Fingerprint Classification sections 5.3 - 5.5

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Fingerprint Classificationsections 5.3 - 5.5

• Fingerprint matching using transformation
  parameter clustering
• R. Germain et al ,IEEE
• And
• Fingerprint Identification Using Delaunay
  Triangulation
• G. Bebis et al ,IEEE

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Performance of fingerprint Classification
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Performance of Classification Techniques (cont..)

• Confusion Matrix

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Accuracy Vs Rejection rate
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• Two Databases
• NIST DB4 - contains 2000 fingerprint pairs
• NIST DB14 contains 27000 fingerprint pairs
• Consist of 8-bit grey level images
• Two different fingerprint instances
• Classified into 5 classes

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Results on NIST DB4
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Results on NIST DB14
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Accuracy Vs Rejection rate

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Fingerprint Indexing and Retrieval

• Problems with classification schemes
• Number of classes is small
• Fingerprints are unevenly distributed
• More than 90 of fingerprints belong to only 3
  classes
• Difficult to search a single fingerprint form the
  large database

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• These problems can be handled with 2 different
  approaches
• Fingerprint sub classification
• Continuous Classification

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Fingerprint Sub Classification
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Continuous Classification and Other Indexing
Techniques

• Uses vectors summarizing their main features
• Feature vectors are created through a similarity
  preserving transformation
• Avoids ambiguous fingerprints
• System efficiency and accuracy will be balanced
  by adjusting the size of the neighborhood.

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Indexing Techniques

• Using Minutae points
• Identifies all the minutae triplets in the
  fingerprints
• Uses geometric hashing to retrieve a similar
  fingerprints from the database
• This is built by quantizing all the possible
  triplets
• If the same fingerprint is hit by more triplets,
  then a voting technique is applied to get the
  final rank

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Other Indexing techniques

• Based on matching scores between the fingerprints
• In some papers, different Indexing techniques are
  combined to improve the performance
• Continuous classification with MKL based
  approaches
• Finger code feature vectors are combined with a
  simplified version of the minutae triplet approach

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Retrieval Strategies

• If exclusive classification is used for indexing
  then,
• Hypothesized class only
• Fixed search order
• Variable search order

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• If continuous classification is used for indexing
  then,
• Fixed radius
• Incremental search order

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Performance of fingerprint Retrieval
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Performance of retrieval strategies
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Performance of retrieval strategies
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Fingerprint matching using transformation
parameter clustering

• Fingerprint Identification Using Delaunay
  Triangulation

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Flash Method

• Flash algorithm uses a higher a dimensional
  indexing scheme than geometric hashing by adding
  invariant properties of the feature subset to the
  index
• Second stage uses, transformation parameter
  clustering to accumulate evidence

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Flash Method

• When adding a model to the database, invariant
  information computed from each subset of feature
  points forms a key or index
• Key labels an entry that is added to a multimap,
• This entry contains the identifier of the model
  that generated the key and information concerning
  the feature subset

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• When servicing a query, each key generated by the
  query object is used to retrieve any items in the
  multimap that are stored under the same index.
• Each item retrieved represents hypothesized match
  between subsets of features in the query object
  and the reference model
• This hypothesized match is labeled by the
  reference model by parameters characterizing the
  geometric transformation bringing the two subsets
  of features into closest correspondence
• Votes for these hypothesized matches accumulate
  in another associative memory structure

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How it applies to fingerprint matching

• In the fingerprint application, class of
  transformations that connects different object
  instances is assumed to be of two-dimensional
  distance preserving transformations
• A least squares estimation methodology is used to
  solve the over constrained pose estimation
  problem for each hypothesized local
  correspondence generated by the index lookup
  process

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Data abstraction and index generation

• Minutae provides a natural choice for feature
  points
• A triplet of numbers (X, Y, ? ) represent each
  feature point

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• Flash matcher uses skeletonized version of the
  ridge pattern on the finger
• If a line is drawn between each pair of minutae,
  the number of ridges crossed by this line can be
  computed
• Ridge counting procedure repeats for each pair of
  minutae in the fingerprint, and the results
  become part of the flash index

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• The flash algorithm uses redundant combination of
  three feature points when forming indices
• This gives some immunity against noise
• To keep the number of indices generated within
  bounds, the algorithm restricts the acceptable
  combinations of feature points used to form an
  index

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• The search engine requires the generation of
  indices used for table lookup
• These indices are descriptive of the objects
  stored in the database.
• Each component of the index is invariant under
  rotations and translations
• The full index consists of nine components
• Length of each side
• Ridge count between each pair
• Angles measures with respect to the sides

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Accumulating evidence

• During the query phase, each index generated by
  the query fingerprint
• This is used to retrieve all the objects in the
  database that are labeled with same index
• Each retrieved model objects represents a
  hypothesized correspondence between 3 points in
  the query print and three in the model

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Algorithm that computes the co-ordinate
transformation
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Accumulating evidence

• If a large number of feature points can be
  brought into correspondence by rigid
  transformation of the coordinate system, all of
  the indices generated by the combinations of
  three feature points belonging to this set
  generate the same coordinate transformation
  parameters

