CN1322465C - Image segmentation and fingerprint line distance getting technique in automatic fingerprint identification method - Google Patents

Abstract

The present invention discloses image segmentation and fingerprint line distance extracting technology in an automatic fingerprint identifying method. The present invention introduces a probability density model of the gray level distribution of the fingerprint images, and provides a new method for the segmentation treatment of the fingerprint images based on the monte carlo simulation of the markov chain referring to the defects of the low adaptation of the quality of fingerprint images and the inaccurate result treatment of the segmentation of the fingerprint images with poor quality. The method can accurately realize the effective segmentation of the fingerprint images even to the fingerprint images of low quality. The present invention uses a two-dimension signal sampling theorem to convert the discrete spectrum of the fingerprint images into a continuous spectrum referring to the problems of large deviation of the fingerprint line distance and the real line distance which are acquired by using a discrete fourier spectrum analysis method and the existing statistical method, and the low adaptability of the image. Accurate and continuous line distances are extracted on the base, and the accuracy rate of the entire fingerprint identifying technology is increased.

Description

Automatically image segmentation in the fingerprint identification method and fingerprint lines are apart from extracting method

Technical field:

The invention belongs to the living things feature recognition field, specifically relate to a kind of finger print image segmentation and fingerprint line distance extractive technique.

Background technology:

Automatically fingerprint identification technology is meant the crestal line that utilizes finger finger surface pattern, a kind of biometrics identification technology that the valley line distribution pattern is confirmed the identifying object identity.Fingerprint is as one of human body essential characteristic, and it has the characteristics of uniqueness, unchangeability and arranged distribution regularity.The human fingerprint that uses has had very long history as the means of identification, and the legitimacy of using fingerprint to identify has also obtained approval widely already.Automatically the application of fingerprint identification technology no longer only is confined to the administration of justice, public security field at present, it can be used as the means that computing machine is confirmed the user, can also be as the information security technology of accesses network resource, it can also be used for the affirmation of bank ATM card and credit card in addition, all kinds of intellective IC cards, employee's work attendance, electronic lock etc.

The research of modern fingerprint identification technology is since 16th century.1864, Britain botanist Nehemiah Graw delivered human first piece of paper that fingerprint identification technology is carried out scientific research, had studied the symmetry of fingerprint ridge ridge, paddy and cavernous structure.Hereafter, a lot of people begin to be devoted to the research of fingerprint identification technology.1788, Mayer published thesis and describes the structure of fingerprint ridge in detail, and the architectural feature of streakline is defined.1809, ThomasBewick brought into use the signet of its fingerprint as him, was considered to the milestone of modernized fingerprint identification technology research.1823, Perkinie proposed the first cover fingerprint classification scheme, and the global structure pattern according to streakline roughly is divided into nine classes with fingerprint.1880, Heney Fauld more scientifically studied the uniqueness problem of fingerprint for the first time.Approximately at one time, Herschel declares that he is engaged in the existing nearly 20 years history of research of fingerprint identification technology.The foundation stone of modern fingerprint identification technology has been established in these researchs.In the 19th-century later stage, Francis Galton has carried out comparatively deep research to fingerprint, and he write articles in 1888 detail characteristics of fingerprints is incorporated into the fingerprint recognition field.It is early stage to have arrived twentieth century, and the notion of fingerprint is known by people, progressively concludes and set up three cardinal rules about fingerprint:

1, different people's fingerprint has different ridges, paddy streakline structure, and everyone fingerprint has uniqueness characteristic.

2, fingerprint global structure pattern varies with each individual, but kind is limited, and it is feasible that fingerprint is classified.

3, to everyone, the global structure pattern of fingerprint and minutia are inherent and lifelong constant.

Article first and the 3rd, principle is the fingerprint base of recognition, and the second principle is the basis of fingerprint classification.

According to realization function separately, automatically fingerprint identification technology can be broken down into following four main modular: (1) fingerprint collecting: be exactly through relevant fingerprint collecting equipment typing and carry out digitized process with the fingerprint ridge distributed architecture; (2) fingerprint characteristic information extraction: exactly the fingerprint image that is collected is handled, extracted the characteristic information that to represent the fingerprint uniqueness; (3) fingerprint classification: specify the respective classified standard according to the global structure pattern that fingerprint ridge is objectively had, the fingerprint that will have identical global structure pattern is summed up in the point that in the same classification; (4) fingerprint matching: judge whether homology of two pieces of fingerprints according to the characteristic information of fingerprint, promptly whether come from same individual's same finger.Early stage fingerprint collecting all produces by being pressed on the paper by printing ink, the 1980s, development along with the optical scanning technology, begin to have occurred the optical finger print sampling instrument, along with the progress of semiconductor technology, novel sensors such as fingerprint sensor, heat sensitive sensor, ultrasonic sensor have appearred successively.The fingerprint image quality of different acquisition method collections exists different difference.The poor quality of fingerprint itself but these acquisition modes can't solve, to the influence of automatic fingerprint identification technology, can't realize to because finger is dry, decortication, wear out, the fingerprint adverse effect of caused poor quality such as band.

