RU2310910C1 - Method for verification and identification of imprints of papillary patterns - Google Patents

Abstract

FIELD: biometry, namely, methods for recognizing and encoding imprints of papillary patterns, possible use in various areas of informational technologies.

SUBSTANCE: in accordance to the invention, passports of fingerprints are formed, standard fingerprint passports are compared with provided passport by comparison of minute parts. Simultaneously with generation of fingerprint passports, filtration encoding of images of fingerprints is performed, which includes repeated mathematical processing of image of papillary pattern. Gabor filter may be used during filtration of the image.

EFFECT: increased speed of operation when comparing and identifying imprints of papillary patterns while preserving high trustworthiness of recognition results.

3 cl, 7 dwg

Description

The present invention relates to the field of biometrics, namely to methods for recognizing and encoding fingerprints of papillary patterns, and can be used to verify and identify fingerprint images in various fields of information technology, such as human identification systems, information security, systems of regulated access control, as well as in the field of forensic medicine and forensics.

Personal identification using biometric technologies is currently one of the most promising, rapidly developing areas, among which methods and tools using fingerprints occupy one of the leading places.

A known method for determining the height of the arc pattern, designed to recognize papillary patterns of fingerprints (see RF patent No. 2204941, IPC 7 AB 5/117, publ. 05.27.2003). The method consists in identifying the most curved papillary line of the arc pattern, marking this line, measuring the angle of its bend and assigning the obtained value of the angle of bending to the category of height of the papillary pattern generally accepted in dermatoglyphics. The method allows to indirectly determine the height of the arc papillary pattern by measuring the bending angle of the most curved papillary line and use this indicator as a characteristic of this type of papillary patterns.

The advantage of the considered method is its high coding rate. However, a significant drawback of the known technical solution is the low accuracy of coding based on the indirect method, and hence the unreliability of recognition, especially when the quality of the compared fingerprints is poor.

A known method for the recognition and encoding of fingerprints of papillary patterns (see RF patent No. 2059979, IPC 6 G06K 9/00, publ. 05/10/1996), which consists in scanning the image of the papillary pattern, highlighting the characteristic features of the image with their subsequent encoding, forming an array of selected characteristic signs and comparing their codes with the codes of the selected characteristic features of the compared fingerprints of papillary lines. A distinctive feature of the known method is that when forming an array of distinguished characteristic features, the flow direction of papillary lines is determined in the vicinity of a point commensurate with the intercostal distance, the flow pattern is smoothed out by replacing the flow direction value with the average of the flow direction values of neighboring points, and the probable position of characteristic features papillary pattern, determine the function of the characteristic features of the papillary pattern and produce sequential calculation The reduction of the characteristic features of the papillary pattern, starting with the sign with the maximum value of the weight function. Thus, in the known method, it is successfully solved not only the problem of determining the position of the features, but also the problem of determining the probability that it is a feature that is defined, and not a noise point. This makes it possible to use only those features that satisfy a certain accuracy criterion for a given level of probability, and not to use dubious features. The method is characterized by a relatively high speed. However, the disadvantage of this method is the low accuracy of coding, and hence the recognition of fingerprints of papillary patterns, due to large errors caused by the spread of the position of the user's finger when taking the print. This may result in insufficient points needed for coding. In addition, there are papillary patterns in which characteristic points are generally absent.

A known method of comparing papillary finger patterns (see RF application No. 94039018, IPC 6 G06K 9/00, 9/68, publ. 09/10/1996), which consists in the fact that when comparing papillary patterns, fingerprints are recorded with the determination of their coordinates and angle directions of the papillary line at the site of formation of the feature. After the list of feature pairs is generated, a compatibility matrix of feature pairs is formed, from which, according to the specified criteria, the most identical pairs are selected and the final unique combination of identical features of the request and archive prints is determined. When comparing the request and archive fingerprints, a differential plane is built on which points are applied, the coordinates of which are defined as the difference between the characteristics of the features of the request and archive fingerprints. For identical fingerprints, these points form a compact set. In case of violation of compactness, primary rejection of archival prints is carried out and their further detailed study is excluded. Obviously, with elastic deformation of the request fingerprint, the compactness of the set of points on the differential plane is violated. In addition, to construct a differential plane, it is necessary to determine the center of coordinates of the request and archive fingerprints. The center of coordinates determines the characteristics of features. When one of the coordinate centers is shifted, the compactness of the set of points on the differential plane is also violated.

Thus, due to deformation or displacement of the coordinate centers, identical fingerprints can be falsely rejected, which is a significant drawback of the method, as it reduces its reliability.

