CN106570445B - A kind of characteristic detection method and device - Google Patents
A kind of characteristic detection method and device Download PDFInfo
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- CN106570445B CN106570445B CN201510657140.0A CN201510657140A CN106570445B CN 106570445 B CN106570445 B CN 106570445B CN 201510657140 A CN201510657140 A CN 201510657140A CN 106570445 B CN106570445 B CN 106570445B
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Abstract
The embodiment of the invention discloses a kind of characteristic detection method and devices, for providing a kind of higher characteristic detection method of accuracy.Method includes: to carry out face location and size detection and facial features localization to first object image, obtains the first crucial point feature；Respectively according to N number of benchmark, regressing calculation is carried out to the described first crucial point feature, obtains N number of first regression result, the N is the integer greater than 1, and the benchmark is the benchmark of face characteristic detection zone；Calculate the similarity of N number of first regression result；If the similarity of N number of first regression result meets condition of similarity, the mean value of N number of first regression result is calculated, fisrt feature testing result is obtained.
Description
Technical field
The present invention relates to field of image processing more particularly to a kind of characteristic detection methods and device.
Background technique
The method that face critical point detection is generally basede on recurrence at present, because the method effect returned is relatively preferable, and
Speed is faster.But the shortcomings that face critical point detection based on recurrence, is not know the effect that finally returns is how, in standard
The demanding application of exactness, the processing result of this method are often not ideal enough.
In the existing face critical point detection technology based on recurrence, the place of the accuracy estimating of a kind of pair of regression algorithm
Reason method is multiple textural characteristics to be extracted around key point, and in addition train a classifier based on these features.It uses
The classifier judges the effect of regression algorithm, takes and is exported by the result of the regression algorithm of classifier.The disadvantages of this solution is,
Just for the regression effect of single frames figure, and in practical applications, due to the posture of face, expression is blocked, and the thousand of the factors such as illumination
Poor ten thousand not so that classification precision be extremely difficult to it is very high, when encountering the case where its training set does not include, be easy make mistake
Conclusion.
Also, during face critical point detection, it is necessary first to, will according to the scale size of facial features localization frame
Target image is normalized into unified mark scale, then according to one average face of parameter initialization of facial features localization frame, so
Afterwards on target image after normalization, since the average face, according to the textural characteristics of each key point peripheral region, carry out
Cascade returns, and obtains final result after multiple regression.This method is more sensitive to initial crucial dot shape, and original shape
It is limited by the size of face characteristic detection block.So, it may also be said to this technology is influenced very greatly by the size of facial features localization frame,
The bad reason of regression effect is greatly because facial features localization frame is too big or too small.
Summary of the invention
The embodiment of the invention provides a kind of characteristic detection method and devices, for providing a kind of higher feature of accuracy
Detection method.
Characteristic detection method provided in an embodiment of the present invention, comprising:
Facial features localization is carried out to first object image, obtains the first crucial point feature；
Respectively according to N number of benchmark, regressing calculation is carried out to the described first crucial point feature, N number of first is obtained and returns
As a result, the N is the integer greater than 1, the benchmark is the benchmark of face characteristic detection zone；
Calculate the similarity of N number of first regression result；
If the similarity of N number of first regression result meets condition of similarity, N number of first regression result is calculated
Mean value obtains fisrt feature testing result.
Feature detection device provided in an embodiment of the present invention, comprising:
Critical point detection unit obtains the first crucial point feature for carrying out facial features localization to first object image；
Unit is returned, for according to N number of benchmark, carrying out regressing calculation respectively to the described first crucial point feature, obtaining
To N number of first regression result, the N is the integer greater than 1, and the benchmark is the station meter of face characteristic detection zone
Degree；
Similarity calculated, for calculating the similarity of N number of first regression result；
Average calculation unit, if the similarity for N number of first regression result meets condition of similarity, calculate described in
The mean value of N number of first regression result, obtains fisrt feature testing result.