Automatically fingerprint identification technology develops into and has moved towards practical application now.But up to the present, still exist some technological difficulties effectively to be solved in the fingerprint identification technology automatically, thereby also on certain program, hindered the widespread use of automatic fingerprint identification technology.At present, fingerprint image dividing processing technology and fingerprint line distance extractive technique in the existing Automated Fingerprint Identification System are not strong to the quality adaptability of fingerprint, can't obtain finger print information accurately when noise is serious, and its overview is described below:

(1) fingerprint image dividing processing technology: the fingerprint image dividing processing is meant effective fingerprint image zone separating treatment from the serious zone of background area and noise, so that reduce the time that subsequent algorithm is handled, reduce the influence of ground unrest, thereby reach the purpose that improves whole Automated Fingerprint Identification System performance the subsequent algorithm result.Fingerprint image generally can be divided into prospect and background two parts, and so-called prospect refers to fingerprint image clearly, and background refers to no streakline part and the very fuzzy part of streakline in the pickup area.The fingerprint image that collects always exist the background area inevitably, and the area of background area often will account for 1/3～1/2 of whole pickup area area.The purpose of separating fingerprint image from background is exactly to determine the effective coverage of fingerprint image, handles targetedly, both can save the processing time greatly, can improve the result in later stage again.The dividing method of existing fingerprint image and background area mainly can be summed up as following two big classes: a class is based on the dividing method of piece level, the another kind of dividing method that is based on pixel level.The two mostly is according to the statistical nature of fingerprint image gray scale (as variance, average) algorithm for design, afterwards, people such as Yin Yilong use again based on quadric fingerprint to be cut apart, the gray variance of fingerprint image, average, direction consistance as index, are realized cutting apart of fingerprint region and background area on a quadric surface.In general, the effect of under normal circumstances cutting apart can be satisfied the demand, but disturbs strong fingerprint segmentation effect unsatisfactory for some.For example, for last time gathering the vestige stay, its paler colour, but shape is as good as with normal fingerprint.If cut apart as index with gray variance, be difficult to it is separated, even may be all bigger than the gray variance of real fingerprint region.Therefore, statistical properties such as variance can not embody the characteristic of fingerprint well, can not make full use of the information that fingerprint image brings, and are characterized as index with variance etc. and carry out fingerprint image and cut apart, and can not well adapt to various situations.

(2) fingerprint line distance extractive technique: the ridge distance information of fingerprint image is the distance between two adjacent crestal lines of fingerprint center.Crestal line, valley line are meant dark and light streakline in the fingerprint image respectively, and the definition of crestal line, valley line and ridge distance as shown in Figure 2.In automatic fingerprint identification technology, the ridge distance information in the image that takes the fingerprint exactly is the basis of fingerprint being carried out effective enhancement process, and in most of fingerprint enhancement algorithms, ridge distance or streakline frequency are all used as an important parameter.In addition, the average ridge distance of fingerprint image also can be used for fingerprint comparison and fingerprint classification, and for two pieces of fingerprints that identical resolution is collected down, if their average ridge distance is obviously different, system can judge directly that these two fingerprints are unmatched.The ridge distance extracting method mainly can be summed up as two classes: based on the ridge distance method of estimation of entire image with based on the ridge distance method of estimation (windowhood method) of piece level.O ' Gorman and Nickerson use the key parameter of ridge distance as wave filter in the design of fingerprint filter line device, and what this method was used is the average statistical of ridge distance, supposes that ridge distance is a constant on the view picture fingerprint image.Lin and Dubes ^[6]Attempt to realize that the automatic statistics of streakline number and supposition ridge distance are constants on the view picture fingerprint image.D.C.Douglas Hung estimates the mean distance of streakline on the view picture fingerprint image.Ridge distance method of estimation based on entire image is to suppose that ridge distance is a constant in the view picture fingerprint image scope, ignored in the fingerprint image difference of ridge distance between different piece fully, and because the average ridge distance that uses average statistical as entire image more, when comprising part inferior quality finger-print region in the image, can cause the reliability of ridge distance estimated result to have a strong impact on.People such as L.Hong have proposed a kind of direction window method of estimating the streakline frequency.Under the good situation more consistent with streakline direction ratio in the direction window of picture contrast, this method can be estimated the streakline frequency reliably.But when the streakline direction was not quite identical in the serious or direction window when noise, the performance of this method can be had a strong impact on.People such as Z.M.Kovacs-Vajna have proposed the geometric method that ridge distance is estimated, this method is also estimated ridge distance at block image, also belongs to the category of windowhood method.An advantage of geometric method is that it does not need the result of calculation of streakline direction as the guide.But because there have a lot of threshold values to need in this method to be accurately selected, these threshold values can change because of the difference of picture quality and the influence of other factors again, and this just makes this method more complicated, and the difficulty of realization is also bigger.

Summary of the invention:

The purpose of this invention is to provide a kind of based on the Markov chain Monte-Carlo simulation fingerprint image dividing method of (MarkovChain Monte Carlo is called for short MCMC).This fingerprint image dividing method can well be realized effectively cutting apart fingerprint image, adapt to the requirement of the fingerprint image of different quality being carried out dividing processing well, under the second-rate condition of fingerprint image, also can extract relatively accurate effective fingerprint image zone.

Another object of the present invention provides the method that a kind of fingerprint line distance of analyzing based on continuous spectrum extracts.The line distance getting technique of this method not only can extract the more continuous ridge distance near actual value, can well adapt to simultaneously the fingerprint image of different quality, under the situation of fingerprint image poor quality, also can obtain fingerprint line distance information relatively more accurately.

