JP2008276758A - Fingerprint singular point extractor and fingerprint singular points extraction method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a fingerprint singular point extractor stably extracting singular points by fetching information regarding angle field to the maximum and accurately carrying out identification of a core point and a delta point. <P>SOLUTION: The fingerprint singular point extractor is provided with: a directional field calculating means 7 calculating a ridge angle θ(x, y) in each point (x, y) in a fingerprint image; a horizontal differentiation means 9 calculating a derivative O<SB>x</SB>(x, y) in a horizontal direction x for each ridge angle θ(x, y); a candidate singular point extracting means 11 carrying out threshold judgement of the derivative O<SB>x</SB>(x, y) by a threshold T<SB>0</SB>and extracting a candidate singular point; a vertical differentiation means 12 calculating a window multiplication derivativeE<SB>y</SB>(x, y) which is derived by multiplying a derivative in the vertical direction y of the ridge angle θ(x, y) by a window function f<SB>w</SB>(θ) in which the absolute value is maximum when the absolute value of the ridge angle θ is π/2 and the absolute value is minimum when the ridge angle Q is 0; and a singular point extraction means 14 extracting a point with the window multiplication derivative E<SB>y</SB>(x, y) in a negative minimum or positive maximum as the singular point. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a fingerprint singular point extraction technique for extracting a singular point from a fingerprint image.

  Fingerprint verification is used in a wide range of fields as an authentication means for performing personal authentication. Minutiae Matching is widely used as a method for fingerprint matching (see Non-Patent Document 1). The minutia matching is a method of performing matching using minutia (end points / branch points of fingerprint ridges) as feature points of a fingerprint ridge image. In minutiae matching, first, noise removal and ridge enhancement processing are performed on a grayscale fingerprint image, and then binarized to generate a ridge image. Further thinning processing is performed on the ridge image to extract the minutiae. Then, a difference in position and direction between the inputted fingerprint image minutia and the registered fingerprint image minutia is calculated. The total number of minutiae pairs whose dissimilarity is less than or equal to a certain threshold value is calculated, and whether or not fingerprints match or not is determined based on whether or not this total number exceeds a predetermined threshold value.

  In the minutia matching, when the input fingerprint image is rotated or moved in parallel, the position and direction of the minutia in the input fingerprint image are greatly shifted. Therefore, when comparing minutiae, it is necessary to perform alignment and rotation correction of the input fingerprint image.

  When performing alignment and rotation correction of the input fingerprint image, a technique is adopted in which singular points of fingerprint ridges such as core points and delta points are detected and affine parameters are determined using these singular points. In this case, a method for stably extracting the singular point of the fingerprint ridge is required.

  As a conventional fingerprint singularity extraction method, a method using a Poincare Index described in Non-Patent Documents 1 and 2 (hereinafter referred to as “Poincare Index Method”) is known.

When extracting a singular point, an angle field is first created from a fingerprint image that has been subjected to ridge enhancement processing. A 3 × 3 Sobel filter is applied to the fingerprint image that has been subjected to the ridge emphasis processing to obtain vertical, horizontal, and vertical and horizontal gradients. _Assuming that the horizontal gradient is G _xx , the vertical gradient is G _yy , and the vertical and horizontal gradients are G _xy , G _xx , G _yy , and G _xy are expressed as follows.

  Using these gradients, the ridge angle θ (x, y) of each point is calculated by the following equation.

  Next, binarization of the fingerprint image that has been subjected to the ridge emphasis processing is performed using the angle field (see Non-Patent Document 3). First, a mask with 9 rows and 7 columns centering on the pixel of interest p (x, y) is created. The image in the mask is rotated so that the row direction coincides with the ridge angle θ (x, y) of the pixel of interest p (x, y). Thereafter, the sum of the pixel values is taken in the row direction, and is 1 if the sum of the center rows is larger than the average value of the sums in the row direction in the mask, and 0 if it is smaller. By performing the above operation for all pixels, the fingerprint image can be binarized. In this method, the pixels are binarized while taking into account the pixel values of the surrounding pixels along the flow of the ridges, so that the discontinuity of the ridges is repaired. Therefore, by creating an angle field again from the binarized image according to Equation (2), an angle field along the ridge flow is created.

