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tensors. This is obtained by successive division of the
q
in (13) by
n
p
for starting from
p
=
k
up to
p
=1, since for all
k
it holds that
i
k
<
n
k
. A series of indices
i
p
is obtained in a
form of residua of such successive divisions. Summarizing, the advantages of the
proposed tensor classes are as follows:
1.
A uniform treatment of the tensor as well as its matrix
n
-modes. A tensor is
stored only in a single chosen mode while other modes are obtained exclusively
by index manipulations.
2.
Tensor proxy objects allow simultaneous manipulation of a tensor in its all
possible
n
-mode flat representations without data copying.
3.
Template implementation allows different types of tensor elements (such as float,
boolean or fixed-point formats).
4.
Object oriented C++ implementation can be easily ported to other OO languages
such as C#, Java, Python, etc.
The described tensor software framework can be accessed from the Internet [11].
5 Experimental Results
The presented object classification framework was implemented in C++. Experiments
were run on a computer with 2GB RAM and Pentium Core 2 T7600 @ 2.33GHz.
Fig. 4.
Exemplary real traffic scenes used in the experiments. The method is able to correctly
recognize signs of different size and orientation.
Fig. 4 and Fig. 5 depict two real traffic scenes with signs correctly detected and
then classified by the presented HOSVD based system. Despite inherent rotation, as
well as variations of tint and different lighting, the signs were recognized correctly.
Fig. 6 Fig. 7 depict the first five tensors
T
and the corresponding five core
tensors
Z
which were computed for the for the “
40 km/h speed limit
” and “
No pass
”
signs, respectively. An inherent rotation added during training is well visible.
An average accuracy of recognition was measured in terms of the error rate
which plot depicts Fig. 8b. However, during the tests it was observed that some
signs cause more errors (such as e.g. the STOP sign), whereas the other can be
recognized very reliably. This is caused mostly by specific pictogram distribution of
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