## Fig a Border points used

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### Fig a Border points used

Fig. 8. (a) Border points used for normalization in OSIRISV4.0, (b) border points used for normalization in OSIRISV4.1, (c) normalized image by OSIRISV4.0, (d) normalized image by OSIRISV4.1.Figure optionsDownload full-size imageDownload high-quality image (390 K)Download as PowerPoint slide
The new normalization follows the following steps. First, let W and H be respectively the width and height of the desired normalized image. Regarding to Daugman’;s approach, we compute a regular sampling of angles θk where k ranges from 0 to W, so that θ0 = 0 and θW = 2π:
equation(1)θk=2πk/W,k&amp;isin;[0,W]θk=2πk/W,k&amp;isin;[0,W]
Let (xp, yp, ?p) and (xi, yi, ?i) respectively be the coordinates of a point of pupil coarse and iris coarse contours where (x, y) are the x-coordinate and y-coordinate of the radius relatively to the estimated center of each coarse contour and ? the angle of the non-regular sampling. ? follows the non-uniform sampling of the coarse contour as explained above. The next step consists in estimating the new point (Xkp,Ykp) with a sampling as close as possible to θk from the coarse pupil contour. To this apexbio dilution end, we interpolate the two nearest points of the coarse contour j and j+1j+1 to θk as follow:
equation(2)Xkp=(1?α)&#183;xpj+α&#183;xpj+1equation(3)Ykp=(1?α)&#183;ypj+α&#183;ypj+1
Table 2.
Summary of works that have used OSIRISV2 and OSIRISV4.1.Full-size tableTable optionsView in workspaceDownload as CSV
This process is illustrated in Fig. 6. In a similar way, the new points (Xki,Yki) of the iris contour are computed. The pupil and the iris centers are not necessarily the same. Often the pupil center has a nasal and inferior position relative to the iris center [22]. To cope with this problem, we define a segment S formed by (Xkp,Ykp) and (Xki,Yki) as shown in Fig. 7.
S is then rescaled so that it fits with the height H of the normalized image. On the normalized image, the pixel on hth row and kth column will take the same value as the pixel located at (xk, h, yk, h) on the original image as follow:
equation(4)xk,h=(1?h/H)&#183;Xkp+(h/H)&#183;Xkiequation(5)yk,h=(1?h/H)&#183;Ykp+(h/H)&#183;Ykiwith h &amp;isin; [0, H]
Compared to OSIRISV4, in OSIRISV4.1 the borders used for normalization are closer to real ones in the sclera area and in the lower eyelid part, as illustrated in Fig. 8. Therefore, the matching points considered in the comparison of two irises are better aligned resulting in increased performance. The flowchart of OSIRISV4.1 is resumed in Fig. 4c.
4. Impact of OSIRIS in the research community
Table 2 gives an overview of the teams that have used OSIRIS reference system in their research. We notice that OSIRIS is used by a large community in different areas of research. We give in Table 2, for each team, the number of papers in which OSIRISV2 and OSIRISV4.1 have been used, with the corresponding field of application. We also cite one reference per team.