As can be seen from the above technical solutions, the embodiment of the present invention has the advantage that
It in embodiments of the present invention, can be respectively according to the base in N number of facial features localization region after completing face characteristic
Object staff degree carries out regressing calculation to the described first crucial point feature, and can reduce people based on multiple facial features localization regions
Face feature detection block initially sets inaccurate brought influence, also, after obtaining N number of first regression result, can calculate
The similarity of N number of first regression result can determine that the setting of N number of benchmark is more accurate if similarity is higher,
It can be exported the mean value of N number of first regression result as the result of facial features localization, improve facial features localization
Accuracy.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings
Obtain other attached drawings.
Fig. 1 is a flow diagram of characteristic detection method in the embodiment of the present invention；
Fig. 2 is a signaling process schematic diagram of characteristic detection method in the embodiment of the present invention；
Fig. 3 is a logical construction schematic diagram of feature detection device in the embodiment of the present invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
It is described in detail separately below.
Description and claims of this specification and term " first ", " second ", " third " " in above-mentioned attached drawing
The (if present)s such as four " are to be used to distinguish similar objects, without being used to describe a particular order or precedence order.It should manage
The data that solution uses in this way are interchangeable under appropriate circumstances, so as to the embodiment of the present invention described herein can in addition to
Here the sequence other than those of diagram or description is implemented.In addition, term " includes " and " having " and their any deformation,
Be intended to cover it is non-exclusive include, for example, containing the process, method of a series of steps or units, system, product or setting
It is standby those of to be not necessarily limited to be clearly listed step or unit, but may include be not clearly listed or for these mistakes
The intrinsic other step or units of journey, method, product or equipment.
The characteristic detection method in the embodiment of the present invention is described below by detailed embodiment, referring to Fig. 1,
One embodiment of characteristic detection method includes: in the embodiment of the present invention
101, facial features localization is carried out to first object image；
Feature detection device carries out facial features localization to first object image, obtains the first crucial point feature.
The first object image is the relatively preceding image in continuous two picture frames.First key point
The feature of feature initial key point；Specifically, crucial point feature can exist for features such as eyes, nose, mouthes in face
Coordinate data in target image.
Specifically, facial features localization method can be Scale invariant features transform (SIFT, Scale-invariant
Feature transform), or other feature extraction algorithms are this time specifically not construed as limiting.
In embodiments of the present invention, the first object image can be the first image in continuous picture frame.
102, respectively according to N number of benchmark, regressing calculation is carried out to the described first crucial point feature；
Feature detection device carries out regressing calculation to the described first crucial point feature, obtains respectively according to N number of benchmark
N number of first regression result, the N are the integer greater than 1, and the benchmark is the benchmark of face characteristic detection zone.
Specifically, regressing calculation can be linear regression, it is also possible to nonlinear regression.
103, the similarity of N number of first regression result is calculated；
Feature detection device calculates the similarity of N number of first regression result, and first regression result is to return fortune
The feature of key point after calculation.
Specifically, the calculating of similarity can be with are as follows:
One, the similarity of corresponding first regression result of two neighboring benchmark is calculated；Such as: 3,3 benchmarks of N
Respectively 1.1S0, S0And 0.9S0, then 1.1S is calculated0And S0Similarity between corresponding first regression result, and
0.9S0And S0Similarity between corresponding first regression result；In practical applications, the setting of N number of benchmark be according to
It is secondary to be incremented by or successively successively decrease；The S0For the real number greater than zero
Two, the similarity between calculating in N number of first regression result two-by-two；Such as: 3,3 benchmarks of N are respectively
1.1S0, S0And 0.9S0, then 1.1S is calculated0And S0Similarity between corresponding first regression result, 0.9S0And S0Respectively
Similarity and 1.1S between corresponding first regression result0And 0.9S0Phase between corresponding first regression result
Like degree.
It is understood that in practical applications, the calculating of similarity is not limited to both the above calculation.
104, judge whether the similarity of N number of first regression result meets condition of similarity；
Feature detection device judges whether the similarity of N number of first regression result meets condition of similarity, if described N number of
The similarity of first regression result meets condition of similarity, thens follow the steps 105；If the similarity of N number of first regression result
It is unsatisfactory for condition of similarity, thens follow the steps 106.
