Model coordinate is xyz 3-dimensional, with the origin at the
center of projection O, and parallels to uv. Where we set the
center of projection O; as position (1, b,, b.) and as rotation (œ,
, K), focal length of cameras as f; and f; respectively. Then
model coordinates of ground point P are observed at O; and O5
as follows with photographic coordinate.
X U,
yx liM (9)
Zz =f
X3 1.0 0 cosp 0 sing
y, |=|0 cosæ —sin@ 0. A 0
Z 0 sing cosc |-sing 0 cose
: : (10)
cosx —sinx O|u, 1
sink cosk« 01% |+jb,
9, 20. dni |»
Then projective transformation of the odd image is as follows.
wi [+
HEH (11)
À x,-1
s © a a (12)
According to the above image rectification process, each
epipolar lines are realigned so as to be parallel to x-direction.
Unknown parameters in the above equations are calculated by
relative orientation process with specified pass points, which
are automatically extracted (Sakamoto 1998). Figure 3 shows
an example of ANM result applied to rectified stereo model,
with the images taken at different time.
Mapping in 1-direction results in inconsistency between
adjacent lines, which can be solved by utilizing edges across
epipolar lines as constraints in the ANM model.
(a) Image A (b) Image B (new) (c) Mapping from A to B
Figure 3. An example of mapping result by ANM
3. ENHANCED ANM MODEL
3.1 A Model for Abrupt Change of Shift Vectors
An enhanced ANM model utilizing edges as contraint was
discussed in our previous study (Sakamoto 2001). In this model,
edges of buildings in a stereo model are detected and matched,
then used to control the mapping process in ANM, which are
extracted from the steps shown in Figure 4. The following
sections will give some brief descriptions of edge constraint
model.
Y
T A Filtering with Geometric
Constraint
Pre-processing
Edge Enhancement
Y
Y
Filtering with Image
Edge Thinning Similarity
Edge Tracing Expansion and Contraction
Y Y
Conjugate Edge Selection |
Edge Line Segmentation
Figure 4. Flow of matched edge detection
3.1.1 Estimation of Initial Registration Position: In ANM
process, mapping obtained at local area is propagated to system
by consensus operation. Therefore even if there are some areas
where mapping falls into local minimum, it may be recovered
by reiteration. However recovery becomes impossible when the
overall system drops into local minimum, which can be avoided
by utilizing initial mapping position formed by matching edges.
3.1.2 Topological Constraints with Detected Edges: By
using detected but un-matched edges, the following rules are
applied according to the type of region.
(i) Detected edge region
Discontinuity of shift vectors is permitted. In the consensus
operation, shift vectors on detected edges are assumed to
change linearly. Therefore linear shift can be estimated by least
squares method and then shifts on detected edges are modified.
(ii) Neighbouring region of edges
In consensus operation, neighbouring regions of both detected
and matched edges where regions are divided into two
parallelogram areas by edge segmentation are evaluated. Only
odd region which has high image similarity is modified to have
the same vector shifts of edges.
3.1.3 Topological Constraints with Matched Edges: In
case of using matched edges, following rules are applied.
(i) Conservation of shifts
The regions of matched edges are fixed in competition and
consensus processes.
(ii) Limitation of processing area
Area sizes for competition and consensus process are restricted
within the range of adjacent matched edges as follows.
Let the i turn’s position of edge be E; and j turn’s position of
non-edge be P; respectively, and define a function S(x) which
returns the shift vector at poison x. Then mapping process of P;
is conducted to satisfying Equation (14) in the condition of
Equation (13).
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