CN114821685A - PSO (particle swarm optimization) based non-contact 3D fingerprint identification method for optimizing Delaunay triangulation - Google Patents
PSO (particle swarm optimization) based non-contact 3D fingerprint identification method for optimizing Delaunay triangulation Download PDFInfo
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- G06V40/12—Fingerprints or palmprints
- G06V40/1382—Detecting the live character of the finger, i.e. distinguishing from a fake or cadaver finger
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Abstract
A PSO-based optimized Delaunay triangularization non-contact 3D fingerprint identification method belongs to the field of fingerprint identification algorithms. In order to make the recognition result of the algorithm of non-contact three-dimensional space fingerprint acquisition and recognition more accurate. Providing a PSO (particle swarm optimization) optimization Delaunay triangulation-based non-contact 3D fingerprint identification method, and estimating a three-dimensional azimuth angle of a three-dimensional minutia point based on the improvement of a principal component analysis technology; constructing an expanded tetrahedral dissection structure; extracting features of the expanded tetrahedral dissection structure; comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons meeting the matching conditions and calculating matching scores, and determining whether the tetrahedrons are matched or not according to the matching scores; optimizing Delaunay triangulated fingerprint comparison algorithm parameters based on an improved particle swarm optimization PSO; and obtaining a final model. According to the invention, by optimizing the identification comparison parameters, a more accurate comparison model can be established, so that the identification precision of the whole fingerprint identification method is improved.
Description
Technical Field
The invention relates to a fingerprint identification method, in particular to a PSO (particle swarm optimization) optimization Delaunay triangulation-based non-contact 3D fingerprint identification method.
Background
The traditional identity authentication methods based on passwords, passwords and the like have the defects of easy forgetting, easy loss and easy counterfeiting, and can not meet the requirements of people on identity authentication and information security. The identification technology based on the fingerprint characteristics is a more convenient and reliable authentication mode.
The traditional contact type fingerprint authentication mode adopts a contact type acquisition mode. The collection equipment that sets up in public places such as all kinds of halls of handling affairs, station carries out the fingerprint collection in-process, and collection equipment can be contacted by many users, and whether the user can worry before the user uses can infect at fingerprint collection surface bacterium, whether has sanitary problem. Moreover, the pressing force of the finger is different every time, the deformation degree of the finger is different, the definition degree of the finger fingerprint image is different, and the identification failure can be caused. Multiple contacts with the acquisition device are required to re-identify. In order to make up for the defects of the contact type acquisition and identification method, and on the basis of obtaining fundation of a natural science fund (No: LH2020F049) project of Heilongjiang province, the invention carries out related research design, establishes a non-contact type three-dimensional space form fingerprint acquisition and identification algorithm, and designs a non-contact type 3D fingerprint identification algorithm based on a particle swarm algorithm and expansion Delaunay triangulation in order to enable identification to be more accurate.
Disclosure of Invention
The invention aims to provide a non-contact 3D fingerprint identification method based on improved PSO (particle swarm optimization) optimized Delaunay triangularization, so that the identification result of a non-contact three-dimensional space fingerprint acquisition and identification algorithm is more accurate.
A non-contact 3D fingerprint identification method based on PSO optimized Delaunay triangulation is realized by the following steps:
estimating a three-dimensional azimuth angle of the three-dimensional minutiae point improved based on a principal component analysis technology;
constructing an expanded tetrahedron subdivision structure;
extracting features based on the expanded tetrahedral dissection structure;
wherein the extracted features include: edges, internal angles, two-dimensional direction angles, three-dimensional azimuth angles, and tetrahedral types;
comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons which accord with the matching conditions, counting the matching scores by using the counting results, and determining whether the tetrahedrons are matched or not according to the matching scores;
optimizing Delaunay triangulated fingerprint comparison algorithm parameters based on an improved particle swarm optimization PSO; optimizing and determining comparison parameters to obtain a final model;
delaunay triangularized Chinese means a triangulation algorithm.
