<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Fast LSIS Pro le Entropy Features for Robot Visual Self-Localization</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Herve GLOTIN</string-name>
          <email>glotin@univ-tln.fr</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Zhong-Qiu ZHAO</string-name>
          <email>zhongqiuzhao@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Emilie DUMONT</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lab. Sciences de l'Information et des Systmes LSIS, UMR USTV CNRS 6168 La Garde-</institution>
          <country country="FR">France</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>School of Computer &amp; Information, Hefei University of Technology</institution>
          ,
          <country country="CN">China</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>University of Sud Toulon-Var</institution>
          ,
          <country country="FR">France</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>In the Robot Vision task, the participants are asked to answer where is the robot using its vision. The robot may be in 5 rooms (BO-One-person o ce, CR-Corridor, EO-Two-persons o ce, KT-Kitchen, PA-Printer Area). In order to train our models we structured the views of each room into several sub-classes: BO-inside, exit, enter; CR-enter, exit, leftstairs, nostairs, rightstairs; EO-enter, exit, inside; KT-enter, exit, cooking hearth, table, television; PA-cabinet, enter, exit. Then an SVM was constructed for each of these 19 sub-classes. After that, we combined the results of SVMs by maximizing to get the nal decision. We run our classi cation models on the new Pro le Entropy Features (PEF) that combines RGB color and texture, yielding to one hundred of dimension, and we compare them to generic Descriptor of Fourier (DF). We also made a fusion of the models on these 2 di erent features. So we got 3 runs. In our experiments, for each decision, we used only the current image, but we do not exploit continuity of the sequences. For this case, a total of 7 teams submitted runs. The o cial evaluation give for the SVM(PEF) run a score of 544, and for SVM(DF) run a score of -32, while their fusion a score of 509.5. Thus our result possesses the 5th rank over the seven. The experiments show that our SVM model works well with little training cost, and PEF feature works much better than DF feature. It could be concluded that PEF is quite e cient: it is very fast to be computed, with around 10 images computed per second on usual pentium, and less of 2 hours of training (compared to 60 hours for the best systems), but still give a competitive results.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        The task addresses the problem of topological localization of a mobile robot using visual
information. Speci cally, participants will be asked to determine the topological location of a robot based
on images acquired with a perspective camera mounted on a robot platform. The details of this
task and dataset are shown in [
        <xref ref-type="bibr" rid="ref9">10</xref>
        ].
      </p>
      <p>We manually classi ed the views of each room into several classes: BO-inside, exit, enter;
CRenter, exit, leftstairs, nostairs, rightstairs; EO-enter, exit, inside; KT-enter, exit, cooking hearth,
table, television; PA-cabinet, enter, exit. Then an SVM was constructed for each small class,
to distinguish this small-calss from all the others and recognize if the robot is currently in this
small-class or not. So we constructed 19 SVMs in total(one per class). After that, we combined
the results of SVMs by maximizing to get the nal decision. We run our classi cation models on
PEF(Pro le Entropy Feature) and DF(Descriptor of Fourier) features and compared them, and
we also made a fusion of the models on these 2 di erent features. So we submitted 3 runs. In our
experiments, for each decision, we used only the current image, but not exploit continuity of the
sequences.
2</p>
    </sec>
    <sec id="sec-2">
      <title>The Pro le Entropy Features</title>
      <p>
        We propose in [
        <xref ref-type="bibr" rid="ref1">1, 2</xref>
        ] a new feature equal to the pixel 'pro le' entropy. A pixel pro le can be a
simple arithmetic mean in horizontal (or vertical) direction. The advantage of such feature is to
combine raw shape and texture representations in a low cpu cost feature.
      </p>
      <p>Let I be an image (or a part of) of L(I) rows, and C(I) columns. The PEF are computed on
these normalized RGB channels : l = (R + G + B)=3, r = R=l, and g = G=l. We consider the
pro les of the orthogonal projections of the pixels to the horizontal X axis, noted oXp, and to the
vertical Y axis ( oYp), where op is a projection operator. This one is either the arithmetic mean of
the pixels (noted :Ari), or their harmonic mean (noted :Harm), as illustrated in Fig.1 and Fig.2.
Thus the length of a given pro le is either S = C(I) or S = L(I).</p>
      <p>
        Then, for each pro le, we estimate its probability distribution function (p^df ) on N bins (where
N = round(pS) as proposed in [
        <xref ref-type="bibr" rid="ref2">3</xref>
        ]).