This drawback is eliminated in the known method for comparing papillary finger patterns (see RF patent No. 2185661, IPC 7 G06K 9/62, published July 20, 2002), which consists in registering numbered features in the area of a clear imprint with determining coordinates, direction angle and crest accounts between the features of the request and archive fingerprints. For each feature, a nest is built, which includes at least two features, all the nests of the request and archive fingerprints located in the database are compared, and at least one of the best pairs of nests containing the request and the archive fingerprint nests is formed. From each selected pair of nests, fragments of the request and archive fingerprints are developed in parallel by the method of transition from one pair of nests to another along the path of the best comparison of nests. Accumulate nest comparison estimates for each fragment development path and select the best path. Comparison of request and archive fingerprint nests is made after their geometrical binding to loops, deltas and curls.

Using the described method for comparing fingerprints of papillary patterns in identifying a person by fingerprints allows us to solve the problem posed by the authors, which is to increase the reliability of comparison of papillary patterns of fingers, which is an undoubted advantage of the method.

However, the disadvantages of the technical solution described above include the low comparison speed of papillary patterns, and, consequently, the lack of recognition speed, which is characteristic of all methods based on the allocation and comparison of minutes. This is due to the large volume of computational operations in the process of identifying the closest papillary patterns.

Closest to the claimed method is a method for comparing papillary finger patterns (see Kukharev GA Biometric systems: Methods and means of identifying a person’s personality. - St. Petersburg: Polytechnic, 2001, p. 27-33), selected as a prototype. The method is based on the allocation and comparison of minutes and includes the following steps:

- improving the quality of the original image of the fingerprint;

- calculation of the orientation field of the papillary lines of the original fingerprint;

- binarization of the fingerprint image;

- thinning of the lines of the image of the print;

- allocation of minutes and recording their parameters in the vector;

- comparison of minutes.

The matchmaking process consists of three parts:

- data registration;

- search for pairs of matching minutes;

- An assessment of the alignment measure of the two matched fingerprints.

In the process of extracting the minutes, determining their type and orientation angle, the coordinates of the detected minutes, as well as the angles of their orientation, are recorded in the vector of minutes. Moreover, in a real situation, two fingerprints of the same finger, obtained one after the other on the same scanner, will differ from each other by rotation relative to one of the axes, offset of the fingerprint pattern relative to the X and Y axes, slightly different deformation of the pattern (or nonlinear distortions) of the pattern, possible changes in the scale of presentation of the prints, and finally, different peripheral areas of the real finger. In this regard, the process of comparing the minutes should not be implemented in one iteration in a complete manner for the whole set, but iteratively for each individual minute. This is due to the high reliability of identification inherent in the described method. However, this same circumstance is the reason for the low speed of the method selected as a prototype. The performance of methods based on fingerprint recognition by comparing minutes is in the range (300 ÷ 2000) comparisons / sec, which is a significant disadvantage of the known method, since it limits the possibilities of its use when working with large databases.

The objective of the invention is to increase the speed of comparison and identification of fingerprints of papillary patterns while maintaining high reliability of recognition results due to the procedure of additional filtering encoding of the fingerprint image, which consists in multiple mathematical processing of the image of the papillary pattern.

To achieve the indicated technical result, a method for verification and identification of fingerprints of papillary patterns is proposed, which, like the method closest to it, chosen as a prototype, consists in recording the data of the reference and presented fingerprints of papillary patterns. Data recording consists of the formation of fingerprint passports by highlighting the minutes, determining their type, coordinates, orientation angles and recording them in the form of the reference and presented vectors of the minutes. Then, reference fingerprint passports are compared with the presented passport by comparing the minutes, which consists in searching for pairs of matching minutes, evaluating the measure of similarity of the fingerprints being compared and comparing it with a threshold.

A feature of the proposed method, distinguishing it from the known method selected as a prototype, is that simultaneously with the formation of passports of the reference and presented fingerprints, additional filtering coding is carried out, which consists in constructing the field of directions of papillary lines by multiple mathematical processing of the image of the fingerprint by projection-dispersive filter followed by processing the modernized median filter, search for characteristic points, determine lenii their types and coordinates, filtering the image in the vicinity of each matched feature point by processing multiple spatially-wave filter with a floating window and retaining the coded data of each fingerprint with fingerprint data obtained in the step of forming passports. When comparing the presented and reference prints of papillary patterns before the minute comparison procedure, an additional code of the presented papillary pattern is compared with additional codes of all standard papillary patterns obtained by additional filtration coding and stored in the database. This comparison is carried out by determining the distance between the two images represented by the vectors of minutes obtained by additional filtering coding for all possible angles, taking the minimum distance as the result corresponding to the maximum similarity of the images of papillary patterns, forming a list of candidate prints, i.e. reference passports having the closest degree of coincidence with the presented fingerprint. After that, each candidate fingerprint is compared with the presented fingerprint by a method based on a comparison of the minutes.

When filtering the image, the Gabor filter can be used.

To form a list of candidate fingerprints, their number is set depending on the size of the base of reference fingerprints.

The essence of the proposed method is as follows.

