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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, Ө ) 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 madeFalse 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