Intelligent Vision
Systems
ENT 496
Object Shape Identification and
Representation
Hema C.R.
Lecture 7
Road Map
• Contour
• Chain codes
• Object Recognition
• Object Representation
• Feature Detection
• Hough Transform
• Fourier Descriptors
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Contour
• Represented as ordered list of
edges or a curve
• Criteria for good contour
– Efficiency: simple and compact
representation
– Accuracy: accurately fit image
features
– Effectiveness: suitable for operations
to be performed at a later stage
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Definitions
• Edge list
– Ordered set of edge points or fragments
• Contour
– Edge list or a curve that is used to represent the
edge list
• Boundary
– Closed contour that surrounds a region
Note: The term edge generally refers to edge points
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Chain Codes
• Notation for recording list of edge points along
contour
• Chain code specifies the direction of the contour
at each edge
• Directions are quantized into one of eight
directions
• These codes are also known as freeman codes
• Are used for the description of pixel border
• Local information of the objects can be obtained
from the chain code
– E.g. where image border turns 90 degrees etc.
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Chain coding example
2 3 4
1
5
8 7 6
3 5 5 5 5 5
3
6
2
6
2
7
1 1 1 1 1 7
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Object Recognition
• Object recognition systems find
objects in the real world from an
image of the world.
• Object recognition can be defined
as a labeling problem based on
models of known objects.
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Components of a object
recognition system
•
•
•
•
Model database – model base
Feature detector
Hypothesizer
Hypothesis verifier
Image
Feature
Detector
Features
Hypothesis
Formation
Candidate
objects
Hypothesis
verification
Object
Class
Modelbase
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Components
• Model Database
– Contains all models known to the system for
recognition –such as size, color, shape, CAD
drawing etc
• Feature Detector
– Applies operators to images and identifies
location of features that help the object
hypothesis
• Hypothesizer
– Assigns likelihood to objects using features
detected and selects object with highest
likelihood
• Hypothesis Verifier
– Uses object models to select most likely object
Note: Depending on the complexity of the problems
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Object Representation
• Observer-Centered Representation
– Applied to objects relatively in stable
positions w.r. to camera
– Global features of a scene are recognized
– Features are selected based on experience of
designer or analyzing features to form object
groups
• Object-Centered Representation
– Uses description of objects based on usually
3D
– Independent of camera parameters
– Used in constructive solid geometry e.g. CAD /
CAM
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Feature Detection
• Global Features
– Characteristic of a region
•
•
•
•
Area
Perimeter
Fourier Descriptors
Moments
• Local Features
– Features on the boundary of an object or a small region
• Curvature
• Boundary segment
• Corners
• Relational Features
– Based on relative positions of different entities like
regions, closed contours etc.
• Distance between features
• Used in defining composite objects
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Recognition Strategies
• Object recognition is a sequence of steps that is
performed after appropriate features have been
detected.
• Not all object recognition techniques require
strong hypothesis formation and verification
steps
Features
Hypothesizer
Classifier
Object
Verifier
Features
Features
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Sequential
Matching
Hypothesizer
Object
Verifier
Object
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Strategies
•
Classification
– Nearest neighbor
• Similar features in a region are clustered, based on a centroid and distance
– Bayesian Classifier
• Used when distribution of objects is not straightforward
• When there is an overlap of features of different objects.
• Probabilistic knowledge about features and frequency of objects is used
– Neural Nets
• Implement a classification approach
• Use nonlinear boundary partition of features
• Boundaries are used by training a net
– Off-line computations
• Computations are done before recognition
• Recognition process can be converted to a look-up table
•
Matching
– Feature Matching
• Known features of the object are matched with unknown objects feature to find
matches
– Symbolic Matching
• Relation among features are matched
• Graph matching
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Hough Transform
• The Hough transform is a feature
extraction technique
• The classical transform identifies lines in
the image, but it has been extended to
identifying positions of arbitrary shapes.
• The transform universally used today was
invented by Richard Duda and Peter Hart
in 1972, who called it a "generalized
Hough transform" after the related 1962
patent of Paul Hough.
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Hough Transform- Theory
• The underlying principle
– there are an infinite number of potential lines that pass through
any point, each at a different orientation.
• The purpose of the transform is to determine which of
these theoretical lines pass through most features in an
image
– that is, which lines fit most closely to the data in the image.
• In order to determine that two points lie on the same
potential line, it is necessary to create a representation
of a line that allows meaningful comparison .
• In the standard Hough transform, each line is
represented by two parameters, commonly called r and
θ (theta)
– which represent the length and angle from the origin of a
normal to the line in question
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Hough Transform- Theory
• By transforming all the possible lines through a point into
this coordinate system
– i.e. calculating the value of r for every possible value of θ - a
sinusoidal curve is created which is unique to that point.
• This representation of the two parameters is sometimes
referred to as Hough space.
• If the curves corresponding to two points are
superimposed, the location (in Hough space) where they
cross correspond to lines (in the original image space)
which pass through both points.
• A set of points which form a straight line will produce
Hough transforms which cross at the parameters for that
line.
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Hough Transform for three data points
Hough Space Graph
Procedure to create a Hough space graph
For each data point
 A number of lines are plotted going through it, all at different
angles. These are shown as solid lines.
 For each solid line a line is plotted which is perpendicular to it and
which intersects the origin. These are shown as dashed lines.
 The length and angle of each dashed line is measured. The
results are shown in tables.
 This is repeated for each data point.
 A graph of length against angle, known as a Hough space graph,
is then created
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Fourier Descriptors
• Fourier descriptors are compact representation for
closed contours
• Boundary of an object can be expressed as a
sequence of co-ordinates
u(n)  [ x(n), y(n)] for n  0,1,2,...N  1.
• Each co-ordinate pair can be represented as a
complex number such that
u(n)  x(n)  jy(n)
(1)
• X axis is treated as the real axis and y axis is
treated as the imaginary axis of a series of
complex numbers
• This sequence is periodic with period N and
boundary is represented in one dimension
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Discrete Fourier Transform
• DFT of a one dimensional sequence u(n)
is defined as
N 1
u ( n )   a ( k )e
j 2kn
N
0  n  N 1
,
(2)
k 0
1 N 1
a ( k )   u ( n )e
N k 0
 j 2kn
N
,
0  n  N 1
(3)
• The Complex coefficients a(k) are called
the Fourier descriptors of the boundary
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Covariance
• Covariance of two features gives a relation
between the two features
• The covariance is computed as





Cov( X , Y )    X i  X  Yi  Y 


i 1 
n
(4)
• Where
n is number of patterns [facial] and

are the mean of features of X and Y
X and Y
respectively
– If covariance value is positive then if X increases Y also
increases
– If covariance value is negative when X increases and Y
decrease
– If covariance is zero there is no relation between X and Y
features
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Intelligent Vision
Systems
Object Shape Identification and
Representation
Hema C.R.
End of Lecture 7