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Neighbourhood filters (introduction)

Prerequisites

Before starting this lesson, you should be familiar with:

Learning Objectives

After completing this lesson, learners should be able to:

  • Understand the basic principle of a neighbourhood filter.

  • Apply a mean filter to an image.

Motivation

Images are quite often noisy or have other issues that make them hard to segment, e.g. by means of a simple intensity threshold. Neighbourhood filters are a very important (maybe the most important) means to enhanced images in a sense of making them more amendable for segmentation.

Concept map

graph TB P(Pixel coordinate) -->NBH(Neighbourhood pixels) SE(Structuring element) --> NBH NBH -->A(Mathematical formula) A -->NP(New pixel value)

Example figure

Image with a pixel neighourhood. Same image filtered with neighborhood filters of different kinds (mean, median, vertical edge) and structuring elements (circular with a radius of 1 pixel, top row; radius of 3 pixels, bottom row).

Neighbourhood filters

Neighborhood filters comprise two ingredients: a definition of the pixel neighbourhood (size and shape) and a mathematical recipe what to compute on this neighbourhood. The result of this computation will be used to replace the value of the central pixel in the neighbourhood. This procedure can be applied to several (all) pixels of an image to obtain a filtered image. The animation shows a square neighbourhoods (3x3) applied to the inner pixels of the image.

There are really tons of different neighborhood filters, and you can invent a new one!

The neighbourhoods

The neighborhood of a pixel is also called a structuring element and can have various sizes and shapes. Here, we use one of the simplest and most widely used neighbourhoods, namely a circular neighborhood, which is defined by a certain radius. We will explore other shapes of structuring elements in more detail in a dedicated module.

The math

There are really many many ways how to cleverly compute on a pixel neighborhood. For example, one class of computations is called convolutional filters, another is called rank filters. Here, we focus on the relatively simple mean filter, which is the mean filter.

Best practice

As usual, everything depends one the scientific question, but maybe one could say to use a filter that changes the image as little as possible.

Activity

Show activity for:

ImageJ Macro & GUI

run("Close All");
// File › Open...
open("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__noisy_two_nuclei.tif");
// Image › Rename...
rename("input");
// Image › Duplicate...
run("Duplicate...", "title=mean_1" );
// Process › Filters › Mean...
run("Mean...", "radius=1");

selectWindow("input");
run("Duplicate...", "title=mean_7" );
run("Mean...", "radius=7");

run("Tile");

Exercises

Show exercises for:

ImageJ Macro & GUI

Exercise 1

  • Open xy_8bit__nuclei_very_noisy.tif
  • Apply a mean filter ([Process > Filters > Mean…]) to the image such that you can binarise the image into exactly three disjoint foreground regions (the three nuclei). It is helpful to first duplicate the image [Image > Duplicate …] or [Ctrl-Shift-D]
    • What is the smallest size for the mean filter that does the job?
    • What happens if the filter size increases?

Solution

run("Close All");

// File › Open...
open("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__nuclei_very_noisy.tif");
// Process › Filters › Mean...
run("Mean...", "radius=2");
// Image › Adjust › Threshold...
setThreshold(29, 255);
setOption("BlackBackground", true);
run("Convert to Mask");

Exercise 2

Sometimes you would like to find out how the structuring-element (the neighbourhood) of a filter looks like. One way to do this is to apply a filter to a single white pixel and look at the resulting form.

Solution

run("Close All");
// File > Open...
open("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit_binary__one_foreground_pixel.tif")
// Duplicate the image Image > Duplicate...
run("Duplicate...", "title=radius2");
// Maximum filter Process › Filters › Maximum...
run("Maximum...", "radius=2");

Assessment

Fill in the blanks

Fill in the blanks, using these words: decrease, increase, size, structuring element, large

Solution

  • A synonym for neighbourhood is structuring element
  • The filter radius characterize the filter size
  • large filter size can cause a loss of details in the filtered image
  • Filter can be used to decrease the noise in an image
  • The usage of filters can increase the quality of image segmentation/binarization

Follow-up material

We recommend reading these modules next:

Learn more: