are usually based upon Poincare index (Plindex), orientation
partitioning, template convolution, the direction of curvature
and mathematical models.
A. Plindex-based methods
Poincare index-based method is the most popular algo-
rithms for singular point detection. Poincare index (a vectorial
ﬁeld wrapped by a curve) was ﬁrst used to extract singular
points by Kawagoe e Tojo , in 1984. For each pixel’s
neighborhood, the sum of differences between the angles is
computed using a sliding window over the directional image
to estimate singularities’ type and location.
The authors in  proposed a modiﬁed Poincare index
technique. In the ﬁrst stage, the input ﬁngerprint image is pre-
processed and, in the next step, ﬁne orientation ﬁeld estimation
is performed. Finally, the singular points are located using the
modiﬁed Poincare index technique described by the authors.
The Plindex is also used by other works in the singularities
detection stage, as can be seen in , .
Even tough such methods are simple, they may lead to the
detection of false singularities in noisy or low-quality ﬁnger-
prints. Additional preprocessing (smoothing the orientation) or
post-processing (combining other information such as quality
check and segmentation) is required to reduce false detections
B. Directional image partitioning methods
Some algorithms create clusters by grouping similar orien-
tations from the directional image. The intersection between
clusters establishes the singular point location, as shown by
, , .
Punnet and Phalguni  proposed a method to compute
a cluster through partitioning of a directional image. A post-
processing step is applied for ﬁne singularities location and to
detect undiscovered deltas. The cluster is validated by Poincare
The method deﬁned in  has three main steps. Firstly, the
ﬁngerprint image is preprocessed for background segmentation
and orientation ﬁeld calculation. Secondly, core and delta
points are clustered using an improvement to Poincare index
method proposed by the authors. Finally, the Gaussian-Hermite
moment distribution of candidate singularity’s surrounding
neighborhood is computed to remove false positives. Using
a sample of 100 randomly selected images from NIST-4
database, the authors achieved accuracies of 95.35% and
85.90% for core and delta points, respectively.
The pattern in ﬁngerprint local ridge orientation map is
analyzed by . The authors segment the orientation values
into 4 areas, where singular points are deﬁned as points
connecting all the different orientation segments. A further step
is performed to recognize core and delta points and remove
false detections. Although the results have shown an average
correct detection rate of 94.05%, their method may not work
properly if a ﬁngerprint is rotated too much.
Such methods also require high-quality images. Noisy
images may cause false intersection points, thus false singular
C. Template-based methods
In template-based methods, a ﬁlter (template) is convolved
over each pixel in a ﬁngerprint image to extract singularities
In , convolutional masks are applied to a ﬁngerprint
image in order to compute gradients, derivatives, and angles
for each pixel. Such information is then used for singular point
extraction as described in the paper. The method is applied
to 75 ﬁngerprint images randomly selected from FVC 2004
(DB4) database. The authors report missing rates of 7.14% and
7.69% for core and deltas, respectively. In addition, 5.71% and
7.69% of false core and deltas are generated by the method.
Complex ﬁlters are used by  for automatic extraction
of singularities in ﬁngerprint images. The ﬁltering is applied
to the orientation ﬁeld in multiple resolution scales estimated
from the global structure of the ﬁngerprint, i.e. the overall
pattern of the ridges and valleys. The DB2 set of FVC2000
database is used to validate the experiments (100 persons with
8 images/person). The correct detection rate is nearly 95%.
However, only core points are detected.
A method for singular point detection using a bank of
discrete Fourier ﬁlters is presented in . The advantages
of Poincare index are ﬁrstly applied for selection of candi-
date blocks in orientation map. A set of 90 discrete Fourier
ﬁlters are then convolved with the orientation image and
the responses are inspected for singular point detection. By
using Fourier transform, the time-consuming problem of Gabor
ﬁlters is avoided. The experimental results showed that the
bank of ﬁlters took about 0.02 seconds for evaluation, instead
of 12 seconds by Gabor transform.
D. Curvature-based methods
The algorithms based on the curvature of the singular
points’ orientation report considerable results to detect singular
points, as acute gradient changes are found around singularities
location . However, such methods are not robust to noise
and false singularities are detected.
The work of  proposes a novel approach for ﬁngerprint
singular points detection based on orthogonal theory. In the
ﬁrst step, the input image is normalized to remove the effects
of sensor noise and deformation due to the ﬁnger pressure
differences. Then, the orientation ﬁeld and double orientation
ﬁeld are estimated to detection of core and delta points. Only a
reduction in computational costs and complexity are reported.
The authors in  described a hybrid technique for sin-
gular point detection based on the Direction of Curvature and
Poincare Index. The modiﬁed DC (called Enhanced Detection
of Curvature, EDC) technique is used to estimate the core and
delta point in a quicker manner and with low computational
cost. On the other hand, the Enhanced Poincare Index (EPCI)
provides a more accurate location of core and delta points. The
paper reports 98.5% of accuracy.
E. Mathematical models
Mathematical models to detect singularities can also be
found in the literature. Usually, such models attempt to de-
scribe core and delta points and deﬁne its location by a