  FIG. 1 is an example of the resulting angular field. The range of the ridge angle θ (x, y) is −π / 2 ≦ θ (x, y) ≦ π / 2. FIG. 2 shows the angle field of FIG. 1 in shades. In FIG. 2, the left part of the line running vertically in the center (red part in the color image in FIG. 2) is an area of θ> 0, and the right part of the line running vertically in the center (blue part in the color image in FIG. 2). ) Indicates a region of θ <0.

Next, the Poincare index method described in Non-Patent Documents 1 and 2 will be described. First, the main value of θ is determined in the range of [0, π] (note that the main value of arctan in equation (2) is [−π / 2, π / 2]). This angle field is quantized in four directions of 0, π / 4, π / 2, and 3π / 4. As shown in FIG. 3, a 3 × 3 block is extracted from the angle field with the pixel (i, j) as the center. From the upper-left corner of the pixel of this _{block, θ 0, θ 1, ...} , referred to as θ _7. For the extracted pixels, the Poincare index P (i, j) defined by the following equation is calculated.

  As shown in FIG. 3A, a core point is obtained when P (i, j) = π, and a delta point when P (i, j) = − π. In all other cases, P (i, j) = 0, indicating that the center of the block is a ridge.

On the other hand, Jain has developed a multi-resolution approach that extracts the north most loop singular point (core) based on the integration of sine components in two adjacent regions Ri and Ru. It has been proposed (see Non-Patent Document 4).
Japanese Patent Laid-Open No. 2001-118065 JP 2001-243465 A Anil K. Jain, Ruud Bolle, Sharath Pankanti, "Biometrics, Personal Identification in Networked Society: Personal Identification in Networked Society", Kluwer Academic Publishers, 1999, Cap. 2. M. Kawagoe and A. Tojo, "Fingerprint pattern classification," Pattern Recognition, Vol. 17, No. 3, pp. 295303, 1984. Kouichi Ito, Ayumi Morita, Akihiro Hayasaka, Takafumi Aoki, “Robust Fingerprint Classification Algorithm Based on Singularity”, The Institute of Electronics, Information and Communication Engineers, 17th Circuit and System, Karuizawa Workshop, April 26, 2004. HL Jain AK, Prabhakar S. and PS Filterbank-based fingerprint matching.IEEE Transactions on Image Processing, 9: 846-859, 2000.

  However, the Poincare index method can extract a singular point well, but has a drawback. In the Poincare index method, most of the information contained in the angle field is discarded by quantizing the ridge angle θ (x, y) into four values, so that the optimal shape and size of the ridge contour can be determined. It is difficult to detect. If the curve is small, many singular points may be extracted by mistake, and if the curve is large, correct singular points may not be extracted. In addition, when the fingerprint is an arch type, the Poincare index method cannot obtain a good result (see Non-Patent Document 3).

  On the other hand, with the above-described multi-resolution method, a better result than the Poincare index method is always obtained, and the center point can be found even with an arched fingerprint. However, since it is a multi-resolution method, it takes a lot of calculation time compared to the Poincare index method. Moreover, since a point can always be extracted, it cannot be determined whether the extracted point is a correct singular point. Furthermore, it is difficult to determine the size of the area. It is also impossible to find a delta point.

  Accordingly, an object of the present invention is to provide a fingerprint singular point extraction technique capable of stably extracting a core point and a delta point by capturing more angle field information.

A first configuration of a fingerprint singularity extraction apparatus according to the present invention is a fingerprint image processing apparatus that extracts a singularity for an input fingerprint image,
Direction field calculating means for calculating a ridge angle θ (x, y) at each point (x, y) of the fingerprint image;
Horizontal differentiation means for calculating a differential coefficient O _x (x, y) in the horizontal direction x of the ridge angle θ (x, y) of each point (x, y);
Candidate singular point extraction means for performing threshold determination on the derivative O _x (x, y) with a predetermined threshold T ₀ and extracting candidate singular points;
For each candidate singular point, the absolute value of the ridge angle θ is π / 2, the absolute value is maximal, and the ridge angle θ is a derivative of the ridge angle θ (x, y) in the vertical direction y. Vertical differentiation means for calculating a windowing differential coefficient E _y (x, y) obtained by integrating the window function f _w (θ) having a minimum value of 0 and an absolute value;
Singular point extraction means for extracting a point where the windowing derivative E _y (x, y) has a negative minimum or a positive maximum as a singular point;
It is provided with.