From patent and scientific literature (see Kukharev G.A. Biometric systems: Methods and means of identifying a person’s personality. - St. Petersburg: Polytechnic, 2001, pp. 19-20), it is known that in each print it is possible to identify the signs of two types used in their identification: global and local. The first type includes signs that can be seen and / or distinguished on the fingerprints with the naked eye: papillary patterns, image area, “core”, “delta” items, type of papillary lines and their number. The second type includes local features called minutes: these are features that are unique to each print and define points of change in the structure of papillary lines (for example, breaking, ending, bifurcation, etc.), the orientation of the papillary lines, and the X and Y coordinates at these points. Each print can be presented in 50-70 minutes. Research and practice confirm that identical global signs can be found in the fingerprints of different people, but the likelihood of the presence of the same micro-blocking minutes in the same fingerprints is very small. As a rule, global features are used for large fingerprint databases at the stages of preliminary classification. And then, at the second stage of recognition, local features are already used.

The identification procedure can conditionally be divided into the following main stages:

- receiving a fingerprint of the user;

- registration of data of the papillary pattern of the fingerprint (formation of the passport of the papillary pattern) and their storage for subsequent identification;

- the actual identification or verification, that is, a comparison of the presented fingerprint of a particular user with the passport (standard) obtained at the data registration stage;

- assessment of the level of similarity of the compared prints of papillary patterns and its comparison with the threshold.

The speed and reliability of the identification procedure substantially depends on the way in which passport prints of papillary patterns are generated. Depending on the tasks set, this procedure, called encoding of the fingerprint image, can be carried out either on the basis of characteristic points (global features), or on the basis of minutes (local features). Moreover, each method has its own advantages and disadvantages described in the section "Prior art" of the proposed application. The general conclusions that can be drawn from a study of the prior art are as follows:

- identification methods based on the encoding of characteristic points are characterized by low accuracy at a high speed of the encoding process and further identification;

- identification methods that use coding and comparison methods based on minutes and their comparison are highly accurate and reliable with a relatively low speed of the process of comparison and identification of fingerprints of papillary patterns.

The identification method chosen as the closest analogue (see Kukharev G.A. Biometric systems: Methods and means of identifying a person’s personality. - St. Petersburg: Polytechnic, 2001, p. 27-33), is based on coding and comparison of minutes and has a limit in speed when comparing feature sets, which is (300 ÷ 2000) comparisons per second. This fundamental limitation is due to the large time costs associated with multiple calculations of the smallest distances between the minutes in order to establish the most similar fingerprints. Naturally, the speed of comparison and identification of papillary patterns encoded by the method described in the prototype will also be low.

In contrast to the indicated technical solution, the claimed method for identifying fingerprints of papillary patterns, possessing, as a prototype, high accuracy and, therefore, reliability of recognition results, has high speed of comparison and identification, which is its significant distinguishing feature.

This feature of the proposed method is provided due to the fact that a new essential feature is introduced into the distinctive part of the formula — additional filtering coding, which consists in the mathematical processing of the image of the papillary fingerprint pattern obtained at the user registration stage. This high-speed procedure is performed simultaneously with the main coding, which is carried out in the process of forming a passport of a papillary pattern. The specified additional coding is carried out by space-wave filtering in the region of characteristic points with a very high speed. Additional coding is carried out in the following sequence given in the claims of the claimed invention, namely:

- construction of the direction field of papillary lines by multiple mathematical processing of the fingerprint image by the projection-dispersion filter;

- subsequent processing of the modernized median filter;

- search for characteristic points, determination of their types and coordinates;

- filtering the image in the vicinity of each characteristic point found by repeatedly processing the space-wave filter with a floating window;

- saving encoded data of the fingerprint of the papillary pattern for subsequent recognition together with the data obtained during the formation of the passport of the user's fingerprint.

An important feature of the proposed method for verifying and identifying a fingerprint of a papillary pattern is that additional fingerprint encoding with a spatial wave resonance filter can also be carried out if there are no characteristic points on the fingerprint (“cores”, “deltas”) (such fingerprints occur).

Thus, as a result of processing the fingerprint of the papillary pattern in the described manner, the additional data set obtained by multiple high-speed mathematical processing of the fingerprint image first by a projection-dispersion filter is added to the main set of data obtained as a result of very accurate coding by highlighting the minutes (basic coding) , then with a modernized median filter and, finally, with a spatially wave resonance filter.

The essential features related to the comparison of additional codes of the presented and reference papillary patterns are signs that reflect the sequence of this procedure, namely:

- determination of the distance between two images represented by vectors of minutes obtained with additional filtering coding for all possible angles;

- adoption of the minimum distance as a result corresponding to the maximum similarity of images of papillary patterns;

- the formation of a list of candidate fingerprints, that is, reference passports having the closest degree of coincidence with the presented fingerprint.

The specified procedure is high-speed and has a significant impact on improving the speed of the proposed method as a whole, thereby contributing to the solution of the problem.