Specifically, in practical applications, meeting condition of similarity and referring to that the parameter phase knowledge and magnanimity for participating in comparing are relatively high；Example
Property, a threshold value can be set, when the similarity of N number of first regression result reaches the threshold value, it may be considered that institute
The similarity for stating N number of first regression result meets condition of similarity；When the similarity of N number of first regression result does not reach this
When threshold value, then condition of similarity is unsatisfactory for.
It is understood that in practical applications, it is similar to judge whether the similarity of N number of first regression result meets
The method of condition can there are many, the embodiment of the present invention only enumerates one way in which.
105, feature testing result is obtained；
If the similarity of N number of first regression result meets condition of similarity, N number of first regression result is calculated
Mean value obtains fisrt feature testing result, and the fisrt feature testing result is cached.
106, the process of feature detection is executed again.
Specifically, in practical applications, if before step 101 is executed to 104 in the embodiment of the present invention, feature detection device
The feature testing result of previous frame target image is not obtained, and current first object image corresponding N number of first returns knot
The similarity of fruit is unsatisfactory for condition of similarity, then does not export and do not retain the detection knot to the current first object image
Fruit, and execute the process of step 101 to 104 again to the target image of next frame, until the corresponding N of target image detected
The similarity of a first regression result meets condition of similarity.
If previous frame target has been obtained in feature detection device before step 101 is executed to 104 in the embodiment of the present invention
The feature testing result of image, and the similarity of current corresponding N number of first regression result of first object image is unsatisfactory for phase
Like condition, then by the feature testing result of previous frame target image, Characteristic Contrast is done with N number of first regression result respectively,
Highest first regression result of characteristic similarity of output and the feature testing result of the previous frame target image, as
Fisrt feature testing result.
It in embodiments of the present invention, can be respectively according to the base in N number of facial features localization region after completing face characteristic
Object staff degree carries out regressing calculation to the described first crucial point feature, and can reduce people based on multiple facial features localization regions
Face feature detection block initially sets inaccurate brought influence, also, after obtaining N number of first regression result, can calculate
The similarity of N number of first regression result can determine that the setting of N number of benchmark is more accurate if similarity is higher,
It can be exported the mean value of N number of first regression result as the result of facial features localization, improve facial features localization
Accuracy.
The characteristic detection method in the embodiment of the present invention is described further below, referring to Fig. 2, the present invention is implemented
One embodiment of characteristic detection method includes: in example
201, facial features localization is carried out to first object image；
Feature detection device carries out facial features localization to first object image, obtains the first crucial point feature.
In embodiments of the present invention, the first object image is the first frame target image in consecutive image.Described first
The feature of crucial point feature initial key point；Specifically, crucial point feature can be the spies such as eyes, nose, mouth in face
The coordinate data in the target image of sign.
Specifically, feature detection device can carry out face location and size detection to the first object image, it is based on
The face location and the size detection are as a result, be normalized operation to the first object image；To normalization operation
The first object image afterwards carries out the extraction of Scale invariant features transform SIFT feature, obtains the first crucial point feature.
202, respectively according to N number of benchmark, regressing calculation is carried out to the described first crucial point feature；
Feature detection device carries out regressing calculation to the described first crucial point feature, obtains respectively according to N number of benchmark
N number of first regression result, the N are the integer greater than 1, and the benchmark is the benchmark of face characteristic detection zone.
Specifically, the N can be 3.
203, the similarity of N number of first regression result is calculated；
Feature detection device calculates the similarity of N number of first regression result, and first regression result is to return fortune
The feature of key point after calculation.
Specifically, the calculating of similarity can be with are as follows:
One, the Euclidean distance of corresponding first regression result of two neighboring benchmark is calculated；Such as: 3,3 station meters of N
Degree is respectively 1.1S0, S0And 0.9S0, it is standard scale S in the scale of the Face datection frame of input illustratively0On the basis of,
Respectively to be greater than standard scale SbigBe less than standard scale Ssmall, the detection of face key point is carried out on three scales respectively,
Sbig=1.10*S0, Ssmall=0.9*S0.The evaluation method of regression effect uses Euclidean distance: d=sqrt (∑ (xi1-xi2) ^
2) xi1 and xi2 respectively indicates two shapes comprising all key points here, wherein xi={ k1, k2, k3 ..., kn }, k1,
K2 ..., kn indicate that n face key point is set.
