CN107273877A - The multiple dimensioned complex-aperture Fingerprint diretion method for building up and classification smoothing algorithm of weighting - Google Patents
The multiple dimensioned complex-aperture Fingerprint diretion method for building up and classification smoothing algorithm of weighting Download PDFInfo
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- CN107273877A CN107273877A CN201710605425.9A CN201710605425A CN107273877A CN 107273877 A CN107273877 A CN 107273877A CN 201710605425 A CN201710605425 A CN 201710605425A CN 107273877 A CN107273877 A CN 107273877A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06V40/00—Recognition of biometric, human-related or animal-related patterns in image or video data
- G06V40/10—Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
- G06V40/12—Fingerprints or palmprints
- G06V40/1347—Preprocessing; Feature extraction
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06V10/00—Arrangements for image or video recognition or understanding
- G06V10/20—Image preprocessing
- G06V10/34—Smoothing or thinning of the pattern; Morphological operations; Skeletonisation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06V10/00—Arrangements for image or video recognition or understanding
- G06V10/40—Extraction of image or video features
- G06V10/44—Local feature extraction by analysis of parts of the pattern, e.g. by detecting edges, contours, loops, corners, strokes or intersections; Connectivity analysis, e.g. of connected components
- G06V10/443—Local feature extraction by analysis of parts of the pattern, e.g. by detecting edges, contours, loops, corners, strokes or intersections; Connectivity analysis, e.g. of connected components by matching or filtering
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Abstract
The invention discloses a kind of multiple dimensioned complex-aperture Fingerprint diretion method for building up of weighting and classification smoothing algorithm.The present invention is by initially setting up a series of Fingerprint diretion OF information under different scale complex-apertures；Then weight of each yardstick in entire series is determined by squared gradient coincident indicator；The OF information integrations under entire series are obtained into a Fingerprint diretion OF finally by weight；The Fingerprint diretion OF of low quality fingerprint image, and the preferably direction in fitting singular point region have effectively been rebuild, the direction of noise region can have accurately been estimated and avoid the skew of singular point position.In addition, the present invention ensure that real singular point position is not offset while handling Fingerprint diretion progress the crestal line structure for having repaired mistake using classification smoothing algorithm.
Description
Technical field
The invention belongs to digital image processing technical field, and in particular to the multiple dimensioned complex-aperture fingerprint side of weighting a kind of
To field method for building up.
Background technology
Fingerprint diretion (Orientation field, OF) shows fingerprint ridge line overall structure information, from macroscopically retouching
The basic configuration, architectural feature and crestal line information of fingerprint are stated.Accurately and reliably OF is handled many follow-up fingerprint images, such as
Fingerprint enhancement, inflection point detection and fingerprint image classification etc., there is important influence.
Gradient method, which calculates fingerprint OF, has the advantages that computation complexity is low and directly perceived, therefore is the fingerprint being most widely used
The field of direction asks for one of algorithm, but also easily by noise jamming.To improve the OF computational accuracies of existing gradient method, need to solve with
Lower Railway Project：
(1) how the size of adaptively selected localized massGradient method was proposed in 1987 earliest, this method block ladder
Vector is spent to calculate OF.Follow-up study person to this method improve obtaining more accurate OF, but these methods are difficult
Balance accuracy and robustness problem.Because the OF that fritter is calculated is more accurate but to noise-sensitive, the OF that bulk is calculated resists
Making an uproar property is strong but accuracy lowers.Therefore, researcher proposes the gradient method of complex-aperture, test result indicates that complex-aperture compared to
Single window, can be better balanced accuracy and robustness problem, but complex-aperture is the problem of but introduce a complexity：How to select
Select the size of interior window and exterior windowExisting method relies on many experiments rule of thumb to select appropriate interior window and exterior window size.
The size of complex-aperture can not be adaptive selected.