Let us now consider how the identification of the presented fingerprint occurs when comparing it with a reference fingerprint encoded using the proposed method.

In the process of comparing the presented and reference prints, the first step is a high-speed comparison of the additional code of the presented papillary pattern with the codes of all papillary patterns in the database obtained by additional filtering coding.

The speed of this comparison, ranging from 3000 to 60,000 comparisons / sec, is several orders of magnitude higher than the speed of fingerprint comparisons based on the comparison of minutes, which is only (300 ÷ 2000) comparisons / sec. The result is a relatively small list of fingerprints - applicants who have the closest degree of coincidence with the submitted fingerprint (their number depends on the size of the base of reference fingerprints). The next step is a longer, but very accurate comparison, during which the presented fingerprint is compared only with the selected fingerprints by the method of matching minutes. Thus, there is a significant increase in the speed of comparison, and therefore identification. This is due to the fact that there is no need to compare the presented fingerprint with each fingerprint stored in the database encoded in an accurate but relatively slow way - a method based on coding and comparison of the minutes selected as a prototype.

The features included in the dependent claims provide specific examples:

- performing the image filtering procedure, for example, using the Gabor filter (see paragraph 2 of the formula);

- forming a list of candidate fingerprints by setting the number of candidate fingerprints depending on the size of the reference fingerprint database (see paragraph 3 of the formula).

Thus, the combination of the above features allows us to solve the tasks.

The proposed method for verification and identification of prints of papillary patterns is illustrated by drawings, which show:

figure 1 is a field of directions of papillary lines, in which each of the four directions corresponds to its own color;

figure 2 - field directions of papillary lines, in which each direction is depicted by lines corresponding to one of four main directions: 0 °, 45 °, 90 °, 135 ° after processing the image of the fingerprint projection-dispersion filter;

figure 3 is a field of directions of papillary lines after processing (filtering, smoothing) of a fingerprint image with a modernized median filter;

figure 4 - determination of the presence of the "core" by a combination of direction fields (changing the direction field of papillary lines around the "core");

figure 5 - determination of the presence of "delta" by a combination of direction fields (changing the direction field of papillary lines around the "delta");

figure 6 - image of the papillary lines of the fingerprint after processing the image with a space-wave filter in the range [0 ° -180 °);

Fig.7 is a filtered image of the papillary lines of the fingerprint, divided into (m × 2n) ring sectors.

The proposed method is as follows.

In the first step of the method, each user must be registered. To do this, on the contact surface of the device for recording fingerprints (optical, capacitive or other type), it is necessary to obtain a fingerprint of each user. As a device for recording fingerprints, any of the following devices can be used:

- models BS1620, BS2024 (Russia), technical solutions are patented by the applicant of the present invention (see RF patent for utility model No. 46914, IPC 7 A61B 5/053, A61B 5/117, publ. 10.08.2005);

- model Fingkey Hamster, Nitgen company (Korea, Seoul),

- models TCR42C, TCRUK, TCEBB1C, UPEK (USA), as well as other models manufactured abroad and in Russia.

The resulting image of the fingerprint of the papillary pattern of the finger is digitized and converted into a unique digital code, which is the reference passport of the registered user and is entered into the database of the system for its storage and subsequent comparison with the presented papillary pattern. This process, which we call conditionally the main coding, should be based on the coding (extraction) of minutes - the most high-precision and reliable method known to date from the prior art.

The main coding consists of several procedures and is performed in the following sequence.

- Improving the quality of the original image of the fingerprint. To do this, either low-pass filtering or normalization is implemented, the purpose of which is to correct the structure of the ridges of papillary lines and improve the sharpness of their boundaries.

- Calculation of the orientation field of papillary lines. Moreover, the whole image is divided into blocks, for example, B × B pixels (B≥5, integer) and for each block (according to the brightness gradients in the block), one orientation angle θ of the papillary lines is calculated.

- Binarization of the fingerprint image. The procedure is implemented by threshold processing.

- Thinning of the lines of the image of the print. It is performed by the process of thinning the lines of a binary image until these lines become equal to one pixel.

- Selecting the minutes and recording their parameters in the vector. This procedure is implemented by local processing of the entire fingerprint image using a mask and counting the number of pixels located around the center of the mask and having nonzero values. The pixel in the center of the mask is taken as a minute if it itself has a non-zero value and if the number of “neighbors” is also non-zero and equal to 1 or 2. In this case, the type of detected minutes (“end” of the ridge or “bifurcation” of the ridge), as well as the coordinates and angle of orientation of the minutes. The found coordinates and their orientation angles are recorded in the vector of minutes.

The described procedures are called in the patent and technical literature the formation of a fingerprint passport (see, for example, application for invention of the Russian Federation No. 2003124350, IPC 7 G06K 19/073, G07C 9/00, G06F 1/00, publ. 02/10/2005) or definition fingerprint standard (see G. Kuharev. Biometric systems: Methods and means of identifying a person’s personality. - St. Petersburg: Polytechnic, 2001, p. 233). Thus, as a result of the formation of the fingerprint passport, its papillary pattern is converted into a unique digital code, which is the reference passport of the registered user and is entered into the system database for its storage and subsequent use when compared with the presented papillary pattern.