Two, the Euclidean distance between calculating in N number of first regression result two-by-two；Such as: 3,3 benchmarks of N are respectively
1.1S0, S0And 0.9S0, then 1.1S is calculated0And S0Similarity between corresponding first regression result, 0.9S0And S0Respectively
Similarity and 1.1S between corresponding first regression result0And 0.9S0Phase between corresponding first regression result
Like degree.
It is understood that in practical applications, the calculating of similarity is not limited to both the above calculation.
204, judge whether the similarity of N number of first regression result meets condition of similarity；
Feature detection device judges whether the similarity of N number of first regression result meets condition of similarity, if described N number of
The similarity of first regression result meets condition of similarity, thens follow the steps 205；If the similarity of N number of first regression result
It is unsatisfactory for condition of similarity, then updates the first object image, executes step 201 again.
Specifically, in practical applications, meeting condition of similarity and referring to that the parameter phase knowledge and magnanimity for participating in comparing are relatively high；Example
Property, a threshold value can be set, when the similarity of N number of first regression result reaches the threshold value, it may be considered that institute
The similarity for stating N number of first regression result meets condition of similarity；When the similarity of N number of first regression result does not reach this
When threshold value, then condition of similarity is unsatisfactory for.
It is understood that in practical applications, it is similar to judge whether the similarity of N number of first regression result meets
The method of condition can there are many, the embodiment of the present invention only enumerates one way in which.
205, feature testing result is obtained；
If the similarity of N number of first regression result meets condition of similarity, N number of first regression result is calculated
Mean value obtains fisrt feature testing result, and the fisrt feature testing result is cached.
206, facial features localization is carried out to the second target image
After fisrt feature testing result has been obtained in feature detection device, feature detection device is to the second target figure
As carrying out facial features localization, the second crucial point feature is obtained.Second target image is to detect to tie with the fisrt feature
The next frame target image of the corresponding target image of fruit.
207, respectively according to N number of benchmark, regressing calculation is carried out to the described second crucial point feature；
Feature detection device carries out regressing calculation to the described second crucial point feature, obtains respectively according to N number of benchmark
N number of second regression result.
208, the similarity of N number of second regression result is calculated；
Feature detection device calculates the similarity of N number of second regression result.
209, judge whether the similarity of N number of second regression result meets condition of similarity；
Feature detection device judges whether the similarity of N number of second regression result meets condition of similarity, if described N number of
The similarity of second regression result meets condition of similarity, thens follow the steps 210；If the similarity of N number of second regression result
It is unsatisfactory for condition of similarity, thens follow the steps 211.
210, the mean value of N number of second regression result is calculated；
If the similarity of N number of second regression result meets condition of similarity, N number of second regression result is calculated
Mean value obtains second feature testing result.
211, highest second regression result of characteristic similarity with the fisrt feature testing result is exported.
If the similarity of N number of second regression result is unsatisfactory for condition of similarity, by the fisrt feature testing result
Characteristic Contrast is done with N number of second regression result respectively, is exported with the characteristic similarity of the fisrt feature testing result most
High second regression result, as second feature testing result.
In embodiments of the present invention, feature detection device judges that the face of single previous frame is crucial according to the similitude of consecutive frame
The accuracy of point testing result, further improves the accuracy of Face datection, this solution is suitble to the face of video flowing to close
The Accuracy evaluation of key point detection.
The feature detection device for executing characteristic detection method in the embodiment of the present invention is illustrated below, referring to Fig. 3,
Include:
Critical point detection unit 301 obtains the first key point spy for carrying out facial features localization to first object image
Sign；
Unit 302 is returned, for according to N number of benchmark, carrying out regressing calculation to the described first crucial point feature respectively,
N number of first regression result is obtained, the N is the integer greater than 1, and the benchmark is the station meter of face characteristic detection zone
Degree；
Similarity calculated 303, for calculating the similarity of N number of first regression result；
Average calculation unit 304 calculates if the similarity for N number of first regression result meets condition of similarity
The mean value of N number of first regression result, obtains fisrt feature testing result.
