PPT s07-machine vision-s2

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

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

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,

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

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

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
)
,
(

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

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

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

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

(example)

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

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

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

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

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

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.

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

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).

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

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

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

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

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
( )

Basic Region Descriptors
(example)

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


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

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

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/)

PPT s07-machine vision-s2

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