(2) how the crestal line information near Exact Reconstruction low quality fingerprint image singular point is without causing singular point position inclined
MoveExisting gradient method is poor for the noise immunity of low quality fingerprint image, in order to rebuild the OF information of low quality fingerprint image,
Researcher proposes many improved gradient method, such as stepwise gradient method, weighted mean method, complex-aperture gradient method, but because
Crestal line curvature near singular point is higher, and these methods can be obtained when low quality fingerprint image OF is reconstructed near singular point
The crestal line structure of mistake causes singular point position to offset.The singular point of skew is used as the characteristic point that subsequent fingerprint is matched or recognized
When, the larger error even mistake of matching and recognition result will be caused.
The content of the invention
For the crestal line information for effectively rebuilding low quality fingerprint image and real singular point position, of the invention first
Purpose, which is that offer is a kind of, can effectively rebuild the Fingerprint diretion OF of low quality fingerprint image, and can accurately estimate noise region
Direction and avoid singular point position skew weighting multiple dimensioned complex-aperture Fingerprint diretion method for building up.
Second object of the present invention is that offer is a kind of and ensures real while can repairing wrong crestal line structure
The Fingerprint diretion classification smoothing algorithm that singular point position is not offset.
In order to realize first purpose of the present invention, built in the multiple dimensioned complex-aperture Fingerprint diretion of this weighting provided
Cube method specifically includes following steps：
S1：A series of Fingerprint diretion set up under different scale complex-apertures；
S2：Weight of each yardstick in entire series is determined by squared gradient uniformity；
S3：Fingerprint diretion information integration under entire series is obtained by a Fingerprint diretion by weight.
Further, a series of direction of fingerprint that the use gradient method in the step S1 is set up under different scale complex-apertures
, specific step is as follows：
A：Ask for the gradient vector [G of entire imagex,Gy]T；
B：Gradient vector is converted into squared gradient vector [Gsx,Gsy]T；
C：Fingerprint image is divided into w × w of non-overlapping copies fritter；
D：Ask for the average vector [G of squared gradient vector in frittermx,Gmy]T；
E：Ask for the angle ψ of average gradient vector；
F：Ask for every piece of fingerprint Block direction θ.
Further, gradient [G is solved in step Ax,Gy]TShi Caiyong dimensional Gaussian local derviations counting method is solved.Using two dimension
Gauss local derviation counting method reduces the noise in Fingerprint diretion, makes result more accurate.
Specifically, the expression formula of the thick Fingerprint diretion described in the step S3 is as follows：
Wherein A and B with following formula (2) and formula (3) respectively by being obtained：
Wherein：Coh (p, q, l) is the squared gradient uniformity that exterior window size is p × p, and θ (p, q, l) is by exterior window size
The field of direction set up by p × p, l=1,2 ..., L represents yardstick；
Coh (p, q, l) can then be obtained by formula (4)：
In formula：P is the length of side of outer window, and q is the length of side of interior window, p=q+l × k；L=1,2 ..., L represents yardstick, k
For different scale coefficient, 3~7 are taken.
In order to realize second object of the present invention, smoothing algorithm, the algorithm are classified in this Fingerprint diretion provided
Comprise the following steps：
S1：Fingerprint diretion is quantified as both direction pattern, isolated direction mode is eliminated, obtains filter mask Mask1；
S2：Different filtering strategies are taken the field of direction to be filtered according to Mask1；
S3：Export one-level filter result；
S4：The step S3 filter results exported are quantified as three direction modes, isolated direction mode is eliminated, is filtered
Mask Mask2；
S5：Different filtering strategies are taken the field of direction to be filtered according to Mask2；
S6：Secondary filter result is exported, Fingerprint diretion is obtained.
The beneficial effects of the invention are as follows：By initially setting up a series of letters of the Fingerprint diretion OF under different scale complex-apertures
Breath；Then weight of each yardstick in entire series is determined by squared gradient coincident indicator；Will be whole finally by weight
OF information integrations under individual series obtain a Fingerprint diretion OF；The direction of fingerprint of low quality fingerprint image is effectively rebuild
Field OF, and the preferably direction in fitting singular point region, can accurately estimate the direction of noise region and avoid singular point position
The skew put.
