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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-11T16:59:32","documenter_version":"1.4.1"}}
{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-14T10:46:46","documenter_version":"1.4.1"}}
2 changes: 1 addition & 1 deletion dev/bc2016/index.html
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\left(\sum_{j \in |\MR_{\Vtheta_λ}\cdot\Vx_λ|} \left([\tilde{\Vx}_λ]_{j}\right)^2\right)\,
\left(\sum_{j \in |\Vy_λ|} \left([\tilde{\Vy}_λ]_j\right)^2\right)
}\notag
\end{align}\]</p><p>The score for a multi-spectral image <span>$\Vx$</span> is the sum of the scores in all spectral channels:</p><p class="math-container">\[\Score_{\Gamma,p}(\Vx) = \sum_λ \Score_{\Gamma,p}(\Vx_λ).\]</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Sanchez2016"><a class="tag is-link" href="#citeref-Sanchez2016">Sanchez2016</a><blockquote><p>J. Sanchez-Bermudez, É. Thiébaut, K.-H. Hofmann, M. Heininger, D. Schertl, G. Weigelt, F. Millour, A. Schutz, A. Ferrari, M. Vannier, D. Mary, J. Young &amp; F. Malbet, F., <em>The 2016 interferometric imaging beauty contest</em> in Optical and Infrared Interferometry and Imaging V, SPIE International Conference, <strong>9907</strong>, 99071D (2016) <a href="https://doi.org/10.1117/12.2231982">doi</a>.</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../general/">« General image metrics</a><a class="docs-footer-nextpage" href="../ic2024/">The 2024&#39; Interferometric Imaging Contest »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Tuesday 11 June 2024 16:59">Tuesday 11 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{align}\]</p><p>The score for a multi-spectral image <span>$\Vx$</span> is the sum of the scores in all spectral channels:</p><p class="math-container">\[\Score_{\Gamma,p}(\Vx) = \sum_λ \Score_{\Gamma,p}(\Vx_λ).\]</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Sanchez2016"><a class="tag is-link" href="#citeref-Sanchez2016">Sanchez2016</a><blockquote><p>J. Sanchez-Bermudez, É. Thiébaut, K.-H. Hofmann, M. Heininger, D. Schertl, G. Weigelt, F. Millour, A. Schutz, A. Ferrari, M. Vannier, D. Mary, J. Young &amp; F. Malbet, F., <em>The 2016 interferometric imaging beauty contest</em> in Optical and Infrared Interferometry and Imaging V, SPIE International Conference, <strong>9907</strong>, 99071D (2016) <a href="https://doi.org/10.1117/12.2231982">doi</a>.</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../general/">« General image metrics</a><a class="docs-footer-nextpage" href="../ic2024/">The 2024&#39; Interferometric Imaging Contest »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 14 June 2024 10:46">Friday 14 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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-1 &amp; \text{if $x &lt; 0$}\\
+1 &amp; \text{if $x &gt; 0$}\\
\phantom{+}0 &amp; \text{if $x = 0$}\\
\end{cases}\]</p><p>Metric parameters <span>$p$</span> and <span>$\gamma$</span> can be chosen depending on the context. According to a human panel<sup class="footnote-reference"><a id="citeref-Gomes2016" href="#footnote-Gomes2016">[Gomes2016]</a></sup>, <span>$p = 1$</span> with <span>$\gamma = 1$</span> best reflect the human perception of image quality.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Gomes2016"><a class="tag is-link" href="#citeref-Gomes2016">Gomes2016</a><blockquote><p>N. Gomes, P. J. V. Garcia &amp; É. Thiébaut, <em>Assessing the quality of restored images in optical long-baseline interferometry</em> in Monthly Notices of the Royal Astronomical Society, vol. <strong>465</strong>, pp. 3823-3839 (2016).</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Image metrics</a><a class="docs-footer-nextpage" href="../bc2016/">The 2016&#39; Interferometric Beauty Contest »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Tuesday 11 June 2024 16:59">Tuesday 11 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{cases}\]</p><p>Metric parameters <span>$p$</span> and <span>$\gamma$</span> can be chosen depending on the context. According to a human panel<sup class="footnote-reference"><a id="citeref-Gomes2016" href="#footnote-Gomes2016">[Gomes2016]</a></sup>, <span>$p = 1$</span> with <span>$\gamma = 1$</span> best reflect the human perception of image quality.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Gomes2016"><a class="tag is-link" href="#citeref-Gomes2016">Gomes2016</a><blockquote><p>N. Gomes, P. J. V. Garcia &amp; É. Thiébaut, <em>Assessing the quality of restored images in optical long-baseline interferometry</em> in Monthly Notices of the Royal Astronomical Society, vol. <strong>465</strong>, pp. 3823-3839 (2016).</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Image metrics</a><a class="docs-footer-nextpage" href="../bc2016/">The 2016&#39; Interferometric Beauty Contest »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 14 June 2024 10:46">Friday 14 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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}{