Preferably, the step of estimating the three-dimensional azimuth angle of the three-dimensional minutiae point improved based on the principal component analysis technology specifically comprises:
(1) acquiring a two-dimensional fingerprint image;
(2) preprocessing the two-dimensional fingerprint image; wherein the preprocessing operation comprises: extracting a fingerprint foreground area, fingerprint ridge line and fingerprint minutiae;
(3) extracting two-dimensional minutiae information on the preprocessed two-dimensional fingerprint image, wherein the two-dimensional minutiae information comprises a coordinate x, a coordinate y and a two-dimensional direction angle theta;
(4) adding a space coordinate z and a three-dimensional azimuth angle phi to the two-dimensional minutiae points to map the two-dimensional minutiae points into three-dimensional minutiae points of a three-dimensional space;
the acquisition process of the space coordinate z is as follows: simulating to form a three-dimensional curved surface through a three-dimensional fingerprint, obtaining the three-dimensional curved surface, and obtaining a position attribute z through xy of a two-dimensional minutia;
(5) estimating a three-dimensional azimuth angle phi of the three-dimensional minutiae added in the last step, specifically:
setting a point F to represent a three-dimensional minutia point;
using all vertices v in m neighbourhood around the three-dimensional minutiae point F i ∈R 3 With these vertices v i As a basis, calculating the normal direction of the three-dimensional minutiae point F by using a principal component analysis method; order to
Wherein the content of the first and second substances,
t represents transposition; r 3 A three-dimensional space is represented in which,
denotes the median value, t denotes v i The number of (2); by
Formed covariance matrix
Wherein T represents transpose; w is a i The weight is represented by a weight that is,
improving an estimation method of the normal direction of a three-dimensional minutiae F through a covariance matrix C, wherein F represents the three-dimensional minutiae, a represents a weight parameter, and m represents the number of neighborhoods;
(6) setting the number of the fingerprint minutiae as k, and then extracting the fingerprint minutiae; the set of fingerprint minutiae is denoted F k ＝(x k ,y k ,z k ,θ k ,φ k ) Wherein (x) k ,y k ,z k ) Is a three-dimensional minutiae space coordinate, (theta) k ,φ k ) The two-dimensional direction angle of the three-dimensional detail point and the three-dimensional azimuth angle of the three-dimensional detail point are obtained;
the feature vectors of the template fingerprint minutiae are represented as: p ═ F i p I 1.. M }, the feature vector of the fingerprint minutiae to be identified is expressed as:
the template minutiae feature set P comprises M minutiae, and the minutiae feature set Q to be identified comprises N minutiae.
Preferably, said step of constructing an extended tetrahedrally subdivided structure is performed by,
the method comprises the following steps of reconstructing an expanded Delaunay tetrahedron subdivision structure by using point cloud Dironey triangulation, and specifically comprises the following steps:
(1) applying a Delaunay triangulation algorithm, and obtaining a tetrahedral structure G ═ { F, E } by adopting the Delaunay triangulation algorithm in a three-dimensional space, wherein E is an edge set of the tetrahedral structure, and F ═ { F ═ F } i 1.. N } represents a three-dimensional minutiae point set of a certain fingerprint; the four vertices of any one tetrahedron are denoted as (F) 1 ,F 2 ,F 3 ,F 4 ) Each vertex is denoted as F k ＝(x k ,y k ,z k )，k＝1,2,3,4；
(2)F i Is a minutia in the F set, N i ＝{F j |(F i ,F j ) E represents in Delaunay triangulated structure G and with F i A detail point set formed by connecting vertexes;
(3) is obtained by Delaunay triangulation algorithm in N i Group G of tetrahedrons of i ＝{N i ,E i In which G is i Is the resulting tetrahedral set, E i Is a set of edges of a tetrahedral structure, N i Representing a set of vertices;
(4) the tetrahedron sets are put together to form an expanded tetrahedron set S, S ═ G- 1 ∪…∪G n And n is the number of minutiae.
Preferably, the step of extracting features of the expanded tetrahedron subdivision structure specifically includes:
let the feature of the tetrahedron be expressed as:
where, t is the number of this tetrahedral type,
denotes the largest of all internal angles in the tetrahedron, l max And l min Respectively representing the longest and shortest edges of the tetrahedron,
indicates the difference between the direction angles of the two vertexes of the longest side,
indicating the difference in the azimuth angle between the two vertices of the shortest side,
representing the difference in azimuth of the two vertices of the longest side,
representing the difference of the azimuth angles of the two vertexes of the shortest side;
the numbering method of the tetrahedron types comprises the following steps:
first of all, the first step is to,
is the largest of all the inner angles in the four faces, the largest of the triangular faces
Is marked as V 1 ；
The vertex of the second largest interior angle in the triangular face is then labeled V 2 The vertex of the smallest interior angle in the triangular surface is marked as V 3 The remaining one vertex of the tetrahedron is marked V 4 ；
Finally, the four vertex types are represented using vectors (t) 1 ，t 2 ，t 3 ，t 4 )，t i Is V i The type number Class of the tetrahedron can be obtained corresponding to the following table.
Preferably, the step of comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons which meet the matching conditions, counting the matching scores by using the counting result, and determining whether the tetrahedrons are matched according to the matching scores; the method specifically comprises the following steps:
(1) comparing each tetrahedron, and judging whether the tetrahedrons are matched:
setting two fingerprints to be compared as a fingerprint A and a fingerprint B, wherein any tetrahedral feature on the fingerprint A is represented as
Any tetrahedral feature on the fingerprint B is represented as
Judging the matching condition:
ΔL max ＝|L max -L' max |，Δθ max ＝|θ-θ'|，Δφ min ＝|φ-φ'|
if t ≠ t', the two tetrahedrons for comparison are considered to be unmatched, and comparison of other characteristics is not carried out any more;
if t is equal to t', continuously judging whether the t is satisfied
ΔL min ＜T L ，Δθ max ＜T θ ，Δθ min ＜T θ ，Δφ max ＜T φ ，Δφ min ＜T φ If yes, the two tetrahedrons are considered to be matched and recorded; wherein the content of the first and second substances,
T L 、T θ 、T φ respectively representing a threshold parameter of a maximum internal angle, a side length threshold parameter of a tetrahedron, a direction angle threshold parameter of two vertexes of an edge and an azimuth angle threshold parameter of the two vertexes of the edge, wherein the values are set;
(2) counting the number of matched minutiae:
if the tetrahedron is matched, marking the four minutiae of the tetrahedron as matching, and counting the number r of the matched minutiae;
(3) and (3) counting the matching scores:
calculating the matching score S of the obtained data r of the matched minutiae by using the formula:
wherein N is A Number of minutiae, N, for fingerprint A B Number of minutiae for fingerprint B;
(4) and (3) recognition results:
matching score S and a set matching score threshold value T S Making a comparison when S>T S If so, matching the fingerprint A with the fingerprint B, otherwise, not matching the two fingerprints; wherein, T S Indicating a match score threshold to be achieved, the value of which is set.