The solution of the present invention comprises the extracting method of fingerprint image dividing processing and fingerprint line distance:

(1) fingerprint image division processing method.

Elder generation's tectonic boundary curve pdf model, again according to internal characteristics that fingerprint image had, construct outer background area probability density function and interior finger-print region probability density function, the Markov model is incorporated in the fingerprint image cutting techniques, form the Markov chain of boundary curve then, adopt the Monte Carlo simulation method to quicken the Markov chain again and converge to optimum solution, realize quick dividing processing fingerprint image, effective fingerprint image is separated from the background area.Suppose to exist a closed curve can realize well in the fingerprint image to fingerprint image ground dividing processing, effective fingerprint image is separated from the background area.At first, this method produces a potential Markov chain, to two state Γ on the Markov chain _i. Γ _I+1, calculate its transition kernel, again with transition probability P (Γ _I+1| Γ _i) determine whether shift, up to obtaining optimum solution, realize effective dividing processing to fingerprint image.This method is obtained cuts apart curve and has realized that well this method can be cut apart the fingerprint image of different quality effectively to the adaptability height of fingerprint image quality simultaneously, the steps include: to effectively the cutting apart of fingerprint image

1. tectonic boundary curve pdf model:

To a closed curve Γ, the outer annular zone territory of Γ is designated as Pout (Γ) at the outer background probability density function of background area, and same, interior fingerprint probability density function is designated as Pin (Γ).The boundary curve probability density function of Γ is designated as PL (Γ), then has: PL (Γ)=Pin (Γ) Pout (Γ);

2. according to the internal characteristics that fingerprint image had, construct outer background area probability density function and interior finger-print region probability density function:

The gray-scale value of pixel obedience is the normal distribution at center with crestal line center gray scale in A, the crestal line zone, and probability density function is defined as: $p\left(i(x,y)\right|\mathrm{ridge})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_l)}^2}{2{\mathrm{\σ}}^2}}$

The gray-scale value of pixel obedience is the normal distribution at center with valley line center gray scale in B, valley line zone and the background area, and probability density function is defined as: $p\left(i(x,y)\right|\mathrm{valley})=p\left(i(x,y)\right|\mathrm{back})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_h)}^2}{2{\mathrm{\σ}}^2}}$

C, for the closed curve Γ that exactly effective finger-print region is separated from background, its perimeter one fixes on background area, then the definition outer background probability density function be:

$\mathrm{Pout}\left(\mathrm{\Γ}\right)=\underset{m=1}{\overset{k}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_h)}^2}{2{\mathrm{\σ}}^2}}$

And its interior zone one fixes on effective fingerprint region, and the pixel on it both may be on the crestal line zone, also may be on the valley line zone, and the intensity profile of valley line is identical with the background intensity profile, crestal line and valley line alternately occur at finger-print region.Therefore, the fingerprint probability density function is in the definition:

$\mathrm{Pin}\left(\mathrm{\Γ}\right)=(1-|1-\frac{2k}{N}\left|\right)\underset{m=1}{\overset{k}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_l)}^2}{2{\mathrm{\σ}}^2}}$

3. construct the Markov chain of fingerprint boundary curve:

A, on the current state lower boundary curve each the some x _i ^kDo Brownian movement, obtain the point on all boundary curves under the next state $x_{i+1}^k=B\left(x_i^k\right);$

B, be docile and obedient preface and connect x _I+1 ^k, obtain the boundary curve under the next state ${\mathrm{\Γ}}_{i+1}^0=\{x_{i+1}^1,x_{i+1}^2,...,x_{i+1}^k,\·\·\·{,x}_{i+1}^{n_1}\};$

C, curve is put in order, removed the circle of some repetitions, thereby obtain the next state on the Markov chain ${\mathrm{\Γ}}_{i+1}=m\left({\mathrm{\Γ}}_{i+1}^0\right);$

4. adopt the accelerating convergence of Monte Carlo simulation method to optimum solution

A, the following transition kernel of employing Metropolis-Hastings method construct:

$P=\left({\mathrm{\Γ}}_{i+1}\right|{\mathrm{\Γ}}_i)=\min \{1,\frac{\mathrm{PL}\left({\mathrm{\Γ}}_{i+1}\right)}{\mathrm{PL}\left({\mathrm{\Γ}}_i\right)}\}$

To two state Γ on the Markov chain _iΓ _I+1, calculate its transition kernel, again with probability P (Γ _I+1| Γ _i) determine whether shift.

If B refuses transfer number＞50 continuously, think then to converge to optimum solution that boundary curve at this moment is the optimum segmentation curve of being asked.Otherwise, continue to calculate its transition probability, judge whether to shift.

(2) fingerprint line distance extracting method:

In order to solve the ridge distance that existing fingerprint line distance acquiring method obtained is discrete value, bigger with respect to the actual value deviation, and to the not high problem of fingerprint image quality adaptability, the present invention is incorporated into the continuous spectrum analytical technology in the fingerprint line distance extractive technique, propose a kind of fingerprint line distance extracting method of analyzing based on continuous spectrum, asked for fingerprint line distance information.This method is at first expressed fingerprint image and is converted to frequency domain presentation by the spatial domain, adopt two-dimentional sampling thheorem that the discrete Fourier spectrum is converted to continuous fourier spectra then, normal direction along streakline adopts little step-length at the enterprising line search of continuous spectrum again, ask for along centrosymmetric two local maximum points, ask for the fingerprint line distance parameter of corresponding region according to the distance between two local maximum points of being tried to achieve at last.The ridge distance that this method is extracted is that this method is strong to the adaptability of fingerprint image quality simultaneously, antinoise interference capability height more near the continuous ridge distance of actual value.