Further,
The critical point detection unit 301 is also used to, and is carried out facial features localization to the second target image, is obtained the second pass
Key point feature；
The recurrence unit 302 is also used to, and respectively according to N number of benchmark, is returned to the described second crucial point feature
Return operation, obtains N number of second regression result；
The similarity calculated 303 is also used to, and calculates the similarity of N number of second regression result；
The average calculation unit 304 is also used to, if the similarity of N number of second regression result meets condition of similarity,
The mean value for then calculating N number of second regression result, obtains second feature testing result；
Described device further include: Characteristic Contrast unit 305, if the similarity for N number of second regression result is discontented
The fisrt feature testing result is then done Characteristic Contrast by sufficient condition of similarity with N number of second regression result respectively, output with
Highest second regression result of the characteristic similarity of the fisrt feature testing result, as second feature testing result.
Specifically, the critical point detection unit 301 is specifically used for:
Face location and size detection are carried out to the first object image；
Based on the face location and the size detection as a result, operation is normalized to the first object image；
The extraction of Scale invariant features transform SIFT feature is carried out to the first object image after normalization operation, is obtained
First crucial point feature.
Specifically, the similarity calculated 303 is specifically used for:
Euclidean distance between calculating separately in N number of first regression result two-by-two；
Or,
Calculate the Euclidean distance of corresponding first regression result of two neighboring benchmark.
Specifically, the Characteristic Contrast unit 305 is specifically used for:
Euclidean distance of the fisrt feature testing result respectively with N number of second regression result is calculated separately, N is obtained
A Euclidean distance calculated result compares the size of N number of Euclidean distance calculated result.
Reference can be made to the above method embodiment for the concrete operations process of above-mentioned each unit, and details are not described herein again.
In several embodiments provided herein, it should be understood that disclosed device and method can pass through it
Its mode is realized.For example, the apparatus embodiments described above are merely exemplary, for example, the division of the unit, only
Only a kind of logical function partition, there may be another division manner in actual implementation, such as multiple units or components can be tied
Another system is closed or is desirably integrated into, or some features can be ignored or not executed.Another point, it is shown or discussed
Mutual coupling, direct-coupling or communication connection can be through some interfaces, the INDIRECT COUPLING or logical of device or unit
Letter connection can be electrical property, mechanical or other forms.
The unit as illustrated by the separation member may or may not be physically separated, aobvious as unit
The component shown may or may not be physical unit, it can and it is in one place, or may be distributed over multiple
In network unit.It can select some or all of unit therein according to the actual needs to realize the mesh of this embodiment scheme
's.
It, can also be in addition, the functional units in various embodiments of the present invention may be integrated into one processing unit
It is that each unit physically exists alone, can also be integrated in one unit with two or more units.Above-mentioned integrated list
Member both can take the form of hardware realization, can also realize in the form of software functional units.
If the integrated unit is realized in the form of SFU software functional unit and sells or use as independent product
When, it can store in a computer readable storage medium.Based on this understanding, technical solution of the present invention is substantially
The all or part of the part that contributes to existing technology or the technical solution can be in the form of software products in other words
It embodies, which is stored in a storage medium, including some instructions are used so that a computer
Equipment (can be personal computer, server or the network equipment etc.) executes the complete of each embodiment the method for the present invention
Portion or part steps.And storage medium above-mentioned includes: USB flash disk, mobile hard disk, read-only memory (ROM, Read-Only
Memory), random access memory (RAM, Random Access Memory), magnetic or disk etc. are various can store journey
The medium of sequence code.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. a kind of characteristic detection method characterized by comprising
Facial features localization is carried out to first object image, obtains the first crucial point feature；
Respectively according to N number of benchmark, regressing calculation is carried out to the described first crucial point feature, obtains N number of first regression result,
The N is the integer greater than 1, and the benchmark is the benchmark of face characteristic detection zone；
Calculate the similarity of N number of first regression result；
If the similarity of N number of first regression result meets condition of similarity, the equal of N number of first regression result is calculated
Value, obtains fisrt feature testing result；
If the similarity of N number of first regression result is unsatisfactory for condition of similarity, the process of facial features localization is executed again.
