Image Segmentation
 Thresholding
• Single level thresholding
Example:
if f(x,y) > T  object point
otherwise  background points
• Multilevel thresholding
if f(x,y) > T2  object1 point
T1 < f(x,y) <= T2  object2 point
f(x,y) < T1  background points
Thresholding
• T function
T = T[x,y, p(x,y), f(x,y)]
where p(x,y) can be certain local value, e.g., average of
neighborhood of (x,y)
Global threshold: T depends only on f(x,y) gray-level value
Local threshold: T depends only on f(x,y) and p(x,y)
Dynamic/Adaptive threshold: T depends on the spatial coordinates (x,y)
Thresholding (cont’d)
• Example of global single threshold algorithm:
Initial estimate for Told
(1) segment image using Told, obtain G1 and G2
(2) compute average u1 for G1, u2 for G2
(3) compute new Tnew = (u1+u2)/2
(4) if | Tnew -Told | > t0  Told = Tnew and goto (1)
Otherwise, goto END
Region growing segmentation
• Group pixels or sub-regions into large regions based on predefined
criteria
• Start with a set of “seed” points
• Criteria for region growing
(1) |fpixel – fseed| < t
(2) The pixel is 8-connected to the region
• Criteria for stopping
-- compare the pixel with the seed
-- compare the pixel with the region average
-- compare the pixel with the pixel neighbors
• Example: multi-modal histogram
Region splitting and Merging
• subdivide an image into a set of arbitrary disjointed regions
• merge and/or split the regions in an attempt to satisfy a certain
condition
R1
R3
R2
R41 R42
R43 R44
Region splitting and Merging
(cont’d)
• Procedure
-- split the image into four disjoint quadrants regions Ri when certain
condition is not satisfied
-- merge adjacent regions Rj and Rk when certain condition is
satisfied
-- stop when no further merging or splitting is possible
• Example:
-- condition:
standard deviation of region Ri < i
or 80% pixels in Ri satisfy | Zj - mi | <= 2 i
Segmentation based on
motion/deformation/Contours
• Motion subtraction
• Deformable template
• Active contour
Image representation and
Description
• External representation: shape, boundary, …
• Internal representation: region, color, texture, …
(1) Chain codes: boundary representation by a connected sequence f
straight-line segments of specified length and direction (4- or 8connectivity)
• definition of direction numbers:
1
2
0
3
4-direction
4
Example:
076666553321212
2
3
1
0
5
6 7
8-direction
Image representation and
Description (cont’d)
(2) Polygon approximations
• Minimum perimeter polygons
-- e.g., rubber band shrinking
• Fit and Split
-- If the maximum perpendicular distance from a boundary
segment to the line (which joins its two end points) exceeds
a certain threshold, the farthest point from the line
becomes a vertex
Image representation and
Description (cont’d)
(3) Thinning (skeletonizing)
• Medial axis transformation
-- property: any point on a medial axis has more than one
closest neighbors on the boundary
Image representation and
Description (cont’d)
(5) Fourier descriptors
• Using small number of frequency components to represent
a set of coordinates, which correspond to a certain shape
• The data reconstructed from Fourier descriptors could be
different with the original data (e.g., loss of fidelity)
(6) Principal component representation
• Eigen vector representation
Image representation and
Description (cont’d)
(7) Relational descriptor
 Rewriting rule (recursive relationship)
Define two primitive elements a and b
a
Example:
b
a
b
a b
Image representation and
Description (cont’d)
(7) Relational descriptor (cont’d)
•
•
•
Rule 1: S aA (starting symbol “S” is replaced by primitive “a” and variable “A”)
Rule 2: A bS (variable “A” is replaced by primitive “b” and starting symbol “S”)
Rule 3: A b (replacing “A” with “b” terminates the procedure)
Example:
a
b
Rule: (1,3)
a b
(1,2,1,3)
a b
(1,2,1,2,1,3)
Image representation and
Description (cont’d)
(7) Relational descriptor (cont’d)
• A phrase structure grammar G = (VN, VT, P, S)
VN : non-terminal vocabularies
VT : terminal vocabularies
V = VN  VT
P: production rewriting rules
S: S  VN Starting symbol
L(G) = {x | x  VT Such that S  x based on grammar G}
(result of production based on grammar G)
Image representation and
Description (cont’d)
(7) Relational descriptor (cont’d)
•
Example of rewriting rule:
production rule P:
VN = {S, A}, VT= {a, b}
S aA
A aA
Ab
G = (VN, VT, P, S)
L(G) = {anb | n=1,2,…}
Image representation and
Description (cont’d)
(7) Relational descriptor (cont’d)
 String description
-- connectivity of primitives can be expressed in a head-to-tail manner
head
Example:
abstracted primitive:
a+b
a –b
ab
a
tail
b
head
tail
a*b
Image representation and
Description (cont’d)
(7) Relational descriptor (cont’d)
 String description
-- PDL (Program description language)
example primitive:
a
b
Example of string description:
e+[[(a+b)*c]+d]
c
(a+b)*c
e
d
Image representation and
Description (cont’d)
(7) Relational descriptor (cont’d)
 Tree description
-- tree description using the relationship “inside of”