ich tasks
can also
rformed
inimizes
of some
; at least
Several
iccuracy
<-project
ontours.
mmetry,
, and so
ISer.
ocedure.
n is first
maining
ed using
stency 1s
de of the
EGIST-
er of vi-
(lady ad-
icted set
hler and
used to
onsistent
ition can
cal solu-
4A-points
veen the
‚ed from
nes with
'€c equa-
1es and a
the rota-
> of lines
was also
1s where
nfigura-
, and pa-
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol XXXV, Part BS. Istanbul 2004
rallel configurations where two planes are parallel, found
closed-form solutions are the intersections of three hyper-
cones in 4-space.
Recent works on the determination of a circle pose from
its projection in a single view led to algebraic (Kanatani
and Liu, 1993) or geometric (Chen and Huang, 1999) so-
lutions. À closed-form solution was also proposed for the
reconstruction of conics from their projections in a couple
of views with known relative orientation (Quan, 1996).
3 THE TWO-STEPS PROCEDURE
3.1 Principle and implementation
The main drawback of a manual registration comes from
the determination of the rotation axis. Therefore we im-
plemented a two-steps procedure which sets up a middle
course between manual registration and features extraction
tasks. First a small set of features is extracted according to
the scene and images geometrical configurations in order
to fix at least two of the three rotation parameters. The
remaining degrees of freedom are then controlled interac-
tively with the mouse.
A set of five configurations is implemented. It is large
enough to cope with most structured scenes already en-
countered, and small enough for a fast appropriation of the
user interface. Three of them require two calibrated views,
the rigid transformation between both views being known.
The two remaining ones use a single view and may also be
used to determine the exterior orientation. These configu-
rations are:
- Stereo line: selection of one visible line in two views.
- Shape of revolution: selection of the occlusion contours
of a shape of revolution in two views.
- Coplanar features: selection of coplanar points or lines
in two views.
- Parallel lines: selection of the projection of two parallel
lines in a single view.
- Orthogonal lines: selection of the projection of three or-
thogonal lines.
The operating mode is sequenced as follows:
= Preliminary tasks : The user first selects the object ©
to be registered, a reference frame R,(P,. Xi Y. Zz. ) on
that object for the interactive manipulation tasks, and the
relevant configuration. Default actions move the object on
à fixed image. It is left possible to change this behaviour
to move the camera position wrt a fixed object and thus de-
termine the camera exterior orientation.
= First step : Visual features are selected to compute a so-
lution R,(P,, xX. Ya, 2) which is used to align A. It is
arranged so that z corresponds to the fixed rotation axis,
P, is defined by the first selected image point, and X, turns
to the viewer. Some configurations admit several solutions.
It was preferred to let the user switch afterwards between
these solutions, rather than asking him to select additional
features to remove possible ambiguities. The closest so-
lution to R, is first proposed. Its axes are then quickly
205
re-arranged if needed.
— Second step : Interactive actions are successively per-
formed until a correct registration is achieved.
3.2 Image features 3-D interpretation
Let P be an image point with coordinates (u. v) wrt the
image reference system. If the camera interior orientatior
is known, we can find its coordinates (L Xe. Yc, Ze) wn
the camera reference system, assuming a unit distance be-
tween the image plane 7 and the optical centre C'. Its coor-
dinates (.X. Y, Z) wrt the world reference system can then
be computed from the exterior orientation matrix. The op-
tical ray £ defined by C and CP is the interpretation line
of P. It is the locus of all the possible interpretations M of
P in the 3-D space.
Figure 1: Point and segment geometry.
Now let S be a segment joining image points A and 3. It
may be the projection of a 3-D line D to be retrieved. AI!
the possible interpretations of S in the 3-D space lie within
a plane P defined by C and normal vector N — CÁACB.
P is the interpretation plane of S.
Implemented configurations are detailed in the following.
For the ones requiring two views, a prime is used to mark
corresponding features on the second view. £; refers to
the interpretation line of the first selected point or segment
end, and P is a point of £; at arbitrary distance & from C.
3.3 Stereo line configuration
This configuration relies on the specification of a visible
edge in two images to retrieve the 3-D line D. Two rotation
and two translation parameters are then fixed to constrain
the interactive registration.
Figure 2: Stereo line geometry.
Let S and S" be the selected segments, and P and P’ their
interpretation planes with normal vectors N and N’. A