This fingerprint image dividing method is compared with existing fingerprint image dividing method, and the advantage that has is: 1. more accurate to cutting apart of fingerprint image, can meticulously effective fingerprint image zone be separated from background; 2. the more important thing is that this method has good adaptability to the fingerprint image quality, at the fingerprint image of various different qualities, this technology can both obtain a desirable segmentation result.

This ridge distance extracting method is compared with existing ridge distance extracting method, its advantage is: the ridge distance value of 1. being extracted is changed into successive value by discrete value, reduced the deviation between the result that asks and the actual value; 2. the ridge distance information asked for of this method is more accurate, can describe the actual ridge distance information of fingerprint image more accurately; 3. this method has good adaptability to the fingerprint image quality, and at the fingerprint image of different quality, this technology can both be tried to achieve desirable ridge distance information.

Description of drawings:

Fig. 1 is that the fingerprint recognition system constitutes block scheme:

Fig. 2 is fingerprint image median ridge line, valley line and ridge distance definition;

Fig. 3 is fingerprint and boundary curve synoptic diagram thereof;

Fig. 4 is the signal of fingerprint border;

Fig. 5 is a fingerprint image;

Fig. 6 is fingerprint image grey level histogram (corresponding to Fig. 4);

Fig. 7 is the inner ring synoptic diagram that needs removal;

Fig. 8 is the outer ring synoptic diagram that needs removal;

Fig. 9 is a width of cloth decortication fingerprint image;

Figure 10 is the actual segmentation result to decortication fingerprint image (Fig. 9);

Figure 11 is a width of cloth residual interference fingerprint image;

Figure 12 is the actual segmentation result to residual interference fingerprint image (Figure 11);

Figure 13 is fingerprint region, pattern district, background area and their pairing spectrums, and ((a) (c) and (e) is respectively fingerprint region, pattern district and background area; (b), (d) and (f) be respectively their pairing spectrums);

Figure 14 is that the discrete spectrum three-dimensional picture of effective finger-print region shows;

Figure 15 is that the discrete spectrum three-dimensional picture of background area shows;

Figure 16 is that the continuous spectrum three-dimensional picture of effective finger-print region shows;

Figure 17 is that the continuous spectrum three-dimensional picture of background area shows;

Figure 18 is the sectional view of three-dimensional continuous spectrum on its normal direction of effective finger-print region;

Figure 19 is that the 216_8 number typical inferior quality fingerprint image in FIDB3_B fingerprint image storehouse carries out the result that ridge distance extracts on the BVC2004 public database to being selected from;

Figure 20 is that the 216_8 number typical inferior quality fingerprint image in FIDB4_B fingerprint image storehouse carries out the result that ridge distance extracts on the BVC2004 public database to being selected from.

Numbering 216 is finger codes, uniquely determines one piece of fingerprint, the 8th, and the repeated acquisition number of times, indicating is that 216 trumpeters are referred to gather resulting fingerprint image the 8th time.

Embodiment:

[embodiment 1] fingerprint image dividing method:

At first, this dividing method tectonic boundary curve pdf model, then construct outer background area probability density function and interior finger-print region probability density function according to the internal characteristics that fingerprint image had, form the Markov chain of boundary curve then, adopt Markov chain Monte-Carlo simulation (MCMC) method to realize dynamic similation at last, ask for optimum boundary curve, thereby realize effectively cutting apart fingerprint image.This fingerprint image cutting techniques can be described as:

1. tectonic boundary curve pdf model:

For a width of cloth fingerprint image, necessarily exist a closed curve successfully fingerprint region and background area to be separated, claim that this curve is a boundary curve.As shown in Figure 3, the realization of curve B success to the separating of fingerprint region and background area, reduced interference residual and decortication simultaneously, and curve A, C, D all can not be accomplished this point simultaneously.Curve B just can be thought the boundary curve of this width of cloth fingerprint.According to the grey scale pixel value of fingerprint image, calculating a closed curve is the possibility of this fingerprint image boundary curve or the size of probability, and then the closed curve of probability maximum is exactly the desired boundary curve that obtains.Boundary curve B as shown in Figure 3, such boundary curve probability density function satisfies:

(1) functional value on the curve on the background area (curve A) is less than boundary curve (curve B).

(2) functional value on the curve (curve C) on the inside, fingerprint region is less than boundary curve (curve B).

(3) pass through functional value on the curve (curve D) of fingerprint region and background area less than boundary curve (curve B).

To every closed curve on the fingerprint image, along curve respectively inwardly, extend outward annular section (as shown in Figure 4).

(1) Shape curve perimeter is just at background area.

(2) Shape curve perimeter is just in the fingerprint region.

To a closed curve Γ, the outer annular zone territory of Γ is designated as Pout (Γ) at the outer background probability density function of background area, and same, interior fingerprint probability density function is designated as Pin (Γ).The boundary curve probability density function of Γ is designated as PL (Γ), has so: PL (Γ)=Pin (Γ) Pout (Γ)

2. construct outer background area probability density function and interior finger-print region probability density function according to the internal characteristics that fingerprint image had.

