Master Thesis - Department of Computer Science

(a) cn(p) = 2 (b) cn(p) = 1 (c) cn(p) = 3
Figure 2.8: (a) Intra-ridge pixel; (b) Termination minutia; (c) Bifurcation minutia
number different from 2. The crossing number [6] cn(p) of a pixel p in a binary image
is defined as half the sum of the differences between pairs of adjacent pixels in the
8-neighborhood of p:
cn(p) = 1
2
�
i=1,..,8
|val(pi mod 8) − val(pi−1)|. (2.20)
where p0, . . . , p7 are the pixels belonging to an ordered sequence of pixels defining
the 8-neighborhood of p and val(p) ∈ {0, 1} is the pixel value. It is simple to note
(Fig. 2.8) that for a pixel p with val(p) = 1, it:
• is an intermediate ridge point if cn(p) = 2;
• corresponds to a termination minutia if cn(p) = 3;
• defines a more complex minutia (bifurcation, crossover, etc.) if cn(p) ≥ 3
Leung et al.’s [76] method extracts the minutiae from thinned binary images but,
instead of using the crossing number, they use a three-layer perceptron neural net-
work. In some approaches, minutiae are detected from binary images without any
intermediate thinning. Weber [129] first performed an image enhancement by band-
pass filtering in the frequency domain and then did binarization via local threshold.
Finally, the minutiae are detected from the thick binary ridges through a ridge track-
ing algorithm. Szekély and Szekély [121] developed a minutiae detection technique
based on the computation of the orientation image divergence.
Miao and Maltoni [82] proposed a direct gray-scale minutiae extraction algorithm,
where the basic idea was to tract the ridge lines in a gray-scale image by “sailing”,
30