The second stage of the implementation of the proposed method is the additional coding of the reference fingerprint of the papillary pattern, which is performed by mathematical processing of the digitized image of the papillary pattern of the registered fingerprint. The second stage is carried out simultaneously with the digital (main) coding performed at the first stage when forming the reference passport of the papillary pattern, and consists in the following.

First, by multiple mathematical processing of the fingerprint image, a projection-dispersion filter determines the direction field of the papillary lines.

To do this, set the size of the floating window n _sws more than one step of papillary lines and having an odd size in the pixel representation. The size of the floating window is determined by the step of the papillary lines of the print, which in turn depends on the resolution of the original image.

Resolution dpi Window size, pixel 500-600 21-25 250-300 11-13

This filter is extremely time consuming. For each point of the original image of size W × H, the following number of operations is performed, not counting the operations of comparison and assignment.

Operation The code The number of operations per point ++ inc 2n ² + 6n-2 + add 6n ² + 10n + 1 - sub 2n ² + 6n-2 * imul 2n + 11 / idiv 4n + 9 = mov 5n ² + 18n + 20 if cmp + jmp 6n ² + 9n + 9 memset lodsb 24n-8

For example, for an image of 456 × 548 pixels, a window of 25 × 25 pixels is selected, therefore, we obtain the following number of calculations:

Operation The code The number of operations per point Number of operations per image ++ inc 1398 349343424 + add 4001 999 801888 - sub 1398 349343424 * imul 61 15243168 / idiv 109 27237792 = mov 3595 898347360 if cmp + jmp 3984 995553792 memset lodsb 592 147933696 TOTAL 3782804544

On a computer with an Intel Pentium processor with a frequency of 2 GHz and a 266 MHz system bus, this operation will be performed for more than 21 s, while it is also necessary to carry out comparison and assignment operations, as well as changing and monitoring cycle counters, which are fourth order by nesting. The time required for the operation is calculated on the basis that reading / writing the result requires one clock of the system bus and a certain number of clock cycles of the processor per operation:

Operation The code The number of measures per operation The number of measures per image Time s ++ inc 3 1048030272 1.837336279 + add 3 2999405664 5.258356546 - sub 3 1048030272 1.837336279 * imul 10 152431680 0.133520983 / idiv 46 1252938432 0.72886693 = mov one 898347360 3.826419394 If cmp + jmp four 3982215168 5.733791013 memset lodsb 2 295867392 0.70407541 TOTAL 11677266240 06/20

Increased productivity can be achieved by slightly reducing the accuracy of the result. To do this, you need to set some step s _{sws of the} floating window, i.e. _iterate over not all points of the original image, but through s _sws points horizontally and vertically.

раз выигрыш по производительности.If you select s _sws <n _sws , then the floating windows overlap, and the filter operation result deteriorates slightly. For s _sws ≥n _{sws, the} picture of the projection dispersion filter begins to degrade quite strongly, and the result is extremely inaccurate. Obviously, with this organization of the filter, we get in

times performance gain.

For almost all types of images of scanned prints, the parameter s _sws can be selected within 4 ... 16.

состоящее из пяти значении.After determining the step and size of the floating window around a certain point of the image with coordinates (x, y) within the size of the floating window, we calculate the variance of the values in four main directions - 0 °, 45 °, 90 °, 135 °. Each direction is encoded by its number, as a result of the filter, a field is displayed in the size direction

consisting of five meanings.

After that, let's ask ourselves the following encoding of directions and background:

g _bg is the index for the background,

g ₀ - index for the direction 0 °,

g ₄₅ - index for the direction of 45 °,

g ₉₀ - index for the direction of 90 °,

g ₁₃₅ - index for the direction of 135 °,

In this case, the following inequality must be satisfied:

g _bg <g ₀ <g ₄₅ <g ₉₀ <g ₁₃₅ .

Next, we do the following calculations:

- calculation of the average value for a floating window:

average brightness value within a floating window around a point (x, y):

If the average value exceeds the brightness threshold for the background, then we accept at this point a result equal to the background index:

g (x, y) = g _bg , with μ≥f _bg .

- calculation of variance in the direction of 0 °:

We calculate the average values for the lines of the floating window:

where k = i.

:We calculate the variance of the values

:

- calculation of variance in the direction of 45 °:

We calculate the average values along the lines of a floating window located at an angle of 45 °:

where k = (i + j) -1.

:We calculate the variance of the values

:

- calculation of variance in the direction of 90 °:

We calculate the average values for the columns of the floating window:

where k = j.

:We calculate the variance of the values

:

- calculation of dispersion in the direction of 135 °:

We calculate the average values along the lines of a floating window located at an angle of 135 °:

where k = (n-1) + (i-j) +1.