Have crestal line zone, valley line zone and background area in the fingerprint image.Comparatively speaking, the gray-scale value of the pixel on the crestal line zone differs very little, and the gray-scale value of the pixel on valley line zone and the background area differs very little.Be reflected on the grey level histogram, gray-scale value will be concentrated at two places and form two peaks (shown in Fig. 5,6, wherein Fig. 6 is the grey level histogram of Fig. 5 fingerprint).Two peak corresponding gray are referred to as crestal line center gray scale and valley line center gray scale respectively.So, can think in the crestal line zone that it is the normal distribution at center that the ash value of pixel is obeyed with crestal line center gray scale, that is:

$p\left(i(x,y)\right|\mathrm{ridge})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_l)}^2}{2{\mathrm{\σ}}^2}}$

Wherein, g _mBe pixel i (x, gray-scale value y), μ _lBe the valley line center gray scale of fingerprint image, σ is a variance.Equally, the gray-scale value obedience of pixel is the normal distribution at center with valley line center gray scale in valley line zone and the background area, promptly has

$p\left(i(x,y)\right|\mathrm{valley})=p\left(i(x,y)\right|\mathrm{back})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_h)}^2}{2{\mathrm{\σ}}^2}}$

Wherein, g _mBe pixel i (x, gray-scale value y), μ _hBe the crestal line center gray scale of fingerprint image, σ is a variance.

For closed curve Γ, if the perimeter at background area, promptly each pixel is all at background area on the perimeter, and all to obey with valley line center gray scale be the normal distribution at center, the perimeter at the outer background probability density function of background area is just so:

$\mathrm{Pout}\left(\mathrm{\Γ}\right)=\underset{m=1}{\overset{k}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_h)}^2}{2{\mathrm{\σ}}^2}}$

Wherein, k is the sum of perimeter pixel, g _mBe the gray-scale value of pixel, μ _hIt is valley line center gray scale.

Yet for the fingerprint region, the pixel on it both may be on the crestal line zone, also may be on the valley line zone, and the intensity profile of valley line is identical with the background intensity profile.Therefore, judge that the index of curve Γ interior zone in the fingerprint region should be the pixel that belongs to the crestal line zone.On a fingerprint region, crestal line and valley line always alternately occur, and can think that the crestal line sum of all pixels roughly also equates with valley line pixel portions number.In other words, the sum of crestal line pixel should probably equal the fingerprint region pixel sum 1/2, too big or too little all not all right.Therefore, interior fingerprint probability density function is:

$\mathrm{Pin}\left(\mathrm{\Γ}\right)=(1-|1-\frac{2k}{N}\left|\right)\underset{m=1}{\overset{k}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(g_m-{\mathrm{\μ}}_l)}^2}{2{\mathrm{\σ}}^2}}$

Wherein, N is the sum of interior zone pixel, and k is the pixel number that belongs to the crestal line zone, g _mBe the gray-scale value of pixel on the crestal line, μ _lIt is crestal line center gray scale.The coefficient of front has guaranteed that the sum of crestal line pixel equals 1/2 o'clock functional value maximum of the sum of fingerprint region pixel, and this also is the feature of fingerprint image, and black or complete entirely white zone all can not be effective finger-print region.

To arbitrary closed curve Γ in the fingerprint image, just can calculate its outer background probability density function Pout (Γ) and interior fingerprint probability density function Pin (Γ), thus computation bound curve probability density function PL (Γ).

PL(Γ)＝Pin(Γ)Pout(Γ)

In fingerprint image, the maximum closed curve of boundary curve probability density function PL (Γ) is exactly separating of fingerprint segmentation effect optimum.Therefore, only need find the closed curve that satisfies boundary curve probability density function PL (Γ) maximum to get final product.A natural idea is, obtains all closed curves, finds out the wherein maximum closed curve of the general density function PL of boundary curve (Γ).But for a width of cloth fingerprint image, it is not in the cards finding out all closed curves.Therefore, need approximate method to realize.Markov chain Monte-Carlo analogy method (Markov Chain Monte Carlo is called for short MCMC) can well address this problem.The MCMC method generally needs in two steps: 1, according to actual needs, and the structure Markov chain.2,, prolong the approximate solution that obtains realistic problem with Monte Carlo simulation according to Markov chain.

3. construct the Markov chain of fingerprint boundary curve:

Suppose the boundary curve sequence number { Γ of fingerprint image ₁, Γ ₂... Γ _nBe a Markov chain that produces at random, know P (Γ by Markov chain character _I+1| Γ _i)=P (Γ _I+1| Γ ₁, Γ ₂... Γ _n), that is to say that next is boundary curve Γ constantly _I+1State only depend on current boundary curve Γ _iState, and do not rely on historic state { Γ ₁, Γ ₂... Γ _I+1.Wherein P (|) is called transition kernel, and it does not rely on time t.Simultaneously, arrive optimum border surely for guaranteeing Markov chain one, the Markov chain of structure also needs to satisfy ergodicity, aperiodicity.Under general rule, Markov chain will be ignored its original state gradually, and finally converge on unique stationary distribution.For fingerprint image, no matter initial border Γ ₀How are position, shape, the most necessarily can converge to a good border of segmentation effect.Present problem is how to produce markovian next state from current state, promptly how from boundary curve Γ ₁Obtain Γ _I+1Brownian movement is a kind of modal stochastic process, to boundary curve Γ ₁Be the Γ that Brownian movement obtains _I+1Satisfy markovian character discussed above, also satisfy ergodicity, aperiodicity.Therefore one converge to optimum solution surely, i.e. the fingerprint boundary curve.If Γ _iBy an x _i ^kForm, ${\mathrm{\&Gamma;}}_i=\{x_i^1,{\mathrm{<figure-callout\; id="2"\; label="x\; i"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">x</figure-callout>}}_i^{},...,x_i^k,...,x_i^{n_i}\}.$

