A Comparison of Classi cation- and Indexing-Based Approaches in .NET

Printer QR Code ISO/IEC18004 in .NET A Comparison of Classi cation- and Indexing-Based Approaches
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A Comparison of Classi cation- and Indexing-Based Approaches
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Parameters and Termination. The key parameters are the population size, the number of generations, the crossover rate, and the mutation rate. The GP stops whenever it nishes the prespeci ed number of generations.
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Indexing
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Our approach for ngerprint indexing is based on the use of triplets of minutiae and ridge counts. However, for identi cation, the indexing and veri cation in our approach are separated. First, we apply indexing techniques to nd the top N hypotheses, and then we apply a veri cation technique to select a hypothesis with the best match. The hypotheses are generated according to the number of corresponding triangles between two ngerprints. Top N hypotheses, sorted in a descending order of the number of potential corresponding triangles, are the indexing results. For indexing, we use features based on minutiae triplets [8] in conjunction with the constraints on the transformation to eliminate the false corresponding triangles. Figure 15.4 shows the block diagram of our indexing approach. During the of ine processing, the features of each template ngerprint are computed and used to construct the indexing space function H( min , med , , , , , ) [8]. r Angles min and med . i s are the three angles in a triplet, where i = 1, 2, 3. min = min{ i }, max = max{ i }, med = 180 min max . r Triangle handedness . Let Zi = xi + jyi be the complex number corresponding to the location (xi , yi ) of point Pi , i = 1, 2, 3. De ne Z21 = Z2 Z1 , Z32 = Z3 Z2 , and Z13 = Z1 Z3 . Let triangle handedness = sign(Z21 Z32 ). Points P1 , P2 , and P3 are noncolinear points, so = 1 or 1.
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Template Fingerprints Query Fingerprint
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Feature Extraction
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Feature Extraction
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For each triplets of minutiae, compute min, med, , , , ,
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For each triplets of minutiae, compute min, med, , , , , Hypotheses generation
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Model database based on the triplets of minutiae
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Generate top N hypotheses according to the number of potential corresponding triangles
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Indexing Results Offline processing Online processing
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Figure 15.4. Block diagram of the indexing approach.
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15.2 Technical Approach
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r Triangle direction . We search the minutiae in the image from top to bottom and left to right. If a minutiae is the start point of the ridge, then = 1; otherwise = 0. Let = 4 1 + 2 2 + 3 , where i is value of point Pi , i = 1, 2, 3 and 0 7. r Maximum side . Let = max{Li }, where L1 = |Z21 |, L2 = |Z32 |, and L3 = |Z13 |. r Minutiae density . In a local area (32 32 pixels) centered at the minutiae Pi . If there exists i minutiae, then the minutiae density for Pi is i . Minutiae density is a 3D vector consisting of all i . r Ridge counts . Let 1 , 2 , and 3 be the ridge counts of sides P1 P2 , P2 P3 , and P3 P1 , respectively. Then, is a 3D vector consisting of all i . During the online processing, we compute the features for the query ngerprint and use them to search the indexing space H( min , med , , , , , ). If the feature values of two triangles, which are from two different ngerprints, are within some error tolerance, then they are potential corresponding triangles. The criteria are: | min min | T min , | med med | T med , = , = , | | T , | i i | T , | i i | T , i = 1, 2, 3, where ( min , med , , , , i , i ) and ( min , med , , , , i , i ) are the local properties of the triangle in different ngerprints; T min , T med , T , T , and T are thresholds to deal with the local distortions.
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