:We calculate the variance of the values

:

Next, an assessment of the direction is carried out, which is as follows. Since the variances calculated from the angles of 45 ° and 135 ° have obviously overestimated values, they must be corrected before comparison. For this, the maximum dispersion is determined, which characterizes the predominant direction of papillary lines at a given point in the image:

where C is the correction factor for the directions 0 ° and 90 °, which for most fingerprint images can be selected in the range from 1.5 ... 2.

The picture of the direction field obtained after applying the projection-dispersion filter, presented in figure 2 and figure 3, will have interference and inaccuracies. To build a smoother directional field, you need to remove the random noise that appears. For this purpose, a special modified median filter is used.

Processing a fingerprint image with a median filter is as follows.

We set the odd size of the floating window n _{sws of the} median filter. Around a certain point of the image with coordinates (x, y) within the size of the floating window, we calculate the number of repetitions of each value taking into account the coefficients specified by the filter matrix of size [n _sws × n _sws ]. The value that has a larger counter value is selected as a filter result. We count the number of repetitions of a certain value, taking into account the coefficients of the filter matrix:

, для всего отображения поля направлений;Where

, for the entire display of the direction field;

with _ij - form a matrix of filter coefficients:

To display the direction field obtained by the projection-dispersion filter with the above values of the size and step of the floating window, one can take n _sws = 3 as the size of the floating window and matrix, and one with _ij = 1 as the values of the matrix elements.

Next, in the vector of counters, we find the maximum value and as the result of filtering at a given point (x, y), select the value that corresponded to this counter:

.

.

After median filtering in the picture of the direction field, random outfalls of the values from the total number will be removed, thereby the picture of the direction field takes on a more “smooth” form (see figure 4). This filter is convergent and for a complete picture it is necessary to perform filtering until the display of the direction field ceases to change, i.e. g (x, y) = f (x, y), for all x and y. Usually the number of iterations does not exceed 10.

After processing the fingerprint image with the modernized median filter, global features (characteristic points) are searched for, the type of characteristic points (core, delta, etc.) and their coordinates are determined. Under global features are understood such features of the papillary pattern, which are stored from image to image and within the allowable noise can be uniquely determined. For example, points like "core" or "delta".

Global features are characterized by a change in the direction field, which around such features as the “core” or “delta” successively changes its value in the range from 0 ° to 360 °. The found points are then used as centers for additional Gabor spatial-wave filtering.

Around such a characteristic point of the papillary pattern as the "core" of the direction of the lines changes from 0 ° to 360 ° counterclockwise. Those. if we consider the direction field we constructed around this point, we will see how it successively counterclockwise changes the values in the direction of increasing the angle - 0 °, 45 °, 90 ° and 135 ° (see figure 5).

Around such a characteristic point of the papillary pattern as the "delta" of the direction of the lines changes from 0 ° to 360 ° clockwise. Those. if we consider the direction field we constructed around this point, we will see how it successively clockwise changes the values in the direction of increasing the angle - 0 °, 45 °, 90 ° and 135 ° (see Fig.6).

After determining global features (characteristic points), their type and coordinates, they search for points of interest and calculate the centers of features.

The first stage of the search for global features is the compilation of a list of points of interest, i.e. such points in the region of which the direction field behaves in a manner characteristic of a global feature.

This search is performed by a 2 × 2 floating window. The window is being built relative to its upper left corner, i.e. except points with coordinates (x, y), also points with coordinates (x + 1, y), (x, y + 1) and (x + 1, y + 1) fall into consideration.

If among four values there is a value of g _bg , then the point is not considered. Similarly, when there is only one or two values within the window, the point is also not considered.

Points for consideration are around which there are three or four different directions. In this case, the sequence of direction changes is analyzed. Starting from the minimum, they must sequentially increase either clockwise - for the "delta", or counterclockwise - for the "core". Such points are stored in arrays of alleged points such as "delta" and "core".

If all four directions are present in the window at once and their sequence corresponds to the "delta" or "core", then this point is taken as the center of this feature. If the window contains only three directions, then this point requires clarification.

The refinement begins with the construction of an array of distances between prospective points of the same type, which complement each other in not enough directions. That is, the distances between all pairs of points of the same type are calculated, in which all four directions are present in total. Such pairs are selected from such an array, the distance between which, firstly, is minimal, and secondly, does not exceed a certain limit value [D] (usually the square of the limit distance does not exceed 9 ... 40).

For pairs satisfying these conditions, the coordinates of the middle position between them are calculated and taken as the coordinates of the center of the singularity.

Further, the image is processed several times by a floating window of odd size n _sws for different directions of wave propagation. The window coefficients are calculated by the formula and depend on the wave propagation angle. The initial wave propagates along the x axis with symmetric exponential decay of the amplitude:

при

at

- частота волн, обратно пропорциональная разрешению;Where

- wave frequency inversely proportional to resolution;

σ ~ dpi is the inverse attenuation coefficient.

