Image Segmentation

1
Image Segmentation

• A process between lowhigh level processes
• (intermediate level)
• The aim is to separate regions wrt brightness,
  color, reflectivity, texture, etc.
• Partial segmentation produces a set of disjoint
  regions (high level info needed to complete
  segmentation)
• For some applications complete segmentation is
  possible (e.g. blood cells, printed characters)

2
Segmentation Methods

• Global knowledge based methods (e.g. thresholding
  using histogram)
• Edge based methods
• Region based methods
• Solution can be based on brightness, texture,
  color, motion, etc.

A dual problem (A region is enclosed in A
boundary)
3
Thresholding

• Thresholding

• Multiple thresholds

if
if
else
if
. .
otherwise
4
Threshold detection methods

• P-tile thresholding Known (estimated)
  foreground/background ratio. Choose pixels with
  low value as foreground so that the estimated
  ratio is satisfied.
• Histogram shape analysis
• Mode method Min between peaks
• Optimal thresholding Consider histogram as a
  weighted sum of prob. densities. Min error.

5
Edge based segmentation

• Edge detection highlights edges (but more work is
  needed to extract meaningful info)
• Nonmaximal supression
• For each edge pixel inspect two adjacent pixels
  pointed by grad direction
• If neighbors have greater edge magnitude mark
  edge pixel for deletion
• Edge relaxation
• Mark edge magnitude greater than as correct
• Scan edge pixels in the range
  (unsure edges)
• If they have adjacent edge pixels then mark them
  as edges.
• Continue until stability

6
Border tracing
7
Hough Transformation

• Line Detection
• Original Hough Transform
• Modified Hough Transform

8
Hough Transform Algorithm

• Quantize the parameter space (I.e. )
• Initialize all cells to zero
• For each foreground point in the image space
  increment the accumulator cells that satisfy the
  equation
• Search for the maxima in the accumulator space

9
Hough Transformation
10
Example
11
Example
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Hough Transformation to detect circles

• Parameter space is the image space
• Accumulation is done for a predetermined range
  of r using edge direction information
• Maxima represents a likely circle

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Hough Transformation to detect circles
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Generalized Hough Transform

• Construct an R-table
• Distances from reference point to border
  points and the border directions are recorded

15
Generalized Hough Transform

• R-table
• Can be modified to include scale and
  rotation

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Gen. Hough Transform Algorithm

• Construct R-table for the desired object
• Initialize accumulator arrays
• For each pixel (x,y) in the gradient image
  determine edge direction find all
  potential reference points and increase
  accumulator values for all and
• Search for maxima in A

17
Region-based Segmentation

• A segmentation is the partition of an image R
  into sub-regions Ri such that
• A region can be defined by a predicate P such
  that P(Ri) TRUE if all pixels within the region
  satisfy a specific property.
• P(Ri ?Rj) FALSE for i ?j.

• Region-Growing
• Start with seed points
• Grow around current seed regions by attaching
  pixels of the same property to the growing
  sub-regions.
• Region splitting and Merging
• Apply the predicate to a sub-region. If it is
  true, stop splitting. Else, split the region.
• Quadtree is one way of splitting.
• Neighboring sub-regions with the same predicates
  can be merged.

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Watersheds Segmentation
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Watersheds Segmentation
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Watersheds Segmentation

• A morphological region growing approach.
• Seed points
• local minima points
• Growing method
• Dilation
• Predicates
• Similar gradient values
• Sub-region boundary
• Dam building
• To avoid over-segmentation
• Use markers

http//cmm.ensmp.fr/beucher/wtshed.html
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Dam Building
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Watershed Segmentation Example
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Over-Segmentation and Use of Marker
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TEXTURE

• An attribute representing the spatial arrangement
  of the gray levels of the pixels in a region.

25
TEXTURE
REGULAR
STATISTICAL ISOTROPIC
STATISTICAL ANISOTROPIC
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STATISTICAL METHODS FOR TEXTURE ANALYSIS
HISTOGRAM
OF OCCURRENCES
FIRST ORDER STATISTICS How often does a given
grey value occur at a pixel in an image.
H(g)
0 255
Single Pixel
GREY VALUES
H (g1,g2)
SECOND ORDER STATISTICS How often do grey values
co-occur at two pixels separated by a
fixed distance and direction ..
(Di,Dj)
OF CO-OCCURRENCES
0 255
(Di,Dj)
255
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STATISTICAL METHODS FOR TEXTURE ANALYSIS
H (g1,g2)
SECOND ORDER STATISTICS How often do grey values
co-occur at two pixels separated by a
fixed distance and direction ..
(Di,Dj)
OF CO-OCCURRENCES
0 255
(Di,Dj)
255
256
256 x 256 2D matrix array where entries
are co-occurrence values
256
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Nth-order STATISTICS
(Di,Dj)
3
(Di,Dj)
2
(Di,Dj)
N-dimensional matrix
1
.
.
(Di,Dj)
n
It has been found that humans can discriminate
textures with different 2nd-order statistics but
are bad at discriminating 3rd order
statistics (Julesz 1981).
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2nd ORDER STATISTICS
256
256 x 256 2D matrix array where entries
are co-occurrence values
256
Since only pixel elements over short distances
are correlated (Di,Dj) is typically small
e.g., (1,0), (0,1), (1,1)
Since for 256 grey values the 2D matrix is
typically sparse, co-occurences are typically
taken over 8 grey value ranges and less (e.g.,
for 256 grey values they are grouped into 8 grey
value bins or less)
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2nd ORDER STATISTICS
SECOND ORDER STATISTICS How often do grey values
co-occur at two pixels separated by a
fixed distance and direction ..
grey values
2D matrix array where entries are co-occurrence
values
grey values
(Di,Dj)
Symmetrize the co-occurrence matrix by adding
itself to its transpose.
T


Besides making this less sensitive to how the
image plane is coordinatized this real positive
symmetric matrix has nice rotational invariants
such as eigenvalues.
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COOCCURANCE MATRIX (Example)
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TEXTURE MEASURES DERIVED FROM THE CO-OCCURRENCE
MATRIX
ENTROPY S S Cij logCij
CONTRAST S S (i - j) Cij
2
ENERGY S S Cij
2
HOMOGENEITY S S Cij / ( 1i-j)
33
Applications of Texture models

• Medical image analysis
• Texture features are used to distinguish between
  different tissues, etc. (e.g. normal/abnormal)

34
Applications of Texture models

• Inspection
• Textiles
• Lumber wood
• Metal surface
• Document processing
• Postal address recognition
• Interpretation of maps

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Applications of Texture models

• Remote sensing
• Land use classification, automated image analysis

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Applications of Texture models

• Content-based image retrieval
• Searching images with a similar content (e.g.
  sunset)