\sum_{j \in Ω_λ} \bigl|[\Vy_λ]_j\bigr|
}
\right)\]</p><p>with</p><p class="math-container">\[\Vtheta_λ = \{\rho_λ,\Vt,\omega_λ\}\]</p><p>the settings for resampling the restored image in spectral channel <span>$λ$</span>. The magnification <span>$\rho_λ$</span> is computed as the ratio of the known pixel sizes of <span>$\Vx_λ$</span> and <span>$\Vy_λ$</span> and, usually, does not depend on <span>$λ$</span>.</p><p>Since there is no closed-form expression of the best scaling factors <span>$α_λ$</span>, for each translation <span>$\Vt$</span>, the score is numerically optimized in the chromatic scaling factors. Since this optimization is separable in the spectral channels, we used Brent&#39;s <code>fmin</code> algorithm to find the scaling factors.</p><p>To find the best shift <span>$\Vt$</span>, the score is computed of a coarse grid of offsets and then continuously maximized starting from the best coarse offset.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Sanchez2016"><a class="tag is-link" href="#citeref-Sanchez2016">Sanchez2016</a><blockquote><p>J. Sanchez-Bermudez, É. Thiébaut, K.-H. Hofmann, M. Heininger, D. Schertl, G. Weigelt, F. Millour, A. Schutz, A. Ferrari, M. Vannier, D. Mary, J. Young &amp; F. Malbet, F., <em>The 2016 interferometric imaging beauty contest</em> in Optical and Infrared Interferometry and Imaging V, SPIE International Conference, <strong>9907</strong>, 99071D (2016) <a href="https://doi.org/10.1117/12.2231982">doi</a>.</p></blockquote></li><li class="footnote" id="footnote-Gomes2016"><a class="tag is-link" href="#citeref-Gomes2016">Gomes2016</a><blockquote><p>N. Gomes, P. J. V. Garcia &amp; É. Thiébaut, <em>Assessing the quality of restored images in optical long-baseline interferometry</em> in Monthly Notices of the Royal Astronomical Society, vol. <strong>465</strong>, pp. 3823-3839 (2016).</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../bc2016/">« The 2016&#39; Interferometric Beauty Contest</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Tuesday 11 June 2024 16:59">Tuesday 11 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\right)\]</p><p>with</p><p class="math-container">\[\Vtheta_λ = \{\rho_λ,\Vt,\omega_λ\}\]</p><p>the settings for resampling the restored image in spectral channel <span>$λ$</span>. The magnification <span>$\rho_λ$</span> is computed as the ratio of the known pixel sizes of <span>$\Vx_λ$</span> and <span>$\Vy_λ$</span> and, usually, does not depend on <span>$λ$</span>.</p><p>Since there is no closed-form expression of the best scaling factors <span>$α_λ$</span>, for each translation <span>$\Vt$</span>, the score is numerically optimized in the chromatic scaling factors. Since this optimization is separable in the spectral channels, we used Brent&#39;s <code>fmin</code> algorithm to find the scaling factors.</p><p>To find the best shift <span>$\Vt$</span>, the score is computed of a coarse grid of offsets and then continuously maximized starting from the best coarse offset.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Sanchez2016"><a class="tag is-link" href="#citeref-Sanchez2016">Sanchez2016</a><blockquote><p>J. Sanchez-Bermudez, É. Thiébaut, K.-H. Hofmann, M. Heininger, D. Schertl, G. Weigelt, F. Millour, A. Schutz, A. Ferrari, M. Vannier, D. Mary, J. Young &amp; F. Malbet, F., <em>The 2016 interferometric imaging beauty contest</em> in Optical and Infrared Interferometry and Imaging V, SPIE International Conference, <strong>9907</strong>, 99071D (2016) <a href="https://doi.org/10.1117/12.2231982">doi</a>.</p></blockquote></li><li class="footnote" id="footnote-Gomes2016"><a class="tag is-link" href="#citeref-Gomes2016">Gomes2016</a><blockquote><p>N. Gomes, P. J. V. Garcia &amp; É. Thiébaut, <em>Assessing the quality of restored images in optical long-baseline interferometry</em> in Monthly Notices of the Royal Astronomical Society, vol. <strong>465</strong>, pp. 3823-3839 (2016).</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../bc2016/">« The 2016&#39; Interferometric Beauty Contest</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 14 June 2024 10:46">Friday 14 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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