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<!doctype html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<title>Image Analysis with Fiji</title>
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<!-- Slide Title -->
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<!-- ---------------------- START OF SLIDES -------------------------- -->
<div class="slides">
<section data-menu-title="Title">
<h1>Deconvolution and Colocalisation</h1>
<h3>Laura Cooper<br>Research Fellow, CAMDU</h3>
<br>
<p>Navigation:
<ul><li> Left/right arrow keys for previous/next slide</li><li>'m' key to get to navigation menu</li><li>Escape for slide overview</li></ul>
</p>
</section>
<section data-menu-title="Acknowledgements" data-state="intro0a">
<h1>Acknowledgements</h1>
<p>Slides adpated from presentations by:
<ul>
<li>Dave Mason, formerly University of Liverpool: <a target="_blank" href="https://pcwww.liv.ac.uk/~dnmason/ia.html">https://pcwww.liv.ac.uk/~dnmason/ia.html</a></li>
<li>Erick Martins Ratamero, formerly University of Warwick</li>
<li>Lewis Mosby, University of Warwick</li>
<li>Philo van Kemenade (<a href="twitter.com/phivk">@phivk</a>)</li>
<li>Some material also from <a href="https://imagej.net/Introduction_into_Macro_Programming">ImageJ website</a></li>
</ul>
</p>
</section>
<section data-menu-title="Deconvolution" data-state="decon">
<h1>Recap</h1>
<ul class="left half">
<li>When aquiring an image, we detect the point spread function (PSF). It blurs every point in the image</li>
<li>Fourier transforms can be used speed up convolution. Convolution in the spatial domain is the same as multiplication in the frequency domain</li>
<li class="fragment">Image formation in the microscope can be understood as convolution between the object being imaged and the PSF of the imaging system</li>
</ul>
<img class="fragment right third" src="img-lc/PSF.png"/>
</section>
<section data-state="decon">
<h1>Approximating the PSF</h1>
<ul class="left half">
<li>PSF are approximated by imaging very small beads. If the beads are smaller than the resolution, the outputs will be the PSF.</li>
<li>Theoretical PSF are sometimes used, often approximated as a Gaussian function.</li>
<li>If we have the PSF and the image can we reconstruct the object?</li>
</ul>
<img class="right third" src="img-lc/PSF.png"/>
</section>
<section data-state="decon">
<h1>Deconvolution</h1>
<ul class="left half">
<li>In the spatial domain, let an image, I, be an object, O, convolved with a PSF, P. i.e. I=O*P</li>
<li>Then, in the frequency domain, we have the F(I)=F(O) x F(P), where F represent the Fourier transform</li>
<li>So F(O)=F(I) ÷ F(P)</li>
<li>By taking the inverse Fourier transform of F(O), we obtain O, the object.</li>
<li>This is known as <b>naive deconvolution</b></li>
</ul>
<img class="right third" src="img-lc/PSF.png"/>
</section>
<section data-state="decon">
<h1>Deconvolution Issues</h1>
<ul>
<li>Extremely sensitive to noise</li>
<li>Can have artifacts if the light source is not constant</li>
<li>More advanced methods are very computationally intesive</li>
</ul>
</section>
<!-- ---------------------- APPLICATIONS COLOCALISTATION -------------------------- -->
<section data-menu-title="Colocalisation Analysis" data-state="apps30z"><style>.apps30z header:after { content: ""; }</style>
<h1>Applications: Co-localisation</h1>
<h4>Use cases, some simple guidance, JaCoP</h4>
</section>
<section data-state="apps30"><style>.apps30 header:after { content: "Colocalisation: Theory"; }</style>
<!-- <p>Colocalisation: the bane of Image Analysts</p> -->
<img class="half" src="img-ia/coloc_00.png"/>
<p class="subtle">Adapted from a slide by <a href="https://twitter.com/fab_cordelieres" target="_blank">Fabrice Cordelieres</a></p>
</section>
<section data-state="apps30"><style>.apps30 header:after { content: "Colocalisation: Theory"; }</style>
<p>Colocalisation is <u>highly</u> dependent upon resolution! Example:</p>
<img class="third" src="img-lc/map.png"/><span> </span><img class="third fragment" src="img-ia/coloc_02b.png"/>
<p class="fragment">Same idea goes for cells. Keep in mind your imaging resolution!</p>
</section>
<section data-state="apps35"><style>.apps35 header:after { content: "Bolte and Cordelieres"; }</style>
