Morphology – Chapter 10

Binary image processing• Often it is advantageous to reduce an image

from gray level (multiple bits/pixel) to binary (1 bit/pixel)– Threshold the gray level image to isolate objects– Edge detect and threshold the edge magnitude map– Special lighting (assembly line manufacturing applications)

• The goal is to separate the image into foreground and background components

Binarization

Binarization

• But, the process is not always perfect (is rarely perfect?)– Foreground objects have holes

(background shows through)

Binarization

• But, the process is not always perfect (is rarely perfect?)– Contours get broken

Morphology

• Morphology is a set of processes that allow us to alter the structure of the binary image

• Foundations in set theory– The image forms one set – the set of pixels that make up the

foreground

– The structuring element forms the other set – much like a convolution kernel

1| pIpF I

1| pHpS SE

Structuring element

• Looks like a convolution kernel– Contains only 0 and 1– Has a designated hot spot (origin)

– The hot spot is placed over the “current pixel” (like the center of the convolution kernel)

– The hot spot need not be in the center– The hot spot can be either 0 or 1

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The operations

• All are based on set theory– Definitions are based on intersections and

unions of the image and the structuring element (logical AND/OR operations)

• The two fundamental operations are– Dilation – growing the foreground of the

image– Erosion – shrinking the foreground of the

image

Dilation

• No need to show the set theory definition – better to just see the words

• Place the hot spot on top of an image pixel that is in the set (a foreground pixel)

• Copy the 1’s of the structuring element into the image set

• Note that this must be done using double buffering (don’t overwrite the original image)

Dilation

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Erosion

• No need to show the set theory definition – better to just see the words

• Place the hot spot on top of an image pixel that is in the set (a foreground pixel)

• Place a 1 in the image only if all of the 1’s of the structuring element align with 1’s in the image

• Note that this must be done using double buffering (don’t overwrite the original image)

Erosion

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Dilation/Erosion usage

• Among other things…– Dilation is good for filling small holes– Erosion is good for removing small tails

• Dilation of the foreground can be achieved by erosion of the background

– See next slide for explanation

HIHI

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Dilation/Erosion

HIHI

*

Dilation operation Erosion operation

H*

Reflection of the structuring element(change coordinates from – to +, + to -)

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Reflect

All this really means is that implementation is easy

Typical…

• The shape of the structuring element is often a circular disk (approximate)– This results in a symmetrical dilation or

erosion (which is often desired)

• There is no easy (i.e. efficient) way to do this stuff– Lots of nested loops is all you can do

Composite operations

• Opening– Erosion followed by dilation (same structuring

element)• Erosion removes small elements (like noise)• Dilation puts the remaining stuff [almost] back to how it was

• Closing – Dilation followed by erosion (same structuring

element)• Dilation removes small holes and notches

• Erosion puts the remaining stuff [almost] back to how it was

Composite operations

• Opening the foreground is equivalent to closing the background– Again, this just means implementation is

easy– To do opening, invert the image (swap

foreground and background) and perform a closing operation

Grayscale morphology

• Instead of checking for values equal to 1 or 0 (and copying into the result image, etc.) you check for minimum and maximum values

• From my experience this isn’t done very much– The book doesn’t go into details– ImageJ doesn’t implement– So I’m going to just move on