Discriminating particles for tracking analysis

<p>After <a class="wikilink" href="/locating_particles_for_nanoparticle_tracking/">locating particles for nanoparticle tracking</a> and <a class="wikilink" href="/refining_the_position_of_nanoparticles_on_an_image/">refining the position of nanoparticles on an image</a>, one must be able to discriminate between particles and noise. Up to this point, we have not rejected any maximum found by the gray dilation method on the images. <a class="litnote tooltip" href="/literature/@crocker1996">@crocker1996<span class="tooltiptext">Methods of Digital Video Microscopy for Colloidal Studies</span></a> propose to use a method based on calculating other moments of the intensity distribution:</p> <p>$$m_0 = \sum_{i^2+j^2\le w^2} A(x+i, y + j)$$</p> <p>and the second order:</p> <p>$$m_2 = \frac{1}{m_0}\sum_{i^2+j^2\le w^2} (i^2+j^2)A(x+i, y+j)$$</p> <p>In the paper, Crocker and Grier observe that most particles fall into a well defined cluster if one looks at the plot $$m_2\textrm{vs}m_0$$ although they also mention that it is hard to anticipate what distribution is expected. In the Fig2, it is clear what they refer to, and <a class="wikilink" href="/trackpy/">trackpy</a> actually builds a feature like this in order to drop some tracks that may be spurious. I wonder what effect may have if one is tracking particles with different anisotropies. </p> <p>The paper also uses the standard deviation of both moments to estimate the accuracy of the location in the z-plane. I do believe that these efforts are because of the technical limitation at the time the paper was written (1996) and nowadays there are other approaches to yield more accurate results.</p>