CN100385451C - Deformation Fingerprint Recognition Method Based on Local Triangular Structure Feature Set - Google Patents

Abstract

This invention relates to an identifying method for deformed fingerprints based on local triangle structure character set, on the basis of the character that relative deformation of fingerprint image is limit in local regions, which expresses fingerprints with a fuzzy character-local triangle structure character sets to convert the computation to integral similarity among fingerprints to similarity balance among character sets, first of all, which puts forward a fuzzy measurement method of similarity between two triangle structures then further makes up of a character vector composed of local similarities of all triangle structures then to map the pair of similarity vectors to a normalized number in the region of [0, 1] to quantize the integral similarity among fingerprint images to further get the matched result.

Description

Deformation Fingerprint Recognition Method Based on Local Triangular Structure Feature Set

technical field

The invention belongs to the field of biometric feature recognition, relates to frontier knowledge such as image processing, pattern recognition, and computer technology, and particularly relates to realizing the recognition of non-linearly deformed fingerprint images by using local feature information and a fuzzy similarity measurement method.

Background technique

At present, the development of biometric identification technology has made fingerprint identification technology more and more mature, and it has been fully practical at present. Due to the sharp drop in the price of automatic fingerprint identification systems, the application of automatic fingerprint identification is no longer limited to the fields of law and public security. It can be used as a means for computers to confirm users, as an information security technology for accessing network resources, and can also be used for confirmation of bank ATM cards and credit cards, double confirmation of various smart IC cards, employee certification and household electronic door locks, etc. .

Due to the advantages of uniqueness and stability, convenient collection and low cost, fingerprints are very suitable to replace traditional passwords as a means of identity authentication. Input the fingerprint image to be matched into the computer, and through the reliable and effective fingerprint recognition algorithm, the identity recognition of anyone can be completed in a short time. With the wide application of fingerprint recognition systems in fields that require identification, our requirements for the accuracy and adaptability of recognition algorithms are also increasing. Fingerprint identification technology mainly includes fingerprint image acquisition, fingerprint image enhancement, fingerprint image feature extraction, data storage, comparison and matching of fingerprint features and other steps. Among them, fingerprint image feature extraction and matching are two key issues in the field of recognition.

During the identification process, the extraction precision and accuracy of fingerprint features directly determine the performance of fingerprint matching. Due to the existence of noise and the incompleteness of image quality enhancement algorithms, the ridge line breaks and Phenomena such as burrs all cause a certain amount of pseudo-feature information in the extracted features, which must be detected from the feature set by an effective, fast, and robust de-pseudo algorithm.

Most of the existing fingerprint collectors are push-type, and elastic deformation is inevitable during the collection process. There are two main reasons for fingerprint deformation. First, the acquisition of fingerprints is a transformation process from three-dimensional to two-dimensional. Different contact centers will produce different deformation models during fingerprint collection. Due to the great difference in the shape and flexibility of different fingertips, it is impossible to establish a unified three-dimensional model to restore this process. Second, the shear force exerted by a person on the collector will cause deformation. Different pressures perpendicular to the collection surface will cause changes in the thickness of the ridge lines of the collected fingerprint images; forces parallel to the collection surface will cause compression and stretching of the image; and torque along the contact center will cause image distortion. distortion. The ubiquity of non-linear deformed fingerprint images seriously affects the accuracy of the fingerprint matching algorithm, resulting in a decline in the overall performance of the fingerprint recognition system

Since the traditional fingerprint matching is generally based on a rigid coordinate system, no or few suitable methods have been found to describe the elastic changes of fingerprints. The original rigid transformation only uses elastic bounding boxes or adjustable parameter thresholds to compensate for the loss of fingerprint stretching that does not correspond to the same detail point in the two images. Because the traditional matching method cannot tolerate a large amount of deformation interference of ridge structure information, the matching criterion depends on the ridge extraction and its connection information, and the matching performance deteriorates with the decline of the quality of the input fingerprint image. Therefore, the matching problem of nonlinear deformed fingerprint images has always been a hot and difficult problem to be solved in this field.

In recent years, more and more scholars have gradually studied the nonlinear deformation of fingerprint features caused by pressure and the dynamic behavior changes with time series, and matched the nonlinear deformation fingerprints. Ratha et al. proposed to directly detect the pressure and torque applied to the scanner, and refuse to collect when the force is excessive, so as to reduce and control the deformation. The method proposed by Dorai et al. detects and estimates the deformation in the fingerprint image. But neither of these two methods can act on the collected fingerprint images. Maio and Maltoni proposed an elastic deformation model to describe the nonlinear deformation that occurs during the online collection of fingerprints, which is very helpful for understanding the deformation process of fingerprints. However, due to the limited information provided by a single fingerprint image and the influence of noise and other factors, it is very difficult to determine the values of the parameters defined in the model. Senior et al adjusted the elastic deformation image before matching to make the ridges equally spaced to improve the accuracy of the algorithm. However, the possibility of equidistant distribution of fingerprint ridges in reality is very small, and this method cannot solve the deformation problem caused by different mapping modes caused by different acquisition areas. proposed a triangle matching algorithm to deal with the large deformation of the fingerprint image. The local deformations of the smaller fingerprints accumulate, resulting in larger deformations of the entire image. However, local small triangular deformations can be combined into a variety of deformation modes. These deformation modes may not be realized in real fingerprint matching at all, but they can match some fingerprints from different fingers, causing misrecognition. Bazen et al. used a thin-plate spline model to describe the nonlinear deformation between two possible matching detail point columns. Ross et al calculated the average deformation of fingerprint images generated by the same finger based on the thin-plate spline model to solve the problem of elastic deformation. But applying the model to "correct" the fingerprints to be matched resulted in two prints becoming more similar regardless of whether they came from the same finger or not.

Based on the above analysis and research, we found that the current research on the matching of nonlinear deformation fingerprints only focuses on finding and describing local registrations, but does not consider the rationality of the global "registration mode" formed by these local matchings. When these methods are used to "correct" the "local deformation", it is possible to recover two fingerprint images from the same finger reasonably, and it is also possible to make some similar fingerprint images from different fingers more similar.