      </p>
      <p>For each channel, and each operator op, we compute :
oXp(I) = p^df ( oXp(I)). Considering that the sources are ergodic, we set P EFX component to the
normalised entropy of this distribution :
P EFX (I) = H( oXp(I))=log(N ),
where N the number of bins of the considered distribution, and H the usual entropy function. We
compute similar PEF on Y axis :
P EFY (I) = H( oYp(I))=log(N ).</p>
      <p>We set a third PEF component to the entropy of the direct distribution of all the pixels in I,
p^df (I) :
P EFB(I) = H(p^df (I))=log(N ),
where N = round(pL(I) C(I)) bins.</p>
      <p>The whole PEF features are the concatenation of P EFX , P EFY and P EFB, with the usual
mean and standard deviation of each channel of I.</p>
      <p>The PEF are computed on three horizontal (noted '=') or vertical ('kk' ) equal segmented
subimages, and on the whole image. For exemple, for a given operator, we have the whole image
plus the three 'kk' subimages, and for each of the 3 channels we have P EFX ;Y ;B , plus their mean
and variance, thus we have 4 3 (3 + 2) = 60 dimensions. We note '#' the concatenation of '='
and 'kk' PEF, without duplication.
3</p>
    </sec>
    <sec id="sec-3">
      <title>Fast classi cation using Least Squares Support Vector</title>
    </sec>
    <sec id="sec-4">
      <title>Machines</title>
      <p>
        In order to design fast image retrieval systems, we use the Least Squares Support Vector Machine
(LS-SVM). The SVM [
        <xref ref-type="bibr" rid="ref4">5</xref>
        ] rst maps the data into a higher dimensional input space by some kernel
functions, and then learns a separating hyperspace to maximize the margin. Currently, because
of its good generalization capability, this technique has been widely applied in many areas such
as face detection, image retrieval, and so on [
        <xref ref-type="bibr" rid="ref5 ref6">6, 7</xref>
        ]. The SVM is typically based on an "-insensitive
cost function, meaning that approximation errors smaller than " will not increase the cost function
value. This results in a quadratic convex optimization problem. So instead of using an "-insensitive
cost function, a quadratic cost function can be used. The least squares support vector machines
(LS-SVM) [
        <xref ref-type="bibr" rid="ref7">8</xref>
        ] are reformulations to the standard SVMs which lead to solving linear KKT systems
instead, which is quite computationally attractive. Thus, in all our experiments, we will use the
LS-SVMlab1.5 (http://www.esat.kuleuven.ac.be/sista/lssvmlab/).
      </p>
      <p>In our experiments, the RBF kernel</p>
      <p>K(x1
x2) = exp( jx1
x2j2= 2)
is selected as the kernel function of our LS-SVM. So there is a corresponding parameter, , to be
tuned. A large value of 2 indicates a stronger smoothing. Moreover, there is another parameter,
, needing tuning to nd the tradeo between to stress minimizing of the complexity of the model
and to stress good tting of the training data points.</p>
      <p>We set these two parameters as
and
2 = [4 25 100 400 600 800 1000 2000]</p>
      <p>= [4 8 16 32 64 128 256 512]
respectively. So hundred of SVMs were constructed for each SVM model, and then we selected
the best SVM using the validation set.
4</p>
    </sec>
    <sec id="sec-5">
      <title>Experimental Results</title>
      <p>
        In this task, the participants are asked to answer 'where are the robots'. The robots may be
in 5 rooms (BO-One-person o ce, CR-Corridor, EO-Two-persons o ce, KT-Kitchen, PA-Printer
Area). We manually classi ed the views of each room into several classes: BO-inside, exit,
enter; CR-enter, exit, leftstairs, nostairs, rightstairs; EO-enter, exit, inside; KT-enter, exit,
cooking hearth, table, television; PA-cabinet, enter, exit (Figure 3). Then an SVM was constructed
for each small class, to distinguish this small-calss from all the others and recognize if the robot is
currently in this small-class or not. So we constructed 19 SVMs in total. After that, we combined
the results of SVMs by maximizing to get the nal decision. We run our classi cation models
on PEF(Pro le Entropy Feature) and DF [
        <xref ref-type="bibr" rid="ref8">9</xref>
        ] features and compared them, and we also made a
fusion of the models on these 2 di erent features. So we got 3 runs. In our experiments, for each
de nition, we used only the current image, but not exploit continuity of the sequences.
      </p>
      <p>The evaluation was performed by the organizer. The following rules are used when calculating
the score for a single test sequence: (1). +1.0 points for each correctly classi ed image Correct
detection of an unknown room is treated the same way as correct classi cation. (2). -0.5 points
for each misclassi ed image (3). 0.0 points for each image that was not classi ed (the algorithm
refrained from the decision) In case several test sequences are used, the scores are calculated
separately for each test sequence and then summarized.</p>
      <p>As the evaluation, we got the SVM+PEF run with the score of 544, and the SVM+DF run
with the score of -32, and the fusion run with the score of 509.5 (Table 4). The best result of us
possesses the 9th rank. The experiments show that our SVM model works well with little training
cost, and PEF feature works much better than DF feature. It could be concluded that PEF is
e cient. Moreover, PEF is fast with around 10 images computed per second on usual pentium.
