![](bg5.png)
Where c
l
=
M
p
l
L
, c
r
=
M
p
r
L
and E =
i<L
|M
p
i
r
−M
p
i
l
|
L
. The Y junction which is formed
by two level-line flows is defined as aprimitive
−→
P
combining three segments. Likewise the L junction
can be approximated by two segments. We define the
principal segment
−→
S
∗
of a primitive as the one sup-
ported by the maximal level-line flow among the three
that join at point p in case of a Y. In case of an L it
corresponds to the first detected flow along with the
image scan. Virtual pixel p is the control point of the
primitive to be further matched. Angles θ
l
and θ
r
are
measured from the principal segment to respectively
the one on its left
−→
S
l
, and the other on the right
−→
S
r
.
The figure 6 shows the primitive associated to the Y
flow junction in figure 5.
−→
P =
p
−→
S
∗
−→
S
l
−→
S
r
θ
l
θ
r
(9)
Figure 6: Definition of primitive.
Note that binding the principal segment of a prim-
itive to the actual image local configuration makes
flow junctions rotation invariant. Moreover, the order
of magnitude of region intensities around the junction
could constrain the matching tighter.
F
−→
P
= V
p
−→
S
i
∈
−→
P
L
i
×E
i
(10)
F
P
appears eventually as the reliability of a primi-
tive, to be used for non-maximum suppression in the
case we extract corners or for multi-round matching
when primitives would be progressively involved ac-
cording to that latter reliability. Let us underline that,
unlike most methods based on points of interest, no
more descriptor − moment, derivative, Fourier para-
meters etc. − needs to be further computed to match-
ing. Next section starts with comparing our results
to Harris’s, and then stresses upon the control of the
junction scattering over an image.
5 RESULTS
The performance of our method is compared to the
one by Harris on real scene images, shown in figure
7(a) ”block image” and figure 10(a) ”house image”.
We select the Harris detector, not SUSAN or others,
for appearing as the more dependable especially with
affine transforms even if it is not the more precise or
robust to noise. The best results of the Harris op-
erator, as found in ”
http://www.cim.mcgill.ca/ dparks/”,
are displayed in figure 7(b) and 10(b) respectively.
By applying our method with E =10, all junctions
extracted from ”block image” before non-maximum
suppression are shown in figure 9(a). Figure 9(b)
displays junctions selected from figure 9(a) as local
maxima by their reliability. Junction points are then
superimposed in ”block image” (figure 7(c)) to com-
pare with the Harris operator. All corners are found
by EFLAM unlike with Harris as indicated by the ar-
rows. This is to the price of more edge-like points.
Our detector is more sensitive to shadows (see cir-
cled points in figure 7(c)). Yet our results are bound
to the selection strategy for E. Increasing E to 14 8,
gets rid of shadow/edge points to the detriment of the
precision of point location. Similarly, by applying
the method to ”house image” all extracted junctions
and sectected junctions are shown in figure 11(a) and
11(b) respectively. Results interpretation remains the
same for 9(b) and (c) as for 7(b) and (c). However
our miss of the upper right corner of the bright verti-
cal window shows the criticity of E , whence the next
kind of experiments about possible loops on E while
matching.
Indeed, another important advantage to stress upon
is that we can control the spread of extracted junc-
tions over the image. That is very important e.g.
for 3D reconstruction. The extraction is performed
as a repetitive process by decreasing the flow exten-
sion E. At the beginning, junctions are extracted with
a high value of E. Then an exclusion zone is de-
fined as a circular area around any extracted junction
point. Next round, the extraction method repeats with
a lesser value of E adding newly found junctions only
in the authorized empty zones. The smaller E, the
more occuring junctions. Note that since the relia-
bility of primitives is computed from the flow exten-
sion E respective to length and variation, primitives
obtained early in the process are likely more reliable.
That turns out to be very useful for multi-round math-
cing.
Figures 12(a) and (b) show an example of ”bust”
stereo images. Extracted junctions from the left and
right images in the first round, where E =20, are
shown in figure 13(a) and (b) respectively. The ex-
tracted junctions cover barely principal structures :
head, eyes, mouth, and nose. Figure 13(c) and (d)
show the second round of extraction, where E =15,
EFLAM: A MODEL TO LEVEL-LINE JUNCTION EXTRACTION
261