<p>We will walk through using JaCoP (Just Another CoLocalisation Plugin) to look at Pearson's and Manders' analysis</p>
<p>If you're doing colocalisation analysis at all, I <u>highly</u> recommend reading the companion paper <a href="https://doi.org/10.1111/j.1365-2818.2006.01706.x" target="_blank">https://doi.org/10.1111/j.1365-2818.2006.01706.x</a></p>
<img class="half" src="img-ia/coloc_00a.png"/>
</section>
<section data-state="apps31"><style>.apps31 header:after { content: "Colocalisation: Pearson's Correlation Coefficient"; }</style>
<p>Pearson's Correlation Coefficient</p>
<img class="third left" src="img-ia/coloc_10.png"/>
<ul class="twothirds">
<li>For each pixel, plot the intensities of two channels in a scatter plot</li>
<li>Ignore pixels with only one channel
<li>P value describes the goodness of fit (-1 to 1)</li>
<ul>
<li>1 = perfect correlation</li>
<li>0 = no positive or negative correlation</li>
<li>-1 = exclusion</li>
</ul></ul>
<p class="subtle clear">Figure from <a href="https://doi.org/10.1111/j.1365-2818.2006.01706.x" target="_blank">https://doi.org/10.1111/j.1365-2818.2006.01706.x</a></p>
</section>
<section data-state="apps31"><style>.apps31 header:after { content: "Colocalisation: Pearson's Correlation Coefficient"; }</style>
<img class="left third" src="img-ia/coloc_11.png"/>
<ul class="twothirds">
<li>Download <a href="material/jacop_.jar"><code>JaCoP</code></a></li>
<li>Run <code>[Plugins > Install Plugin...]</code> or <code>[Plugins > Install...]</code> point to the jar file and then save</li>
<li>Restart Fiji</li>
<li>Open <a href="material/11-colocA.tif"><code>11-colocA.tif</code></a> and <a href="material/12-colocB.tif"><code>12-colocB.tif</code></a></li>
<li>Run <code>[Plugins > JaCoP]</code>, uncheck everything except Pearsons, select the same image for both channels</li>
<li>Repeat for different combinations of these images and also <a href="material/13-colocA_half.tif"><code>13</code></a> and <a href="material/14-colocB_quarter.tif"><code>14</code></a></li>
</ul>
</section>
<section data-state="apps32"><style>.apps32 header:after { content: "Colocalisation: Problems with Pearson's"; }</style>
<img class="left quart" src="img-ia/coloc_10.png"/>
<ul class="twothirds">
<li>Great for complete colocalisation</li>
<li>Unsuitable if there is a lot of noise or partial colocalisation (see below)</li>
<li>Midrange P-values (-0.5 to 0.5) do not allow reliable conclusions to be drawn</li>
<li>Bleedthrough can be particularly problematic (as they will always correlate)</li>
</ul>
<br>
<img class="clear half" src="img-ia/coloc_12.png"/>
</section>
<section data-state="apps33"><style>.apps33 header:after { content: "Colocalisation: Manders'"; }</style>
<!-- <img class="twothirds" src="img-ia/coloc_13.png"/> -->
<p>Manders' Overlap Coefficient</p>
<ul class="twothirds">
<li>Removes some of the intensity dependence of Pearson's and provides channel-specific overlap coefficients (M1 & M2)</li>
<li>Values from 0 (no overlap) to 1 (complete overlap)</li>
<li>Defined as <i>"the ratio of the summed intensities of pixels from one channel for which the intensity in the second channel is above zero to the total intensity in the first channel"</i></li>
</ul>
</section>
<section data-state="apps33"><style>.apps33 header:after { content: "Colocalisation: Manders'"; }</style>
<img class="third" src="img-ia/coloc_11.png"/>
<ul class="twothirds">
<li>Use the same images from last time (<a href="material/11-colocA.tif"><code>11</code></a>, <a href="material/12-colocB.tif"><code>12</code></a>,<a href="material/13-colocA_half.tif"><code>13</code></a> and <a href="material/14-colocB_quarter.tif"><code>14</code></a>)</li>
<li>Run <code>[Plugins > JaCoP]</code>, check both Pearsons and Manders</li>
<li>Run for different combinations of these images</li>
<li>Note the differences in coefficients especially in images 13 and 14</li>
<li class="fragment">[BONUS] add some noise <code>[Process > Noise > Add Noise]</code> or blur your images <code>[Process > Filters > Gaussian Blur]</code> and see how that affects the coefficients</li></ul>
</section>
</div> <!-- ---------------------- END OF SLIDES -------------------------- -->
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