This document discusses various shape features that can be used for machine vision and image segmentation. It covers thresholding techniques, identifying object boundaries using chain codes and Fourier descriptors, and describing regions using basic descriptors like area and perimeter or moment invariants. Segmentation is described as an important but difficult task, and thresholding, discontinuities and region similarity are presented as common segmentation approaches. Examples are provided to illustrate different shape feature extraction methods.

1. Course: Machine Vision
Shape Features
Session 08
D5627 – I Gede Putra Kusuma Negara, B.Eng., PhD

2. Outline
• Thresholding
• Identifying Boundary
• Chain Code
• Fourier Descriptor
• Identifying Region
• Moments

3. Thresholding

4. Segmentation
• Segmentation: subdivides an image into its constituent region or
objects
• The purpose of image segmentation is to decompose the image into
parts that are meaningful with respect to a particular application
• Example, automatic PCB (printed circuit board) inspection,

5. Segmentation
• Segmentation is one of the most difficult tasks in image processing
• Segmentation accuracy determines the success or failure of
automated analysis procedure
• Considerable care should be taken to improve the probability of
rugged segmentation

6. Segmentation
Image segmentation generally are based on basic properties of intensity
values:
1. Discontinuity: partition an image based on abrupt changes in
intensity, such as edges
2. Similarity: partition image into regions that are similar according to
a set of predefined criteria

7. Thresholding
• Thresholding is a fundamental approach to segmentation
• Popular in applications where speed is an important factor
• Single value thresholding can be given mathematically as follows:






T
y
x
f
if
T
y
x
f
if
y
x
g
)
,
(
0
)
,
(
1
)
,
(

8. Thresholding (example)
• For example, we are going to build poker playing robot
• This robot should be able to visually interpret the card in its hand

9. What is the Correct Threshold?
• Wrong threshold leads to disastrous results

10. Basic Global Thresholding
• Partition the image histogram using a single global
threshold
• The basic global threshold, T, is calculated as follows:
1. Select an initial estimate for T (typically the average grey level
in the image)
2. Segment the image using T to produce two groups of pixels: G1
consisting of pixels with grey levels >T and G2 consisting pixels
with grey levels ≤ T
3. Compute the average grey levels of pixels in G1 to give μ1 and
G2 to give μ2

11. Basic Global Thresholding
4. Compute a new threshold value:
5. Repeat steps 2 – 4 until the difference in T in successive
iterations is less than a predefined limit T∞
• This algorithm works very well for finding thresholds when the
histogram is suitable
2
2
1 
 

T

12. Basic Global Thresholding
(example)

13. Problems with Single Value
Thresholding
• Single value thresholding only works for bimodal histograms
• Images with other kinds of histograms need more than a single
threshold

14. Thresholding (example)
• For example, we want to
isolate the contents
of the bottles
• Think about what the
histogram for this
image would look like
• Single threshold value can’t be used
in this problem
• The second picture shows the single
value thresholding result

15. Double Value Threshold
• We need a double value to
segment this kind of image
• There are two objects in this
image, bottle and liquid
• After we applied double
threshold value, we can
distinguish bottle and liquid

16. Identifying Boundary

17. Object Descriptor
• Objects are represented as a collection of pixels in an image
• To support the object recognition, we need to describe the
properties of group pixels  object descriptor
• Two forms of object descriptor:
1. Boundary descriptor: characterize an arrangement of pixels in
the object perimeter or boundary
2. Region descriptor: characterize an arrangement of pixels within
the area of the object

18. Important Properties
of Object Descriptor
1. Complete set: two objects must have the same descriptors if and only
if they have the same shape
2. Congruent: able to recognize similar objects when they have similar
descriptors
3. Convenient: they have invariant properties (position, rotation, scale,
or affine/perspective changes)
4. Compact set: represent the essence of an object in an efficient way

19. Boundary
• Boundary: a region describes contents that are surrounded
by a boundary (or perimeter)  region’s contour
• The boundary found by following the object contour:
– First, find one point on the contour
– Progress round the contour either in a clockwise/anticlockwise
direction, finding the nearest (or next) contour point.

