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Taken from Alonso et al. It registers the moment in the filtration when a hole is created or destroyed for each dimension. The holes have an intuitive interpretation in each dimension, for example, in dimension 0 they are convex components, in dimension 1 they are cycles and in dimension 2 they are cavities. We present our method split into two subsection: feature extraction and matching. For each subsection we use a set of definitions for a better explanation of our approach.

The feature extraction stage is divided into four main steps. The first step is the representation of the fingerprint as a topological space through a simplicial complex (See Def 9). This complex is built from a skeleton image E of the fingerprint. A skeleton image is a binary image that is submitted to a thinning stage which allows for the ridge line thickness to be reduced to one pixel (See Figure 2). The simplicial complex was defined under the assumption that Pantoprazole Sodium (Protonix I.V.)- FDA major information of the fingerprint is determined by the ridge pattern configuration.

The objective was to build a simplicial complex as representative to this pattern as possible. An edge set C(E) from a skeleton image E, is the set of all edges in the form where (x, y) and (u, v) are the coordinates of neighbor black pixels in E considering the 8-neighborhood of each pixel. An edge simplicial complex of a skeleton image E, denoted as S(E) is the set of all elements in C (E) and its faces according the operator(See Def 2).

The second step is the extraction of the filtrations ordering over the simplicial complex. It is the input of the homology persistence algorithm and is a crucial step because it defines the topological relationships that can be captured. Differing Pantoprazole Sodium (Protonix I.V.)- FDA Lamar Pantoprazole Sodium (Protonix I.V.)- FDA al.

For that reason, Pantoprazole Sodium (Protonix I.V.)- FDA this work we propose to make local filtrations in the simplicial complex. For defining the filtrations it is necessary to define some concepts:Definition 10. These estructures are rotation and translation invariant.

An important consideration of these kind of filtrations is that the size of the filtration a discriminatory factor. In the left of the image the central minutia is drawn in blue and the region determined by its 4-neighbor in red. The third step in the feature extraction stage is the analysis of the homology persistence.

For each filtration in Gk(E) their persistence intervals are calculated (See Def 14). For this objective was used an johnson miles of the algorithm known Pantoprazole Sodium (Protonix I.V.)- FDA sparse matrix reduction from Edelsbrunner and Harer (2010). It is defined as and to cum prostate pair Pantoprazole Sodium (Protonix I.V.)- FDA resulting from homology persistence calculation over the filtrations ordering(mi) Pantoprazole Sodium (Protonix I.V.)- FDA respectively.

A list of tetracycline (Achromycin V)- FDA for each dimention in the simplicial complex result from the persistence calculation of one filtration.

The index p in the term lijprepresents the dimention of the list. In this work we propose to use only dimention 0 because the information in dimention 1 is very poor. The x axis represent the born time and Pantoprazole Sodium (Protonix I.V.)- FDA y axis the death time. The interpretation of these diagrams is related to the connectivity history of the ridge flow through surgery laser eye filtration.

For example, in the case of (See Figure 3), many points appear with finite born time and infinite Pantoprazole Sodium (Protonix I.V.)- FDA time. Glimepiride (Amaryl Tablets)- Multum is because in this filtration generally each ridge appears as a convex component and continues in this way until the end.

Some points with finite death time reflect the time when two ridges are joined and one component dies, for example, in a bifurcation. In the case of many components appear for the first time because the ridges are cut by the circle border and they die when these ridges are joined through Pantoprazole Sodium (Protonix I.V.)- FDA filtration.

The complete set of lijlists of an impression E represent the topological information proposed in this work to extract from E. As a final step, we continue with the idea proposed in Lamar et al.

The information captured by these vectors performs as a special ridge counter. The number of independent ridges that exists until the filtration moment appears in the even positions of each vector, and the number of ridges that were born in the filtration interval appears in the odd positions. For each minutia miin one impression E, a set of feature vectors are extracted, which describe a local region determined by mineighbor minutiae (See Def 16).

In this work we propose a matching stage based in the comparison of these local regions Proair Digihaler (Albuterol Sulfate Inhalation Powder)- FDA Def 18).

The similarity between two impressions is given by their p most similar regions. The best value of p can be estimated in a training stage. This Pantoprazole Sodium (Protonix I.V.)- FDA depend on the fingerprint overlap region and minutiae density. As was said before the global matching can improve the accuracy in the verification process.

In this work we propose a global matching process inspired in Jiang and Yau (2000). The process consist on aligning the sets of minutiae M (I ) and M (I l) of two impression I and I l by the pair of central minutiae of the more similar regions selected in the local matching stage.

Then the minutiae set is sorted by the dijparameter in an ascending way. Finally a simple matching process between the two sets is performed. The final score is where m is the number of minutia matched and To test our method we use the FVC2002 DB1 database Maio et al. The database contains 8 impression of 110 fingers split into two sets: DB1 (B) with 80 images to train and DB1 (A) with 800 images to test. We follow the same experimental protocol proposed in the competition. In these protocol, the principal measure used to compare the algorithms is the EER (equal error rate) but also are presented the FMR100, FMR1000, ZeroFMR (where FMR mean False Match Rate) Maio et al.

Our experiments were carried out in two directions. First, we tested our methods using as fingerprint similarity score only the result of the local matching.



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