Preferably, the improved particle swarm optimization PSO-based optimized Delaunay triangularization fingerprint comparison calculationA method parameter; optimizing and determining the comparison parameters to obtain the final model, wherein the fingerprint comparison algorithm parameters comprise a threshold parameter for optimizing the maximum internal angle
Edge length threshold parameter T of tetrahedron L Direction angle threshold parameter T of two vertexes of an edge θ The azimuth angle threshold parameter T of two vertexes of the edge φ And a matching score threshold T S (ii) a The method specifically comprises the following steps:
establishing a plurality of matched fingerprint pairs and unmatched fingerprint pairs as training sets, and acquiring optimal parameters by using a particle swarm algorithm PSO; utilizing particle swarm optimization PSO to carry out threshold parameter on maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S Optimizing the five parameters; wherein, the optimizing process is as follows:
(1) initializing particle swarm size to be 40, iterating times to be 200, searching threshold parameters of optimal maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S Defining the position and velocity of the particle swarm;
(2) determining fitness function
Wherein N represents the number of training samples, and ACC represents the identification accuracy of the training samples;
(3) updating individual optimal positions p im And the population optimum position p gm ；
(4) Updating the speed and position of the particle;
wherein, ω represents the inertial weight; m is an element of [1, M ]]，i∈[1,40]；v im And x im Respectively representing the speed and the position of the m-th particle; c. C 1 And c 2 Is a learning factor; r is 1 ,r 2 ∈[0,1]Is a random number; p is a radical of formula im And p gm Respectively representing the individual optimal position and the group optimal position searched by the i particle at present; updating particle positions
(5) If the error is less than 0.01 or the maximum iteration times are reached, ending the optimization of the particle swarm optimization algorithm to obtain the optimal particle position as the threshold parameter of the optimal maximum internal angle
Optimal length threshold parameter T L Optimal direction angle threshold parameter T θ Optimal azimuth angle threshold parameter T φ Optimal matching score threshold T S Therefore, an optimized three-dimensional fingerprint comparison algorithm based on the extended Delaunay triangulation is obtained.
The invention has the beneficial effects that:
the invention adopts non-contact type to collect fingerprints, thereby avoiding cross infection among users.
The fingerprint identification algorithm designed by the invention has the advantage of high operation speed, and the time required by identification is reduced.
Firstly, the invention carries out a novel tetrahedron type coding method, and particularly relates to a process of adding a space coordinate z and a three-dimensional azimuth angle phi to a two-dimensional minutia to map the two-dimensional minutia into a three-dimensional minutia of a three-dimensional space, then constructing an expanded tetrahedron subdivision structure and extracting characteristics, and designing a unique tetrahedron type number in the process. In the subsequent comparison process, once the numbers of the tetrahedrons are not matched, the comparison of other information is not carried out, so that the method makes the model matching more efficient. Therefore, the invention has higher calculation efficiency and reduces 60-70% of the time required for identification.
In addition, the invention adds the step of optimizing the Delaunay triangularization fingerprint comparison algorithm parameters based on the improved PSO, and is used for optimizing the identification comparison parameters to establish a more accurate comparison model, thereby improving the identification precision of the whole fingerprint identification method, and the identification precision reaches more than 98%. Specifically, the point cloud Dironi triangulation is introduced to obtain a tetrahedron of the three-dimensional fingerprint minutiae, and matching is performed on the obtained tetrahedron of the three-dimensional fingerprint minutiae. This can greatly reduce the amount of computation, but when false minutiae occur or minutiae are lost, it can cause tetrahedral structure errors, and thus tetrahedral matching errors. In order to overcome the problem, an expanded tetrahedron set is provided, and the robustness in tetrahedron matching is improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of an expanded tetrahedron subdivision scheme in accordance with the present invention;
FIG. 3 is a schematic illustration of a tetrahedron in the extended tetrahedron subdivision arrangement of the present invention;
FIG. 4 is a flow chart of a three-dimensional fingerprint matching algorithm according to the present invention;
FIG. 5 is an example of features involved in the step of extracting features involved in the present invention;
FIG. 6 is an example of a 2D fingerprint image to which the present invention relates;
FIG. 7 is a diagram of the extraction of two-dimensional minutiae points on a two-dimensional fingerprint image according to the present invention;
FIG. 8 is a ROC curve relating to a simulation experiment of the present invention.