Contents of the invention

The purpose of the present invention is to propose and implement an automatic fingerprint recognition algorithm for fingerprint images with large deformations obtained in fingerprint collection, which can accurately, efficiently and robustly recognize them, and reduce the number of points and ridges caused by deformation. The phenomenon of misrecognition and refusal of recognition caused by the irregular deviation of the line.

In order to achieve the above object, the technical solution of the present invention is to provide a deformation fingerprint recognition method based on local triangular structure feature set, which selects a kind of fuzzy feature quantity—local minutiae point triangle structure to represent fingerprint; The similarity between fingerprints is used to describe the overall similarity between fingerprints; the relative distance between the minutiae points, the angle difference between the connection line and the direction of the surrounding ridges are selected to define the local triangular structure; the fuzzy similarity measurement method is introduced for the two triangular structures, and a Contains the vectors of all triangular structure similarities between two fingerprint images; finally, the algorithm maps each pair of similarity vectors to a normalized value, that is, the overall similarity of the fingerprint images is quantified as a scalar in the interval [0, 1] .

The described deformation fingerprint identification method based on the local triangular structure feature set comprises steps:

(1) Preprocessing of the fingerprint image: Enhance, refine and binarize the fingerprint image, remove the interference of various noises in the image, restore the ridge structure of the fingerprint, and make the texture accurate and clear, so that the subsequent operations can be correct carry out effectively;

(2) minutiae extraction and false removal processing: extract the information template of the minutiae feature points from the preprocessed image, and remove the false minutiae points from the extracted minutiae points according to the position law of the false minutiae points;

(3) Fuzzy feature representation: based on the distribution of minutiae points, define its local triangular structure feature vector, including information templates of all triangular feature structures in the image, and each fingerprint image can be represented by a corresponding feature vector set;

(4) On the real matching fingerprint image database, calculate the corresponding deformation parameters, and obtain the deformation parameter distribution in the true matching space;

(5) Fuzzy feature matching: use the deformation parameters in the true matching space to calculate the difference between it and the feature vector set of the image to be matched, and obtain the feature vector that can accurately measure the correlation between the fingerprints to be matched, and apply the fuzzy principle , which maps the similarity vector into a scalar in the interval [0, 1], representing the quantized value of the overall similarity between images.

The described deformation fingerprint identification method based on the local triangular structure feature set, in its (2), according to the position rule that the false minutiae point appears, is a kind of rule that judges the authenticity of the minutiae point simply and efficiently, and the specific steps include:

(1) Determine whether the minutiae is close to the edge of the fingerprint image: extract the fingerprint template, calculate the distance d from the minutiae to the edge of the fingerprint image, if d<threshold T1, determine that the point is a false minutiae;

(2) Take the minutiae i as the center of the circle, and the threshold r is the radius of the circle to search for the minutiae, and obtain the quantity value n of the minutiae;

(3) If n≥threshold T2, it is judged that the point i is a false minutiae, otherwise, it is considered as a true minutiae.

In the described deformation fingerprint recognition method based on local triangular structure feature set, in (3), each fingerprint image is represented by a corresponding feature set T={T ₁ , T ₂ ,..., T _N }, where T _k (k=1, 2...N) is the feature quantity of all local triangular structures detected from the fingerprint image.

In the deformation fingerprint recognition method based on the local triangular structure feature set, the feature quantity of the triangular structure, if the length of each side of the triangle formed by the minutiae points is less than the preset threshold Thr _d , then define the feature of the local triangular structure The quantity is T _k = {d _ij , d _ik , d _jk , θ _i , θ _j , θ _k , M _i , M _j , M _k , α _i , α _j , α _k }, and d _ij represents two minutiae points The distance between i and j, _{θ i} represents the angle between the direction from minutiae i to j and the direction from minutiae i to k; The mean value of the direction difference between each pixel and point i, α _i represents the angle between the direction of detail point i and the bisector of the interior angle of angle i;

_Mi is calculated by the following formula, where O(i, j) is the direction field of pixel (i, j):

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; o</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; o</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}}$

组成参数空间，由下式计算：The described deformation fingerprint identification method based on the local triangular structure feature set, true matching in (4) refers to the matching between fingerprint images from the same finger, which is carried out on the deformation fingerprint image set under the true matching mode Parameter training, four deformation parameter vectors

Composing the parameter space, calculated by the following formula:

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; en</span>}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

These deformation mode parameters constitute the deformation feature vector A true matching deformation pattern parameter space is obtained.

The described deformable fingerprint recognition method based on the local triangular structure feature set, in (5), in the fingerprint image matching, a similarity vector is defined to describe the feature difference between the fingerprint images: make T={T _t : 1≤t≤a} represents the template fingerprint image, I={T _i : 1≤i≤b} represents the input fingerprint image,

For every T _t ∈ T, $l_t^I=\max \left\{C(T_t-T_i)\right|i=1..b\},$ ${\stackrel{\&Right\; Arrow;}{l}}^I={[{l_1}^I,{l_2}^I,\&Center\; Dot;\&CenterDot;\&CenterDot;,{l_a}^I]}^T$

For each T _i ∈ I, $l_i^T=\max \left\{C(T_i-T_t)\right|t=1..a\},$ ${\stackrel{\&Right\; Arrow;}{l}}^T={[{l_1}^T,{l_2}^T,\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,{l_b}^T]}^T$

是局部三角特征结构的相似度测量函数。A (a+b)-dimensional similarity vector is defined for T and I ${\stackrel{\&Right\; Arrow;}{L}}^{(T,I)}={[L_1,L_2,\&CenterDot;\&Center\; Dot;\&CenterDot;,L_{a+b}]}^T,$ in, $L_i=\left\{\begin{array}{cc}{l_i}^I& i<=a\\ {l_{i-a}}^T& a<i<a+b\end{array}\right.,$

is the similarity measurement function of the local triangular feature structure.

