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Affine Invariant Shape Matching using Histogram of Radon Transform
and Angle Correlation Matrix
Makoto Hasegawa
1
and Salvatore Tabbone
2
1
Tokyo Denki University, 5 Senju Asahi-cho, Adachi-ku, Tokyo 120-8551 Japan
2
LORIA, UMR 7503, Universit
´
e de Lorraine, 54506 Vandoeuvre-l
`
es-Nancy, France
Keywords:
Shape Descriptor, Affine Invariance, Radon Transform, Dynamic Time Warping Distance, Beam Search.
Abstract:
An affine invariant shape matching descriptor using the histogram of Radon transform (HRT) and the dynamic
time warping (DTW) distance is proposed. Our descriptor based on the Radon transform is robust to shape
rotation, uniform scaling, and translation. For non-uniform scaling and shearing, our descriptor has a non-
linear sparse and dense distortion relative to the angle coordinates. Therefore, we apply DTW on a cost matrix
to be robust to these transformations. This cost matrix is defined as an angle correlation matrix based on the
product of two matrices only. Moreover, based on the beam search algorithm, we speed-up the time complexity
of our method. Experimental results show that our approach is fast to compute and competitive compared to
well-known descriptors.
1 INTRODUCTION
Geometric invariant shape descriptors are very impor-
tant for shape recognition. Usually shape descriptors
need to be invariant to classical geometric transfor-
mations like rotation, scaling and translation. How-
ever these transformations are not enough in several
applications. Recently, a shape recognition applica-
tion using a portable digital camera has been pro-
posed in (Liang et al., 2005) where shapes (included
in the photos) are deformed following affine distor-
tions. Therefore, it is necessary to be invariant to such
distortions.
RST invariant descriptors have been proposed for
shapes description and matching. Fourier transform
has been used as the starting point for the proposal of
many shape descriptors. The generic Fourier descrip-
tor (GFD) proposed by D. Zhang and G. Lu (Zhang
and Lu, 2002) is a typical one, and it is invariant to
rotation. However, in the case of translation and scal-
ing, GFD needs normalizations. The phase-only cor-
relation function (POC) proposed by C. Kuglin et al.
(D., 1975) has been shown to be effective for shape
matching. The Fourier–Mellin transform (FMT) pro-
posed by Chen et al. (Chen et al., 1994) is a typi-
cal Fourier descriptor invariant to RST transforma-
tions. Fourier descriptors have proved their robust-
ness to RST transformations and many applications
have been developed using these descriptors (Arafat
et al., 2009; Yuyama and Mitsuhashi, 2008; Ouyang
et al., 2006).
Many shape descriptors using the Radon trans-
form (Deans, 1993) have been defined in the liter-
ature by Tabbone et al. (Tabbone et al., 2006). A
method called the histogram of Radon transform
(HRT) (Tabbone et al., 2008) has been proposed us-
ing the Radon transform and a two-dimensional his-
togram. This descriptor encodes the shape length
at each orientation; it is invariant to the shape scal-
ing and translation, and the shape rotation is pro-
jected to a horizontal translation on the domain.
Recently, the Amplitude-only log Radon transform
(ALR) (Hasegawa and Tabbone, 2012) has been de-
fined. This descriptor is based on the Radon trans-
form, amplitude extraction, and log mapping. It is
invariant to shape translation; shape rotation and scal-
ing are projected into a two-dimensional translation.
To keep the invariance to these transformations (ro-
tation and scaling) the phase-only correlation func-
tion is used where the computation of several Fourier
transforms are needed. Combined with the DTW, this
descriptor is in addition invariant to any affine distor-
tions. The reported results on recognition rates are
very good compared to the literature but the complex-
ity of the approach is very high. A method proposed
by K.C. et al. (Santosh et al., 2011) combined the
Radon transform and the dynamic time warping. The
authors apply directly the dynamic time warping to
21
Hasegawa M. and Tabbone S..
Affine Invariant Shape Matching using Histogram of Radon Transform and Angle Correlation Matrix.
DOI: 10.5220/0004787000210029
In Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods (ICPRAM-2014), pages 21-29
ISBN: 978-989-758-018-5
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)