According to this configuration, first, by determining the threshold value of the horizontal differential coefficient O _x (x, y) of the ridge angle θ (x, y), a candidate for a singular point is selected from the entire points on the ridge. Narrow down candidate singularities. As candidate singular points obtained here, the center of the ridge vortex and the bent line of the curved ridge (the line connecting the maximum bent points of the ridge) are extracted.

FIG. 4 is an example of the angular field of the ridge of the fingerprint image. 4, red (region indicated by “R” in FIG. 5) indicates θ> 0, and blue (region indicated by “B” in FIG. 6) indicates θ <0. FIG. 7 shows the result of calculating the horizontal derivative O _x (x, y) for the angular field of FIG. Red (the linear portion indicated by “R” in FIG. 8) is O _x (x, y)> 0, and blue (the linear portion indicated by “B” in FIG. 8) is O _x (x, y) < Indicates 0. 4 and 5, it can be seen that O _x (x, y) is maximized in the vicinity of the vortex of the ridge, the branch point of the ridge, and the bent line.

Next, the windowed derivative E _y (x, y) is calculated by integrating the window function f _w (θ) to the derivative in the vertical direction y of the ridge angle θ (x, y) for the narrowed candidate singular points. To do. Window function f _{w (θ),} the absolute value and ridge angle theta absolute value maximum at [pi / 2 of the ridge angle theta is a function of the absolute value becomes minimum at 0. The derivative in the vertical direction y of the ridge angle θ (x, y) takes a large value at the vortex point, the branch point of the ridge line, and the end point of the bending line. Further, the ridge angle θ (x, y) takes a value close to π / 2 at the end point of the vortex or the bend line, and the ridge angle θ (x, y) close to 0 at a point on the bend line other than the end point. Value (see FIG. 1). Accordingly, the windowing derivative E _y (x, y) has a large negative maximum value at the end points of the vortex and the bend line, and a large positive maximum value at the center point of the ridge branch.

FIG. 9 shows the result of calculating the windowing derivative E _y (x, y) for the angle field of FIG. Red (indicated by "R" in FIG. 10) is _E y (x, y) large value is positive, blue (indicated in Figure 10 by "B") is _E y (x, y) is negative Indicates a large value.

Accordingly, the threshold _{T core} following negative windowing differential coefficient _E y (x, y) core points obtained by extracting the minimum point, the threshold _{T delta} more positive windowing differential coefficient _E y (x, The delta point can be extracted by extracting the local maximum point of y).

  In addition, in this method, when calculating the derivative of the ridge angle θ (x, y) at each point of interest, information on the ridge angle of a point in the vicinity of the point of interest is also captured, so the above Poincare index method is used. Compared to this, more information on the angle field can be captured. Therefore, it is robust against the image capturing state and noise, and the core point and delta point can be stably extracted.

  In this method, unlike the multi-resolution method, it is possible to extract a delta point or a lower center point (re-south loop type core point).

In addition, the candidate singular points are first narrowed down by the horizontal differential coefficient O _x (x, y), and then the singular points are extracted by the windowing differential coefficient E _y (x, y). Thus, it is possible to reduce the amount of calculation required for singular point extraction and extract singular points at high speed.

  Here, the “ridge line” refers to a line formed by a series of convex portions of the concave / convex pattern of the fingerprint. “Ridge angle” refers to the angle of a ridge to a horizontal line. A “singular point” refers to a point where the direction of the ridge changes rapidly, that is, a discontinuous point in the direction field. Singular points include core points and delta points. The “core singular point” is the center point (vortex point) of the vortex when the ridge is winding, and the center point (upper center) of the fold when the ridge is curved Point or lower center point). The “upper center point” means the point at the center of the ridge when the ridge has an upward convex curvature, and the “lower center point” means that the ridge has a downwardly convex curvature. The point at the center of the curve. A “delta singular point” refers to a branch point when a ridge is branched.

Further, as the window function f _w (θ), in addition to the cotangent function cos (θ), for example, f _w (θ) = 1−exp (−αθ ² ) (α: constant) and the like [−π / 2, π / 2] is a function in which absolute value | f _w (θ) | becomes maximum when θ = −π / 2 and π / 2, and absolute value | f _w (θ) | becomes minimum when θ is 0. Anything is acceptable.

The second configuration of the fingerprint singularity extracting apparatus according to the present invention is characterized in that, in the first configuration, the window function f _w (θ) is a cosine function of a ridge angle θ. The fingerprint singularity extraction device described.