The described deformation fingerprint identification method based on the local triangular structure feature set, the calculation method of the fingerprint image similarity vector is to introduce the fuzzy feature measurement method, and define the similarity measurement function of the local triangular feature structure. The specific steps include:

定义模糊特征集

的中心为集合中各元素的均值；(1) All the elements in the true matching deformation pattern parameter space constitute the fuzzy feature set

Define fuzzy feature set

center of is the mean value of each element in the set;

相对于模糊特征序列

的隶属程度，采用Cauchy函数的改进形式，定义隶属度函数C： $\tilde{D}\&RightArrow;\left[\mathrm{0,1}\right]$ 如下：(2) Measurement vector

Relative to the sequence of fuzzy features

The membership degree of , using the improved form of the Cauchy function, defines the membership degree function C: $\widetilde{\mathrm{D.}}\&Right\; Arrow;\left[\mathrm{0,1}\right]$ as follows:

中的每个元素小于

中相应的元素时， $C\left(\stackrel{\&RightArrow;}{f}\right)=1;$ when

Each element in is less than

When the corresponding elements in $C\left(\stackrel{\&Right\; Arrow;}{f}\right)=1;$

otherwise, $C\left(\stackrel{\&Right\; Arrow;}{f}\right)={[1+{(\mathrm{\&alpha;}*||\stackrel{\&Right\; Arrow;}{f}-\stackrel{\&Right\; Arrow;}{d}|\left|\right)}^{\mathrm{\&beta;}}]}^{-1};$ in, $\stackrel{\&Right\; Arrow;}{f}\&Element;\widetilde{\mathrm{D.}},$ β and α∈R, β>0, α>0, α is inversely proportional to the width of the function.

中的各元素加权向量w累积，来量化指纹图像间的整体相似度；结合应用了区域最优、中心最优及角度均匀性最优配置，将权向量

定义为：The described deformable fingerprint recognition method based on the local triangular structure feature set, in (5), in the fingerprint image matching, the similarity vector

The weighted vector w of each element in is accumulated to quantify the overall similarity between fingerprint images; combined with the application of the optimal configuration of the region, the center, and the uniformity of the angle, the weight vector

defined as:

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}}$

为输入指纹图像和模板指纹图像的正常区域百分比，

与三角结构到邻近的指纹图像中心点的距离正比，

与三角结构中角度间的均匀性成正比；p_A、p_B、p_C(p_A+p_B+p_C＝1)调整了

和

的比重，将模板和输入指纹图像的整体相似度量化为：in,

is the normal area percentage of input fingerprint image and template fingerprint image,

Proportional to the distance from the triangle structure to the center point of the adjacent fingerprint image,

It is proportional to the uniformity between the angles in the triangular structure; p _A , p _B , p _C (p _A +p _B +p _C ＝1) adjusted

and

The proportion of the overall similarity between the template and the input fingerprint image is quantified as:

$\mathrm{<span\; class="notranslate">\; Sim</span>}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; *</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}$

The core idea of the present invention is to realize fingerprint identification based on the local triangular feature structure in the fingerprint image. The algorithm chooses a kind of fuzzy feature quantity—local minutiae triangular structure to represent the fingerprint. Calculate the similarity between fuzzy feature quantities to describe the overall similarity between fingerprints. The local triangular structure is defined by selecting the relative distances of the minutiae points, the angle difference of connecting lines and the directions of the surrounding ridges. A fuzzy similarity measurement method is introduced for two triangular structures, and a vector containing the similarity of all triangular structures between two fingerprint images is constructed. Finally, the algorithm maps each pair of similarity vectors into a normalized value, that is, the overall similarity of the fingerprint image is quantified into a scalar in the interval [0, 1].

Based on the above ideas and purposes, the identification process of fingerprint images is divided into several steps, and the key issues that need to be paid attention to when performing each step are briefly introduced to design and improve our system and establish the final identification of elastic deformation fingerprint images Theoretical framework and system prototype. The implementation process of the invention obtained after integrating the research results into the existing algorithm is as follows:

Fingerprint image preprocessing: enhance, refine and binarize the fingerprint image, remove the interference of various noises in the image, restore the ridge structure of the fingerprint, make the texture accurate and clear, and make the following details point extraction, matching and other operations be carried out correctly and effectively.

Minutiae extraction and de-false processing: Extract the information template of the minutiae feature points from the preprocessed image, and propose a simple and effective algorithm to de-falseize the minutiae set according to the position law of the pseudo-details.

Fuzzy feature representation: Due to the limited deformation in the local area of the fingerprint image, the local triangular feature structure set is selected to represent the fingerprint image, and the feature vector set corresponding to each fingerprint is obtained, including information templates of all triangular feature structures in the image.

Fuzzy feature matching: Calculate the maximum degree of membership between any triangular feature structure and another fingerprint, and obtain a feature vector that can accurately measure the correlation between the fingerprints to be matched. Applying the fuzzy principle, the similarity vector is mapped to a scalar in the interval [0, 1], which represents the overall similarity quantification value between images (1 represents a complete match, and 0 represents a complete mismatch).

Our fingerprint image recognition method can remove the false minutiae of the original fingerprint image due to the influence of noise, record the feature information of the fingerprint as accurately as possible, and can also identify fingerprint images with poor quality. Obviously, when matching excessively deformed fingerprint images, it is not feasible to measure the similarity between the images to be matched only by the overall structure of the fingerprint, because the irregular offset of the corresponding minutiae points and ridge lines may be large, beyond beyond the tolerance range of traditional algorithms. According to the characteristic that the deformation of the local area of the fingerprint image is small and the accumulation leads to large deformation, the local triangular structure of the minutiae is selected as the fuzzy feature that is approximately unchanged before and after deformation for fingerprint registration and recognition, which ensures the accuracy of the algorithm. Considering the different numbers of minutiae points extracted from different fingerprint images and the ambiguity of the matching process, the fuzzy theory can be applied to the similarity calculation. The corresponding feature quantity cannot be divided by a single threshold, nor can the image to be matched The simple judgment is two cases of matching or not matching.

Through the evaluation of the performance of the algorithm, we found that the selected feature quantity can well distinguish the irregular offset of feature points and ridges caused by false matching and excessive deformation, and has strong robustness. Since the triangular structure information of local features is independent of the overall transformation such as rotation and translation of the fingerprint image, our recognition algorithm does not need to calibrate the original image, which simplifies the steps of the algorithm and improves the efficiency of the algorithm.