(1) to each some x _i ^kDo Brownian movement. $x_{i+1}^k=B\left(x_i^k\right)$

(2) be docile and obedient preface and connect x _I+1 ^k ${\mathrm{\&Gamma;}}_{i+1}^0=\{x_{i+1}^1,x_{i+1}^2,...,x_{i+1}^k,...,x_{i+1}^{n_l}\}$

(3) put curve in order, remove the circle of some repetitions.Shown in Fig. 7,8. ${\mathrm{\&Gamma;}}_{i+1}=m\left({\mathrm{\&Gamma;}}_{i+1}^0\right)$

4. Monte Carlo simulation:

The Markov chain Monte-Carlo method is a kind of special monte carlo method, and it is incorporated into the Markov process in the stochastic process in the Monte Carlo simulation, realizes dynamic similation.The central issue of MCMC is the problem of choosing of transition kernel.The Metropolis-Hastings method that adopts has mostly also all obtained good effect in the practice at present.

In fingerprint image, the obvious closed curve that boundary curve probability density function PL (Γ) is big more " approaching " optimum solution more.Therefore, the following transition kernel of structure:

$P\left({\mathrm{\&Gamma;}}_{i+1}\right|{\mathrm{\&Gamma;}}_i)=\min \{1,\frac{\mathrm{PL}\left({\mathrm{\&Gamma;}}_{i+1}\right)}{\mathrm{PL}\left({\mathrm{\&Gamma;}}_i\right)}\}$

To two state Γ on the Markov chain _i, Γ _I+1Calculate its transition kernel, again with notion rate P (Γ _I+1| Γ _i) determine whether shift.So far, can be summarised as following a few step to the MCMC method:

(1) produces a potential Markov chain.

(2) suppose that current state is Γ _i, according to (1) step generation Γ _I+1Calculate transition kernel P (Γ _I+1| Γ _i).

(3) go up equally distributed stochastic variable u of generation in [0,1].

(4) if P is (Γ _I+1| Γ _i) 〉=u, Markov chain enter next time Γ _I+1, repeating step 2.

(5) if P is (Γ _I+1| Γ _i)＜u, the Markov chain refusal shifts, i.e. Γ _I+1=Γ _i, repeating step 2.

(6) refusal transfer number＞50, program stops.

By the MCMC theory, the Markov chain one of Chan Shenging arrives optimum solution surely like this.Boundary curve Γ _iOne converges to the maximum closed curve of boundary curve probability density function PL (Γ), the i.e. best border of segmentation effect surely.Figure 10,12 is respectively the actual segmentation result to decortication fingerprint (Fig. 9), residual interference fingerprint (Figure 11).

[embodiment 2] fingerprint line distance extracting method

At first, this method is the fingerprint image piecemeal, specifically be with a pending fingerprint image be divided into non-overlapping copies, size is the piece of NXN, generally gets N=32; Then to every image g (i, j) carry out fast two-dimensional fourier transformation obtain corresponding discrete spectrum G (u, v); Then to every discrete spectrum G (u, v), by sampling thheorem obtain continuous frequency spectrum function G (x, y); Next adopt Rao method [9], ask for streakline direction θ, and be θ+pi/2 in direction, radius is on N/12-N/14, and (x y) searches for, and obtains local extremum radius corresponding r to the continuous spectrum function G to adopt the long step of small step; Estimate that at last this piece fingerprint image ridge distance is d=N/r.

This line distance getting technique specifically describes and is:

1. fingerprint image being handled piecemeal handles: fingerprint one width of cloth fingerprint image is divided into non-overlapping copies here, size is the piece of N * N, generally gets N=32.

2. to every image g (i, j) carry out two-dimentional fast Flourier spectral transformation obtain discrete spectrum G (u, v), transformation for mula is as follows:

$G(u.v)=\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}g(i,j){\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">e</figure-callout>}}^{2\mathrm{\&pi;}{j}^{\text{'}}N<(i.j)(u.v)>}$

From the part, fingerprint image is a kind of regular veins image, it is done Fourier transform after, pairing fourier spectra has reflected the frequency and the directional information of streakline.Distance between bright spot is directly proportional with the streakline frequency, is inversely proportional to ridge distance; The line direction of bright spot is vertical with the streakline direction, should embody this feature with the parallel leaf of streakline normal direction.