Our SVM model on PEF works well, with medium performances, needing much less training time
than other systems (around 50 times less). It could be concluded that our system with PEF feature
is e cient for this task. We also noticed that the best result of those who used the continuity
information, which is from SIMD group, attains a much higher score: 916.5. So in the future, we
will combine in our system the continuity information through HMM optimisation, which shall
results in a signi cant enhancement.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgment</title>
      <p>This work was supported by French National Agency of Research (ANR-06-MDCA-002) and
Research Fund for the Doctoral Program of Higher Education of China (200803591024).
[1] Glotin, H.: Information retrieval and robust perception for a scaled multi-structuration, Thesis
for habilitation of research direction, University Sud Toulon-Var, Toulon (2007)</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [2]
          <string-name>
            <surname>Glotin</surname>
            ,
            <given-names>H.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zhao</surname>
            ,
            <given-names>Z.Q.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Ayache</surname>
            ,
            <given-names>S.:</given-names>
          </string-name>
          <article-title>E cient Image Concept Indexing by Harmonic</article-title>
          &amp;
          <source>Arithmetic Pro les Entropy</source>
          ,
          <source>2009 IEEE International Conference on Image Processing, Cairo, Egypt, November</source>
          <volume>7</volume>
          -
          <issue>11</issue>
          ,
          <year>2009</year>
          (
          <year>2009</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [3]
          <string-name>
            <surname>Moddemeijer</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          :
          <article-title>On estimation of entropy and mutual information of continuous distributions</article-title>
          ,
          <source>Signal Processing</source>
          ,
          <volume>16</volume>
          (
          <issue>3</issue>
          ),
          <volume>233</volume>
          {
          <fpage>246</fpage>
          (
          <year>1989</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [4]
          <string-name>
            <surname>Vapnik</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          :
          <article-title>The nature of statistical learning theory</article-title>
          . Springer-Verlag, New York (
          <year>1995</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [5]
          <string-name>
            <surname>Vapnik</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          :
          <article-title>Statistical learning theory</article-title>
          . John Wiley, New York (
          <year>1998</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [6]
          <string-name>
            <surname>Waring</surname>
            ,
            <given-names>C.A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Liu</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          :
          <article-title>Face detection using spectral histograms and SVMs</article-title>
          .
          <source>IEEE Transactions on Systems, Man, and Cybernetics</source>
          ,
          <string-name>
            <surname>Part</surname>
            <given-names>B</given-names>
          </string-name>
          ,
          <volume>35</volume>
          (
          <issue>3</issue>
          ),
          <volume>467</volume>
          {
          <fpage>476</fpage>
          (
          <year>2005</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [7]
          <string-name>
            <surname>Tong</surname>
            <given-names>S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Edward</surname>
          </string-name>
          , Chang:
          <article-title>Support vector machine active learning for image retrieval</article-title>
          .
          <source>In Proceedings of the ninth ACM international conference on Multimedia Ottawa</source>
          , Canada, pp.
          <volume>107</volume>
          {
          <issue>118</issue>
          (
          <year>2001</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [8]
          <string-name>
            <surname>Suykens</surname>
            ,
            <given-names>J.A.K.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Vandewalle</surname>
          </string-name>
          , J.:
          <source>Least Squares Support Vector Machine Classi ers Neural Processing Letters</source>
          ,
          <volume>9</volume>
          , 293{
          <fpage>300</fpage>
          (
          <year>1999</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [9]
          <string-name>
            <surname>Smach</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lemaitre</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          , Gauthier,
          <string-name>
            <given-names>J.P.</given-names>
            ,
            <surname>Miteran</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            ,
            <surname>Atri</surname>
          </string-name>
          ,
          <string-name>
            <surname>M.</surname>
          </string-name>
          :
          <article-title>Generalized Fourier Descriptors with Applications to Objects Recognition in SVM Context, 30</article-title>
          , J.
          <source>Math Imaging Vis</source>
          <volume>43</volume>
          {
          <fpage>71</fpage>
          (
          <year>2008</year>
          )
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [10]
          <string-name>
            <surname>Caputo</surname>
            <given-names>B.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Pronobis</surname>
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Jensfelt</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          :
          <article-title>Overview of the CLEF 2009 robot vision track</article-title>
          ,
          <source>CLEF working notes 2009</source>
          , Corfu, Greece (
          <year>2009</year>
          )
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>