Detailed Description
The first specific implementation way is as follows:
in the embodiment, as shown in fig. 1, the non-contact 3D fingerprint identification method based on PSO optimized Delaunay triangulation is implemented by the following steps:
step one, because the geometric coordinates of the vertex of the three-dimensional fingerprint surface are easily disturbed by noise, the normal direction of the vertex can be changed, and the estimation error of the three-dimensional azimuth angle of the three-dimensional minutiae point is larger. The invention is presented herein:
estimating a three-dimensional azimuth angle of the three-dimensional minutiae point improved based on a principal component analysis technology; the method is used for improving the precision of three-dimensional azimuth estimation;
step two, constructing an expanded tetrahedron subdivision structure;
step three, extracting characteristics based on the expanded tetrahedral subdivision structure;
wherein the extracted features include: edges, internal angles, two-dimensional direction angles, three-dimensional azimuth angles, and tetrahedral types;
as shown in FIG. 5, the azimuth angle is θ and the azimuth angle φ, the azimuth angle θ is the direction on the X-Y plane; the azimuth angle phi is a direction in space;
comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons which accord with the matching conditions, counting the matching scores by using the counting results, and determining whether the tetrahedrons are matched or not according to the matching scores;
fifthly, optimizing Delaunay triangularized fingerprint comparison algorithm parameters based on an improved Particle Swarm Optimization (PSO); optimizing and determining comparison parameters to obtain a final model;
delaunay triangularized Chinese means a triangulation algorithm.
The method provided by the invention verifies the identification accuracy through the acquired three-dimensional data. The simulation result shows that the method has the advantages of high operation speed and short identification time.
The invention provides a 3D fingerprint identification algorithm based on improved particle swarm optimization and expanded Delaunay triangulation, which has the following effects:
the expanded Delaunay triangulation is proposed to perform tetrahedrization on the three-dimensional fingerprint minutiae, so that the influence of wrong minutiae on the whole fingerprint triangulation is reduced, and the robustness of a tetrahedral structure is improved.
And 2, optimizing parameters in the three-dimensional fingerprint matching model by utilizing a particle swarm optimization algorithm to obtain the parameters of the optimal matching model, thereby greatly improving the identification precision of the model.
3, the novel tetrahedron type coding makes the model matching more efficient and has higher calculation efficiency.
The second embodiment is as follows:
different from the specific embodiment, in the non-contact 3D fingerprint identification method based on PSO optimized Delaunay triangulation of the present embodiment, the step of estimating the three-dimensional azimuth angle of the three-dimensional minutiae based on the principal component analysis technology improvement specifically includes:
(1) acquiring a two-dimensional fingerprint image; the two-dimensional fingerprint image is shown in FIG. 6;
(2) preprocessing the two-dimensional fingerprint image; wherein the preprocessing operation comprises: extracting a fingerprint foreground area, fingerprint ridge line and fingerprint minutiae;
(3) extracting two-dimensional minutiae information on the preprocessed two-dimensional fingerprint image, wherein the two-dimensional minutiae information comprises a coordinate x, a coordinate y and a two-dimensional direction angle theta; wherein the two-dimensional minutiae plot is shown in FIG. 7;
(4) adding a space coordinate z and a three-dimensional azimuth angle phi to the two-dimensional minutiae points to map the two-dimensional minutiae points into three-dimensional minutiae points of a three-dimensional space;
the acquisition process of the space coordinate z is as follows: simulating to form a three-dimensional curved surface through a three-dimensional fingerprint, obtaining the three-dimensional curved surface, and obtaining a position attribute z through xy of a two-dimensional minutia;
(5) estimating a three-dimensional azimuth angle phi of the three-dimensional minutiae added in the last step, specifically:
in order to improve the estimation accuracy of the three-dimensional azimuth angle of the three-dimensional minutiae, setting a point F to represent the three-dimensional minutiae;
using all vertices v in m neighbourhood around the three-dimensional minutiae point F i ∈R 3 With these vertices v i As a basis, calculating the normal direction of the three-dimensional minutiae point F by using a principal component analysis method; order to
Wherein the content of the first and second substances,
t represents transposition; r 3 To representThe three-dimensional space is a space with three-dimensional,
denotes the median value, t denotes v i The number of (2); by
Formed covariance matrix
Wherein T represents transpose; w is a i The weight is represented by a weight that is,
improving an estimation method of the normal direction of a three-dimensional minutiae F through a covariance matrix C, wherein F represents the three-dimensional minutiae, a represents a weight parameter, and m represents the number of neighborhoods;
(6) setting the number of the fingerprint minutiae as k, and then extracting the fingerprint minutiae by the conventional method for extracting the fingerprint minutiae; the set of fingerprint minutiae is denoted F k ＝(x k ,y k ,z k ,θ k ,φ k ) Wherein (x) k ,y k ,z k ) Is a three-dimensional minutiae space coordinate, (theta) k ,φ k ) The two-dimensional direction angle of the three-dimensional minutiae and the three-dimensional azimuth angle of the three-dimensional minutiae are obtained;
the feature vectors of the template fingerprint minutiae are represented as: p ═ F i p I 1.. M }, the feature vector of the fingerprint minutiae to be identified is expressed as:
the template minutiae feature set P comprises M minutiae, and the minutiae feature set Q to be identified comprises N minutiae.