In addition, convolution (1)~formula (3), Fingerprint diretion method for building up provided by the present invention is also achieved adaptively
Method select the field of direction weight of each window and integrate to obtain the final field of direction, it is to avoid the master of experimental method selection
The property seen and the big deficiency of workload.
In addition, Fingerprint diretion OF is quantified as two kinds of direction modes by classification smoothing algorithm provided by the present invention first,
Eliminate isolated direction mode to obtain filtering mask, covered according to filtering and both direction Pattern Filter is carried out to Fingerprint diretion OF；
Then, obtained Fingerprint diretion OF is quantified as three different directions patterns, eliminates isolated block and obtain mask, then basis is covered
Film carries out three direction modes to Fingerprint diretion OF and filtered, and finally obtains accurate and smooth Fingerprint diretion OF, this method
It ensure that real singular point position is not offset while the crestal line structure for having repaired mistake.
Brief description of the drawings
Fig. 1 is the flow chart of the multiple dimensioned complex-aperture Fingerprint diretion method for building up of weighting provided by the present invention；
Fig. 2 is the flow chart that Fingerprint diretion provided by the present invention is classified smoothing algorithm；
Fig. 3 is the experimental result comparison diagram one of the invention with existing Fingerprint diretion method for building up；
Fig. 4 is the experimental result comparison diagram two of the invention with existing Fingerprint diretion method for building up；
Fig. 5 is the experimental result comparison diagram three of the invention with existing Fingerprint diretion method for building up；
Fig. 6 is the experimental result comparison diagram four of the invention with existing Fingerprint diretion method for building up.
Embodiment
In order to which technical scheme is better described, it is further described in conjunction with the embodiments with accompanying drawing herein.
Provided herein is a kind of multiple dimensioned complex-aperture Fingerprint diretion method for building up of weighting, and this method can have
The Fingerprint diretion OF for rebuilding low quality fingerprint image is imitated, and the crestal line structure of dislocation can be repaired and ensure that the singular point for being really
Position is not offset；In addition, method provided by the present invention also selects the interior window and exterior window of complex-aperture by adaptive approach
Size, the problem of effectively prevent the subjectivity and big workload of experimental method selection.The flow chart of this method is as shown in figure 1, tool
Body comprises the following steps：
S1：A series of Fingerprint diretion set up under different scale complex-apertures；Setting up the Fingerprint diretion can be using existing
Any method having is set up, and the specific method that the application is used herein is：Set up using gradient method, in fingerprint side
Setting up process to field needs to carry out following handle：
A, the gradient vector [G for asking for using relationship below view picture fingerprint imagex,Gy]T；
Wherein：G (x, y, δ) represents the two-dimensional Gaussian function that yardstick is δ,WithX directions and y directions are represented respectively
Partial derivative.Herein in order to reduce interference of the noise to result of calculation, therefore two-dimensional Gaussian function is used to carry out view picture fingerprint image
Processing；
B, gradient vector by relationship below is converted into squared gradient vector [Gsx,Gsy]T；
C, the view picture fingerprint image extracted divided；It is the mutual of w × w that it can be divided into, which to be divided into exterior window size,
Nonoverlapping fingerprint-block；
D, the squared gradient vector asked for using relationship below in every piece of fingerprint-block average vector [Gmx,Gmy]T；
E：The angle ψ of average gradient vector is asked for by following relation；
F：Every piece of fingerprint Block direction θ is asked for by following relation；
S2：Weight of each yardstick in entire series is determined by squared gradient uniformity；Squared gradient uniformity with
Relation between weight is：Squared gradient uniformity is directly proportional to weight, and squared gradient uniformity is big, then weight is big；Otherwise also
So；
S3：Fingerprint diretion information integration under entire series is obtained by a Fingerprint diretion by weight；This place
The thick Fingerprint diretion obtained can be expressed by any expression formula, the thick Fingerprint diretion that the application is set up
Expression formula is：
Wherein A and B with following formula (2) and formula (3) respectively by being obtained：
Wherein：Coh (p, q, l) is the squared gradient uniformity that exterior window size is p × p, and θ (p, q, l) is by exterior window size
The field of direction set up by p × p, l=1,2 ..., L represents yardstick；
Coh (p, q, l) can then be obtained by formula (4)：
In formula：P is the length of side of outer window, and q is the length of side of interior window, p=q+l × k；L=1,2 ..., L represents yardstick, k
For different scale coefficient, for a series of various sizes of exterior window directional informations, when the squared gradient corresponding to it always
When information coh (p, q, l) is larger, illustrate that the direction set up under this yardstick is more reliable, it is corresponding it in entire series yardstick
In shared ratio it is higher than the yardstick at squared gradient sexual intercourse bottom always.