20. Chain Code
• We can represents a contour with the coordinates of a sequence of
pixels in the image
• Alternatively, we can just store the relative position between
consecutive pixels. This is the basic idea behind chain code
• The set of pixels in the border of a shape is translated into a set of
connections between them

21. Chain Code: Example

22. Start Point Invariance
in Chain Code
• Chain code will be different when the start point changes
• We need start point invariance. This can be achieved by considering the
elements of the code to constitute the digits in an integer.
• We can shift the digits cyclically (replacing the least significant digit with
the most significant one, and shifting all other digits left one place).

23. Fourier Descriptor
• Let x[m] and y[m] be the coordinates of the m-th pixel on the boundary
of a given 2D shape containing pixels, a complex number can be formed
as z[m]=x[m]+jy[m], and the Fourier Descriptor (FD) of this shape is
defined as the DFT of z[m]:
• FD is independent of its location, scaling, rotation and starting point
• We could use M < N FDs corresponding to the low frequency
components of the boundary to represent the 2D shape
Z[k]= DFT[z[m]]=
1
N
z[m]e- j2pmk/N
m=0
N-1
å

24. Fourier Descriptor
(example)
25-Jun-21 Image Processing and Multimedia Retrieval 24
Original shape Reconstructed
Using 9 FD
Reconstructed
Using 19 FD
Reconstructed
Using 29 FD

25. Fourier Descriptor Properties
• Fourier descriptors inherit several properties from the Fourier transform.
• Translation invariant: no matter where the shape is located in the image,
the Fourier descriptors remain the same.
• Scaling invariant: if the shape is scaled by a factor, the Fourier descriptors
are scaled by that same factor.
• Rotation and starting point invariant: rotating the shape or selecting a
different starting point only affects the phase of the descriptors.
25-Jun-21 Image Processing and Multimedia Retrieval 25

26. Identifying Region

27. Region
There are two main region descriptors:
1. Basic: characterize the geometric properties of the region
2. Moment: characterize the density of the region

28. Basic Region Descriptors
• A region can be described by considering scalar measures based on its
geometric properties
Descriptor Formula
Area
Perimeter
Compactness
Dispersion
A(S) = I(x, y)DA
y

x

P(S) = (xi - xi-1)2
+(yi - yi-1)2
i
å
C(S) =
A(s)
P2
(s) / 4p
IR(S) =
max (xi - x)2
+(yi - y)2
( )
min (xi - x)2
+(yi - y)2
( )

29. Basic Region Descriptors
(example)

30. Moments
• Moments describe a shape’s layout, a bit like combining area,
compactness, irregularity, and higher-order descriptions together
• The moment of order p and q, mpq of a function I(x,y) is defined as
• Example
mpq = xp
yq
y

x
 I(x, y)DA
m00 = I(x, y)DA
y

x
 m10 = xI(x, y)DA
y

x
 m01 = yI(x, y)DA
y

x


31. Centralized Moments
• General formula:
• Example
• This moment descriptors are translation invariant
mpq = (x - x)p
(y - y)q
y

x
 I(x, y)DA
m01 = m01 -
m01
m00
m00
m10 = m01
m20 = m20 -
m10
2
m00

32. Centralized Moments: Example

33. Invariant Moments
• Centralized moments are only translation invariant
• Normalized central moments are invariant to translation, scale and
rotation
hpq =
mpq
m00
g
where g=
p + q
2
"p+ q ³ 2

34. Invariant Moments (cont.)

35. Invariant Moments: Example

36. Acknowledgment
Some of slides in this PowerPoint presentation are adaptation from
various slides, many thanks to:
1. Dr. Brian Mac Namee, School of Computing at the Dublin Institute
of Technology (http://www.comp.dit.ie/bmacnamee/gaip.htm)
2. James Hays, Computer Science Department, Brown University,
(http://cs.brown.edu/~hays/)

37. Thank You