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Accuracy Issues

• Four scenarios are possible
• H0 is true, and test says H0 is true
• H0 is false, and test says H0 is true
• H1 is true, and test says H1 is true
• H1 is true, and test says H1 is true
• Two distinct types of errors can be made
• False Negative incorrectly assigned mated to
  non mated
• False Positive incorrectly assigned
  non mated to mated
• The number of matching triangles that generate a
  consistent rigid transformation serves as the
  basis for assigning pairs to the mated or
  non-mated pair population

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• With the decision criteria, it is straightforward
  to determine the two error rates from the
  conditional probability densities computed from
  the test populations
• The error rate for incorrectly assigning a mated
  pair to the nonmated population is given by
• The error rate for incorrectly assigning a
  nonmated pair to the mated population is given by

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• Consider one to many identification query
• The candidate list of hypothesized matches is
  formed by taking all prints from the reference
  database
• Assuming the presence of one mate to the query,
  the FPR and FNR for and identification search
  against a database N is shown below
• The FPR increases drastically with database size
  because each additional entry in the database
  provides another opportunity to randomly achieve
  a high score

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Results

• Data set
• 97492 inked dab images
• 657 queries, against this database
• Query set of prints was a subset of the models
• They made 657 X 97492 comparisons of pairs
• These pairs divided into 3 groups
• identical fingerprints(657 pairs)
• diff. impressions of the same finger( 768
  pairs)
• impressions of different fingers( 64,050,819
  pairs)

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Fingerprint identification using Delaunay
triangulation
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Advantages of using this technique

• Preserves index selectivity
• Reduces memory requirements
• Improves recognition time
• Considers only O(N) minutae triangles

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Important issues to be consider when using
Indexing

• memory requirements
• In the case of fingerprints, memory requirements
  can become much higher since fingerprints contain
  more features on the average than typical objects
• Index selectivity
• relates to the discrimination power of the groups
  considered for indexing
• groups with low discrimination power give rise to
  very similar indices
• large number of hypothetical matches are
  generated during recognition

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• To deal with this problems
• Increasing index dimensionality using large size
  groups
• Additional information can be computed from each
  group and added to index

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• Indexing based methods have two phases of
  operation
• Preprocessing
• features which remain unchanged under geometric
  transformations are extracted from groups of
  model points and used to form indices
• Indexed locations are filled with entries
  containing references to the models
• Recognition
• Features from groups of image points are
  extracted and used to form indices again
• The models listed in the indexed entries are
  collected into a list of candidate models and the
  most often indexed models are selected for
  further verification

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Background on Delaunay Triangulation
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• Delaunay triangulation has certain properties
• Non degenerate set of points is unique
• A circle through the three points of a Delaunay
  triangle contains no other points
• The minimum angle across all the angles in all
  the triangles in a delaunay triangulation is
  greater than the minimum angle in any other
  triangulation of the same points

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Indexing using Delaunay Triangulation

• Minutae triangulation

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Building the Index Table

• The index table is built by considering the
  minutae triangles formed by the Delaunay
  triangulation
• From each minutae triangle, information invariant
  to similarity transformations is computed.
• Then, an index is formed using the invariants and
  appropriate information is stored in the indexed
  table location
• the Delaunay triangulation, yields O(N).

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• Given a minutae triangle,
• Compute 3 invariants
• These based on sides and angles of the triangle
• First sort the sides of the triangle to avoid
  considering all possible orders of three points

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• Following invariants are computed

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• After the invariants have been computed followed
  by quantization yields an integer index
• The entries stored in the table have the
  following format

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• Identification step
• Each index generated by a query fingerprint is
  used to retrieve all model fingerprints
• To account for noise, we also retrieve entries
  stored in a small neighborhood

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• Verification step
• Performed by aligning the two fingerprints using
  the transformation computed and by computing the
  amount of overlap
• A list of candidate fingerprints which possibly
  match query fingerprints is generated
• If a large number of minutae from the candidate
  fingerprint are close, then it is very likely
  that the two fingerprints come from the same
  fingerprint

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• Although we use similarity transformations,
  differences in the pressure of the finger on the
  sensor or skin elasticity produce deformations
  which are not modeled very well by similarity
  transformations
• alignment is improved by computing the similarity
  transformation using affine transformations

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Experimental results

• Data set
• 300 fingerprints, captured from 30 individuals
  (10 images per finger for each individual)
• Size is 400 X 400 pixels
• No restriction on the position and the
  orientation of fingers

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Experiments

• First set of experiment
• Vary the number of imprints stored in the
  database for each person
• Experimented with storing 3, 5 ,and 7 images per
  person
• In each case, 6 experiments were conducted
• In the first five experiments, images stored in
  the database are chosen randomly and in the last
  one, best one is chosen

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• Classify results into 4 categories
• Correct query correctly matched to one or more
  fingerprints from the same person
• False positive - query matched to one or more
  fingerprints from the an incorrect person
• False negative - query has not been matched to
  any fingerprints from the database
• Mixed there is not enough evidence to assign
  the query fingerprint to one of the previous
  categories

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Results
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Conclusions from the results

• Recognition accuracy depends on the number of
  imprints stored in the database for each person
• Last row of each table shows that if the imprints
  stored in the database are of good quality,
  recognition accuracy improved significantly
• Number of false negatives are relatively high
  compared to number of false positives

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• Second experiment
• How false positives increase with the database
  size
• Tested how the system performs on fingerprints
  from people not represented in the database
• Five experiments were conducted