3. to every discrete spectrum G (i, j), by sampling thheorem obtain continuous frequency spectrum function G (x, y):

Discrete Fourier spectrum to fingerprint image adopts the 2D signal sampling thheorem, and discrete spectrum is converted into continuous spectrum.Sampling thheorem is played a great role in signal Processing, and is suitable equally for the picture signal of two dimension.Here, the sampling thheorem of 2D signal can be described below:

L ²(R ₂) on function f (x ₁, x ₂) Fourier transform F (s ₁, s ₂) be tight propping up, promptly F is zero outside the D of bounded domain, D can be expressed as rectangle ((s ₁, s ₂), | s ₁|≤Ω, | s ₂|≤Ω }.During easy, suppose Ω=π earlier.F (x1, fourier series x2) can be expressed as:

$F(S_1,S_2)=\underset{n_1}{\mathrm{\&Sigma;}}\underset{n_2}{\mathrm{\&Sigma;}}{C}_{n_1\&CenterDot;n_2}{e}^{-{\mathrm{jn}}_1{s}_1-{\mathrm{jn}}_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}$

Wherein $C_{n_1,{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^2}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{\mathrm{ds}}_1{\mathrm{ds}}_2{e}^{{\mathrm{jn}}_1{s}_1+{\mathrm{jn}}_2{s}_2}F(s_1,s_2)=\frac{1}{2\mathrm{\&pi;}}f(n_1,n_2)$

Draw immediately

$f(x_1,x_2)=\frac{1}{2\mathrm{\&pi;}}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{\mathrm{ds}}_1{\mathrm{ds}}_2{e}^{{\mathrm{jx}}_1{s}_1+{\mathrm{jx}}_2{s}_2}F(s_1,s_2)$

$=\frac{1}{2\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{\mathrm{ds}}_1{\mathrm{ds}}_2{e}^{{\mathrm{jx}}_1{s}_1+{\mathrm{jx}}_1{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}\underset{n_1}{\mathrm{\&Sigma;}}\underset{n_2}{\mathrm{\&Sigma;}}{C}_{n_1,n_2}{e}^{-{\mathrm{jn}}_1{s}_1-{\mathrm{jn}}_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}$

$=\frac{1}{2\mathrm{\&pi;}}\underset{n_1}{\mathrm{\&Sigma;}}\underset{n_2}{\mathrm{\&Sigma;}}{C}_{n_1,{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{\mathrm{ds}}_1{\mathrm{ds}}_2{e}^{{\mathrm{jx}}_1{s}_1+{\mathrm{jx}}_2{s}_2}{e}^{-{\mathrm{jn}}_1{s}_1-{\mathrm{jn}}_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}$

$=\frac{1}{2\mathrm{\&pi;}}\underset{n_1}{\mathrm{\&Sigma;}}\underset{n_2}{\mathrm{\&Sigma;}}{C}_{n_1,{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{\mathrm{ds}}_1{e}^{j(x_1-n_1)s_1}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{\mathrm{ds}}_2{e}^{j(x_2-n_2){\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}$

$=\underset{n_1}{\mathrm{\&Sigma;}}\underset{n_2}{\mathrm{\&Sigma;}}{C}_{n_1,{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C20051009072300231.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}\frac{\sin \mathrm{\&pi;}(x_1-n_1)}{\mathrm{\&pi;}(x_1-n_1)}\frac{\sin \mathrm{\&pi;}(x_2-n_2)}{\mathrm{\&pi;}(x_2-n_2)}$

Like this, discrete signal C _{N1, n2}Just can revert to continuous signal f (x by sampling thheorem ₁, x ₂).Any fingerprint image, the discrete frequency spectrum with fast fourier transform obtains can revert to continuous spectrum.Figure 16,17 is respectively that discrete spectrum among Figure 14,15 is adopted step-length is 0.1 to recover the continuous spectrum that obtains.

4. adopt rao method [9], ask for streakline direction θ, and adopt the long step of small step to ask for Local Extremum:

Analysis to continuous spectrum is found, " bright spot " that we are concerned about, and just Local Extremum always appears at certain zone.Direction must be on the direction of streakline normal, and radius also has relative scope.Can obtain by the ridge distance formula: r=N/d, ridge distance is probably between 4-12 pixel as can be known by experience, and the radius that extreme point occurs is at N/12-N/4.Therefore, at first adopt improved Rao method by propositions such as L.Hong, calculate the directional information θ of every fingerprint image, be θ+pi/2 in direction then, radius adopts the long step of small step to continuous spectrum function G (x on N/12-N/4, y) search for, ask for accurate Local Extremum, and obtain local pole and plant radius corresponding r, wherein step-size in search step generally is taken as 0.01.

5. estimate this piece fingerprint image ridge distance d=N/r, then the d that is tried to achieve is the ridge distance of the corresponding region that we ask.Figure 18 has described the sectional view of continuous spectrum on its normal direction in a fingerprint image zone, is 4.71 corresponding to the radius of extreme point, and then the ridge distance of being asked is d=N/4.71=32/4.71=6.79.Figure 19, the 20th asks for the ridge distance result to two width of cloth typical images, and the numeral on the figure is the ridge distance value of corresponding region.