Description of drawings

Fig. 1 fingerprint identification processing flowchart of the present invention;

Figure 2 Schematic diagram of pseudo-detail points of low-quality images: (a) is the original image; (b) is the thinned image after (a) image enhancement; (c) and (d) are the original images; (d) is (c ) of the enhanced thinning image; there are often other pseudo-detail points appearing near the pseudo-detail points, as shown in the ellipse area, and the pseudo-detail points often appear on the edge of the image, as shown in the rectangular area;

Figure 3 A pair of fingerprint images with large deformation: (a) is the original image a; (b) is the original image b; (c) is the correspondence between the minutiae points in the images (a) and (b); (d) is The image (a) is artificially optimally calibrated and superimposed on the image (b), the corresponding detail points in the upper ellipse area are basically consistent, but the corresponding detail points in the lower ellipse area are offset by more than 100 pixels;

The partial triangular structure schematic diagram of Fig. 4 fingerprint image;

Figure 5 is a schematic diagram of true matching mode parameter training: (a) template fingerprint image; (b) input fingerprint image; (c) true matching mode;

Fig. 6 the experimental result of the inventive method on the NIST24 fingerprint database;

Fig. 7 is the experimental result of the inventive method on the FVC2004 DB1 fingerprint database.

Detailed ways

The steps included in the deformed fingerprint recognition algorithm based on the local triangular feature structure proposed by the present invention are introduced below, especially the two parts of image feature extraction and local feature matching. First of all, we introduce some assumptions, based on which the research and analysis of the recognition algorithm are carried out: do not distinguish the terminal point and the bifurcation point, they are all regarded as point features; point features are evenly distributed in the fingerprint, but the different detail points Undetermined regions may overlap; correlations of minutiae pairs are independent and each correlation is equally important; fingerprint image quality is not explicitly considered in the model. The detailed steps are as follows:

1) Fingerprint image preprocessing

The specific processing operations include: 1. Equalization of gray scale, which can eliminate the contrast difference between different images. 2. Use a simple low-pass filter algorithm to remove speckle noise and Gaussian noise. 3. Calculate the boundary of the image and crop the image. This reduces the computational workload in the next step and increases the speed of the system. 4. Estimation of the direction field, calculate the direction of each pixel of the fingerprint image. 5. Binarization, according to the direction of each pixel, the fingerprint image is processed into an image with only black and white pixels. 6. Thinning, according to the binarized image, the ridge line width of the fingerprint is thinned to only one pixel, and a fingerprint thinning map is generated. 7. Post-thinning processing, remove some obvious broken lines in the thinned image, obvious bridges between ridges, burrs on ridges, too short ridges and single spots and other bad ridge structures.

2) Extraction of detail feature points and de-fake processing

From the preprocessed fingerprint skeleton, track and extract the minutiae points. According to our experience, the distance between two true minutiae points is generally greater than a certain threshold, and there are generally other false minutiae points near the false minutiae points. And false minutiae points can often be extracted in the edge area of the fingerprint image. Figure 2 shows an example of pseudo minutiae point extraction in a low-quality fingerprint image.

The following algorithm is used to extract pseudo minutiae points. In this process, a few true minutiae points will be considered as false minutiae points, but this does not affect the subsequent matching process.

1. Determine whether the minutiae point is close to the edge of the fingerprint image. Extract the fingerprint template and calculate the distance d from the minutiae point to the edge of the fingerprint image. If d is less than the threshold T1, the point is a pseudo minutiae point.

2. Search within the range of the circle with the minutiae i as the center and the threshold r as the radius, and the number of minutiae points obtained is n.

3. If n is greater than the threshold T2, the point is a false minutiae, otherwise, the point is a true minutiae.

Among them, T1, T2, and r are empirical values, which can be selected according to the situation of the fingerprint image. This is a simple and efficient method for detecting false minutiae points, and all detected pseudo minutiae points will not participate in the subsequent matching process.

3) Fuzzy feature representation of fingerprints

A fuzzy feature quantity-minutiae local triangular structure is selected to characterize the features of the fingerprint. Firstly, the parameters that can reflect the local features of the fingerprint are selected to define the triangular structure. In the proposed algorithm, fingerprint local triangular structure features are the matching primitives. Define the feature quantity T _k of the local triangular point _structure as T _k = {d _ij , d _ik , d _jk , θ _i , θ j , θ _k , M _i , M _j , M _k , α _i , α _j , α _k }, d _ij represents the distance between two detail _points i and j, θ _i represents the angle between the direction from detail point i to j and the direction from detail point i to k; Direction difference, α _i represents the angle between the direction of minutia point i and the bisector of the interior angle of angle i. With minutiae i as the center, the pixels in the area with radius r constitute the area of minutiae i. M _i is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; o</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; o</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}}$

where r is the radius of the region, O(i, j) is the direction field at point (i, j).

The meaning of the parameters {d _ik , d _jk , θ _j , θ _k , M _j , M _k , α _j , α _k } is similar to that of {d _ij , θ _i , M _i , α _i }. Obviously, the feature quantity T _k of the local triangular point is independent of the rotation and translation of the fingerprint. Figure 4 shows the local triangular point structure of the fingerprint.

There is a constraint condition in the process of constructing local triangle points: the maximum length of the distance between minutiae points in the triangle is less than Thr _d . For a fingerprint image with a large deformation, due to the accumulation of deformation in each area between the minutiae points, the overall deformation of the image is relatively large.

Thus, the feature set T={T ₁ , T ₂ ,...,T _N } corresponding to each fingerprint image is obtained, where T _k (k=1, 2...N) is all the local parts detected on the fingerprint image The characteristic quantity of the triangular structure. The overall similarity measurement problem between the template and the input fingerprint image is transformed into the similarity calculation problem between the two corresponding feature sets.

Then, through a series of true matching (true matching refers to the matching between fingerprint images from the same finger) training to obtain the parameter space of the true deformation mode, which is used to select an appropriate threshold for discrimination in the following fingerprint feature matching.

