Latent Fingerprint Indexing - Computer Science and Engineering

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Figure 2. Overview of the proposed indexing scheme.In summary, given a set of minutiae points, the featurevector extracted for every possible triplet t with sides withinthe range [l min ,l max ] — in our implementation, 20 and 150respectively — is given byF t =(L max ,L min ,L med ,θ 1 ,θ 2 ,θ 3 ,φ). (1)These features are quantized into bins (bin size is 20 forboth triplet side lengths and directional differences, and φ,which can be either −1 or 1, is mapped to {0, 1}). A keyis associated with each bin. During the indexing or search,triplets in reference prints with the same key as triplets inthe latents are considered as matched triplets.Latent examiners can usually position a latent very closeto its true position in the finger based on their knowledgeof fingerprints. Also, rolled prints in background databasesusually present a small rotation deviation compared to thefinger upright position. Thus, an additional step is addedto further improve the indexing performance of the tripletsby constraining the possible rotation between two matchedtriplets. We call this the constrained triplets approach.Given a matched triplet pair, the differences in the directionof the corresponding three minutiae are averaged andtaken as the rotation for that matched triplets pair. If thisdifference is larger than a threshold (60 degrees in our implementation),then that triplet pair is excluded from the setof matched triplets. The triplet indexing score between thelatent and a reference print in the background database isgiven by the number of matched triplets between them.4.2. Minutia Cylinder Code (MCC) IndexingIn [5], the authors proposed an indexing technique basedon a local minutiae descriptor, called Minutia CylinderCode (MCC). MCC descriptor represents the neighborhoodminutiae information in the form of a 3D function (cylinder).Each level of the cylinder corresponds to a directiondifference range, and for each direction difference range,the descriptor contains spatial information about the neighboringminutiae relative to the center minutia.Hash functions are utilized to calculate an indexing scorefor two given fingerprints (search and reference prints). Theindexing score is computed by averaging the estimate of theHamming distance between the descriptors, and this estimateis based on the collisions between two descriptors underthe hash functions so that the indexing is more efficientthan directly comparing the descriptors.More specifically, given two fingerprint templates T 1 andT 2 , with V 1 and V 2 being the sets of cylinders for each minutiaein each template, the indexing score proposed in [5] isgiven by∑S M (T 1 ,T 2 ) ∼ v∈V=1(max vj ∈V 2{C F (v, v j )}) p h, (2)∣V 1 ∣×(H M ) p hwhere ∣V 1 ∣ is the number of cylinders in the search print,H M is the number of hash tables, h is the number of bitsselected in each hash table, p is a parameter of the distancefunction (set to 30), and C F represents the number of collisionsover all hash functions between cylinders v and v j .We used MCC SDK provided by the authors [5] with the defaultparameters, with the exception of the number of hashtables that was increased to 64 instead of the default 32 becausewe found that the former worked better for the latentindexing case.4.3. Orientation Field Descriptor IndexingGiven a set of minutiae M and orientation field f(x, y),aset of descriptors O = {o 1 , o 2 ,...,o N } is extracted, where
N is the number of minutiae, o i = {o i,1 ,o i,2 ,...,o i,n } isthe descriptor for the i th minutia and n is the total numberof sample points in the orientation descriptor [19].Given a minutia, L concentric circles are centered at theminutia with the j th circle of radius R×jL, and K j samplepoints are equally spaced on each circle starting from theprojection location of the reference minutia along its directionon the circle. In this paper, the number of circles L is4 and the numbers of sample points from the inner circle toouter circle are 10, 16, 22 and 28, respectively, and the maximumradius R for the outer most circle is 80 pixels. So,the total number of sample points for each orientation descriptoris n = ∑ Lj=1 K j =76. The feature value for eachsample point is computed as the counter-clock wise rotationangle from local orientation field at the sample point to thelocal orientation at the central minutia.In the index table generation, a set of l pairs of samplepoints {(h j ,b j )} l j=1 from the orientation descriptor is randomlygenerated, where h j ,b j ∈{1, 2,...,n} and h j ∕=b j . Then, a bit vector r = {r 1 ,r 2 ,...,r l }, is generated as{ 1 if oi,hj >or j = i,bjj =1, 2,...,l. (3)0 otherwiseThe random generation of the bit vectors is repeated sothat the total number of hash functions is H O , and the numberof bits in each hash function is fixed (l). Each bit vectorcorresponds to a decimal number, which is then used as oneof the index keys. The sample points and hash functionsrandomly chosen in the index table generation step are thenused to obtain the bit vectors from the search print. Giventwo sets of orientation descriptors O 1 and O 2 , similar to theMCC index score computation, the index score for orientationdescriptor is computed as∑S O (T 1 ,T 2 ) ∼ r∈O=1(max rj ∈O 2{C F (r, r j )}) p l, (4)∣O 1 ∣×(H O ) p lwhere C F represents the number of collisions over all hashfunctions as in Equation 2.4.4. Singular PointsSingular points provide useful characterization of a fingerprint.Given a list of core points and delta points witheach singular point containing coordinates and direction information,three types of singular point pair features can beextracted [6]: 1) core pair; 2) delta pair; and 3) core-deltapair.To order the singular points in a pair of singular points,each core point pair generates two pairs with each core pointbeing ranked first once; for delta pairs, the delta points areordered based on x-coordinates; and for core-delta pairs, thecore points are ordered first. For each singular pair, threefeatures are computed: 1) the distance (d) between the singularpoints; 2) the counter-clock wise rotation angle (α)from the direction of the first singular point to the line connectingsingular points; 3) the counter-clock wise rotationangle (β) from the direction of the second singular point tothe line connecting singular points.The singular pair similarity score between latent and referenceprint isS SP = 1N∑SPN SPi=1max s i,j (5)jwhere N SP is the number of singular pairs in latent ands i,j is the similarity between the i th singular pair in latentand the j th singular pair of the same type in reference print,which can be computed ass i,j = 1 (f20,60 (Δd i,j )+f π63, π (Δα π3i,j)+f6 , π (Δβ 3 i,j) )(6)where Δd i,j is the distance difference, Δα i,j and Δβ i,j arethe angle differences between the first and second singularpoints, respectively, and f a,b (x) is a piece-wise linear function⎧⎨ 1 xb,⎩otherwise.b−xb−aIf no singular pair of the same type in the reference printcan be found, then the singular pair similarity s i is set tozero.4.5. Ridge PeriodGiven a fingerprint (either latent or reference print), theaverage ridge period is computed within a circle of radius10 blocks centered at the core point, with each block being16 × 16 pixels; only foreground blocks are used. If there isno core point in the print, the center point of the foregroundregion is used. The ridge period similarity is then computedas(S R =exp − ∣R )l − R r ∣(8)σ Rwhere R l and R r are the average ridge periods in the latentand the reference print, respectively, and σ R is a normalizationterm which is usually set to the average of ∣R l − R r ∣.In this paper, σ R is set to 2.4.6. Fusion of Indexing ScoresThe indexing scores based on different features (triplets,MCC, orientation field descriptor, singular points and ridgeperiod) take values in different ranges. Thus, normalizationof individual indexing scores is done before the fusion.Let s = {s 1 ,s 2 ,...,s N R} be the list of scores correspondingto a latent, and N R be the number of reference(7)
Page 1 and 2: Latent Fingerprint Indexing: Fusion
Page 3: RolledPlainLatentLiang et al. [13]
Page 7 and 8: Table 2. Increase in hit rate (HR)

Latent Fingerprint Indexing - Computer Science and Engineering

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