The third concrete implementation mode:
different from the specific embodiment, in the non-contact 3D fingerprint identification method based on PSO optimized Delaunay triangulation according to the embodiment, the step of constructing the extended tetrahedron subdivision structure specifically,
the matching problem of minutiae can be understood as the best correspondence between the elements in the set P and the set Q, resulting in a matching score. The existing matching method usually needs to align elements in two sets, and the alignment operation has high calculation complexity. This reduces the computation by 60-70%, but when false minutiae occur or minutiae are missing, it leads to tetrahedral structure errors and thus tetrahedral matching errors. In order to overcome the problem, an expanded tetrahedron set is provided, and the robustness in tetrahedron matching is improved.
The method comprises the following steps of reconstructing an expanded Delaunay tetrahedron subdivision structure by using point cloud Dironey triangulation, and specifically comprises the following steps:
(1) applying the existing Delaunay triangulation algorithm, and obtaining a tetrahedral structure G (F, E) by adopting the Delaunay triangulation algorithm in a three-dimensional space, wherein E is an edge set of the tetrahedral structure, and F (F) i N represents a three-dimensional minutiae set of a certain fingerprint; the four vertices of any one tetrahedron are denoted as (F) 1 ,F 2 ,F 3 ,F 4 ) Each vertex is denoted as F k ＝(x k ,y k ,z k )，k＝1,2,3,4；
(2)F i Is a minutia in the F set, N i ＝{F j |(F i ,F j ) E represents in Delaunay triangulated structure G and with F i A detail point set formed by connecting vertexes;
(3) is obtained by Delaunay triangulation algorithm in N i Group G of tetrahedrons of i ＝{N i ,E i In which G is i Is the resulting tetrahedral set, E i Is a set of edges of a tetrahedral structure, N i Representing a set of vertices;
(4) putting these tetrahedron sets together to form an expanded tetrahedron set S, S ═ G- 1 ∪…∪G n And n is the number of minutiae.
The extended tetrahedron set S includes not only the original tetrahedron join G, but also the set N of vertices i A generated tetrahedron set; higher matching scores may also be obtained when a loss of minutiae occurs.
The fourth concrete implementation mode:
different from the third specific embodiment, in the non-contact 3D fingerprint identification method based on PSO optimization Delaunay triangulation according to the third embodiment, the step of extracting features based on an extended tetrahedral subdivision structure specifically includes:
let the feature of the tetrahedron be expressed as:
where, t is the number of this tetrahedral type,
denotes the largest of all internal angles in the tetrahedron, l max And l min Respectively representing the longest and shortest edges of the tetrahedron,
indicates the difference between the direction angles of the two vertexes of the longest side,
indicating the difference in the azimuth angle between the two vertices of the shortest side,
representing the difference in azimuth of the two vertices of the longest side,
representing the difference of the azimuth angles of the two vertexes of the shortest side;
the tetrahedron type number t is a new type table and represents the combination type of the detail nodes, and each detail node can be divided into two types of end points or branch points; each tetrahedron can construct 16 types of numbers according to the detail point types of four vertexes of each tetrahedron;
the numbering method of the tetrahedron types comprises the following steps:
first of all, the first step is to,
is the largest of all the inner angles in the four faces, the largest of the triangular faces
Is marked as V 1 ；
The vertex of the second largest interior angle in the triangular face is then labeled V 2 The vertex of the smallest interior angle in the triangular surface is marked as V 3 The remaining one vertex of the tetrahedron is marked V 4 ；
Finally, the four vertex types are represented using vectors (t) 1 ，t 2 ，t 3 ，t 4 )，t i Is V i The type number Class of the tetrahedron can be obtained corresponding to the following table. For example, assuming that the type of four vertices of a tetrahedron is represented as (e, e, e, b), e represents that the point type is an end point, and b represents that the point type is a bifurcation point, the tetrahedron has a corresponding type number of 2.
The fifth concrete implementation mode:
different from the first, second, or fourth specific embodiments, in the PSO-optimized Delaunay triangulation-based non-contact 3D fingerprint identification method of the present embodiment, the steps of comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons that meet the matching conditions, counting the matching scores according to the counting results, and determining whether to match according to the matching scores are specifically:
(1) comparing each tetrahedron, and judging whether the tetrahedrons are matched:
setting two fingerprints to be compared as a fingerprint A and a fingerprint B, wherein any tetrahedral feature on the fingerprint A is represented as
On the fingerprint BAny one of the tetrahedral features is represented as
Judging the matching condition:
ΔL max ＝|L max -L' max |，Δθ max ＝|θ-θ'|，Δφ min ＝|φ-φ'|
if t ≠ t', the two tetrahedrons for comparison are considered to be unmatched, and comparison of other characteristics is not carried out any more;
if t is equal to t', continuously judging whether the t is satisfied
ΔL max ＜T L ，ΔL min ＜T L ，Δθ max ＜T θ ，Δθ min ＜T θ ，Δφ max ＜T φ ，Δφ min ＜T φ If yes, the two tetrahedrons are considered to be matched and recorded; wherein the content of the first and second substances,
T L 、T θ 、T φ respectively representing a threshold parameter of a maximum internal angle, a side length threshold parameter of a tetrahedron, a direction angle threshold parameter of two vertexes of an edge and an azimuth angle threshold parameter of the two vertexes of the edge, wherein the values are set;
(2) counting the number of matched minutiae:
if the tetrahedron is matched, marking the four minutiae of the tetrahedron as matching, and counting the number r of the matched minutiae;
(3) and (3) counting the matching scores:
calculating the matching score S of the obtained data r of the matched minutiae by using the formula:
wherein N is A Number of minutiae for fingerprint A，N B Number of minutiae for fingerprint B;
(4) and (3) recognition results:
matching score S and a set matching score threshold value T S The comparison is performed, as shown in fig. 4, in which the threshold is set in the process of comparing two fingerprints. When S is>T S If so, matching the fingerprint A with the fingerprint B, otherwise, not matching the two fingerprints; wherein, T S Indicating a match score threshold to be achieved, the value of which is set.