由下式计算：Suppose I _k = {d′ _ij , d′ _ik , d′ _jk , θ′ _i , θ′ _j , θ′ _k , M′ _i , M′ _j , M′ _k , α′ _i , α′ _j , α ′ _k } is the local triangle point feature of the input fingerprint, T _k = {d _ij , d _ik , d _{jk ,} θ _i , θ j , θ _k , M _i , M _j , M _k , α _i , α _j , α _k } is the local triangle point feature in the fingerprint template. Four deformation formal parameter vectors

Calculated by the following formula:

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; en</span>}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; jk</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}_{\mathrm{<span\; class="notranslate">\; diff</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \}</span>$

为了研究真匹配模式参数，我们在形变指纹图像集上训练得到一个真形变模式的参数空间。这个图像集从FVC2004DB1的B库中提取。指纹图像通过“CrossMatchV300”光学采集仪获得。图像的大小为640×480象素，在500DPI的条件下。指纹库B含有从10个不同手指捕获的80个指纹图像，每个手指8幅图像。在这个指纹库中，从同一个手指得到的指纹图像间的形变是很大的。图3显示了FVC2004 DB1中的一对形变较大的指纹图像。对来自相同手指的形变指纹图像进行匹配，计算出真形变模式对应的参数空间中的形变参数。图5显示了在FVC2004 DB1中的两幅指纹图像的一个真形变模式。These deformation formal parameters constitute the formal feature quantity

In order to study the true matching pattern parameters, we train on the deformable fingerprint image set to obtain a parameter space of true deformable patterns. This image set is extracted from the B library of FVC2004DB1. The fingerprint image is obtained by the "CrossMatchV300" optical acquisition device. The size of the image is 640×480 pixels, under the condition of 500DPI. Fingerprint library B contains 80 fingerprint images captured from 10 different fingers, 8 images per finger. In this fingerprint library, the deformation between fingerprint images obtained from the same finger is very large. Figure 3 shows a pair of deformed fingerprint images from FVC2004 DB1. The deformed fingerprint images from the same finger are matched, and the deformation parameters in the parameter space corresponding to the true deformation mode are calculated. Figure 5 shows a true deformation pattern of two fingerprint images in FVC2004 DB1.

4) Fuzzy feature matching

定义模糊特征集

的中心

为集合中各元素的均值。A fuzzy similarity measurement method is introduced for two triangular feature structures, and a vector including the similarity of all triangular structures between two fingerprints is constructed. All elements in the parameter space of the true deformation model constitute the fuzzy feature set

Define fuzzy feature set

center of

is the mean of each element in the set.

In fact, it is the average value of all elements in the feature set, which may not be the elements in the feature set. The averaging of all elements in the feature set can increase the robustness of fuzzy features, and at the same time, the loss of useful information is also hidden in the continuous process, because a set of feature vectors is drawn into a single feature vector.

相对于模糊特征序列

的隶属程度。Suppose T _k = {d _ij , d _ik , d _jk , θ _i , θ _j , θ _k , M _i , M _j , M _k , α _i , α _j , α _k ,} represent the local triangular structure of the template fingerprint, I _k = {d′ _ij , d′ _ik , d′ _jk , θ′ _i , θ′ _j , θ′ _k , M′ _i , M′ j , M′ _k , α′ _i , α′ _{j ,} α′ _k } represents the local triangular structure of the input fingerprint, and the similarity between T _k and I _k is measured by the following method. First, the eigenvectors of the deformation modes are computed Then, measure the vector

Relative to the sequence of fuzzy features

degree of membership.

Constructing or selecting an appropriate membership function depends on its application field. The most commonly used types of membership functions are cone, exponential and Cauchy. In this algorithm, we adopt the improved form of Cauchy function, which has a good expression form and high calculation efficiency.

Define the membership function C: $\widetilde{\mathrm{D.}}\&Right\; Arrow;\left[\mathrm{0,1}\right]$ as follows:

中的每个元素小于

中相应的元素时， $C\left(\stackrel{\&RightArrow;}{f}\right)=1;$ 否则， $C\left(\stackrel{\&RightArrow;}{f}\right)={[1+{(\mathrm{\&alpha;}*||\stackrel{\&RightArrow;}{f}-\stackrel{\&RightArrow;}{d}|\left|\right)}^{\mathrm{\&beta;}}]}^{-1}.$ 其中， $\stackrel{\&RightArrow;}{f}\&Element;\tilde{D},$ β和α∈R，β＞0，α＞0，α与函数的宽度成反比。β决定函数的平滑程度。对于确定的α，模糊度随β值的减少而增加。对固定的β，模糊度随α值的增大而下降。很明显，特征矢量距离矢量串的中心越远，模糊特征的相关程度就越低。when

Each element in is less than

When the corresponding elements in $C\left(\stackrel{\&Right\; Arrow;}{f}\right)=1;$ otherwise, $C\left(\stackrel{\&Right\; Arrow;}{f}\right)={[1+{(\mathrm{\&alpha;}*||\stackrel{\&Right\; Arrow;}{f}-\stackrel{\&Right\; Arrow;}{d}|\left|\right)}^{\mathrm{\&beta;}}]}^{-1}.$ in, $\stackrel{\&Right\; Arrow;}{f}\&Element;\widetilde{\mathrm{D.}},$ β and α∈R, β>0, α>0, α is inversely proportional to the width of the function. β determines how smooth the function is. For a certain α, the ambiguity increases as the value of β decreases. For a fixed β, the ambiguity decreases as the value of α increases. Obviously, the farther the feature vector is from the center of the vector string, the less correlated the fuzzy features are.

Then, the similarity vector is mapped to a scalar in the interval [0, 1], which represents the overall similarity quantization value between images.

