region-based segmentation
TRANSCRIPT
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Mestrado em Ciência de ComputadoresMestrado Integrado em Engenharia de Redes e
Sistemas Informáticos
VC 14/15 – TP9Region-Based Segmentation
Miguel Tavares Coimbra
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VC 14/15 - TP9 - Region-Based Segmentation
Outline
• Region-based Segmentation• Morphological Filters
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VC 14/15 - TP9 - Region-Based Segmentation
Topic: Region-based Segmentation
• Region-based Segmentation• Morphological Filters
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VC 14/15 - TP9 - Region-Based Segmentation
Why Region-Based Segmentation?
• Segmentation– Edge detection and
Thresholding not always effective.
• Homogenous regions– Region-based
segmentation.– Effective in noisy
images.
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VC 14/15 - TP9 - Region-Based Segmentation
Definitions
• Based on sets.• Each image R is a set
of regions Ri.– Every pixel belongs to
one region.– One pixel can only
belong to a single region.
S
iiRR
1
ji RR
R1
R3R2
R4
R6
R5
R7
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VC 14/15 - TP9 - Region-Based Segmentation
R1
R3
R2
R4
R6
R5
R7
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VC 14/15 - TP9 - Region-Based Segmentation
Basic FormulationLet R represent the entire image
region. Segmentation partitions R into n subregions, R1, R2, ..., Rn, such that:
a)
b)
c)
d)
e)
a) Every pixel must be in a region
b) Points in a region must be connected.
c) Regions must be disjoint.
d) All pixels in a region satisfy specific properties.
e) Different regions have different properties.
n
ii RR
1
.21 region, connected a is , ..., n, i Ri
jijiRR ji , and allfor
.,...,2,1for )( niTRUERP i
.for )( jiFALSERRP ji
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VC 14/15 - TP9 - Region-Based Segmentation
How do we form regions?
• Region Growing• Region Merging• Region Splitting• Split and Merge• Watershed• ...
What a computer sees
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VC 14/15 - TP9 - Region-Based Segmentation
Region growing• Groups pixels into
larger regions.• Starts with a seed
region.• Grows region by
merging neighboring pixels.
• Iterative process– How to start?– How to iterate?– When to stop?
InitialRegions Iterations Stop
Condition
Finish
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VC 14/15 - TP9 - Region-Based Segmentation
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VC 14/15 - TP9 - Region-Based Segmentation
Region merging
• Algorithm– Divide image into an initial set of regions.
• One region per pixel.– Define a similarity criteria for merging
regions.– Merge similar regions.– Repeat previous step until no more merge
operations are possible.
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VC 14/15 - TP9 - Region-Based Segmentation
Similarity Criteria
• Homogeneity of regions is used as the main segmentation criterion in region growing.– gray level – color, texture – shape – model – etc.
Choice of criteria affects segmentation results dramatically!
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VC 14/15 - TP9 - Region-Based Segmentation
Gray-Level Criteria
• Comparing to Original Seed Pixel– Very sensitive to choice of seed point.
• Comparing to Neighbor in Region– Allows gradual changes in the region.– Can cause significant drift.
• Comparing to Region Statistics– Acts as a drift dampener.
• Other possibilities!
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VC 14/15 - TP9 - Region-Based Segmentation
Region splitting• Algorithm
– One initial set that includes the whole image.
– Similarity criteria.– Iteratively split regions
into sub-regions.– Stop when no more
splittings are possible.
R1
R1 R2
R3 R4
R1 R2
R3R4
R6
R5
R7
R1 R3R2
R4 R6R5 R7
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VC 14/15 - TP9 - Region-Based Segmentation[Machine Vision; David Vernon]
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VC 14/15 - TP9 - Region-Based Segmentation
Split and Merge• Combination of both
algorithms.• Can handle a larger
variety of shapes.– Simply apply previous
algorithms consecutively.
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VC 14/15 - TP9 - Region-Based Segmentation
The Watershed Transform• Geographical inspiration.
– Shed water over rugged terrain.
– Each lake corresponds to a region.
• Characteristics– Computationally complex.– Great flexibility in
segmentation.– Risk of over-segmentation.
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VC 14/15 - TP9 - Region-Based Segmentation
The Drainage Analogy
• Two points are in the same region if they drain to the same point.
Courtesy of Dr. Peter Yim at National Institutes of Health, Bethesda, MD
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VC 14/15 - TP9 - Region-Based Segmentation
The Immersion Analogy
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VC 14/15 - TP9 - Region-Based Segmentation
[Milan Sonka, Vaclav Hlavac, and Roger Boyle]
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VC 14/15 - TP9 - Region-Based Segmentation
Over-Segmentation
• Over-segmentation.– Raw watershed segmentation produces a
severely oversegmented image with hundreds or thousands of catchment basins.
• Post-Processing.– Region merging.– Edge information.– Etc.
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VC 14/15 - TP9 - Region-Based Segmentation
Topic: Morphological Filters
• Region-based Segmentation• Morphological Filters
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VC 14/15 - TP9 - Region-Based Segmentation
Mathematical Morphology
• Provides a mathematical description of geometric structures.
• Based on sets.– Groups of pixels which
define an image region.
• What is this used for?– Binary images.– Can be used for post-
processing segmentation results!
• Core techniques– Erosion, Dilation.– Open, Close.
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VC 14/15 - TP9 - Region-Based Segmentation
Tumor Segmentation using Morphologic Filtering
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VC 14/15 - TP9 - Region-Based Segmentation
Dilation, Erosion• Two sets:
– Image– Morphological kernel.
• Dilation (D)– Union of the kernel with
the image set.– Increases resulting area.
• Erosion (E)– Intersection.– Decreases resulting area.
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VC 14/15 - TP9 - Region-Based Segmentation
Dilation
• Example using a 3x3 morphological kernel
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VC 14/15 - TP9 - Region-Based Segmentation
Erosion
• Example using a 3x3 morphological kernel
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VC 14/15 - TP9 - Region-Based Segmentation
Opening, Closing• Opening
– Erosion, followed by dilation.
– Less destructive than an erosion.
– Adapts image shape to kernel shape.
• Closing– Dilation, followed by
erosion.– Less destructive than a
dilation.– Tends to close shape
irregularities.
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VC 14/15 - TP9 - Region-Based Segmentation
Opening
• Example using a 3x3 morphological kernel
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VC 14/15 - TP9 - Region-Based Segmentation
Closing
• Example using a 3x3 morphological kernel
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VC 14/15 - TP9 - Region-Based Segmentation
Core morphological operators
Dilation Erosion
Closing Opening
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VC 14/15 - TP9 - Region-Based Segmentation
Example: Opening
Tresholding
Opening
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VC 14/15 - TP9 - Region-Based Segmentation
Example: Closing
Closing
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VC 14/15 - TP9 - Region-Based Segmentation
Connected Component Analysis
• Define ‘connected’.– 4 neighbors.– 8 neighbors.
• Search the image for seed points.
• Recursively obtain all connected points of the seeded region.
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VC 14/15 - TP9 - Region-Based Segmentation
Resources
• Gonzalez & Woods - Chapter 7 and 8