CN107180412A - Transverse and longitudinal based on floor projection and seed point constraint K mean cluster shreds scraps of paper method for reconstructing - Google Patents
Transverse and longitudinal based on floor projection and seed point constraint K mean cluster shreds scraps of paper method for reconstructing Download PDFInfo
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- 239000012634 fragment Substances 0.000 claims abstract description 75
- 238000004364 calculation method Methods 0.000 claims abstract description 12
- 238000013467 fragmentation Methods 0.000 claims abstract description 7
- 238000006062 fragmentation reaction Methods 0.000 claims abstract description 7
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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- G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
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- G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract
The invention discloses it is a kind of based on floor projection and seed point constraint K mean cluster transverse and longitudinal shred scraps of paper method for reconstructing, the image of file fragmentation is projected to horizontal direction, with projection come one-dimensional signal carries out cluster in lines.The initial seed point in K mean cluster is constrained as seed point using the one-dimensional signal that the first fragment of every a line is transformed, branch clusters using K mean algorithms.The distance between fragment in often row is calculated apart from calculation formula using introducing penalty coefficient, and sets up the adjacency matrix of distance between fragment, so that Bonding Problem in the row of fragment is converted into traveling salesman problem.Using ant colony optimization for solving by going the traveling salesman problem that interior Bonding Problem is transformed, introduce and merge and divide-and-conquer strategy improves splicing precision in row.Finally the splicing of row fragment is realized using the characteristic vector matching of row fragment.
Description
Technical field
The invention belongs to image processing field, refer to a kind of text information that scraps of paper image is shredded based on transverse and longitudinal and restore
Joining method, is the application of floor projection, seed point limited K mean cluster and ant colony method in a scrap of paper splicing.
Technical background
The inspection of document is a medicolegal important subdomains, and it is with criminal, military, civil, government's law enforcement, the administration of justice etc. leads
There is great contact in domain.The key of the inspection of document is to apocrypha using a series of known standards and the method for applied science
Test contrast, such as signature verification, handwriting verification.In order to obtain reliable result, legal medical expert worker must be by guarantor
Deposit complete file.
Many times apocrypha can may be torn off corner, damage by worms, soak by different degrees of breaking-up, file, with
And tear up.In a kind of last situation, file may be torn to pieces by human hand or machine, no matter which kind of situation, legal medical expert workers
It is required for reparation file to complete following appraisal.Powder is repaired by the size and number of fragment in a manual manner
Broken file needs the substantial amounts of time, and several days or even several all times may be needed by repairing several papers.And file reparation is spelled
It is a very boring dull job to connect, therefore one efficient autofile restorative procedure of design seems unusual necessity.
Shredder is used as the instrument for protecting user's paper document information security, it is desirable to which shredding documents information can not be reconditioned.
File is ground into the small bulk of transverse and longitudinal by most shredders, therefore research transverse and longitudinal chopping scraps of paper restorative procedure can instruct broken simultaneously
The upgrade design of paper machine, preferably protects the information security of user.
The content of the invention
The present invention is directed to propose a kind of reconstruction transverse and longitudinal chopping scraps of paper joining method, this method relatively existing method both at home and abroad
Possess higher precision, more automate.This method is greatly improved operating efficiency compared to artificial splicing.
Particular technique content is as follows：
1.1. floor projection is carried out to each fragment, each fragment is converted into an one-dimensional signal；
1.2. according to the one-dimensional signal of fragment, the K mean cluster algorithm being limited using seed point realizes that the branch of fragment gathers
Class；
1.3. each row is ranked up, Bonding Problem in row of tiles is converted into traveling salesman problem, using ant colony method
Solve this traveling salesman problem；
1.4. the characteristic vector FC=[a of row fragment are used1, a2, a3, a4] carry out the splicing that row fragment is realized in matching.
2. described in step 1.1 include：
2.1. the image of each a scrap of paper is carried out binary conversion treatment, the two-value when the gray value of pixel is more than threshold value
1 is turned to, two-value turns to 0 when gray value is less than threshold value；
2.2. it is the number of the pixel of black during from left to right accumulated image is per a line, the mathematic(al) representation of the process is such as
Shown in lower：
Wherein f (y) represents the number of image pixel of black in y rows；I (x, y) represents ashes of the image I at point (x, y) place
Angle value, when the point is black, the gray value of the point is 0, and when the point is white, the gray value of the point is 1；N represents fragmentation pattern
The horizontal resolution of picture；
2.3. step 2.2. is passed through, fragmentation pattern is converted into an one-dimensional vector d for having m to tie up as ii, wherein m represents fragmentation pattern
The vertical resolution of picture.
