Juliang Shao
A a b 0|[A]
B'|=|e d 0!||R (1)
€. de f lC
where (4°, B', C^) and (A, B, C) are the coefficients of the corresponding lines in two images, while a, b, c, d, e, and f
are the coefficients of the affine dual transform. To solve the six elements of the line affine model, at least three pairs of
matched lines are required. It should be noted that to avoid singularity, the three lines in the reference image for the line
affine element determination must exclude lines intersecting in a single point, and the case of three parallel lines with an
effective intersection at infinity.
Uo —
EM.
N
E
N
Fig. 4: Candidate prediction (L^) in object image derived from L in
reference image by the nearest segments: 1 - 1’; 2 - 2°; and 3 - 3°
which are the initial and one to one corresponding matches.
3.2 Extension via Prediction
Once the affine coefficients are determined, a feature position can be predicted and a search can be conducted for that
feature within specified error bounds. When a candidate is located, a final verification step is performed using grey
level intensity values and information on contour orientation. If, on the other hand, no feature is found at this location, a
refined segment detection can be iteratively performed through a lowering of threshold values.
Shown in Fig. 5 is the extension of the initial segment matching (Fig. 2) in which additional matched segments have
been located. The lines whose numbers are larger than 2 indicate the additional matches obtained via a change of the
threshold in the contour extractor for all images.
a
Fig. 5: Additional corresponding segments obtained via prediction.
Each segment may have several ambiguous candidates. To eliminate ambiguities, relationships among the neighbouring
segments in the same image, and among the candidates in overlapping images, are formulated to enable local
consistency checks. This aspect is discussed in the next section.
4 A RELAXATION PROCESS FOR LOCAL CONSISTENCY CHECKS
To eliminate ambiguities in feature-based matching, a relaxation process has been adopted. This technique has
previously proved a useful tool in vision processes (Atalay and Yilmaz, 1998; Barnard and Thompson, 1980; Kittler,
1993). Probabilities are employed in the relaxation process. Firstly, the initial probabilities are estimated from similarity
measures and they are then updated iteratively so as to impose local consistency conditions. That is, the probability of a
point is increased if its compatible neighbours have high probability values. A recursive procedure can be continued
either until the probabilities reach a steady state or a pre-set number of iterations has been carried out. This is thus
840 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
