ISPRS Commission III, Vol.34, Part 3A »Photogrammetric Computer Vision“, Graz, 2002
4. Object symmetry: Man-made objects, like buildings,
have usually strong symmetry property. We adapt a
measure introduced in (Colliot et al., 2002) by com-
puting the symmetry score for different positions of
the symmetry axis (II) passing through the centroid :
0<S(Z,en(Z)) = IZuen(Z)|
2 EUM “ar
where |.| denotes the cardinality of a set, and en(Z)
is the mirror reflection of the set Z with respect to
the II axis. The measure counts the number of pix-
els that have a symmetric counterpart with respect to
the IT axis. One searches for the optimum orientation
of the axis, which corresponds to the position where
the maximum number of pixels have their matching
counterparts across the II axis. For a rectangle two
maxima are found located at 04 and 05 and with am-
plitude A; and As. Then we derive two measures :
1.2
ms; = 5 > rlAsni Ar
=1
exp(—a * |0ref,i — 0:|) (7)
1. 2
m$ — 5 > (1 — |Aref,i — Ail) *
I
=
(1 —ax sin (0c; — 0;))* (8)
1. The uniformity and contrast of the segment: We intu-
itively expect that a segmented object be “more uni-
form" as compared to "its surroundings". We ob-
tain the surrounding region Z as the dilation of the
object's bounding box, shown in figure 1 (pixels in
white). The notions of "object uniformity" and of
"object contrast" are quantified as follows
Oz
du = 2 (11)
Z
dy = luz — uz| (12)
0707
where pz and o2, are the mean and variance of the
object.
Figure 1: A segmented form (rectangle in black) and its
surround (in white) obtained by dilating its bounding box.
2. Contour regularity: We define this notion as the mean
where ref denotes the ground-truth values, and * is
the positive part of the function.
5. Histogram differences : We expect the histogram of a
correctly segmented object to follow very closely that
of its ground-truth object histogram. Low resolution
histograms, H, with only 16 gray levels, were calcu-
lated since the data available from small objects may
be very limited. The discrepancy between the gray-
level histograms is estimated by using the x? and Lo
metrics (Erdem et al., 2001), normalized to the range
[0:1]:
y RiHi(j)— R2 Ho(j)?
j=1 Hı(j)+H2(j) (9)
d,2(Hı, Hz) = Ng + Nr
1 2
absolute curvature as in (Chassery and Montanvert,
1991):
1 N
C4 = — S^ |ca | (13)
p i
where p is the perimeter of the boundary and c, ; is the
fourth order curvature (see figure 2) of the ith edge
pixel.
2 Et ; NS Pa
+
Figure 2: Curvature (c4,;) of point P; defined as the angle
b xh ; 12
dio(Hi, H3) — VM (j) - R3 H3 )] (10) formed by the line (P;_4 P;) and (P; P;,4) (P;4, P; and
NSg, + NSH,
where b = 16 denotes the number of bins in the
histogram, the scaling parameters KR; and RA» are
used to normalize the data when the total num-
ber of elements in the two histograms are different,
Ry = 2 and R; — 1/Rs.
3.0.2 The extrinsic features The extrinsic feature set
deals with appearance of the object, and not with its
ground-truthed geometric characteristics. They penalize or
reward the generic goodness of the segmented region.
A - 201
P; 4 belong to the boundary).
3. Object contrast: Well segmented objects must have
distinct gray levels with respect to the background. In
the definition of contrast, given in (Erdem et al., 2001)
one computes the mean grey level over blocks "just
inside’ (N 7) and "just outside" (N 2) for j points reg-
ularly spaced along the boundary. These blocks, typ-
ically 3x3 or 5x5, "just inside' and "just outside' are
drawn on the two sides of the j normal to the bound-
ary.
1 Z
dne SN EE (14)