The overall similarity of the fingerprint image is composed of the similarity of the local triangular structure. Let T={T _t : 1≤t≤a, a represents the number of all triangle points detected from the template fingerprint image} represents the template fingerprint image, I={T _i : 1≤i≤b, b represents the The number of all triangle points detected on the input fingerprint image} denotes the input fingerprint image. For each T _t ∈ T, we define the similarity method, I as

${\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; \}</span>$

Combine l _t ^I together to get a vector

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span>{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; ,</span>{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

Similarly, for each $\stackrel{\&Right\; Arrow;}{f}{T}_i\&Element;I,,$ We define the similarity method, T as

${\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \}</span>$

Combine l _i ^T together to get a vector

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span>{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

描述了冲的个体模糊特征与I中全部模糊特征间的相似度，

显示了I中个体模糊特征与冲全部模糊特征间的相似度。因此，我们为T和I定义了一个(a+b)维的相似度矢量 ${\stackrel{\&RightArrow;}{L}}^{(T,I)}={[L_1,L_2,\&CenterDot;\&CenterDot;\&CenterDot;,L_{a+b}]}^T,$ 其中 $L_i=\left\{\begin{array}{cc}{l_i}^I& i<=a\\ {l_{i-a}}^T& a<i<a+b\end{array}\right.,$ 所有元素都取值为[0，1]区间内的实数。Obviously,

Describes the similarity between the individual fuzzy features of Chong and all the fuzzy features in I,

Shows the similarity between individual fuzzy features in I and all fuzzy features. Therefore, we define a (a+b)-dimensional similarity vector for T and I ${\stackrel{\&Right\; Arrow;}{L}}^{(T,I)}={[L_1,L_2,\&Center\; Dot;\&Center\; Dot;\&CenterDot;,L_{a+b}]}^T,$ in $L_i=\left\{\begin{array}{cc}{l_i}^I& i<=a\\ {l_{i-a}}^T& a<i<a+b\end{array}\right.,$ All elements take values as real numbers in the interval [0, 1].

中的各元素加权累积来衡量指纹图像间的整体相似度。FFM算法计算权向量w和相似度向量

的内积。有很多种选择来挑选权向量w。我们可以考虑三角结构的位置并给临近指纹图像中心(中心最优配置，假设邻近图像中心的三角结构更可信)的三角结构分配较高的权值。另一个选择是区域配置，利用三角结构覆盖的区域面积来确定权值，理论依据是所占区域面积合适的三角结构更可信。我们还采用了三角结构中角度间的均匀性作为加权依据。权向量

定义为：similarity vector

Each element in is weighted and accumulated to measure the overall similarity between fingerprint images. The FFM algorithm calculates the weight vector w and the similarity vector

inner product. There are many options for picking the weight vector w. We can consider the location of the triangular structures and assign higher weights to the triangular structures near the center of the fingerprint image (the center is optimally configured, assuming that the triangular structures near the center of the image are more credible). Another option is regional configuration, which uses the area covered by the triangular structure to determine the weight. The theoretical basis is that a triangular structure with an appropriate area is more credible. We also use the uniformity between angles in the triangular structure as a weighting basis. weight vector

defined as:

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}}$

包括输入指纹图像和模板图像的正常区域百分比，

包括正常的权值(邻近图像中心的感兴趣的三角点)，

与三角结构中角度间的均匀性成正比。p_A、p_B、p_C(p_A+p_B+p_C＝1)调整了

的比重。in,

includes the normal area percentage of the input fingerprint image and the template image,

Include normal weights (triangle points of interest adjacent to the center of the image),

Proportional to the uniformity between the angles in the triangular structure. p _A , p _B , p _C (p _A +p _B +p _C ＝1) adjusted

proportion.

Finally, the algorithm quantifies the overall similarity between the template and the input fingerprint image as:

$\mathrm{<span\; class="notranslate">\; Sim</span>}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; *</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}$

Train the parameters on the true matching pattern library, observe the sample points in the parameter space, and find the value corresponding to the concentrated distribution area as the threshold for discrimination.

The test results on the fingerprint database show that the algorithm solves the problem of nonlinear deformation very well. Even if the fingerprint image from the same finger is excessively deformed, the algorithm can better distinguish it from false matches, with good accuracy and robustness.

Example

We apply this method to the fingerprint image processing system designed and implemented by ourselves. The fingerprint image processing system developed by us is based on Window98/95, adopts object-oriented design method and software engineering specification, realizes with C++ language, and is an image processing and analysis system oriented to the field of fingerprint identification. The fingerprint identification processing flow of the present invention is shown in Figure 1. This system has rich graphic image processing and analysis functions, not only has perfect two-dimensional image processing and analysis functions, but also can dynamically load various fingerprint identification algorithms. The system provides a series of functions such as image input, image storage, image processing, algorithm loading, file conversion, and FVC testing tools.

The algorithm is tested in the fingerprint library of NIST24 and FVC2004, and the recognition algorithm standard of the international fingerprint recognition competition is used for evaluation. Since the fingerprints in the library have significant elastic deformation, it can be used to determine the adaptability of the system to significant elastic deformation. The experimental results are shown in Figures 6 and 7.

A large number of experiments prove that this algorithm solves the problem of nonlinear deformation very well. For deformed fingerprints, compared with traditional matching methods, this algorithm gives quite accurate discrimination results, and has high reliability, practicability and admissibility.

Claims (9)

1. A deformation fingerprint identification method based on a local triangle structure characteristic set is characterized in that a local minutiae triangle structure is selected to represent a fingerprint; calculating the similarity among the fuzzy characteristic quantities to depict the overall similarity among the fingerprints; selecting the relative distance of the detail points, the angle difference of the connecting lines and the directions of the peripheral ridge lines to define a local triangular structure; introducing a fuzzy similarity measurement method into the two triangular structures, and constructing a vector containing all the triangular structure similarities between the two fingerprint images; finally, the algorithm maps each pair of similarity vectors into a normalized value, i.e., the overall similarity of the fingerprint image is quantized into a scalar quantity within a [0, 1] interval.

