Find Maxima

The interactive Watershed Fiji plugin provides an interactive way to explore local maxima and threshold values while a resulting label map is updated on the fly.

After the user has found a reliable parameter configuration, it is possible to apply the same parameters to other images in a headless mode, for example via ImageJ macro scripting.

Maxima finding algorithm implemented in Python recreated from implementation in Fiji(ImageJ)

This is a re-implementation of the java plugin written by Michael Schmid and Wayne Rasband for ImageJ. The original java code source can be found in: https://imagej.nih.gov/ij/developer/source/ij/plugin/filter/MaximumFinder.java.html 

This implementation remains faithful to the original implementation but is not 100% optimised. The java version is faster but this could be alleviated by compiling c code for parts of the code. This script is simply to provide the functionality of the ImageJ find maxima algorithm to individuals writing pure python script.

The algorithm works as follows:

The first stage in the maxima finding algorithm is to find the local maxima. This involves processing the image with a 3x3 neighbourhood maximum filter. Once filtered this image is compared back to the original, where the pixels are the same value represents the locations of the local maxima. Typically there are far too many local maxima to be meaningful so the goal is then to merge and prune this maxima using some kind of measure of quality. In the case of algorithm a single parameter is used, the noise tolerance (Prominence). If a maxima is close to another then the maxima will be merged or removed based on the below criteria.

Starting with the brightest maxima and working down the intensities:

• Expand out (‘flood fill’) from each maxima location. Neighbouring pixels within a noise tolerance (notl) of the maxima are scanned until the region within tolerance is exhausted.
  • If the pixels are equal to the maxima, mark this as equal.
  • If a greater maxima is met, ignore the active maxima.
  • If the pixels are less than maxima, but greater than maxima minus the noise tolerance, mark as listed.
  • Mark all ‘listed’ pixels 'processed' if they are included within a valid peak region, otherwise reset them.
  • From the regions containing a peak, calculate the best pixel to be considered as maxima based on minimum distance calculation with all those maxima considered equal.
     

For a video detailing how this algorithm works please see:

https://youtu.be/f9vXOMKOlaY

Or for examples of it being used in practise, please see:

https://youtu.be/9wvPsEzRWzI

Various ways are proposed in different websites for example:

• Count the number of foci
• IJ Forum: How to utilize ImageJ to count foci per nucleus
• PDF: Two Ways to Count Cells with ImageJ

Here, a workflow template using ImageJ's build-in Find Maxima ( Process -> Find Maxima) is explained. It can be used for many 2D counting-related tasks.

For counting small, bright foci (dots), set Output type to be Point Selection. If too many points are detected, the number may be reduced using one or more of the following methods:

Apply a filter to reduce noise, e.g. Process -> Filters -> Gaussian Blur... prior to running Find Maxima Set a minimum threshold with Image -> Adjust -> Threshold... prior to running Find Maxima, then use the Above lower threshold option within the dialog box Increase the Noise tolerance value (which effectively acts as a local threshold)

The resulting point selection can be modified (points added/removed) by the Multi-Point tool.

After the points are available, final measurements can be made using Analyze -> Measure.