2. the method according to claim 1, wherein it is described obtain fisrt feature testing result after, further includes:
Facial features localization is carried out to the second target image, obtains the second crucial point feature；
Respectively according to N number of benchmark, regressing calculation is carried out to the described second crucial point feature, obtains N number of second regression result；
Calculate the similarity of N number of second regression result；
If the similarity of N number of second regression result meets condition of similarity, the equal of N number of second regression result is calculated
Value, obtains second feature testing result；
If the similarity of N number of second regression result is unsatisfactory for condition of similarity, the fisrt feature testing result is distinguished
Characteristic Contrast is done with N number of second regression result, is exported highest with the characteristic similarity of the fisrt feature testing result
One the second regression result, as second feature testing result.
3. the method according to claim 1, wherein it is described to first object image carry out facial features localization,
Obtain the first crucial point feature, comprising:
Face location and size detection are carried out to the first object image；
Based on the face location and the size detection as a result, operation is normalized to the first object image；
The extraction of Scale invariant features transform SIFT feature is carried out to the first object image after normalization operation, obtains first
Crucial point feature.
4. the method according to claim 1, wherein the similarity for calculating N number of first regression result,
Include:
Euclidean distance between calculating separately in N number of first regression result two-by-two；
Or,
Calculate the Euclidean distance of corresponding first regression result of two neighboring benchmark.
5. according to the method described in claim 2, it is characterized in that, by the fisrt feature testing result respectively with it is described N number of
Second regression result does Characteristic Contrast, comprising:
Euclidean distance of the fisrt feature testing result respectively with N number of second regression result is calculated separately, N number of Europe is obtained
Formula compares the size of N number of Euclidean distance calculated result apart from calculated result.
6. a kind of feature detection device characterized by comprising
Critical point detection unit obtains the first crucial point feature for carrying out facial features localization to first object image；
Unit is returned, for according to N number of benchmark, carrying out regressing calculation respectively to the described first crucial point feature, obtaining N number of
First regression result, the N are the integer greater than 1, and the benchmark is the benchmark of face characteristic detection zone；
Similarity calculated, for calculating the similarity of N number of first regression result；
Average calculation unit calculates described N number of if the similarity for N number of first regression result meets condition of similarity
The mean value of first regression result obtains fisrt feature testing result；If the similarity of N number of first regression result is unsatisfactory for phase
Like condition, then triggers the critical point detection unit and execute facial features localization again.
7. device according to claim 6, which is characterized in that
The critical point detection unit is also used to, and carries out facial features localization to the second target image, obtains the second key point spy
Sign；
The recurrence unit is also used to, and respectively according to N number of benchmark, carries out regressing calculation to the described second crucial point feature,
Obtain N number of second regression result；
The similarity calculated is also used to, and calculates the similarity of N number of second regression result；
The average calculation unit is also used to, if the similarity of N number of second regression result meets condition of similarity, calculates institute
The mean value for stating N number of second regression result, obtains second feature testing result；
Described device further include: Characteristic Contrast unit, if the similarity for N number of second regression result is unsatisfactory for similar item
The fisrt feature testing result is then done Characteristic Contrast, output and described first by part with N number of second regression result respectively
Highest second regression result of the characteristic similarity of feature testing result, as second feature testing result.
8. device according to claim 6, which is characterized in that the critical point detection unit is specifically used for:
Face location and size detection are carried out to the first object image；
Based on the face location and the size detection as a result, operation is normalized to the first object image；
The extraction of Scale invariant features transform SIFT feature is carried out to the first object image after normalization operation, obtains first
Crucial point feature.
9. device according to claim 6, which is characterized in that the similarity calculated is specifically used for:
Euclidean distance between calculating separately in N number of first regression result two-by-two；
Or,
Calculate the Euclidean distance of corresponding first regression result of two neighboring benchmark.
10. device according to claim 7, which is characterized in that the Characteristic Contrast unit is specifically used for:
Euclidean distance of the fisrt feature testing result respectively with N number of second regression result is calculated separately, N number of Europe is obtained
Formula compares the size of N number of Euclidean distance calculated result apart from calculated result.
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