As described above, when the cosine function cos (θ) of the ridge angle θ is used as the window function f _w (θ), the upper center point (the northernmost loop type core point on E _y (x, y) as a result of the experiment. ) Is easily localized.

According to a third configuration of the fingerprint singularity extraction apparatus according to the present invention, in the first or second configuration, the singularity extraction unit includes:
The windowing derivative E _y (x, y) is a negative minimum point, and the minimum point is a dividing line SL1 in which the ridge angle θ (x, y) changes from positive to negative in the x-axis direction. If it is an upper point, the minimum point is determined as the upper center point,
If the windowing derivative E _y (x, y) is a positive maximum point and the maximum point is a point on the dividing line SL1, the maximum point is determined as a delta point;
The windowing derivative E _y (x, y) is a positive maximum point, and the maximum point is a dividing line SL2 in which the ridge angle θ (x, y) changes from negative to positive in the x-axis direction. In the case of an upper point, the maximum point is determined as the lower center point.

As shown in FIG. 9, the windowing differential coefficient E _y (x, y) is a minimum point (blue) whose upper center point is negative. It is also clear that the delta point is a positive maximum point (red). If the fingerprint is a spiral, there are two center points, and the upper center point is a negative minimum point on E _y (x, y), but both the lower center point and the delta point are positive maximum points. is there. Accordingly, when only E _y (x, y) is viewed, it is difficult to distinguish the difference between the lower center point and the delta point, and the ridge angle θ (x, y) is referred to in order to extract a necessary singular point. There is a need.

  As shown in FIG. 4, the angle field is divided into several regions according to the value of the ridge angle θ (x, y). There are usually two regions above the upper center point, the left region has a ridge angle θ (x, y) greater than 0, and the right region has a ridge angle θ (x, y) less than 0. . A dividing line between these two regions is a dividing line SL1 (see a red line in FIG. 7). The upper center point exists on the dividing line SL1. It can also be seen that there is a dividing line SL1 below the delta point.

  On the other hand, the lower center point is not on the dividing line SL1. Below this lower center point, there are usually two regions, the left region has a ridge angle θ (x, y) smaller than 0, and the right region has a ridge angle θ (x, y) greater than 0. large. A dividing line between these two regions is a dividing line SL2 (see the blue line in FIG. 7). The lower center point exists on the dividing line SL2.

The dividing line SL1 and the dividing line SL2 can be calculated by calculating the differential coefficient O _x (x, y) in the horizontal direction x of the ridge angle θ (x, y).

  From the above, according to the third configuration of the present invention, the extracted singular points can be classified into an upper center point, a lower center point, and a delta point.

A fingerprint singularity extraction method according to the present invention is a fingerprint image processing method for extracting a singularity for an input fingerprint image,
A direction field calculating step of calculating a ridge angle θ (x, y) at each point (x, y) of the fingerprint image;
A horizontal differentiation step of calculating a differential coefficient O _x (x, y) in the horizontal direction x of the ridge angle θ (x, y) of each point (x, y);
A candidate singularity extraction step of extracting a candidate singularity by performing threshold determination with the predetermined coefficient O _x (x, y) wp predetermined threshold T ₀ ;
For each candidate singular point, the absolute value of the ridge angle θ is π / 2, the absolute value is maximal, and the ridge angle θ is the derivative of the ridge angle θ (x, y) in the vertical direction y. A vertical differentiation step for calculating a windowing differential coefficient E _y (x, y) obtained by integrating the window function f _w (θ) having an absolute value of 0 at a minimum;
A singular point extraction step of extracting a point where the windowing derivative E _y (x, y) has a negative minimum or a positive maximum as a singular point;
It is provided with. .

As described above, according to the present invention, in extracting a singular point of a fingerprint image, after narrowing down candidate singular points by a horizontal differential coefficient O _x (x, y), a windowing differential coefficient E _y (x, y ), The core point and the delta point can be stably extracted by taking in the maximum amount of angle field information.

  The best mode for carrying out the present invention will be described below with reference to the drawings.

