, (b) x-
difference, (c) correlation coefficient, and (d) rank
differences. The first two items control the geometric side
and the last two items control the semantic part of the
matching operations. For each of these items membership
functions are defined by an experienced photogrammetric
operator.
TABLE 1. Linguistic variables and labels for the fuzzy based
image matching operation.
Linguistic Linguistic
Variables Labels
fn Very Small, Small, Large,
Ÿ Difference er Small Small, Large
; : : Very Large
SA Very Small, Small, Medium
5 'y Small, Small, Medium,
X Difference ery Sm a edit
Large, Very Large
Input - -
; ; Very Week, Week, Medium,
Correlation a nn
Radiometric Good, Fine, Excellent
Texture Diff Very Small, Small, Medium,
Ü rr Large. Very Large
oy i - ; Not, Probably Not,
Output Conjugate Conjugation Probably Yes Yes
4. EXPERIMENTS AND RESULTS
The potential of the proposed method is evaluated using a
real periapical and panoramic dental radiograms (Figure. 3).
Registration process is performed hierarchically using five-
layer image pyramids. Each pyramid layer has four times
reduced resolution in relation to its previous layer.
Table 2 shows the independent results for each pyramid layer
obtained by the fuzzy logic process. A comparison between
the number of the detected features in each layer and the
number of matched points (see Table 2) clearly indicates how
the fuzzy reasoning process has eliminated some of the
points in each layer. These are the points for which the
geometric and the radiometric conditions have not been
satisfied according to the fuzzy parameters settings.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
Panoramic radiogram
Periapical radiogram
Figure 3. Evaluation data set
Table 2. The number of matched points and the
corresponding residual errors on different layers
Reference | Target Matcli
Layer Image Image ; Method Order
; ; Points
Points Points
5 10 7 5 P2=P4
4 19 13 11 P2-P4 2
3 28 25 19 P2=P4 2
2 37 32 29 P2#P4 2
1 49 41 38 P2zP4 2
Figure 4. shows the final result of registration of prepaical
radiogram to panoramic radiogram base on the formulation
of last layer of matching process (layer -1).
Figure 4. Registration result
CONCLUSION
The proposed automatic image registration method discussed
in this paper, has proved to be very efficient and reliable for
automatic registration of different dental radiograms. The
implemented methodology
has
characteristics
of a)
Utilization of a multiresolution representation of information
and mathematical models, b) Employing a fuzzy reasoning
system for conjugate feature identification and modelling.
In spite of the success which is gained in the implementation
of the presented method, the topic by no means is exhausted
and still a great deal of research works are needed. These
research works should be focused mainly on the development
of a more sophisticated fuzzy reasoning system, interest
operator and matching strategy. All of these are currently
under investigation in our institute.
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