2. The method for identifying deformed fingerprints based on the local triangular structure feature set according to claim 1, comprising the steps of:

(1) preprocessing a fingerprint image: the fingerprint image is enhanced, refined and binarized, the interference of various noises in the image is removed, the ridge line structure of the fingerprint is recovered, the texture is accurate and clear, and the subsequent operation can be correctly and effectively carried out;

(2) detail point extraction and false removal processing: extracting an information template of detail characteristic points from the preprocessed image, and removing pseudo-fine nodes from the extracted detail point set according to the position rule of the pseudo-fine nodes;

(3) fuzzy feature representation: based on the distribution of the minutiae, defining the feature vectors of the local triangular structure of the minutiae, including information templates of all triangular feature structures in the image, wherein each fingerprint image can be represented by a corresponding feature vector set;

(4) calculating corresponding deformation parameters on a true matching fingerprint image library to obtain deformation parameter distribution in a true matching space;

(5) fuzzy feature matching: and calculating the difference between the true matching space and the feature vector set of the image to be matched by using the deformation parameters in the true matching space to obtain a feature vector capable of accurately measuring the correlation between the fingerprints to be matched, and mapping the similarity vector into a scalar in a [0, 1] interval by applying a fuzzy principle to represent the quantization value of the overall similarity between the images.

3. The method for identifying deformed fingerprints based on the local triangular structure feature set according to claim 2, wherein in the step (2), the rule for simply and efficiently judging the authenticity of the minutiae according to the position rule of the pseudo minutiae is a specific step comprising:

(1) judging whether the minutiae are close to the edge of the fingerprint image: extracting a fingerprint template, calculating the distance d from the minutiae to the edge of the fingerprint image, and if d is less than T1, judging the minutiae as pseudo minutiae;

(2) searching minutiae in the range of a circle with the minutiae i as the center of the circle and the threshold r as the radius to obtain the number value n of the minutiae;

(3) if n is larger than or equal to T2, judging the point i as a pseudo minutia, otherwise, considering the point i as a true minutia;

wherein: wherein T1, T2 and r are empirical values and are selected according to the condition of the fingerprint image.

4. The method for fingerprint identification based on local triangle feature set as claimed in claim 2, wherein in the step (3), each fingerprint image is identified by the corresponding feature set T ═ T₁，T₂，…，T_NDenotes wherein T_k(k ═ 1, 2 … N) is a feature quantity of all local triangular structures detected from the fingerprint image.

5. The method for fingerprint identification based on the deformation of the feature set of the local triangle structure as claimed in claim 4, wherein the feature quantity of the triangle structure is determined if the length of each side of the triangle formed by the minutiae is smaller than the threshold Thr_dThen, the feature quantity defining the local triangle structure is T_k＝{d_ij，d_ik，d_jk，θ_i，θ_j，θ_k，M_i，M_j，M_k，α_i，α_j，α_k}，d_ijDenotes the distance, θ, between two minutiae points i and j_iRepresenting the included angle between the direction from the detail point i to j and the direction from the detail point i to k; m_iThe mean value of the direction differences, alpha, between each pixel in a square region with a side length of 2r and the point i, centered on the minutiae point i, is shown_iRepresenting the included angle between the direction of the minutiae point i and the inner angle bisector of the angle i;

M_iis calculated by the following equation, where O (i, j) is the directional field of pixel (i, j):

<math><mrow> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mi>x</mi> <mn>0</mn> <mo>-</mo> <mi>r</mi> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mi>x</mi> <mn>0</mn> <mo>+</mo> <mi>r</mi> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mi>x</mi> <mn>0</mn> <mo>-</mo> <mi>r</mi> </mrow> <mrow> <mi>j</mi> <mo>=</mo> <mi>x</mi> <mn>0</mn> <mo>+</mo> <mi>r</mi> </mrow> </munderover> <mo>|</mo> <mi>O</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>O</mi> <mrow> <mo>(</mo> <mi>x</mi> <mn>0</mn> <mo>,</mo> <mi>y</mi> <mn>0</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mrow> <mn>2</mn> <mi>r</mi> <mo>*</mo> <mn>2</mn> <mi>r</mi> </mrow> </mfrac> </mrow></math>

wherein Thr is_dIs an empirical value and is set according to the condition of the fingerprint image.

6. The method for identifying deformed fingerprints based on the local triangle structure feature set as claimed in claim 2, wherein the true matching in (4) refers to matching between fingerprint images from the same finger, the parameter training is performed on the deformed fingerprint image set in the true matching mode, and four deformed parameter vectors are used

A composition parameter space, calculated by:

<math><mrow> <mover> <mi>l</mi> <mo>&RightArrow;</mo> </mover> <msub> <mi>en</mi> <mi>diff</mi> </msub> <mo>=</mo> <mo>{</mo> <mo>|</mo> <msub> <mi>d</mi> <mi>ij</mi> </msub> <mo>-</mo> <msup> <msub> <mi>d</mi> <mi>ij</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>d</mi> <mi>ik</mi> </msub> <mo>-</mo> <msup> <msub> <mi>d</mi> <mi>ik</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>d</mi> <mi>jk</mi> </msub> <mo>-</mo> <msup> <msub> <mi>d</mi> <mi>jk</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>}</mo> </mrow></math>

<math><mrow> <msub> <mover> <mi>&theta;</mi> <mo>&RightArrow;</mo> </mover> <mi>diff</mi> </msub> <mo>=</mo> <mo>{</mo> <mo>|</mo> <msub> <mi>&theta;</mi> <mi>ij</mi> </msub> <mo>-</mo> <msup> <msub> <mi>&theta;</mi> <mi>ij</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>&theta;</mi> <mi>ik</mi> </msub> <mo>-</mo> <msup> <msub> <mi>&theta;</mi> <mi>ik</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>&theta;</mi> <mi>jk</mi> </msub> <mo>-</mo> <msup> <msub> <mi>&theta;</mi> <mi>jk</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>}</mo> </mrow></math>

<math><mrow> <msub> <mover> <mi>M</mi> <mo>&RightArrow;</mo> </mover> <mi>diff</mi> </msub> <mo>=</mo> <mo>{</mo> <mo>|</mo> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>-</mo> <msup> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>M</mi> <mi>j</mi> </msub> <mo>-</mo> <msup> <msub> <mi>M</mi> <mi>j</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>M</mi> <mi>k</mi> </msub> <mo>-</mo> <msup> <msub> <mi>M</mi> <mi>k</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>}</mo> </mrow></math>