In addition, in formula (2) and formula (3)Then determine weight, i.e., the squared gradient of every piece fingerprint-block
The squared gradient uniformity of uniformity divided by all fingerprint-blocks it is cumulative.
And in order to the effective crestal line structure for repairing mistake and ensure that real singular point position is not offset, the application
Subsequent treatment is carried out to the Fingerprint diretion set up by the above method, the processing mode used is classified for Fingerprint diretion
Smoothing algorithm, the flow chart of the algorithm is as shown in Figure 2；Specifically process step is：
S1：Both direction pattern is quantified as to the Fingerprint diretion set up in above-mentioned Fingerprint diretion method for building up, disappeared
Except isolated direction mode, filter mask Mask1 is obtained；Both direction pattern in the step in thick Fingerprint diretion can be appointed
Meaning, the both direction pattern that the application is used herein is respectively ω1 1And ω2 1, wherein ω1 1Represent that angle is less than 90 ° of direction
Pattern, and ω2 1Then represent that angle is more than or equal to 90 ° of direction mode；
S2：Different filtering strategies are taken the field of direction to be filtered according to Mask1；The filtering strategies can use any
One kind, the application is as follows in the filtering strategies that this is used：
InvestigateDirection mode in neighborhoodWithNumberWithIfForWith
Both maximums；So halve the variance δ of the gauss low frequency filter in direction mode filtering1Obtained by following formula：
Wherein δ1=empty represents not take any filtering process；In the decile direction mode filtering of the present invention, n's
It is worth for n=1,2,3；NeighborhoodIt is taken as respectivelyWith
Wherein int () represents floor operation；
S3：Export one-level filter result；
S4：The step S3 filter results exported are quantified as three direction modes, isolated direction mode is eliminated, is filtered
Mask Mask2；Three direction modes in the step in thick Fingerprint diretion can be arbitrary, three sides that the application is used
It is respectively to patternWithWhereinRepresent that orientation angle is less than 60 ° of direction mode；Represent orientation angle etc.
In or more than 60 ° and the direction mode less than 120 °；Represent that direction is equal to or more than 120 ° of direction mode；
S5：Different filtering strategies are taken the field of direction to be filtered according to Mask2；The filtering strategies can use any
One kind, the application is as follows in the filtering strategies that this is used：
IfWithRepresent respectivelyDirection mode in neighborhoodWithNumber；With For
WithIn maximum, then trisection direction mode filtering in gauss low frequency filter variance δ2Obtained by following formula：
In the trisection direction mode filtering of the present invention, n value is n=1,2；NeighborhoodIt is taken as respectively
With
S6：Secondary filter result is exported, the final accurate fingerprint field of direction is obtained.
In order to verify finger that the multiple dimensioned complex-aperture Fingerprint diretion method for building up of weighting provided by the present invention is set up
The performance of the line field of direction, and checking classification smoothing algorithm provided by the present invention can effectively repair the crestal line structure of mistake
And ensure the effect that real singular point position is not offset.Here, the application devises following three groups of experiments, wherein experiment one is
Contrast between Fingerprint diretion method for building up provided by the present invention and conventional fingerprint field of direction method for building up；Experiment two is this
Contrast between the provided classification smoothing algorithm of invention and traditional Fingerprint diretion processing method；Experiment three refers to for the present invention
Contrast between line field of direction method for building up+classification smoothing algorithm and conventional fingerprint field of direction method for building up+classification smoothing algorithm.
