5th Intensive Course on Soil Micromorphology Naples 2001 12th - 14th September Image Analysis Lecture 8 Introduction to Binary Morphology.

5th Intensive Course on Soil Micromorphology

Naples 2001

12th - 14th September

Image Analysis

Lecture 8

Introduction to Binary Morphology

5th Intensive Course on Soil Micromorphology - Naples 2001Image Analysis - Lecture 8: Binary Morphology

•Erosion/Dilation

•Opening/Closing

•Kernel Shapes

Applications in Particle / Void Size Distribution

Introduction to Binary Morphology Methods

Requires Segmentation of Image into Binary Form

(may require manual editting).

Foreground pixels are coded 1 - background 0

i.e. Particles 1 (white), voids 0 (black)or Voids 1 (white), particles 0 (black)


Erosion

strips one layer of foreground pixels at edges of particles

criteria

based on number of surrounding background pixels

can be any number 1 - 8

pixel of interest is redwhite - foregroundblack - background

a) 8 pixels b) 7 pixels

c) 6 pixels d) 5 pixels

e) 4 pixels f) 3 pixels

g) 2 pixels h) 1 pixel


a) foreground pixel removed for all criteria.

h) foreground pixel removed only if criteria is set to 1 pixel.

a) 8 pixels

h) 1 pixel

Criteria may also specify that diagonal erosion is (or is not permitted).

Erosion not permitted if diagonals not allowed in (j)

i) j)


4 - point connectivity 8 - point connectivity

Connectivity:

4 - point connectivity

allows connection only up/down and side to side


allows connection on diagonals

In 4 - point connectivity, foreground and background are uniquely separated.

In 8 - point connectivity is background or foreground continuous across diagonal? Both are not possible


Erosion of original by one layer

criterion - a single touching background pixel

4 - point connectivity8 - point connectivity


Erosion by 2 and 3 layers


Some residual parts of largest particle remain.

Erosion by 2 and 3 layers


All foreground features will disappear.

Until particles disappear the residues are less rough


Dilation

- the reverse of erosion

Once again similar criteria apply



Individual features will merge


X

X

X

X X

X

X

X X

8 - point connectivity erosion

Equivalent to passing a 3 x 3 kernel over binary image.

Where central point of kernel hits background, all pixels covered by kernel are set to background

X


4 - point connectivity erosion

Equivalent to passing a 3 x 3 kernel over binary image.

Where central point of kernel hits background, all pixels covered by kernel are set to background

X

X

X X

X X

X

X

X X


Non-standard Kernels may be used for special effects

X


Consider effect of one erosion followed by one dilation.

This is known as an “OPENING”


Red: Residual after erosion

Yellow: Recovered after dilation

Blue: Complete particles lost

Green: Roughness lost on large particles

Using careful housekeeping it is

possible to identify proportion of

particles lost completely and

“roughness” lost from large

particles.


2 cycles of erosion

(8 - point connectivity)

2 cycles of erosion followed by 2 cycles of dilation

(8 - point connectivity)

Components of “opening” - see next slide


Light Green: Roughness cycle 1

Dark Green: Roughness cycle 2

Red: Residue after 2 cycles

Yellow: Recovery cycle 1

Orange: Recovery cycle 2

Blue: Particles lost cycle 1

Purple: Particles lost cycle 2


2 cycles of 3 x 3 kernel are equivalent to 1 cycle by a 5 x 5 kernel.

Can be used for efficiency

Alternative kernel for 5 x 5 which approximates more closely to a circle (i.e. corner pixels are omitted)

Kernel for 3 cycles giving a good approximation to a circle / octagon).


Standard Kernels for 9 x 9 array

These 4 shapes can be propagated to any size


Procedure for feature size analysis

•Erode n cycles•Dilate n cycles

•Determine pixels lost as roughness

•Determine pixels lost from particles which disappear

n = 1

Are particle residues left

Yes

No

n = n + 1

Summarise results

Schematic Representation of one erosion and one dilation

Grey Level Image Binary Version


BINARY MORPHOLOGY

• During successive opening, features tend towards circles.

• At each stage, protrusions are lost and this loss is related to the shape and roughness of grains.

• Finally, the remaining feature is lost and this is related to the size of the feature.

• Careful housekeeping is needed to differentiate between two types of loss, but procedure is well established in some branches of microscopy.

The difficulty in achieving a reliable threshold makes the

method generally unsuitable for analysing images of cores.




Binary Morphology used to determine Particle size Distribution



Roundness

Often defined relating to sharpness of asperities on a grain

Sometimes roundness is defined by drawing circles,

but when exactly should on draw a circle?


Grain is successively “opened” with different radii.

The lighter colours (yellow) show parts lost first.

Ultimately remainder of grain disappears when inscribed circle is as shown in blue.

If octagonal or square “structuring” elements are used, then grain degenerates to these shapes.


Grain is successively subjected to “opening” of different radii.

The edge of the grain are shown in colour where light colours (e.g. yellow represent areas lost first - i.e. sharp), and dark colours (e.g. dark blue are lost last.

Can be used as a more objective measure of roundness.

5th Intensive Course on Soil Micromorphology Naples 2001 12th - 14th September Image Analysis Lecture 8 Introduction to Binary Morphology.

Documents

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image analysis lecture

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soil micromorphology