![](bg2.png)
Though conceptually elegant, it suffers from sus-
ceptibility to speckled noise which leads to distor-
tions of the sym-axes, and it generates local rela-
tions only, meaning the sym-axes are formed only be-
tween immediately neighboring contours. However,
what it also requires are global relations (or group-
ings) between contours, whereby irrelevant contours
may lie in-between (e.g. speckled noise). The study
by Bileschi and Wolf is a step toward that direction
(Bileschi and Wolf, 2007): it relies on finding group-
ing principles from pixel correlations, that however
are time intensive (ca. 80 secs/image). Instead, a
grouping by contours would be less intensive and po-
tentially more powerful, yet has been hardly pursued.
That is the novelty of this study. To pursue such a
contour-based approach, it requires a method which
can reliably identify contours. We thereby use the
method described in (Rasche, 2009), that is summa-
rized in subsection 2.1. Subsection 2.2 explains the
grouping procedure tested in this study.
2 MODEL
2.1 Contour Description, Partitioning
and Extraction
The contour description is derived from distance dis-
tributions that in turn are obtained from systematic
measurements along the contour. For an arbitrary
contour a so-called local/global (LG) space is cre-
ated, which is a description analogous to the scale
space (fine/coarse space) but does not involve low-
pass filtering (Rasche, 2009). The contour’s global
geometry is classified into either arc (a) or alternat-
ing (w), whereby the values are scalar and express the
strength of these aspects. The contour’s local aspects
are described by the curvature parameter (b), that ex-
presses the circularity and amplitude of the arc and
alternating contour respectively; the edginess param-
eters, that expresses the sharpness of a curve (L fea-
ture or bow); the symmetry parameter, that expresses
the ’eveness’ of the contour.
Contours are partitioned as follows: if a contour
contains an ’end’ - a turn of 180 degrees - it is par-
titioned at its point of highest curvature. After ap-
plication of this rule, any contour appears either as
elongated in a coarse sense and can thus be classified
as either alternating or curved (w or a). An excep-
tion to this rule are smooth arcs, whose arc length is
larger than 180 degrees; they are extracted separately.
Exemplifying these two partitioning steps on the Ω
shape: the shape is havened and its circular part is
extracted.
An alternating contour may span several objects
(or parts) and that can be very characteristic to a
category (as for instance the vertical wiggly contour
for a person). Yet, its individual curved and straight
segments can form potentially useful groupings with
other contours of the structure. Thus, further parti-
tioning for the purpose of grouping meant also losing
potential category specificity. In this study, such al-
ternating contours are not further partitioned but any
straight or reasonably smooth, curved segment of suf-
ficient arc length is extracted from it. Such elemen-
tary segments can be identified using the LG space.
For a wiggly, natural contour such segments hardly
exist, but many object silhouettes contain multiple
such segments. Thus, the decomposition process does
not strictly partition the contours into separate seg-
ments, but will create partially overlapping segments
to some extent. Taking the Ω shape as the example
again, it is partitioned into 5 segments: one smooth
arc segment; two L features representing the corners;
and two straight segments (if of sufficient arc length).
The left graph in Figure 1 shows an example out-
put of this decomposition. The long smooth arc out-
lining the wheel shows multiple segment extractions
(straight and curved) because a) the segment is an el-
lipse, and b) due to the aliasing problem and the asso-
ciated difficulty of discriminating between a smooth
arc and a circularly aligned (open) polygon, that is
discriminating between circle and hexagon for in-
stance. Filtering techniques could resolve this latter
issue (Lowe, 1989), but would introduce additional
computation time, which we think can be avoided as
we merely intend to find the semantic content of the
image and not a precise reconstruction. In addition to
those contours (denoted as c), we use the symmetric-
axis descriptors a as in (Rasche, 2009).
2.2 Grouping
Relating all contours with each other is excessive and
leads to an unspecific structural description. Thus,
there need to be some constraints that reduce the num-
ber of all possible relations to a smaller set of mean-
ingful groupings. Such constraints have already been
described by Lowe for the purpose of determining the
orientation of objects in 3D space (Lowe, 1985). For
instance, closely spaced contour endpoints or paral-
lel lines are ’salient’ groupings which point to certain
object poses. In case of a description for an arbitrary
structure, the issue of grouping is more complexas es-
sentially any spatial arrangement of two contours can
be very category specific. Thus, the aim is therefore
to find criterions that eliminate irrelevant pairings and
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