Morphological filters

Requirements

• Neighbourhood filters
• Rank filters

Motivation

This module explains how filters can be used to change size and shape of objects in the image.

Learning objectives

• Understand how to design morphological filters using rank filters
• Execute morpholofical filters on binary or grayscale images and explain the output

Concept map

graph TD
    image --> max1[max]
    image --> min1[min]
    image --> max2[max]
    image --> min2[min]
    image --> d 
subgraph rank filter sequence
    max2 --> min3[min]
    min2 --> max3[max]
    max1
    min1
    d[max - min]
    end
    max1 --> dilation
    min1 --> erosion
    max3 --> opening
    min3 --> closing
    d --> gradient
    subgraph morphological filter name
    dilation
    erosion
    opening
    closing
    gradient
    end

[*] Concept map above assumes bright objects on dark background. For dark objects on bright background effect of min and max filters inverses

Activity: Explore erosion and dilation on binary images

• Open image: xy_8bit_binary__two_spots_different_size.tif
• Explore how structures grow and shrink, using erosion and dilation

Activity: Explore opening and closing on binary images

• Open image: xy_8bit_binary__for_open_and_close.tif
• Explore effects of morphological closing and opening:
  • closing can fill holes
  • closing can connect gaps
  • opening can remove thin structures

Formative assessment

Fill in the blanks, using those words: shrinks, increases, decreases, enlarges.

1. An erosion _____ objects in a binary image.
2. An erosion in a binary image _____ the number of foreground pixels.
3. A dilation in a grayscale image _____ the average intensity in the image.
4. A dilation _____ objects in a binary image.

True of false? Discuss with your neighbour!

1. Morphological openings on binary images can decrease the number of foreground pixels.
2. Morphological closings on binary images never decreases the number of foreground pixels.
3. Performing a morphological closing a twice in a row does not make sense, because the second closing does not further change the image.

Learn more

• https://en.wikipedia.org/wiki/Morphological_gradient
• https://imagej.net/MorphoLibJ#Grayscale_morphological_filters