  FIG. 11 is a diagram illustrating the configuration of the fingerprint singularity extraction apparatus 1 according to the first embodiment of the invention. The fingerprint singularity extraction device 1 is a device that extracts a singularity of a fingerprint image input from the fingerprint input device 2 and outputs it to the output device 3. The fingerprint singularity extraction apparatus 1 includes an input image storage unit 4, a ridge extraction unit 5, a ridge data storage unit 6, a direction field calculation unit 7, a direction field data storage unit 8, a horizontal differential calculation unit 9, and a horizontal differential coefficient storage. Unit 10, candidate singularity extraction unit 11, vertical differential calculation unit 12, windowing derivative storage unit 13, and singularity extraction unit 14.

  The input image storage unit 4 stores a fingerprint image input from the fingerprint input device 2. The ridge extraction unit 5 reads the fingerprint image stored in the input image storage unit 4, extracts ridge data, and stores it in the ridge data storage unit 6.

  The direction field calculation unit 7 reads out the ridge data stored in the ridge data storage unit 6 and calculates the ridge angle θ (x, y) of each pixel point by the calculation shown in equations (a) and (2). Is calculated and stored in the direction field data storage unit 8.

The horizontal differential calculation unit 9 reads out the ridge angle stored in the direction field data storage unit 8 and derives the differential coefficient O _x (x, y) in the horizontal direction x of the ridge angle θ (x, y) of each pixel point. ) And is stored in the horizontal differential coefficient storage unit 10.

The candidate singularity extraction unit 11 extracts candidate singularities from which the differential coefficient O _x (x, y) is equal to or less than a predetermined threshold value T ₀ .

For each candidate singular point, the vertical differential calculation unit 12 adds the window function f _w (θ) to the derivative in the vertical direction y of the ridge angle θ (x, y), and the windowed differential coefficient E _y (x , Y) is calculated and stored in the windowing derivative storage unit 13. Here, in this embodiment, cos (θ) is used as the window function f _w (θ).

Singular point extraction unit 14, windowing derivative stored in the windowing derivative storage unit 13 E _{y (x, y)} read out, windowing differential coefficient E _{y (x, y)} is negative minimum or positive A point having a maximum is extracted as a singular point, and the extracted singular point is output to the output device 3.

  The fingerprint singularity extraction apparatus 1 of the present embodiment may be configured by hardware, or each component is created as a program module and executed by the computer to functionally extract the fingerprint singularity from the computer. You may comprise so that it may function as the apparatus 1. FIG.

  The operation of the fingerprint singularity extraction apparatus 1 according to this embodiment configured as described above will be described below.

  First, a fingerprint is input from the fingerprint input device 2 and stored in the input image storage unit 4. The ridge extraction unit 5 extracts ridges from the stored fingerprint image. A known method can be used for this ridge extraction process.

  For example, the method shown in Non-Patent Document 3 can be used. That is, first, dispersion of pixel values is obtained for each 3 × 3 block. Next, the variance is binarized by 1/4 of the average value of the obtained variances. As a result, only the ridges of the fingerprint emerge, so a mask for extracting the fingerprint is created using a morphological filter. Next, an average is calculated for each block of 11 × 11 size, and the central pixel of the block is binarized using this as a threshold value. Thereby, a ridge is emphasized. Also, processing such as blur correction processing is performed as necessary.

  Next, the direction field calculation unit 7 calculates the ridge angle θ (x, y) by calculating the expressions (1) and (2) at each pixel point (x, y) based on the ridge image. calculate. The window size used here is 8 × 8.

  The ridge extraction unit 5 binarizes the fingerprint image that has been subjected to the ridge enhancement process using the data of the calculated ridge angle θ (x, y), as described in the prior art. Then, the direction field calculation unit 7 may calculate the ridge angle θ (x, y) again.

Next, in order to create a center point mask, the horizontal differential calculation unit 9 performs a differential calculation of the following equation for each ridge angle θ (x, y) to calculate a differential coefficient O _x (x, y). .

Further, in order to generate the center point mask, the candidate singular point extraction unit 11 removes points whose values are smaller than the threshold T ₀ from the calculated differential coefficients O _x (x, y). Here, a 2.5 as the threshold value _{T 0.} Furthermore, morphological operations are performed to remove isolated points and spurs (short branch lines).

Next, the vertical differential calculation unit 12 performs the following windowed differential calculation on each ridge angle θ (x, y) to calculate a windowed differential coefficient E _y (x, y).

Finally, the singular point extraction unit 14 applies a center point mask to the windowing derivative E _y (x, y). The minimum point is the center point and the maximum point is the delta point. Here, a threshold value T _core is set, and it is determined whether the center point is correct or incorrect. If the value of the minimum point is larger than T _core , it is assumed that there is no center point.