The sixth specific implementation mode:
different from the fifth embodiment, in the non-contact 3D fingerprint identification method based on PSO optimized Delaunay triangulation of the present embodiment, the improved particle swarm optimization PSO optimized Delaunay triangulation based fingerprint comparison algorithm parameters; in the step of optimizing and determining the comparison parameters to obtain the final model, the fingerprint comparison algorithm parameters include a threshold parameter for optimizing the maximum internal angle
Edge length threshold parameter T of tetrahedron L Direction angle threshold parameter T of two vertexes of an edge θ The azimuth angle threshold parameter T of two vertexes of the edge φ And a matching score threshold T S (ii) a The method specifically comprises the following steps:
threshold parameter due to maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S The accuracy of the image recognition algorithm is set, so that a plurality of matched fingerprint pairs and unmatched fingerprint pairs are established as a training set, and the Particle Swarm Optimization (PSO) is used for obtaining the optimal parameters; utilizing particle swarm optimization PSO to carry out threshold parameter on maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S Optimizing the five parameters, and further improving the accuracy of fingerprint identification based on the extended Delaunay triangulation; wherein, the optimizing process is as follows:
(1) combining the requirement of a Delaunay triangularization fingerprint comparison algorithm, initializing the particle swarm size to be 40, the iteration number to be 200, and searching for the threshold parameter of the optimal maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S Defining the position and velocity of the particle swarm;
(2) determining fitness function
Wherein N represents the number of training samples, and ACC represents the identification accuracy of the training samples;
(3) updating individual optimal positions p im And the population optimum position p gm ；
(4) Updating the speed and position of the particle;
wherein, ω represents the inertial weight; m is an element of [1, M ]]，i∈[1,40]；v im And x im Respectively representing the speed and the position of the m-th particle; c. C 1 And c 2 Is a learning factor; r is 1 ,r 2 ∈[0,1]Is a random number; p is a radical of formula im And p gm Respectively representing the individual optimal position and the group optimal position searched by the i particle at present; updating particle positions
(5) If the error is less than 0.01 or the maximum iteration times are reached, ending the optimization of the particle swarm optimization algorithm to obtain the optimal particle position as the threshold parameter of the optimal maximum internal angle
Optimal length threshold parameter T L Optimal direction angle threshold parameter T θ Optimal azimuth angle threshold parameter T φ Optimal matching score threshold T S Therefore, an optimized three-dimensional fingerprint comparison algorithm based on the extended Delaunay triangulation is obtained.
Simulation verification:
collecting experimental data:
a structured light three-dimensional fingerprint acquisition system which is designed and built by taking a DLP4500 type three-dimensional scanner and a Grasshopper3 camera as main components is used for acquiring a large amount of three-dimensional fingerprint data through the system, and the identification accuracy of the method is verified through the acquired three-dimensional data. As shown in fig. 8, the change in receiver operating characteristic curve (ROC) is shown. The first method is a point matching method, and the second method is a fingerprint identification method related to the application. It can be found from experiments that in the collected data set, method one and method two, their corresponding Equal Error Rates (EER) are 0.16 and 0.13, respectively. The fingerprint identification method has the advantages of lower equal error rate and better identification performance.
The embodiments of the present invention are disclosed as the preferred embodiments, but not limited thereto, and those skilled in the art can easily understand the spirit of the present invention and make various extensions and changes without departing from the spirit of the present invention.
Claims (6)
1. A non-contact 3D fingerprint identification method based on PSO optimization Delaunay triangulation is characterized in that: the method is realized by the following steps:
estimating a three-dimensional azimuth angle of the three-dimensional minutiae point improved based on a principal component analysis technology;
constructing an expanded tetrahedron subdivision structure;
extracting features based on the expanded tetrahedral dissection structure;
wherein the extracted features include: edges, internal angles, two-dimensional direction angles, three-dimensional azimuth angles, and tetrahedral types;
comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons which accord with the matching conditions, counting the matching scores by using the counting results, and determining whether the tetrahedrons are matched or not according to the matching scores;
optimizing the fingerprint comparison algorithm parameters of Delaunay triangulation based on the improved particle swarm optimization PSO; optimizing and determining comparison parameters to obtain a final model;
the Delaunay triangularization Chinese meaning is a triangulation algorithm.