<math><mrow> <msub> <mover> <mi>&alpha;</mi> <mo>&RightArrow;</mo> </mover> <mi>diff</mi> </msub> <mo>=</mo> <mo>{</mo> <mo>|</mo> <msub> <mi>&alpha;</mi> <mi>i</mi> </msub> <mo>-</mo> <msup> <msub> <mi>&alpha;</mi> <mi>i</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>&alpha;</mi> <mi>j</mi> </msub> <mo>-</mo> <msup> <msub> <mi>&alpha;</mi> <mi>j</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>-</mo> <msup> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>&prime;</mo> </msup> <mo>|</mo> <mo>}</mo> </mrow></math>

these deformation mode parameters constitute the deformation eigenvectors <math><mrow> <mover> <mi>f</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>l</mi> <mo>&RightArrow;</mo> </mover> <msub> <mi>en</mi> <mi>diff</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&theta;</mi> <mo>&RightArrow;</mo> </mover> <mi>diff</mi> </msub> <mo>,</mo> <msub> <mover> <mi>M</mi> <mo>&RightArrow;</mo> </mover> <mi>diff</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&alpha;</mi> <mo>&RightArrow;</mo> </mover> <mi>diff</mi> </msub> <mo>)</mo> </mrow> </mrow></math> And obtaining a deformation mode parameter space which is truly matched.

7. The method for shape-changing fingerprint identification based on local triangle structure feature set as claimed in claim 2, wherein in the step (5), in fingerprint image matching, a similarity vector is defined to describe the feature difference between fingerprint images: let T be { T ═ T_t: 1 ≦ T ≦ a } representing the template fingerprint image, I ═ T ≦ T_i: 1 i ≦ b represents an input fingerprint image,

for each T_t∈T， $l_t^I=\max \left\{C(T_t-T_i)\right|i=1..b\},$ <math><mrow> <msup> <mover> <mi>l</mi> <mo>&RightArrow;</mo> </mover> <mi>I</mi> </msup> <msup> <mrow> <mo>[</mo> <msup> <msub> <mi>l</mi> <mn>1</mn> </msub> <mi>I</mi> </msup> <mo>,</mo> <msup> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>I</mi> </msup> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msup> <mrow> <mo>,</mo> <msub> <mi>l</mi> <mi>a</mi> </msub> </mrow> <mi>I</mi> </msup> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow></math>

For each T_i∈I， $l_i^T=\max \left\{C(T_i-T_t)\right|t=1..a\},$ <math><mrow> <msup> <mover> <mi>l</mi> <mo>&RightArrow;</mo> </mover> <mi>T</mi> </msup> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msup> <msub> <mi>l</mi> <mn>1</mn> </msub> <mi>T</mi> </msup> <mo>,</mo> <msup> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>T</mi> </msup> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msup> <msub> <mi>l</mi> <mi>b</mi> </msub> <mi>T</mi> </msup> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow></math>

Defining a (a + b) -dimensional similarity vector for T and I <math><mrow> <msup> <mover> <mi>L</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>T</mi> <mo>,</mo> <mi>I</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>L</mi> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow></math> Wherein <math><mrow> <msub> <mi>L</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msup> <msub> <mi>l</mi> <mi>i</mi> </msub> <mi>I</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>&le;</mo> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <msup> <msub> <mi>l</mi> <mrow> <mi>i</mi> <mo>-</mo> <mi>a</mi> </mrow> </msub> <mi>T</mi> </msup> <mo>,</mo> <mi>a</mi> <mo>&lt;</mo> <mi>i</mi> <mo>&lt;</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow></math>

is a similarity measure function of the local trigonometric feature.

8. The method for identifying deformed fingerprints based on the local triangular feature set according to claim 7, wherein the method for calculating the similarity vector of the fingerprint image introduces a fuzzy feature measurement method to define the similarity measurement function of the local triangular feature set, and the method comprises the following steps:

(1) all elements in the true matching deformation mode parameter space constitute a fuzzy feature set

Defining a set of fuzzy featuresOf (2) center

Is the average value of each element in the set;

(2) measurement vectorRelative to fuzzy feature sequencesThe degree of membership of the Cauchy function is defined by adopting an improved form of the Cauchy function <math><mrow> <mi>C</mi> <mo>:</mo> <mover> <mi>D</mi> <mo>~</mo> </mover> <mo>&RightArrow;</mo> <mo>[</mo> <mn>0,1</mn> <mo>]</mo> </mrow></math> The following were used:

when in useEach element of (1) is less than

When the corresponding elements are used in the formula (I), <math><mrow> <mi>C</mi> <mrow> <mo>(</mo> <mover> <mi>f</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>;</mo> </mrow></math> if not, then, <math><mrow> <mi>C</mi> <mrow> <mo>(</mo> <mover> <mi>f</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>*</mo> <mo>|</mo> <mo>|</mo> <mover> <mi>f</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <mi>d</mi> <mo>&RightArrow;</mo> </mover> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mi>&beta;</mi> </msup> <mo>]</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>;</mo> </mrow></math> wherein, <math><mrow> <mover> <mi>f</mi> <mo>&RightArrow;</mo> </mover> <mo>&Element;</mo> <mover> <mi>D</mi> <mo>~</mo> </mover> <mo>,</mo> </mrow></math> β and α ∈ R, β > 0, α being inversely proportional to the width of the function.

9. The method for fingerprint identification based on deformation of local triangle structure characteristic set according to claim 2, wherein in the step (5), similarity vector is used in fingerprint image matchingThe weighted vectors w of each element in the fingerprint image are accumulated to quantize the overall similarity among the fingerprint images; combining the optimal configuration of the area, the optimal center and the optimal angle uniformity, and applying the weight vector

Is defined as:

<math><mrow> <mover> <mi>w</mi> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>p</mi> <mi>A</mi> </msub> <msub> <mover> <mi>w</mi> <mo>&RightArrow;</mo> </mover> <mi>A</mi> </msub> <mo>+</mo> <msub> <mi>p</mi> <mi>B</mi> </msub> <msub> <mover> <mi>w</mi> <mo>&RightArrow;</mo> </mover> <mi>B</mi> </msub> <mo>+</mo> <msub> <mi>p</mi> <mi>C</mi> </msub> <msub> <mover> <mi>w</mi> <mo>&RightArrow;</mo> </mover> <mi>C</mi> </msub> </mrow></math>

Images