For wave propagation in an arbitrary direction at an angle φ, we have the following dependence:

и

where χ = xcosφ-ysinφ, for

and

For a discrete grid of a floating window, we obtain the following expression:

,

, при

и

Where

,

at

and

χ _ij = x _j cosφ-y _i sinφ.

The resulting mapping is calculated as follows:

The calculation is carried out in n directions in the range [0,180), numbered for definiteness counterclockwise. As a result, we obtain n filtered images (see Fig. 7).

In the vicinity of each characteristic point found, by means of Gabor spatial-wave filtration, the characteristic numerical features of the fingerprint image (minutes) are calculated.

To calculate the characteristic numerical features of the image - the minutes, the filtered images are divided into m rings, numbered for definiteness, starting from the center, and 2n sectors around the geometric center of global features, which for definiteness are numbered counterclockwise. Thus, on each of the n filtered images, we get m × 2n areas (see Fig. 8), in each of which we calculate the average value:

, при

at

where O _kij is the region of the k-th image, the i-th ring and the j-th sector;

- число отсчетов изображения находящихся в области O_kij.

- the number of samples of the image located in the region O _kij .

Next, for each such region, the absolute mean deviation is calculated:

, при

at

As a result of the calculations, we obtain the vector of minutes M, consisting of n × m × 2n = 2n ² m numbers, which is internally divided into n matrices of size m × 2n.

If the grid element goes beyond the boundaries of the image or the background was determined on the original image at this place by the projection-dispersion filter, then -1 is written as the value. And then it does not participate in the comparison function.

Thus, the encoding procedure described above consists of two parallel steps: primary and secondary encoding and can be called combined encoding.

The fingerprint pattern data encoded in this manner is stored for subsequent identification along with the reference data obtained in the first step of generating the fingerprint passport.

Let us now examine how the presented fingerprint is identified when comparing it with a reference fingerprint encoded using the combined method, which includes primary and secondary filtering coding. The presented fingerprint is encoded in a high-precision way, based on the coding of the minutes (main coding), and additional filtering coding (additional coding) is carried out in parallel. The coding result is a passport of the presented papillary pattern, which should be identified by reference passports stored in the database.

All stages of the encoding procedure (primary and secondary) are carried out identically and in the same sequence as the procedures described above, carried out during the formation of the reference passport of the papillary pattern, described in detail at the beginning of the section "Implementation of the method" on pages 13-26 of the proposed application.

The next step in the implementation of the proposed method is the comparison of the presented and reference passports of fingerprints of papillary patterns, with the first step being a high-speed comparison of the additional code of the presented papillary pattern with the codes of all papillary patterns in the database obtained by additional filtering coding.

Image comparison is based on the use of global features, which allows you to get rid of the degrees of freedom associated with displacement when comparing images. In addition, by plotting the minutes around the base point in polar coordinates, the rotation around the center is replaced by a shift.

The distance Ω between the two images represented by the vectors of the minutes M ₁ and M ₂ is calculated by the formula:

where Δ is the absolute average deviation of the sector brightness;

2n is the number of sectors around the geometric center of global features;

m is the number of rings.

Since we do not know at what angle one image is rotated relative to another, it is necessary to calculate the distance between the images for all possible 2n angles and select the minimum as the resulting value. To do this, a circular shift of the m × 2n matrices is performed sequentially inside one of the compared vectors, for example, the vector M ₂ , so that the latter becomes the first - this corresponds to the selected numbering of the filtration directions counterclockwise. It is also necessary to rotate the columns inside each of the n matrices of the shifted vector so that the latter becomes the first, which corresponds to the selected sector numbering counterclockwise.

Having thus obtained “2n” distances, it is necessary to take the minimum as the result, which corresponds to the assumption of maximum image similarity. The normalized result in the range (0,1], where zero corresponds to the absolute dissimilarity of the images, and the unit to full correspondence, is obtained from the expression:

where ρ is the degree of dissimilarity of the images,

(x, y) belong to the image.

The two in the denominator is obtained from considerations that the Gabor filter has coefficient values within [-1, 1], therefore, the filtered image g [x, y) can have values within [-f _max , f _max ]. Further, the average value of μ _kij also falls into the range [f _max , f _max ]. But the absolute average deviation Δ _kij can vary in the range [0.2f _max ].

The speed of this comparison, which ranges from 3,000 to 60,000 comparisons / sec, is several orders of magnitude higher than the speed of comparing fingerprints in coding based on the comparison of minutes. The result is a relatively small list, for example, several dozen prints - applicants who have passed the threshold and have the closest degree of coincidence with the presented print. The threshold is set based on the calculation of the optimal ratio of the probability of skipping "strangers" and not skipping "friends" and depends on the size of the base of reference prints.