Claims (4)

1, image segmentation and the fingerprint line distance extracting method in a kind of automatic fingerprint identification method, it is characterized in that fingerprint image dividing method is first tectonic boundary curve pdf model, again according to internal characteristics that fingerprint image had, construct outer background area probability density function and interior finger-print region probability density function, form the Markov chain of boundary curve then, adopt the Monte Carlo simulation method to quicken the Markov chain again and converge to optimum solution, realization is to the quick dividing processing of fingerprint image, effective fingerprint image is separated from the background area, the steps include:

1. tectonic boundary curve pdf model:

To a closed curve Γ, the outer annular zone territory of Γ is designated as Pout (Γ) at the outer background probability density function of background area, equally, interior fingerprint probability density function is designated as Pin (Γ), the boundary curve probability density function of Γ is designated as PL (Γ), then has: PL (Γ)=Pin (Γ) Pout (Γ);

2. according to the internal characteristics that fingerprint image had, construct outer background area probability density function and interior finger-print region probability density function:

The gray-scale value of pixel obedience is the normal distribution at center with crestal line center gray scale in A, the crestal line zone, and probability density function is defined as: $P\left(i(x,y)\right|\mathrm{ridge})=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{-\frac{{(g_m-{\mathrm{\&mu;}}_l)}^2}{2{\mathrm{\&sigma;}}^2}}$

The gray-scale value of pixel obedience is the normal distribution at center with valley line center gray scale in B, valley line zone and the background area, and probability density function is defined as:

$P\left(i(x,y)\right|\mathrm{valley})=P\left(i(x,y)\right|\mathrm{back})=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{-\frac{{(g_m-{\mathrm{\&mu;}}_k)}^2}{2{\mathrm{\&sigma;}}^2}}$

C, for the closed curve Γ that exactly effective finger-print region is separated from background, its perimeter one fixes on background area, then the definition outer background probability density function be:

$\mathrm{Pout}\left(\mathrm{\&Gamma;}\right)=\underset{m=1}{\overset{k}{\mathrm{\&Pi;}}}\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{-\frac{{(g_m-{\mathrm{\&mu;}}_k)}^2}{2{\mathrm{\&sigma;}}^2}}$

And its interior zone one fixes on effective fingerprint region, and the pixel in effective fingerprint region both may be on the crestal line zone, also may be on the valley line zone, and the intensity profile of valley line is identical with the background intensity profile, crestal line and valley line alternately occur at finger-print region, therefore, the fingerprint probability density function is in the definition:

$\mathrm{Pin}\left(\mathrm{\&Gamma;}\right)=(1-|1-\frac{2k}{N}\left|\right)\underset{m=1}{\overset{k}{\mathrm{\&Pi;}}}\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{-\frac{{(g_m-{\mathrm{\&mu;}}_l)}^2}{2{\mathrm{\&sigma;}}^2}}$

3. construct the Markov chain of fingerprint boundary curve:

A, on the current state lower boundary curve each the some x _i ^kDo Brownian movement, obtain the point on all boundary curves under the next state $x_{i+1}^k=B\left(x_i^k\right);$

B, be docile and obedient preface and connect x _I+1 ^k, obtain the boundary curve under the next state ${\mathrm{\&Gamma;}}_{i+1}^0=\{x_{i+1}^1,x_{i+1}^2,...,x_{i+1}^k,\&CenterDot;\&CenterDot;\&CenterDot;,x_{i+1}^{n_1}\};$

C, curve is put in order, removed the circle of some repetitions, thereby obtain the next state on the Markov chain ${\mathrm{\&Gamma;}}_{i+1}=m\left({\mathrm{\&Gamma;}}_{i+1}^0\right);$

4. adopt the accelerating convergence of Monte Carlo simulation method to arrive optimum solution:

A, the following transition kernel of employing Metropolis-Hastings method construct:

$P\left({\mathrm{\&Gamma;}}_{i+1}\right|{\mathrm{\&Gamma;}}_i)=\min \{1,\frac{\mathrm{PL}\left({\mathrm{\&Gamma;}}_{i+1}\right)}{\mathrm{PL}\left({\mathrm{\&Gamma;}}_i\right)}\}$

To two state Γ on the Markov chain _i, Γ _I+1, calculate its transition kernel, again with probability P (Γ _I+1| Γ _i) determine whether shift;

If B refuses transfer number＞50 continuously, then to think to converge to optimum solution, boundary curve at this moment is the optimum segmentation curve of being asked, otherwise, continue to calculate its transition probability, judge whether to shift;

The fingerprint lines is that the continuous spectrum analytical technology is incorporated in the fingerprint line distance extractive technique apart from extracting method, at first fingerprint image is expressed by the spatial domain and be converted to frequency domain presentation, adopt two-dimentional sampling thheorem that the discrete Fourier spectrum is converted to continuous fourier spectra then, normal direction according to streakline adopts little step-length at the enterprising line search of continuous spectrum again, ask for along centrosymmetric two local maximum points, ask for the fingerprint line distance parameter of corresponding region according to the distance between two local maximum points of being tried to achieve at last.

2, image segmentation and the fingerprint line distance extracting method in the automatic fingerprint identification method according to claim 1 is characterized in that: fingerprint image is divided into non-overlapping copies, and size is the piece of N * N, gets N=32.

3, image segmentation and the fingerprint line distance extracting method in the automatic fingerprint identification method according to claim 1, it is characterized in that to every image g (i.j) carry out two-dimentional fast Flourier spectral transformation obtain discrete spectrum G (u, v).

4, according to image segmentation and fingerprint line distance extracting method in claim 1 or the 3 described automatic fingerprint identification methods, it is characterized in that: the discrete Fourier spectrum to fingerprint image, adopt the 2D signal sampling thheorem, discrete spectrum is converted into continuous spectrum.

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