2. The PSO-based optimized Delaunay triangulation-based non-contact 3D fingerprint identification method as claimed in claim 1, wherein: the three-dimensional azimuth angle estimation method based on the improved three-dimensional minutiae of the principal component analysis technology specifically comprises the following steps:
(1) acquiring a two-dimensional fingerprint image;
(2) preprocessing the two-dimensional fingerprint image; wherein the preprocessing operation comprises: extracting a fingerprint foreground area, fingerprint ridge line extraction and fingerprint minutiae;
(3) extracting two-dimensional minutiae information on the preprocessed two-dimensional fingerprint image, wherein the two-dimensional minutiae information comprises a coordinate x, a coordinate y and a two-dimensional direction angle theta;
(4) adding a space coordinate z and a three-dimensional azimuth angle phi to the two-dimensional minutiae points to map the two-dimensional minutiae points into three-dimensional minutiae points of a three-dimensional space;
the acquisition process of the space coordinate z is as follows: simulating to form a three-dimensional curved surface through a three-dimensional fingerprint, obtaining the three-dimensional curved surface, and obtaining a position attribute z through xy of a two-dimensional minutia;
(5) estimating a three-dimensional azimuth angle phi of the three-dimensional minutiae added in the last step, specifically:
setting a point F to represent a three-dimensional minutia point;
using all vertices v in m neighbourhood around the three-dimensional minutiae point F i ∈R 3 With these vertices v i As a basis, calculating the normal direction of the three-dimensional minutiae point F by using a principal component analysis method; order to
Wherein the content of the first and second substances,
t represents transposition; r 3 A three-dimensional space is represented in which,
denotes the median value, t denotes v i The number of (2); by
Formed covariance matrix
Wherein T represents transpose; w is a i The weight is represented by a weight that is,
improving an estimation method of the normal direction of a three-dimensional minutiae F through a covariance matrix C, wherein F represents the three-dimensional minutiae, a represents a weight parameter, and m represents the number of neighborhoods;
(6) setting the number of the fingerprint minutiae as k, and then extracting the fingerprint minutiae; the set of fingerprint minutiae is denoted F k ＝(x k ,y k ,z k ,θ k ,φ k ) Wherein (x) k ,y k ,z k ) Is a three-dimensional minutiae space coordinate, (theta) k ,φ k ) The two-dimensional direction angle of the three-dimensional minutiae and the three-dimensional azimuth angle of the three-dimensional minutiae are obtained;
the feature vectors of the template fingerprint minutiae are represented as: p ═ F i p I 1.. M }, the feature vector of the fingerprint minutiae to be identified is expressed as:
the template minutiae feature set P comprises M minutiae, and the feature set Q of the minutiae to be identified comprises N minutiaeAnd (5) minutiae points.
3. The PSO-based optimized Delaunay triangulation-based non-contact 3D fingerprint identification method as claimed in claim 2, wherein: the process of the step of constructing an extended tetrahedrally subdivided structure is described,
the method comprises the following steps of reconstructing an expanded Delaunay tetrahedron subdivision structure by using point cloud Dironey triangulation, and specifically comprises the following steps:
(1) applying a Delaunay triangulation algorithm, and obtaining a tetrahedral structure G ═ { F, E } by adopting the Delaunay triangulation algorithm in a three-dimensional space, wherein E is an edge set of the tetrahedral structure, and F ═ { F ═ F } i N represents a three-dimensional minutiae set of a certain fingerprint; the four vertices of any one tetrahedron are denoted as (F) 1 ,F 2 ,F 3 ,F 4 ) Each vertex is denoted as F k ＝(x k ,y k ,z k )，k＝1,2,3,4；
(2)F i Is a minutia in the F set, N i ＝{F j |(F i ,F j ) E represents in Delaunay triangulated structure G and with F i A detail point set formed by connecting vertexes;
(3) is obtained by Delaunay triangulation algorithm i Group G of tetrahedrons of i ＝{N i ,E i In which G is i Is the resulting tetrahedral set, E i Is a set of edges of a tetrahedral structure, N i Representing a set of vertices;
(4) the tetrahedron sets are put together to form an expanded tetrahedron set S, S ═ G- 1 ∪…∪G n And n is the number of minutiae.
4. The PSO-based optimized Delaunay triangulation-based non-contact 3D fingerprint identification method as claimed in claim 3, wherein: the step of extracting features of the expanded tetrahedron subdivision structure specifically comprises the following steps:
let the feature of the tetrahedron be expressed as:
where, t is the number of this tetrahedral type,
denotes the largest of all internal angles in the tetrahedron, l max And l min Respectively representing the longest and shortest edges of the tetrahedron,
indicates the difference between the direction angles of the two vertexes of the longest side,
indicating the difference in the azimuth angle between the two vertices of the shortest side,
representing the difference in azimuth of the two vertices of the longest side,
representing the difference of the azimuth angles of the two vertexes of the shortest side;
the numbering method of the tetrahedron types comprises the following steps:
first of all, when a user wants to use the apparatus,
is the largest of all the inner angles in the four faces, the largest of the triangular faces
Is marked as V 1 ；
The vertex of the second largest interior angle in the triangular face is then labeled V 2 The vertex of the smallest interior angle in the triangular surface is marked as V 3 One vertex remaining in the tetrahedron is marked V 4 ；
Finally, the four vertex types are represented using vectors (t) 1 ，t 2 ，t 3 ，t 4 )，t i Is V i The type number Class of the tetrahedron can be obtained corresponding to the following table.
