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Generalized Torsion-Curvature Scale Space Descriptor for
3-Dimensional Curves
Lynda Ayachi, Majdi Jribi and Faouzi Ghorbel
CRISTAL Laboratory, GRIFT Research Group, Ecole Nationale des Sciences de l’Informatique (ENSI),
La Manouba University, 2010, La Manouba, Tunisia
Keywords:
3D Curve Description, Invariant 3D Descriptor, Space Curves.
Abstract:
In this paper, we propose a new method for representing 3D curves called the Generalized Torsion Curvature
Scale Space (GTCSS) descriptor. This method is based on the calculation of curvature and torsion measures
at different scales, and it is invariant under rigid transformations. To address the challenges associated with
estimating these measures, we employ a multi-scale technique in our approach. We evaluate the effectiveness
of our method through experiments, where we extract space curves from 3D objects and apply our method to
pose estimation tasks. Our results demonstrate the effectiveness of the GTCSS descriptor for representing 3D
curves and its potential for use in a variety of computer vision applications.
1 INTRODUCTION
In the field of computer vision, the ability to accu-
rately describe curves is essential for numerous ap-
plications, including object recognition, image seg-
mentation, motion estimation, and tracking. In two-
dimensional images, contours can be represented as
two-dimensional curves. Over the years, a variety of
methods and techniques have been developed for de-
scribing these curves in a concise and effective man-
ner. These curve descriptors are essential for many
computer vision tasks, as they enable the extraction
of useful information from images and enable algo-
rithms to better understand the shape and structure of
objects within an image. Two categories of methods
have been proposed in the literature: global and local.
These terms refer to the scope of the features that are
extracted from contours. Global methods typically
focus on extracting high-level, overall characteristics
of the contour, such as its length or overall shape.
Local methods, on the other hand, focus on extract-
ing more detailed, fine-grained features that capture
the local structure of the contour, such as the angles
between adjacent points or the curvature at different
points along the contour. These two types of methods
have different strengths and weaknesses, and they are
often used in combination to achieve the best perfor-
mance in contour description and analysis tasks. In
the global set of algorithms, there are several meth-
ods that have been applied to the task of contour de-
scription. One such method is the Fourier descrip-
tor, which has been used in a number of works, in-
cluding (Persoon and Fu, 1977) and (Ghorbel, 1998).
These methods focus on extracting global features
of contours, but other methods have been developed
that focus on local features instead. For example, the
method proposed in (Hoffman and Richards, 1984)
partitions the curve into segments at points of neg-
ative curvature, which improves the performance of
object recognition. In a more recent work, (Yang and
Yu, 2018) introduces a multiscale Fourier descriptor
that is based on triangular features. This method com-
bines global and local features, addressing the limita-
tions of existing Fourier descriptors in terms of lo-
cal shape representation. Triangle area representation
(TAR) is a multi-scale descriptor that was introduced
in (Alajlan et al., 2007). It is based on the signed ar-
eas of triangles formed by boundary points at differ-
ent scales. Another multiscale approach is the Angle
Scale Descriptor, which was proposed in (Fotopoulou
and Economou, 2011) and is based on computing
the angles between points of the contour at different
scales. In (Sebastian et al., 2003), a method called
Curve Edit was proposed that characterizes the con-
tour using two intrinsic properties: its length and the
variations in its curvature. This method has been used
for contour registration and matching. Another no-
table method is the Shape Context algorithm, which
was introduced in (Belongie et al., 2002). (Pedrosa
et al., 2013) introduced the Shape Saliences Descrip-
tor (SSD), which is based on the identification of
points of high curvature on the contour. These points,
known as salience points, are represented using the
relative angular position and the curvature values at
Ayachi, L., Jribi, M. and Ghorbel, F.
Generalized Torsion-Curvature Scale Space Descriptor for 3-Dimensional Curves.
DOI: 10.5220/0011895500003411
In Proceedings of the 12th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2023), pages 185-190
ISBN: 978-989-758-626-2; ISSN: 2184-4313
Copyright
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2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
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