  As described above, the singular point of the fingerprint image is extracted.

It is a figure which shows the example of the angle field of a fingerprint image. It is the figure which showed the angle field of FIG. 1 by the color coding. It is a figure explaining the extraction method of the singular point by the Poincare index method. It is a figure which shows the example of the angle field of the ridgeline of a fingerprint image. It is auxiliary explanatory drawing of FIG. It is auxiliary explanatory drawing of FIG. It is a figure which shows the result of having calculated the differential coefficient _Ox (x, y) of the horizontal direction about the angle field of FIG. It is auxiliary explanatory drawing of FIG. It illustrates windowing differential coefficient E _{y (x, y)} The results of calculating the the angle field of FIG. It is auxiliary explanatory drawing of FIG. It is a figure showing the structure of the fingerprint singularity extraction apparatus 1 which concerns on Example 1 of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Fingerprint singularity extraction apparatus 2 Fingerprint input apparatus 3 Output apparatus 4 Input image storage part 5 Ridge line extraction part 6 Ridge line data storage part 7 Direction field calculation part 8 Direction field data storage part 9 Horizontal differentiation calculation part 10 Horizontal differential coefficient storage Unit 11 Candidate Singularity Extraction Unit 12 Vertical Differential Operation Unit 13 Windowing Derivative Coefficient Storage Unit 14 Singularity Extraction Unit

Claims (4)

A fingerprint image processing apparatus that extracts a singular point for an input fingerprint image,
Direction field calculating means for calculating a ridge angle θ (x, y) at each point (x, y) of the fingerprint image;
Horizontal differentiation means for calculating a differential coefficient O _x (x, y) in the horizontal direction x of the ridge angle θ (x, y) of each point (x, y);
Candidate singular point extraction means for performing threshold determination on the derivative O _x (x, y) with a predetermined threshold T ₀ and extracting candidate singular points;
For each candidate singular point, the absolute value of the ridge angle θ is π / 2, the absolute value is maximal, and the ridge angle θ is the derivative of the ridge angle θ (x, y) in the vertical direction y. Vertical differentiation means for calculating a windowing differential coefficient E _y (x, y) obtained by integrating the window function f _w (θ) whose absolute value is minimum at 0;
Singular point extraction means for extracting a point where the windowing derivative E _y (x, y) has a negative minimum or a positive maximum as a singular point;
A fingerprint singularity extraction apparatus characterized by comprising: The fingerprint singularity extracting apparatus according to claim 1, wherein the window function f _w (θ) is a cosine function of a ridge angle θ. The singular point extraction means includes:
The windowing derivative E _y (x, y) is a negative minimum point, and the minimum point is a dividing line SL1 in which the ridge angle θ (x, y) changes from positive to negative in the x-axis direction. If it is an upper point, the minimum point is determined as the upper center point,
If the windowing derivative E _y (x, y) is a positive maximum point and the maximum point is a point on the dividing line SL1, the maximum point is determined as a delta point;
The windowing derivative E _y (x, y) is a positive maximum point, and the maximum point is a dividing line SL2 in which the ridge angle θ (x, y) changes from negative to positive in the x-axis direction. 3. The fingerprint singular point extraction apparatus according to claim 1, wherein, when the point is an upper point, the maximum point is determined as a lower center point. A fingerprint image processing method for extracting a singular point for an input fingerprint image,
A direction field calculating step of calculating a ridge angle θ (x, y) at each point (x, y) of the fingerprint image;
A horizontal differentiation step of calculating a differential coefficient O _x (x, y) in the horizontal direction x of the ridge angle θ (x, y) of each point (x, y);
A candidate singularity extracting step of extracting a candidate singularity by determining the threshold value of the derivative O _x (x, y) with a predetermined threshold T ₀ ;
For each candidate singular point, the absolute value of the ridge angle θ is π / 2, the absolute value is maximal, and the ridge angle θ is the derivative of the ridge angle θ (x, y) in the vertical direction y. A vertical differentiation step for calculating a windowing differential coefficient E _y (x, y) obtained by integrating the window function f _w (θ) having an absolute value of 0 at a minimum;
A singular point extraction step of extracting a point where the windowing derivative E _y (x, y) has a negative minimum or a positive maximum as a singular point;
A method for extracting a fingerprint singularity characterized by comprising: