Morphology – Chapter 10. Binary image processing Often it is advantageous to reduce an image from...
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Transcript of Morphology – Chapter 10. Binary image processing Often it is advantageous to reduce an image from...
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
• But, the process is not always perfect (is rarely perfect?)– Foreground objects have holes
(background shows through)
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)
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)
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
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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