The next step is a longer, but very accurate comparison based on the comparison of the minutes. During this comparison, the presented (current) fingerprint that has been registered is compared only with fingerprints selected at the previous stage by the method of matching minutes, which is as follows.

As mentioned above, at the stage of user registration and the formation of a reference fingerprint database, the coordinates of the detected minutes, as well as the angles of their orientation, are recorded in the vector of minutes, which can be represented in the following form:

W ^(p) = [(x ₁ , y ₁ , θ ₁ ), (x ₂ , y ₂ , θ ₁ ), (x ₃ , y ₃ , θ ₃ ), ..., (x _p , y _p , θ _p )],

where the parameter "p" determines the number of minutes.

At the stage of user registration, this vector defines the standard E ^(p) , which is recorded in the database of standards. At the recognition stage, the vector determines the current (presented) fingerprint O ^(q) and its parameters. Next, it is necessary to determine such parameters of affine transformations as the angle of rotation, scale, and shifts (Δx and Δy) at which some minute of the vector O ^(q) will be consistent with some minute of the vector E ^(p) . In order to solve this problem (under the condition q ≠ p), it is necessary to recalculate the coordinates of each minute from the vector O ^(q) for all possible values of the rotation, scale and shift parameters. The total number of coordinates recalculations of only one minute will be 2F MNL,

where f is the angle of rotation at which two fingerprints can be rotated relative to each other;

M is the maximum shift along the x axis;

N is the maximum shift along the y axis;

L is the maximum zoom of the print.

Then, pairs of matching minutes are searched for, for which at each step (of 2 M MNL possible) the coordinates of the minutes from the vector O ^(q) undergo affine transformations, and the new coordinates obtained are compared with each of the minute coordinates of the vector E ^(p) . Agreed pairs of minutes are not involved in further iterations (if we are not talking about a new standard). After that, the conformity assessment of the two matched fingerprints is evaluated. In the process of searching for pairs of minutes, the information on the parameters {Δх, Δy, Δk, Δφ}, at which a pair is found, is stored in the memory, and the number of found pairs of minutes is also calculated. If the same information on the parameters {Δx, Δy, Δk, Δφ} is repeated quite often, then this indicates a high quality of correspondence of the fingerprints and determination of the true parameters of affine transformations connecting the two fingerprints with each other.

If the comparison was performed in the task of fingerprint verification, then the whole process ends. If the task was to identify the fingerprints, then the described process must be repeated, but not for all fingerprints, as in the prototype, but only for fingerprints - candidates who have passed the threshold and have the closest degree of coincidence with the presented fingerprint.

Thus, there is a significant increase in the speed of comparison, since there is no need to compare the presented fingerprint with each of the reference fingerprints encoded in the exact, but relatively slow way - the encoding method based on the minutes, selected as a prototype.

In conclusion, it should also be noted that the use in the proposed method for verification and identification of fingerprints of papillary patterns of additional filtering coding, implemented at the level of software or hardware, can significantly increase the speed of the identification process of the presented fingerprint compared to the prototype, while maintaining high reliability of the method, selected as a prototype.

Claims (3)

1. The method of verification and identification of fingerprints of papillary patterns, which consists in recording the data of the reference and presented fingerprints of papillary patterns, consisting of generating passports of fingerprints by extracting the minutes, determining their type, coordinates, orientation angles and recording them in the form of the reference and presented vectors of minutes, respectively , comparing the reference passports of fingerprints and the presented passport by comparing the minutes, consisting in the search for pairs of matching mine assessing the similarity measure of the compared fingerprints and comparing it with a threshold, characterized in that simultaneously with the formation of passports of the reference and presented fingerprints, additional filtering coding is carried out, which consists in constructing the directions field of papillary lines by multiple mathematical processing of the fingerprint image by a projection-dispersion filter with subsequent processing of the modernized median filter, the search for characteristic points, determining their types and coordination t, filtering the image in the vicinity of each characteristic point found by repeatedly processing the space-wave filter with a floating window and storing the encoded data of each fingerprint of the papillary pattern along with the data obtained at the stage of forming the passports, moreover, when comparing the presented and reference fingerprints of papillary patterns before the matching procedure minutes perform a comparison of the additional code of the presented papillary pattern with additional codes of all the reference pops illary patterns obtained by additional filtration coding and stored in the database by determining the distance between two images represented by vectors of minutes obtained by additional filtration coding for all possible angles, taking the minimum distance as the result corresponding to the maximum similarity of images of papillary patterns, forming list of fingerprints of candidates, that is, reference passports having the closest degree of coincidence with presenting ennym print, and then comparing the presented fingerprint with each fingerprint of a candidate by a method based on a comparison of Minucius. 2. The method according to claim 1, characterized in that when filtering the image, a Gabor filter is used. 3. The method according to claim 1 or 2, characterized in that for forming a list of candidate fingerprints, their number is set depending on the size of the reference fingerprint database.

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