The specific setting of three groups of experiments is as follows：
Experiment one：
This experiment have chosen two width low quality fingerprint images as shown in Figure 3 and Figure 4.(a) in wherein Fig. 3 and Fig. 4, (b),
(c), (d) and (e) represents fingerprint artwork, traditional gradient method, laminated gradient method, ballot gradient method and the inventive method and rebuild respectively
Fingerprint diretion OF result.Fig. 3 (a) is wet finger print image, and the crestal line of fingerprint image, which occurs, to be adhered and valley line is not clear
Aobvious situation.Fingerprint artwork in Fig. 4 (a) is influenceed by finger overdrying, and the most of region of former fingerprint image is simultaneously not present bright
The phenomenon that aobvious ridge valley line is alternately present.It can be seen that from Fig. 3 and Fig. 4, method proposed by the present invention can preferably be fitted singular point
The direction in region, can accurately estimate the direction of noise region and avoid the skew of singular point position.
Experiment two：
It is as shown in Figure 5 that this experiment have chosen several low quality fingerprint images.(a), (b), (c) and (d) difference in wherein Fig. 5
Represent the knot for the Fingerprint diretion OF that fingerprint artwork, anisotropic diffusion filtering, the calculus of variations are filtered and the inventive method is set up
Really；The smooth calculation of classification is also carried out in the experiment to it after thick Fingerprint diretion has been set up using method provided by the present invention
Method processing.The crestal line information for mistake marked for singular point, great circle that wherein small circle is marked.As can be seen from Figure 5, use
The smooth method of classification can effectively correct error message, while not causing singular point position to shift.
Experiment three：
It is as shown in Figure 6 that this experiment have chosen several low quality fingerprint images.(a), (b), (c) and (d) difference in wherein Fig. 6
Represent the weighted multiscale of fingerprint artwork, ballot gradient method+classification exponential smoothing, laminated gradient method+classification exponential smoothing and the present invention
Gradient method+classification exponential smoothing.Red area represents singular point region in figure, and yellow area is the region in wrong crestal line direction.From
Fig. 6 can be seen that the OF that method proposed by the present invention is rebuild reflects the trend of true crestal line exactly, in the absence of the direction of mistake
Information, and singular point position also do not shift.
Fingerprint diretion classification smoothing algorithm provided herein can be applied not only to fingerprint provided herein
The field of direction, can be also used for other Fingerprint diretions, and it simply is applied into Fingerprint diretion foundation side provided herein
In the Fingerprint diretion that method is set up, effect more preferably more can effectively rebuild low-quality Fingerprint diretion.
The principle that the application is used is：Artwork → matlab → image normalization → STFT is analyzed → asks for frequency
Image and directional image, then respectively to image travel direction consistency treatment, by Butterworth trap bandpass filter and
Gaussian band-pass filter is smoothed, so as to obtain Fingerprint diretion.
Although the foregoing describing the embodiment of the present invention, those skilled in the art should be appreciated that this
It is merely illustrative of, various changes or modifications can be made to present embodiment, without departing from the principle and essence of the present invention,
Protection scope of the present invention is only limited by the claims that follow.
Claims (5)
1. the multiple dimensioned complex-aperture Fingerprint diretion method for building up of weighting, it is characterised in that：This method is comprised the following steps that：
S1：A series of Fingerprint diretion set up under different scale complex-apertures；
S2：Weight of each yardstick in entire series is determined by squared gradient uniformity；
S3：Fingerprint diretion information integration under entire series is obtained by a Fingerprint diretion by weight.
2. the multiple dimensioned complex-aperture Fingerprint diretion method for building up weighted as claimed in claim 1, it is characterised in that：The step
A series of Fingerprint diretion that use gradient method in rapid S1 is set up under different scale complex-apertures, specific step is as follows：
A：Ask for the gradient vector [G of entire imagex,Gy]T；
B：Gradient vector is converted into squared gradient vector [Gsx,Gsy]T；
C：Fingerprint image is divided into w × w of non-overlapping copies fritter；
D：Ask for the average vector [G of squared gradient vector in frittermx,Gmy]T；
E：Ask for the angle ψ of average gradient vector；
F：Ask for every piece of fingerprint Block direction θ.
