Question 10 – Pattern Recognition
(patterns, classification, object recognition)
Image analysis is a process of discovering, identifying, and understanding patters that are relevant to
the performance of an image-based task.
One of the principle goals of image analysis by computer is to endow a machine with the capability to
approximate, in some sense, a similar capability in human beings. For example, in a system for
automatically reading images of typed documents, the patterns of interest are alphanumeric characters,
and the goal is to achieve character recognition accuracy that is as close as possible to the superb
capability exhibited by human beings for performing such tasks.
Thus an automated image analysis system should be capable of exhibiting various degrees of
intelligence. The concept of intelligence is somewhat vague, particularly with reference to a machine.
However, conceptualizing various types of behavior generally associated with intelligence is not
difficult. Several characteristics come to mind: (1) the ability to extract pertinent information from a
background of irrelevant details; (2) the capability to learn from examples and to generalize this
knowledge so that it will apply in new and different circumstances; and (3) the ability to make
inferences from incomplete information.
Image analysis systems with these characteristics can be designed and implemented for limited
operational environments. However, we do not yet know how to endow these systems with a level of
performance that comes even close to emulating human capabilities in performing general image
analysis functions.
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Elements of Image Analysis
Dividing the spectrum of techniques in image analysis into three basic areas is conceptually useful.
These areas are (1) low-level processing, (2) intermediate-level processing, and (3) high-level
processing. Although these subdivisions have no definitive boundaries, they do provide a useful
framework for categorizing the various processes that are inherent of an autonomous image analysis
system. Figure 1 illustrates these concepts, with the overlapping dashed lines indicating that clear-cut
boundaries between processes do not exist. For example Thresholding may be viewed as an
enhancement (pre-processing) or a segmentation tool, depending on the application.
Intermediate-level processing
Segmentation
Representation
& description
Recognition
&
interpretation
Pre-processing
Knowledge base
Image
acquisition
High-level processing
Low-level processing
Figure 1. Elements of Image Analysis
Low-level processing  deals with functions that maybe viewed as automatic reactions, requiring no
intelligence on the part of the image analysis system.
Intermediate-level processing  deals with the tasks of extracting and characterizing components
(say, regions) in an image resulting from a low-level process.
High-level processing  involves recognition & interpretation.
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1. Patterns and Pattern Classes
The ability to perform pattern recognition is fundamental to image analysis.
A pattern is a quantitative or structural description of an object or some other entity of interest in an
image.
In general a patter is formed by one or more descriptors. In other words a pattern is an arrangement of
descriptors (The name ‘features’ is often used in the pattern recognition literature to denote
descriptors.). A patter class is a family of patterns that share some common properties. Pattern classes
are denoted w1, w2, ….., wM, where M is the number of classes.
Pattern recognition by machine involves techniques for assigning patterns to their respective classes –
automatically and with as little human intervention as possible.
The three principle pattern arrangements used in practice are vectors (for quantitative descriptions) and
strings and trees (for structural descriptions).
Pattern vectors are represented by bold lowercase letters, such as x, y, z, and take the form:
 x1 
x 
 2
x  .  --------------------- (Equation 1)
 
. 
 xn 
 
Where each component, xi, represents the ith descriptor and n is the number of such descriptors.
Pattern vectors are represented as columns, hence equation 1 can also be written as: x = (x1, x2, ….,
xn)T, where T indicates transposition.
The nature of the components of a pattern vector x depends on the measurement technique used to
describe the physical itself. For example, suppose that we want to describe three types of iris flowers
by measuring the widths and lengths of their petals. In this case we would be dealing with 2-D vectors
of the form:
 x1 
x    ----------------------- (Equation 2)
 x2 
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Where x1 and x2 correspond to petal length and width, respectively. The three pattern classes in this
case are denoted w1, w2 and w3 and correspond to the three verities of flowers (setosa, virginica and
versicolor).
Petals of flowers vary in width and length to some degree, the pattern vectors describing these flowers
also vary, not only between different classes, but also within a class. Figure 2 (9.2) shows length and
width measurements for several samples of each type, plotted as points in 2-D Euclidean space.
As can be seen from the figure (2) that Iris Setosa class is adequately separated from the other two
classes but the other two classes are not. This result illustrates the classic feature selection problem, in
which the degree of class separability depends strongly on the choice of pattern measurements selected
for an application.
Figure 2. Two measurements performed on three types of iris
Can also talk about Strings pattern (staircase example) and Tree pattern (city picture example).
2. Decision-Theoretic Methods
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Decision (or discriminant) functions are designed such that if a pattern x belongs to class wi then:
di(x) > dj(x), j= 1, 2, . . . , M; j = 1, 2, …. M; j  0 ---------------------- (Equation 3)
For each pattern all decision functions are evaluated and the highest value wins.
2.1 Matching (Minimum Distance Classifier)
Assume each pattern class is represented by a prototype (or mean) vector:
mj =
1
N
 x............ j  1,2,....., M
------------------ (Equation 4)
xw j
Euclidian distance to the nearest prototype determines the class membership. The decision boundary
between classes wi and wj for a minimum distance classifier is:
dij (x) = di(x) – dj(x) = xT (mi - mj) – ½ (mi - mj)T (mi - mj) = 0 ---------- (Equation 5)
2.2 Matching by Correlation
Correlation between f(x, y) and w(x, y), where f (x, y) is the image and w(x, y) is the sub-image is
given as:
c( s, t )   f ( x, y ) w( x  s, y  t ) -------------------- (Equation 6)
x
y
Where s = 0, 1, 2, ….. M-1, t = 0, 1, 2, … N-1, and the summation is taken over the image where w and
f overlap.
Optimum Statistical Classifiers
Bayes classifier for Gaussian pattern class
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