![](bg1.png)
A GENERAL ALGORITHM FOR CALCULATING FORCE
HISTOGRAMS USING VECTOR DATA
Daniel Recoskie, Tao Xu and Pascal Matsakis
School of Computer Science, University of Guelph, Guelph, Ontario, Canada
Keywords: Relative position descriptors, Shape descriptors, Polygonal objects.
Abstract: The histogram of forces is a generic relative position descriptor with remarkable properties, and it has found
many applications, in various domains. So far, however, the applications involve objects in raster form. The
fact is that several general algorithms for the computation of force histograms when dealing with such
objects have been developed; on the other hand, there is no general algorithm available for objects in vector
form, and the algorithms for raster objects cannot be adapted to vector objects. Here, the first general
algorithm for calculating force histograms using vector data is presented.
1 INTRODUCTION
The histogram of forces is a generic relative position
descriptor with high discriminative power and
remarkable properties. It was introduced by Matsakis
and Wendling (1999) with the aim of developing
new models of directional relations (such as right,
left, above, below) between 2-D objects. The spatial
organization of 2-D objects is a subject of interest in
many disciplines (e.g., computer science, cognitive
science, linguistics, geography), with applications in
various domains (e.g., medical imaging, robot navi-
gation, content-based image retrieval, geographic
information systems). The histogram of forces has
been used, e.g., in a geospatial information retrieval
and indexing system (Shyu et al., 2007); for scene
matching (Sjahputera and Keller, 2007); to interpret
human-to-robot commands and generate robot-to-
human feedback (Skubic et al., 2004); along with a
land cover classification system (Vaduva et al., 2010).
Many other applications are mentioned in a recent
paper by Matsakis et al. (2011): the classification of
skull orbits and sinuses; the recognition of graphical
symbols in technical line drawings; the translation of
hand-sketched route maps into linguistic descrip-
tions; etc. The above-mentioned applications deal
with 2-D objects in raster form. These objects can be
crisp or fuzzy, connected or disconnected, with or
without holes, disjoint or overlapping. The fact is
that several general algorithms for the computation
of force histograms when dealing with such objects
have been developed. The traditional algorithm
(Matsakis and Wendling, 1999) runs in O (Kk
2
N
√
N)
time, where K is the number of directions in which
forces are considered, k is the number of nonzero
membership degrees and N is the number of pixels
in the image. A variant runs in O (KkN
√
N) time.
Another runs in O (KN
√
N) (Wang et al., 2004). A
completely different algorithm is in O (N logN) (Ni
and Matsakis, 2010). Which algorithm or variant
performs better under which conditions is an issue
discussed by Ni and Matsakis (2010). As these
authors acknowledge, however, the algorithms
above cannot be adapted to objects in vector form,
and there is no general algorithm for the compu-
tation of force histograms in the case of vector
objects (Matsakis et al., 2011). The present paper
fills this important lacuna. The concept of the
histogram of forces is described in Section 2. The
new algorithm is introduced in Section 3.
Experimental results follow in Section 4, and
Section 5 concludes the paper.
2 BACKGROUND
2.1 Objects
Consider a fuzzy subset A of the Euclidean plane.
Every point p of the plane has therefore a grade of
86
Recoskie D., Xu T. and Matsakis P. (2012).
A GENERAL ALGORITHM FOR CALCULATING FORCE HISTOGRAMS USING VECTOR DATA.
In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, pages 86-92
DOI: 10.5220/0003781600860092
Copyright
c
SciTePress