3. the multiple dimensioned complex-aperture Fingerprint diretion method for building up weighted as claimed in claim 2, it is characterised in that：Step A
Middle solution gradient [Gx,Gy]TShi Caiyong dimensional Gaussian local derviations counting method is solved.
4. the multiple dimensioned complex-aperture Fingerprint diretion method for building up of the weighting as described in claim 1 or 2 or 3, it is characterised in that：
The expression formula of thick Fingerprint diretion described in the step S3 is as follows：
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<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<mi>c</mi>
<mi>o</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>&theta;</mi>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>+</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>......</mn>
<mo>+</mo>
<mfrac>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<mi>c</mi>
<mi>o</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>&theta;</mi>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mi>L</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：Coh (p, q, l) is the squared gradient uniformity that exterior window size is p × p, θ (p, q, l) be by exterior window size be p ×
The field of direction that p is set up, l=1,2 ..., L represents yardstick；
Coh (p, q, l) can then be obtained by formula (4)：
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>,</mo>
<mi>q</mi>
<mo>,</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mo>-</mo>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mo>-</mo>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>d</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>)</mo>
<mo>,</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>d</mi>
<mi>y</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mrow>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mo>-</mo>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mo>-</mo>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>p</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>d</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>)</mo>
<mo>,</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>d</mi>
<mi>y</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
1
In formula：P is the length of side of outer window, and q is the length of side of interior window, p=q+l × k；L=1,2 ..., L represent yardstick, and k is chi
Coefficient of variation is spent, 3~7 are taken.
5. a kind of Fingerprint diretion is classified smoothing algorithm, it is characterised in that：The algorithm comprises the following steps：
S1：Fingerprint diretion is quantified as both direction pattern, isolated direction mode is eliminated, obtains filter mask Mask1；
S2：Different filtering strategies are taken the field of direction to be filtered according to Mask1；
S3：Export one-level filter result；
S4：The step S3 filter results exported are quantified as three direction modes, isolated direction mode is eliminated, obtains filter mask
Mask2；
S5：Different filtering strategies are taken the field of direction to be filtered according to Mask2；
S6：Secondary filter result is exported, Fingerprint diretion is obtained.
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| CN110579804A (en) * | 2019-10-10 | 2019-12-17 | 中国石油化工股份有限公司 | Diffusion filtering method under structure tensor trace constraint based on absolute square gradient |
| CN113313627A (en) * | 2021-06-08 | 2021-08-27 | 中国科学院大学 | Fingerprint image reconstruction method and fingerprint image feature extraction method and device |
| CN116883292A (en) * | 2023-09-07 | 2023-10-13 | 上海海栎创科技股份有限公司 | pseudo-Gaussian-based image direction field acquisition method, system and computer equipment |
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| CN107977653A (en) * | 2017-12-22 | 2018-05-01 | 云南大学 | The multiple dimensioned inflection point detection algorithm being combined with reference to complex filter and PI values |
| CN110579804A (en) * | 2019-10-10 | 2019-12-17 | 中国石油化工股份有限公司 | Diffusion filtering method under structure tensor trace constraint based on absolute square gradient |
| CN113313627A (en) * | 2021-06-08 | 2021-08-27 | 中国科学院大学 | Fingerprint image reconstruction method and fingerprint image feature extraction method and device |
| CN113313627B (en) * | 2021-06-08 | 2023-10-20 | 中国科学院大学 | Fingerprint image reconstruction method, fingerprint image feature extraction method and device |
| CN116883292A (en) * | 2023-09-07 | 2023-10-13 | 上海海栎创科技股份有限公司 | pseudo-Gaussian-based image direction field acquisition method, system and computer equipment |
| CN116883292B (en) * | 2023-09-07 | 2023-11-28 | 上海海栎创科技股份有限公司 | pseudo-Gaussian-based image direction field acquisition method, system and computer equipment |
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