Pattern Recognition Concepts

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Pattern Recognition Concepts
Dr. Ramprasad Bala Computer and Information
Science UMASS Dartmouth CIS 585 Image
Processing and Machine Vision
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Pattern Recognition Problem

• In many practical problems, there is a need to
  make some decision about the content of an image
  or about the classification of an object that it
  contains.
• Character recognition on a PDA
• ATM face recognition
• In general we will accommodate an unknown state.

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Pattern Recognition

• Definition The process of matching an object
  instance to a single object prototype or class
  definition is called verification.
• One definition of recognition is to know again
• A recognition system must contain some memory of
  the objects that it is to recognize.

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Image Memory

• This memory representation might be
• built-in (a frogs model of a fly)
• Taught by a large number of samples (a student
  learning the alphabets)
• Programmed in terms of specific image features.

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Common Model for Classification

• 1. Classes
• There is a set of m known classes of objects
  (either programmed or trained).
• There will be a reject class for objects that
  cannot be placed in one of the known classes.
• An ideal class is a set of objects having some
  important common property, a class to which an
  object belongs is denoted by some class label.
  Classification is a process that assigns a label
  to an object according to the properties of the
  object. A classifier is a device or algorithm
  that performs takes an object as input and
  outputs the object label.

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Common Model

• 2. Sensor/Transducer
• There must be some device that captures the
  object and provides a digital representation
  (image) of the object as an input to the
  classifier.
• Generic devices off the shelf devices
• For computer vision digital color cameras.

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Common Model

• 3. Feature Extractor
• The feature extractor extracts information
  relevant to classification by the sensor. Usually
  done in software. Can also be done in hardware.
• 4. Classifier
• The classifier uses the features extracted from
  the sensed object data to assign the object one
  of the m designated classes C1, C2, , Cm-1, Cm ,
  Cr where Cr denotes the reject class.

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A d-dimensional input feature vector is processed
by the m classes. K is the knowledge of the
class. Finally the results are compared and a
decision made on the class label.
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Building a classification system

• Each part of this system has many alternate
  implementations.
• Chapter 2 image sensors
• Chapter 3 binary image features
• Chapter 5 gray-scale image features
• Chapter 6 color image features
• Chapter 7 texture features

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Evaluation of System Error

• The error rate of a classification system is one
  measure of how well the system solves the problem
  for which it is designed.
• Other factors are speed, cost (h/w, s/w),
  developmental cost etc.
• The classifier makes a classification error
  whenever it classifies the input object as class
  Ci when the true class is Cj ( i .ne. j and Ci
  .ne. Cr).

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• The empirical error rate of a classification
  system is the number of errors made on
  independent test data divided by the number of
  classifications attempted.
• The empirical reject rate of a classification
  system is the number of rejects made on
  independent test data divided by the number of
  classifications attempted.
• Independent test data are sample objects with
  true class known, includes objects from the
  reject class, that were not used in designing the
  feature extraction and classification algorithms.

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False Alarms and False Dismissals

• Some problems are special two-class problems
• Good objects vs bad objects
• Object present vs abscent
• Person has disease vs does not have disease
• In each case false-positives and false-negatives
  have different consequences.

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Receiver Operating Curve
In order to increase the percentage of objects
correctly recognized, one usually has to pay a
cost of incorrectly passing along objects that
should be rejected.
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Precision versus Recall

• In document retrieval(DR) or image retrieval, the
  objective is to retrieve interesting objects of
  class C1 and not too many of uninteresting class
  C2 according to features supplied.
• The precision of a DR system is the number of
  relevant documents retrieved divided by the total
  number of documents retrieved.
• The recall of a DR system is the number of
  relevant documents retrieved by the system
  divided by the total number of relevant documents
  in the DB.

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Features used for Representation

• What representation or encoding of the object is
  used in the recognition process?
• Consider the case of a handwriting CR system
• The area of the character in units of black
  pixels
• The height and width of the bounding box
• The number of holes inside the character
• The center (centroid) of the set of pixels
• The best axis direction through the pixels as the
  axis of inertia
• The second moments of the pixels about the axis
  of least inertia and most inertia.

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Assuming there is no error in computing the
features, a sequential Decision procedure can be
used to classify instances of these 10 Classes.
The algorithm 4.1 outlines this procedure. This
structure Is called a decision tree.
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Feature Vector Representation

• Objects maybe classified based on their
  representation as a vector of measurements.
• Suppose each object is represented by exactly d
  measurements.
• The similarity or closeness, between the feature
  vectors can be described using the Euclidean
  distance between the vector.

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Implementing the Classifier

• Assume there are m classes of objects, not
  including the reject class, and there are ni
  sample vectors for class i.
• In our character recognition example, we had m
  10
• n 100 (say)
• d 8 (features)

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Nearest Class Mean

• A simple classification algorithm is to summarize
  the sample data for each class using the class
  mean vector or centroid.
• An unknown object with feature vector x is
  classified as class i if it is closer to the mean
  vector of class i than to any other class mean.
• x could be put into the reject class if it is not
  close enough to any of the classes.

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Returning to Figure 4.2, we now have a definition
of the function boxes. The ith function box
computes the distance between unknown Input x and
the mean vector of the training samples from that
class.
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• While simple to implement nearest class mean does
  not work well for a variety of problems.

• The classes are not regular and in one case is
  multi-modal.
• In such cases a scaled Euclidean distance may be
  considered.

