). The new
ch is deter-
on, its local
mental dis-
er after the
or of edge
se the tem-
w in the im-
; reached).
nd 9x9 pix-
; in greater
Ss increase
ar features
ed method
tioning ac-
:stablished
al analysis
its perfor-
alized pro-
;e and fails
ine break
JUARES
matching,
ic informa-
) a globally
)g strategy
ich the ob-
road, land
menu and
ons of ob-
define a
Selection of Object Class i
Manual Selection of Outline Breakpoints p
Automatic Template Generation i
Globally Enforced Least Squares Template Matching
Fig. 5: Globally enforced least squares template
matching strategy
polygonic approximation of the edge contour. By in-
terpolating between the polygonic approximation
nodes at user-specified intervals, numerous points
are extracted, roughly outlining the current object of
interest. These points are then used as approxima-
tions for the subsequent precise edge positioning
through least squares template matching. The syn-
thetic matching template is automatically generated
as the 2-D ramp edge which best fits image profiles
extracted perpendicular to the polygonic approxima-
tion at the interpolated positions. The matching solu-
tion, however, will no longer proceed independently
for the various points of the same outline. Instead,
the mathematical model presented in section 5 is ex-
tended to provide a simultaneous global matching so-
lution, whereby globality refers to all matching
candidates pertaining to a single object.
More specifically, individual edge positions, detected
by least squares template matching along a single
object outline, will have to fulfill a certain geometric
condition, describing the acceptable outline geome-
try. For example, it is typical for houses to have edges
formed by straight linear segments, while for roads
Smooth splines are suitable. By defining such a geo-
metric relationship, we are able to tie together the
matching adjustment solution of independent points.
Assuming straight linear edges for instance, and us-
Ing the notation of the previous section, it is obvious
that edge points along the same line should satisfy
the condition
A y;- Axtang, - 0 (23)
which in matrix form is expressed as
Vector X includes the transformation parameters of
all matching templates referring to different locations
along the same linear edge segment. The associated
weights can vary from zero (i.e. constraint virtually re-
moved) to infinity (i.e. constraint strictly enforced). By
adding these constraints, the final solution is ob-
tained in analogy to equation (22) as
E T T T T =
X » (A'PA« BIP,B, * BIP,B, « BI P,B)
T T T T
(A PI- B, P lp B.P t7 B, P, (25)
The above matrices include information from all in-
volved templates, and obviously matrices in equation
(22) are actually submatrices of their counterparts in
equation (25).
For curvilinear features now (e.g. roads), splines are
used to ensure piecewise continuity and smooth-
ness. A discrete approximation of this constraint can
be given as
2AX;- AX;_,-AX;,, = 0 (26)
2Ay;- Ay; ,-Ay;,4, 70 (27)
2A9,-A9; ,-A9,,, 70 (28)
Such conditions can be properly fomulated and in-
cluded as geometric constraints in the global adjust-
ment in lieu of equation (24), and the solution is
again given by equation (25). The employment of the
appropriate set of constraints is determined by the
operator's object class selection at the beginning of
the procedure.
By modifying least squares template matching in
such manner, its inherent high edge positioning pre-
cision and well established mathematical foundation
are retained and further improved by the infusion of
global geometry information similarly to the snake ap-
proach. Thus, the advantages of both techniques are
optimally combined providing precise and reliable re-
sults.
7. EXPERIMENTS
The semi-automatic strategy for road extraction using
wavelet transformed SPOT imagery has been suc-
cessfully implemented in our Institute on a digital
photogrammetric station and Fig. 6, 7 and 8 show a
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