the central area of the reference image to the matched image
(or vice versa) using the similarity distance defined by (45),
which yields an approximate parallax vector for this central
area. Parallax vector for each integer-indexed position of this
central area can then be fine-tuned also by using (45). Known
parallax vectors can then be propagated from the central area
to the outer rings, ring by ring, until the boundary of partial
correspondence is reached, and this can be done fully au-
tomatically. Gross errors of the resultant parallax field can
be detected and corrected automatically by using the local
continuity constraint.
5.2 Hierarchical Parallax Propagation
After image matching on a higher (7 4- 1)-th level, the parallax
field should then be propagated to the next lower (finer) j-th
level. The initial parallax field on the current j-th level can be
obtained by interpolating the parallax field at the (5 + 1)-th
level. The inverse of the similarity distance of (45) for each
position on the higher level may be taken as the weighting
factor for linear or nonlinear interpolation.
‘After matching through intermediate levels, a number of ho-
mologous matched point pairs can then be selected automat-
ically, the focal length of each image and five relative orien-
tation parameters can then be solved via a direct closed-form
solution [Pan et al, 1995] from these pure image coordinates.
Note that the standard aerial stereo pairs with closely parallel
principal axes correspond to a degeneracy of that direct so-
lution. The solution of two focal lengths is sensitive, though
indeed solvable. For robotic stereo images with an essential
vergence angle, the solution is robust enough.
5.3 An Example of Real Aerial Images
The complete procedure consists of complex wavelet trans-
form, spiral matching on the top level, and hierarchical
matching through intermediate levels, solving the two focal
lengths and relative orientation, up to surface reconstruction
and visualization. This procedure has been implemented and
tested with real images. Fig.4-6 show an example of matching
a pair of real aerial images. Through visual checking of each
matched position pairs, no gross error is found. As we only
match regular points to normal and diagonal regular points,
the matching errors bound to 0.5 pixel on each level. This
wavelet-based approach can in principle reach a resolution of
2 x 2. We shall leave the final pixel-level or subpixel-level
matching to least-square global matching, to which, wavelet
features may still be useful.
6 CONCLUSIONS
This paper presents a basic theory of uniform full-informatin
image matching using complex conjugate wavelet pyramids.
The basic procedure including the bottom-up wavelet mul-
tiresolution analysis and top-down image matching has been
implemented and tested with real images. The result is
promising. The feasibility of this approach is confirmed.
Rotation-invariant image matching is not discussed here due
to the length limit, which is the main focus of our current
research.
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