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Nearest Neighbor

• A more flexible but expensive method is to
  classify unknown feature vector x into the class
  of the individual sample closes to it.
• This is the nearest-neighbor rule.
• NN classification can be effective even when
  classes have complex structure in d-space and
  when classes overlap.
• The algorithm uses only the existing training
  samples. A brute force approach computes the
  distance from x to all samples in the database of
  samples and remembers the minimum distance.

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• A better classification decision can be made by
  examining the nearest k-feature vectors in the
  DB.
• Using larger k depends on a larger number if
  samples in each neighborhood of the space to
  prevent us from searching too far from x.
• In a two-class problem, using k 3, we would
  classify x into the class that has 2 of the three
  samples nearest x.
• If there are more than two classes then there are
  more combinations possible and the decision is
  more complex.

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Structural Techniques.
Consider the two images above. They both have the
same bounding box, the same centroid, same number
of strokes and hole pixels and the same moments.
Each has two bays (intrusions of the
background into the character). Each bay has a
lid (a virtual line that closes the bay). The
difference is the placement of the lids
(structural relations).
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Statistical PR

• Traditionally represents entities by feature
  vectors (set of real and Boolean values).
• These values measure some global aspect of the
  entities, such as area or spatial moments.
• Our example even took into account holes and
  strokes (do we know how to find them?)

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Structural PR

• An entity is represented by its primitive parts,
  their attributes and their relationships as well
  as by its global features.

Structural properties -4 major strokes -2
vertical or slanted - 2 horizontal -one hole or
lake on top -one bay -lake and bay separated by a
horizontal line.
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Graphical representation

• When the relationships are binary, a structural
  description of an entity can be viewed as a graph
  structure.
• Define
• CON specifies the connection of two strokes
• ADJ specifies that a stroke is immediately
  adjacent to a lake or bay region
• ABOVE specifies that one hole (lake or bay)
  lies above another.
• We can then construct a graph of the structure.

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In this example we use three binary relations.
Even ternary or quaternary relations can be used
for stronger constraints. For example A ternary
relation exists between the lake, the horizontal
line and the bay.
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Structural PR

• Structural PR is often achieved through
  graph-matching algorithms.
• However, the relationship between two primitives
  can itself be considered an atomic feature and
  thus can be used in feature vector (the number of
  such relationships can be used as a feature) for
  statistical PR.
• Structural methods are useful for recognizing
  complex patterns involving sub-patterns. They
  also offer understanding of a scene, especially
  when multiple objects are present.

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The Confusion Matrix

• The confusion matrix is often used to report
  results of classification experiments.
• The entry in row i, column j records the number
  of times that an object labeled to be truly of
  class i was classified as j.
• The diagonal indicates success. High off-diagonal
  numbers indicate confusion between classes and
  forces us to reconsider our feature extraction or
  classification procedures.

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Decision Trees

• When the PR task is complex, computing
  similarities between feature vectors can become
  very expensive (or impossible).
• In such cases one should consider using a
  decision tree. A decision tree is a compact
  structure that uses one feature (or a small set)
  at a time to split the search space.
• Algorithm 4.1 presented a simple decision tree.
• Each branching node has nodes that represents
  different features of the feature vector. At each
  stage a feature is selected for the decision.

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Binary Decision Tree

• A binary decision tree is a binary tree structure
  that has a decision function associated with each
  node. The decision function is applied to the
  unknown vector and determines whether the next
  node to be visited is the left child or right
  child of the current node.
• Each leaf node stores names of a pattern class.

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Automatic Construction of DT

• Decision trees are not unique for a specific
  problem. Several trees may yield the same result.
• One simple but effective method is grounded in
  information theory. The most basic concept in
  information theory is entropy.
• Definition the entropy of a set of events is
  given by

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• Entropy can be interpreted as the average
  uncertainty of the information source.
• IT allows us to measure the information content
  of an event. In particular, the information
  content of a class w.r.t. each of the feature
  events.
• The information content I(CF) of the class
  variable C with possible values c1,c2,,cm
  w.r.t. the feature variable F with possible
  values f1,f2,,fd is
• where P(Cci) is the probability of class C
  having value ci, P(Ffj) is the probability of
  feature F having fj and P(Cci, Ffj) is their
  joint probability.

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• These probabilities can be estimated from the
  frequency of the associated events in the
  training data.
• In the previous example, since class I occurs in
  two out of the four training samples P(CI)
  0.5. Since three of the four training samples
  have 1 for feature X, P(X1) 0.75.
• We can use this information content measure to
  decide which feature is best one to select at the
  root of the tree.
• We calculate I(C,F) for each of the three
  featuresX,Y and Z.

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Since Y has the largest information content, it
is chosen as the root.
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Character Classification

• Now consider a more complex example handwritten
  numerical digits.
• Characters with bays, lakes and lids.
• The following features can be computed
• lake_num the number of lakes
• bay_num the number of bays
• bay_above_bay Boolean feature (T or F)
• lid_rightof_bay Boolean feature
• bay_above_lake Boolean feature
• lid_bottomof_image Boolean feature

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Bayesian Decision Making
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The practical difficulty is in coming up with the
probabilities. Empirically we collect enough
samples for each class and fit a distribution
and can find the probabilities in that
fashion. For example if we find enough sample for
each class and construct a Histogram, we can
normalize the histogram to obtain a
probability distribution function.
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Decisions Using Multidimensional data

• Understanding the multidimensional space will go
  a long way in understanding the classification.
• All the techniques we have seen so far form a
  basic type of machine learning called supervised
  learning. We assumed that labeled samples were
  available for all the classes that were to be
  distinguished.
• In unsupervised learning the machine must also
  determine the class structure.