5. The PSO-based optimized Delaunay triangulation-based non-contact 3D fingerprint identification method as claimed in claim 4, wherein: the method comprises the following steps of comparing each tetrahedron to be matched according to the extracted features, counting the tetrahedrons which accord with the matching conditions, counting the matching scores by using the counting results, and determining whether the tetrahedrons are matched according to the matching scores, wherein the steps are as follows:
(1) comparing each tetrahedron, and judging whether the tetrahedrons are matched:
setting two fingerprints to be compared as a fingerprint A and a fingerprint B, wherein any tetrahedral feature on the fingerprint A is represented as
Any tetrahedral feature on the fingerprint B is represented as
Judging the matching condition:
ΔL max ＝|L max -L' max |，Δθ max ＝|θ-θ'|，Δφ min ＝|φ-φ'|
if t ≠ t', the two tetrahedrons for comparison are considered to be unmatched, and comparison of other characteristics is not carried out any more;
if t is equal to t', continuously judging whether the t is satisfied
ΔL max ＜T L ，ΔL min ＜T L ，Δθ max ＜T θ ，Δθ min ＜T θ ，Δφ max ＜T φ ，Δφ min ＜T φ If so, the two are consideredThe tetrahedra are matched and recorded; wherein the content of the first and second substances,
T L 、T θ 、T φ respectively representing a threshold parameter of a maximum internal angle, a side length threshold parameter of a tetrahedron, a direction angle threshold parameter of two vertexes of an edge and an azimuth angle threshold parameter of the two vertexes of the edge, wherein the values are set;
(2) counting the number of matched minutiae:
if the tetrahedron is matched, marking the four minutiae of the tetrahedron as matching, and counting the number r of the matched minutiae;
(3) and (3) counting the matching scores:
calculating the matching score S of the obtained data r of the matched minutiae by using the formula:
wherein N is A Number of minutiae, N, for fingerprint A B Number of minutiae for fingerprint B;
(4) and (3) recognition results:
matching score S and a set matching score threshold value T S Making a comparison when S > T S If so, matching the fingerprint A with the fingerprint B, otherwise, not matching the two fingerprints; wherein, T S Indicating a match score threshold to be achieved, the value of which is set.
6. The PSO-based optimized Delaunay triangulation-based non-contact 3D fingerprint identification method as claimed in claim 5, wherein: the improved particle swarm optimization PSO is used for optimizing the Delaunay triangularization fingerprint comparison algorithm parameters; in the step of optimizing and determining the comparison parameters to obtain the final model, the fingerprint comparison algorithm parameters include a threshold parameter for optimizing the maximum internal angle
Edge length threshold parameter T of tetrahedron L The direction angle threshold value of two vertexes of the edgeNumber T θ The azimuth angle threshold parameter T of two vertexes of the edge φ And a matching score threshold T S (ii) a The method specifically comprises the following steps:
establishing a plurality of matched fingerprint pairs and unmatched fingerprint pairs as training sets, and acquiring optimal parameters by using a particle swarm algorithm PSO; utilizing particle swarm optimization PSO to carry out threshold parameter on maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S Optimizing the five parameters; wherein, the optimizing process is as follows:
(1) initializing particle swarm size to be 40, iterating times to be 200, searching threshold parameters of optimal maximum internal angle
Length threshold parameter T L Direction angle threshold parameter T θ Azimuth angle threshold parameter T φ Matching score threshold T S Defining the position and velocity of the particle swarm;
(2) determining fitness function
Wherein N represents the number of training samples, and ACC represents the identification accuracy of the training samples;
(3) updating individual optimal positions p im And the population optimum position p gm ；
(4) Updating the speed and position of the particle;
wherein, ω represents the inertial weight; m is an element of [1, M ]]，i∈[1,40]；v im And x im Respectively representing the speed and the position of the m-th particle; c. C 1 And c 2 Is a learning factor; r is 1 ,r 2 ∈[0,1]Is a random number; p is a radical of im And p gm Respectively represent i particlesThe current searched individual optimal position and the group optimal position; updating particle positions
(5) If the error is less than 0.01 or the maximum iteration times are reached, ending the optimization of the particle swarm optimization algorithm to obtain the optimal particle position as the threshold parameter of the optimal maximum internal angle
Optimal length threshold parameter T L Optimal direction angle threshold parameter T θ Optimal azimuth angle threshold parameter T φ Optimal matching score threshold T S Therefore, an optimized three-dimensional fingerprint comparison algorithm based on the extended Delaunay triangulation is obtained.
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