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<title>Ordenação do DIBCO</title>
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<div class="stackedit__html"><h1 id="dibco-metrics-sorting">DIBCO metrics sorting</h1>
<h2 id="obtain-averages-vector-v_m-for-each-metric">Obtain averages vector (<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>V</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">V_{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.83333em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathit" style="margin-right: 0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span class="" style="top: -2.55em; margin-left: -0.22222em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">m</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span></span>) for each metric</h2>
<ol>
<li>For each <strong>algorithm</strong> <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.43056em; vertical-align: 0em;"></span><span class="mord mathit">a</span></span></span></span></span>, obtain <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>A</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">A_{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.83333em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathit">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">m</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span></span></li>
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<li>Average of the results of metric <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.43056em; vertical-align: 0em;"></span><span class="mord mathit">m</span></span></span></span></span> for <strong>all</strong> images</li>
<li>Para cada imagem, obter <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mi>M</mi><mi>m</mi><mi>i</mi></msubsup></mrow><annotation encoding="application/x-tex">M_{m}^{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 1.07166em; vertical-align: -0.247em;"></span><span class="mord"><span class="mord mathit" style="margin-right: 0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.824664em;"><span class="" style="top: -2.453em; margin-left: -0.10903em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">m</span></span></span></span><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">i</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.247em;"><span class=""></span></span></span></span></span></span></span></span></span></span> (desempenho da imagem)</li>
<li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>M</mi><mi>m</mi></msub><mo>=</mo><mfrac><mrow><msub><mo>∑</mo><mi>i</mi></msub><msubsup><mi>M</mi><mi>m</mi><mi>i</mi></msubsup></mrow><mi>N</mi></mfrac></mrow><annotation encoding="application/x-tex">M_{m} = \frac{\sum_{i} M_m^i}{N}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.83333em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathit" style="margin-right: 0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span class="" style="top: -2.55em; margin-left: -0.10903em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">m</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 1.51147em; vertical-align: -0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.16647em;"><span class="" style="top: -2.655em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right: 0.10903em;">N</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.53501em;"><span class="pstrut" style="height: 3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop op-symbol small-op mtight" style="position: relative; top: -5e-06em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.149647em;"><span class="" style="top: -2.17856em; margin-left: 0em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathit mtight">i</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.321439em;"><span class=""></span></span></span></span></span></span><span class="mspace mtight" style="margin-right: 0.195167em;"></span><span class="mord mtight"><span class="mord mathit mtight" style="margin-right: 0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.902086em;"><span class="" style="top: -2.214em; margin-left: -0.10903em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathit mtight">m</span></span></span><span class="" style="top: -2.931em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathit mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.286em;"><span class=""></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.345em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>
<blockquote>
<p><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi><mo>=</mo><mtext mathvariant="italic">imagem</mtext></mrow><annotation encoding="application/x-tex">i = \textit{imagem}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.65952em; vertical-align: 0em;"></span><span class="mord mathit">i</span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 0.8623em; vertical-align: -0.19444em;"></span><span class="mord text"><span class="mord textit">imagem</span></span></span></span></span></span><br>
<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>m</mi><mo>=</mo><mrow><mtext mathvariant="italic">m</mtext><mover accent="true"><mtext mathvariant="italic">e</mtext><mo>ˊ</mo></mover><mtext mathvariant="italic">trica</mtext></mrow></mrow><annotation encoding="application/x-tex">m = \textit{métrica}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.43056em; vertical-align: 0em;"></span><span class="mord mathit">m</span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 0.69444em; vertical-align: 0em;"></span><span class="mord text"><span class="mord textit">m</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.69444em;"><span class="" style="top: -3em;"><span class="pstrut" style="height: 3em;"></span><span class="mord textit">e</span></span><span class="" style="top: -3em;"><span class="pstrut" style="height: 3em;"></span><span class="accent-body" style="left: -0.25em;">ˊ</span></span></span></span></span></span><span class="mord textit">trica</span></span></span></span></span></span><br>
<span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>N</mi><mo>=</mo><mrow><mtext mathvariant="italic">n</mtext><mover accent="true"><mtext mathvariant="italic">u</mtext><mo>ˊ</mo></mover><mtext mathvariant="italic">mero</mtext><mtext> </mtext><mtext mathvariant="italic">de</mtext><mtext> </mtext><mtext mathvariant="italic">imagens</mtext></mrow></mrow><annotation encoding="application/x-tex">N = \textit{número de imagens}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.68333em; vertical-align: 0em;"></span><span class="mord mathit" style="margin-right: 0.10903em;">N</span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 0.88888em; vertical-align: -0.19444em;"></span><span class="mord text"><span class="mord textit">n</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.69444em;"><span class="" style="top: -3em;"><span class="pstrut" style="height: 3em;"></span><span class="mord textit">u</span></span><span class="" style="top: -3em;"><span class="pstrut" style="height: 3em;"></span><span class="accent-body" style="left: -0.25em;">ˊ</span></span></span></span></span></span><span class="mord textit">mero de imagens</span></span></span></span></span></span></p>
</blockquote>
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</ul>
<ol start="2">
<li>Resultados: <span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>V</mi><mi>m</mi></msub><mo>=</mo><mo>{</mo><msubsup><mi>M</mi><mi>m</mi><mn>1</mn></msubsup><mo separator="true">,</mo><msubsup><mi>M</mi><mi>m</mi><mn>2</mn></msubsup><mo separator="true">,</mo><msubsup><mi>M</mi><mi>m</mi><mn>3</mn></msubsup><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>}</mo></mrow><annotation encoding="application/x-tex">V_m = \{M_{m}^{1}, M_m^2, M_m^3, ...\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.83333em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathit" style="margin-right: 0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span class="" style="top: -2.55em; margin-left: -0.22222em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 1.06411em; vertical-align: -0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathit" style="margin-right: 0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -2.453em; margin-left: -0.10903em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">m</span></span></span></span><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.247em;"><span class=""></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathit" style="margin-right: 0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -2.453em; margin-left: -0.10903em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">m</span></span></span><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.247em;"><span class=""></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathit" style="margin-right: 0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.814108em;"><span class="" style="top: -2.453em; margin-left: -0.10903em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathit mtight">m</span></span></span><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 0.247em;"><span class=""></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mclose">}</span></span></span></span></span></li>
</ol>
<ul>
<li><span class="katex--inline"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>a</mi><mo>=</mo><mtext mathvariant="italic">algoritmo</mtext></mrow><annotation encoding="application/x-tex">a = \textit{algoritmo}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.43056em; vertical-align: 0em;"></span><span class="mord mathit">a</span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 0.88888em; vertical-align: -0.19444em;"></span><span class="mord text"><span class="mord textit">algoritmo</span></span></span></span></span></span></li>
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