Image Segmentation - INTELLIGENCE: Lab Description
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Transcript Image Segmentation - INTELLIGENCE: Lab Description
Image Segmentation
• Segmentation is the process of partitioning an
image into regions
– region: group of connected pixels with similar
properties
– properties: gray levels, colors, textures, motion
characteristics (motion vectors), edge continuity …
• There are two approaches to segmentation
– region segmentation
– edge segmentation
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Edges and Regions
• In ideal images, a region is bounded by a
closed contour
– the close contours may be obtained from the
regions by edge detection
– the regions may be obtained from the closed
contours by boundary-filling
• In real images, it is rare to obtain regions
from contours directly and vice versa
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Regions and Objects
• Regions are important for the interpretation of
images because they may correspond to objects in
a scene
• An image may contain several objects and each
object may contain several regions corresponding
to different parts of an object
• Due to a number of factors (noise, bad
illumination, 3D world etc.) segmentation is
usually not perfect
• Image Interpretation requires object specific
knowledge
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• Image with many objects
• Each object consists of several regions
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Region Segmentation
• Region Segmentation: the pixels of the
same object are grouped together and are
marked to indicate that they form a region
• Criteria for region segmentation: pixels may
be assigned to the same region if they have
similar intensity values and they are close to
one another
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Edge Segmentation
• Find all pixels on region boundaries
• Canny Operator
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apply Gaussian smoothing
apply edge detection
remove false edges (e.g., noise)
thin the edge boundary is 1 pixel wide
fill the gaps recover missing edges
put boundary pixels in order all pixels in a list
• Ideally closed boundaries
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Edge Following
• There may exist gaps and noisy edges in the
output of Canny
• Fill gaps and follow the edge in many directions
– there may exist more than one regions meeting each
other
– not all directions are promising
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continuity
proximity
intensity
length
direction
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Edge Following as a Graph
Traversal Problem
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Graph Traversal
• Edge following on a graph can be viewed as a
minimization (or maximization) problem
– the most promising path is the one which maximizes a
function Φ(i,j)
– promising paths correspond to strong edges
• Graph search can be hard combinatorial
Can become very slow
– Dynamic Programming (DP)
– Heuristics
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Criterion Φ(C)
• The edge C with maximum Φ is the most
promising
– Φ(C) = Σφ(i,j) over all points on a curve
– Σφ(i,j) = average{intensity} - average{angle}
– takes averages over all points on a path
• In places where the curve splits into 2 or more
directions (paths), follow the direction with the
maximum φ
– this situation changes after a while and may be
necessary to backtrack to an earlier point
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edges
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directions
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7 4
3
5
1
6
1
6
6
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first path
second path
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5
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7
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φ=14/3-π/(4*3)
3 φ=17/3-0
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1 promising
7 promising
at 7
at 6
1
6
φ=22/6-0
φ=33/66
2*π/(4*6)
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Using the maximum cost Φ criterion to find the cell boundaries
in microscope images
a. a stage in the search process
b. the completed boundary
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Region Segmentation
• Analyze the grey value
distribution (histogram) of
the image
– assumption: objects are
dark against a light
background
– their grey-value
distributions can be
separated putting thresholds
between them
– convert a grey-level image
into a binary one by
applying carefully selected
thresholds
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Many Regions
• One threshold two regions
– black pixels: object
– white pixels: background
• More than two thresholds more than two regions with
different intensity values
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(1) Peakiness Detection Algorithm
1. Find the two highest local maxima gi, gj in the
histogram that are at least at distance d apart
d is user defined
2. Find the lowest point gk in the histogram between gi
and gj
3. Peakiness = min{H(gi),H(gj)}/H(gk)
4. Take the combination (gi,gj,gk) with the highest
peakiness
5. Threshold the image at T=gk
6. N thresholds: take the N greater peakinesses (Ti=gki)
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(2) Iterative Algorithm
1. Compute a threshold T
T: mean gray value of image
2.
3.
4.
5.
Partition the image into R1, R2 using T
Compute the mean values μ1,μ2 of R1,R2
Select a new threshold T=1/2(μ1+μ2)
Repeat steps 2-4 until μ1, μ2 do not change
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(3) Adaptive Thresholding
• The same threshold is not usable everywhere in
the image
• e.g., uneven illumination
1. Partition the image into mxm subimages
2. Select a threshold Tij for each subimage
apply 1st or 2nd threshold selection algorithm
3. Compute the union of the thresholded subimages
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a. original image with
uniform illumination
b. histogram of a
c. simulated uneven
illumination
d. image a with uneven
illumination added
e. histogram of image d
f. thresholding at T=72
failed!!
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(4) Double Thresholding
1. Select threshold T1 (apply 1st or 2nd algorithm)
2. Set T2 = T1 + ε (ε is user defined)
3. Compute regions R1, R2, R3:
a. R1: pixels with gray values less than T1
b. R2: pixels with gray values between T1 and T2
c. R3: pixels with gray values above T2
4. Visit each pixel of R2: if the pixel has a neighbor
in R1, reassign it to R1
5. Repeat step 4 until no pixels of R2 are reassigned
6. Reassign all pixels remaining in R2 to R3
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