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DTU Compute Image Analysis Plenty of slides adapted from Thomas Moeslunds lectures Rasmus R. Paulsen Tim B. Dyrby DTU Compute [email protected] http://www.compute.dtu.dk/courses/02502
DTU Compute
Image Analysis
Plenty of slides adapted from Thomas Moeslunds lectures
Rasmus R. Paulsen
Tim B. Dyrby
DTU Compute
http://www.compute.dtu.dk/courses/02502
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2021Image Analysis2 DTU Compute, Technical University of Denmark
Lecture 4b – Morphology
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What can you do after today?
Describe the similarity between filtering and morphology
Describe a structuring element
Compute the dilation of a binary image
Compute the erosion of a binary image
Compute the opening of a binary image
Compute the closing of a binary image
Apply compound morphological operations to binary images
Describe typical examples where morphology is suitable
Remove unwanted elements from binary images using morphology
Choose appropriate structuring elements and morphological operations based on image content
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Morphology
The science of form, shape and structure
In biology: The form and structure of animals and plants
Common leaf morphologies
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Mathematical morphology
Developed in 1964
Theoretical work done in Paris
Used for classification of minerals in cut stone
Initially used for binary images
Do not worry! We use a much less theoretical approach!
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Relevance?
Point wise operations
Filtering
Thresholding
– Gives us objects that are separated by the background
Morphology
– Manipulate and enhance binary objects
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What can it be used for?
Remove noise
– Small objects
– Fill holes
Isolate objects
Customized to specific shapes
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How does it work?
Grayscale image
Preprocessing
– Inversion
Threshold => Binary image
Morphology
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Filtering and morphology
Filtering
– Gray level images
– Kernel
– Moves it over the input image
– Creates a new output image
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Filtering and morphology
Filtering
– Gray level images
– Kernel
– Moves it over the input image
– Creates a new output image
Morphology
– Binary images
– Structuring element (SE)
– Moves the SE over the input image
– Creates a new binary output image
Disk
Box
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1D Morphology
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
(SE)
?Output Image
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1D Morphology : The hit operation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
(SE)
?Output Image
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• If just one 1 in the SE match with the input
• output 1
• else
• output 0
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1D Morphology : The fit operation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
(SE)
?Output Image
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• If all 1 in the SE match with the input
• output 1
• else
• output 0
0
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1D Morphology : Dilation
Dilate : To make wider or larger
– Dansk : udvide
Based on the hit operation
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1D Dilation example
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1Output Image
111
• If just one 1 in the SE match with the input
• output 1
• else
• output 0
Hit
to make bigger
𝑔 𝑥 = 𝑓(𝑥)⨁𝑆𝐸
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0Output Image
111
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0 1Output Image
111
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0 1 1Output Image
111
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0 1 1 1Output Image
111
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0 1 1 1 1Output Image
111
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0 1 1 1 1 1Output Image
111
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Example for Dilation
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
1 0 1 1 1 1 1 1Output Image
111
The object gets bigger and holes are filled!
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1D Morphology : Erosion
Erode : To wear down (Waves eroded the shore)
– Dansk : tære, gnave
Based on the fit operation
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Example for Erosion
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
0Output Image
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12 2 SESE _ _ _
• If all 1 in the SE match with the input
• output 1
• else
• output 0
Fit
to make smaller
𝑔 𝑥 = 𝑓(𝑥)⊖ 𝑆𝐸
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Example for Erosion
1 0 0 0 1 1 1 0 1 1Input image
Structuring Element
0 0 0 0 1 0 0 0Output Image
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The object gets smaller
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Structuring Element (Kernel)
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Structuring Elements can have varying sizes
Usually, element values are 0 or 1, but other values are possible (including none!)
Structural Elements have an origin
Empty spots in the Structuring Elements are don’t cares!
Disk Box
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Structuring Element Origin
The origin is not always the center of the SE
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Special structuring elements
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Structuring elements can be customized to a specific problem
LineDiamond
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Dilation on images - diskHoles are closed
SE
Object is bigger𝑔 𝑥, 𝑦 = 𝑓(𝑥, 𝑦)⨁𝑆𝐸
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Dilation – the effect of the SE
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Dilation Example
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• Round structuring element (disk)
• Creates round corners
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Erosion on images - disk
SE
Object is smaller𝑔 𝑥, 𝑦 = 𝑓(𝑥, 𝑦) ⊖ 𝑆𝐸
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Erosion on images – box (square)
SE
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𝑔 𝑥, 𝑦 = 𝑓(𝑥, 𝑦) ⊖ 𝑆𝐸
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Erosion example
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Counting Coins
Counting these coins is difficult because they touch each other!
Solution: Threshold and Erosion separates them!
More on counting next time!
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Compound operations
Compound
– made of two or more separate parts or elements
Combining Erosion and Dilation into more advanced operations
– Finding the outline
– Opening
Isolate objects and remove small objects (better than Erosion)
– Closing
Fill holes (better than Dilation)
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Finding the outline
1. Dilate input image (object gets bigger)
2. Subtract input image from dilated image
3. The outline remains!
𝑔 𝑥, 𝑦 = 𝑓 𝑥, 𝑦 ⨁𝑆𝐸 − 𝑓(𝑥, 𝑦)
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Opening
Motivation: Remove small objects BUT keep original size (and shape)
Opening = Erosion + Dilation
– Use the same structuring element!
– Similar to erosion but less destructive
Math:
Opening is idempotent: Repeated operations has no further effects!
_𝑔 𝑥, 𝑦 = 𝑓 𝑥, 𝑦 ∘ 𝑆𝐸 = (𝑓(𝑥, 𝑦) ⊖ 𝑆𝐸)⊕ 𝑆𝐸
𝑓 𝑥, 𝑦 ∘ 𝑆𝐸 = (𝑓 𝑥, 𝑦 ∘ 𝑆𝐸) ∘ 𝑆𝐸
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Opening
Original Eroded Dilated
SEOpening = erosion+dilation
𝑔 𝑥, 𝑦 = (𝑓(𝑥, 𝑦) ⊖ 𝑆𝐸)⊕ 𝑆𝐸
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Opening Example
9x3 and 3x9 Structuring Elements
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Opening example
Size of structuring element should fit into the smallest object to keep
Structuring Element: 11 pixel disc
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Closing
Motivation: Fill holes BUT keep original size (and shape)
Closing = Dilation + Erosion
– Use the same structuring element!
– Similar to Dilation but less destructive
Math:
Closing is idempotent: Repeated operations has no further effects!
_𝑔 𝑥, 𝑦 = 𝑓 𝑥, 𝑦 𝑆𝐸 = 𝑓 𝑥, 𝑦 ⊕ 𝑆𝐸 ⊖ 𝑆𝐸
𝑓 𝑥, 𝑦 ∘ 𝑆𝐸 = (𝑓 𝑥, 𝑦 ∘ 𝑆𝐸) ∘ 𝑆𝐸
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Closing
Original
SE
Dilated Eroded
Closing = dilation + erosion
𝑔 𝑥, 𝑦 = 𝑓 𝑥, 𝑦 ⊕ 𝑆𝐸 ⊖ 𝑆𝐸
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Closing Example
Closing operation with a 22 pixel disc
Closes small holes
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Next week: Blob Analysis and object classification