3. described in step 1.2 include：
3.1. according to the left part of first fragment in every row fragment be this white feature determine first fragment per a line and
Its one-dimensional signal CVF1...CVFt, it is that this white feature is determined per a line according to the right part of last fragment in every row fragment
Last fragment and its one-dimensional signal CVL1...CVLt, wherein t represents the pulverized line number of fragment；
3.2. the corresponding one-dimensional signal CVF of the first fragment of every row1...CVFtAs in cluster initial in clustering algorithm
Heart vector C1...Ct；
3.3. the one-dimensional vector di to all kinds of center C of each fragment is calculated using Euclidean distance calculation formula1...Ct's
Distance, the mathematical expression form of the step is as follows：
disted(di, Cj)=| | di-Cj||2
Wherein disted(di, Cj) represent fragment i one-dimensional vector diWith cluster centre CjThe distance between；
3.4. fragment i is clustered in from the corresponding classifications of cluster centre j minimum with a distance from it；
3.5. the cluster result in 3.4 steps recalculates cluster centre, and calculation formula is as follows：
Wherein | Ci| represent to be clustered into the number of i fragment, C 'iCluster centre C after expression is updatedi, d represents to be clustered
To cluster centre CiThe one-dimensional vector of the fragment of corresponding class；
3.6. iterative step 3.3.-3.5. until in each class fragment no longer change；
3.7. cluster result is returned.
4. described in step 1.3 include：
4.1. each class in cluster branch result is all individually handled, and a scrap of paper of every row is abstracted into the top in graph theory
Matching degree between point, chip edges matrix is abstracted into the distance between summit；
4.2. summit i is calculated to summit j (apart from d using formulam(i, j), i.e. a scrap of paper i right hand edge and a scrap of paper j
Left hand edge；Calculate the distance between any summit and obtain a complete weighted graph；
Wherein p is a penalty coefficient, and penalty coefficient is defined as follows：
Wherein xiRepresent the vector corresponding to the right hand edge of a scrap of paper i images；xjRepresent that the left hand edge of a scrap of paper j images is corresponding
Vector；xjuRepresent vector xiCorresponding gray value, x at the u of positionjuWith xiuIt is similar；T is a constant, wherein can pass through examination
Determination is tested, is found through overtesting, is that 0 (i.e. the pixel is when M is arranged in the row fragment longitudinal edge pixel gray value
It is black) number average value when splicing precision it is higher.
4.3. ant colony method result of calculation is used, the parameter of ant colony method is set to α=1, β=5, ρ=0.5, (wherein α generations
Table heuristic factor, β is represented from the inspiration amount factor, ρ representative informations element residual coefficients) the ant quantity in ant colony method be set to it is broken
The quantity of the scraps of paper.
4.4. the result for fragment of going on a journey is rebuild according to ant colony result of calculation.
5. described in step 1.4 include：
If being 5.1. white at the top of row a scrap of paper, incomplete literal line, order are not present in row fragment top
Row fragment i characteristic vector FCiOne-component a1=0；
If 5.2. the top the first row word of row a scrap of paper is complete, a is made1=0, the i.e. coboundary of the style of writing word
It is overlapping with the coboundary of row a scrap of paper；Otherwise a is made1=l1, wherein l1It is the bottom of incomplete literal line at the top of row fragment broken
The position of the scraps of paper；
If 5.3. the bottom of row a scrap of paper is white, incomplete literal line, order is not present in the bottom of the row fragment
a4=0；
If 5.4. bottom last column word of row a scrap of paper is complete, a is made4=0, (i.e. the style of writing word is upper
Border is overlapping with the lower boundary of row a scrap of paper)；Otherwise a is made4=l4, wherein l4It is the top of the imperfect literal line in row fragment bottom
Position in a scrap of paper；
If 5.5. making a comprising the word that any a line is complete in row a scrap of paper2=l2, a3=l3, wherein l2It is most to lean on
Position of the coboundary of the complete word of that row of nearly row a scrap of paper bottom in a scrap of paper, l3It is closest to a scrap of paper bottom
Position of the lower boundary of the complete word of that row in a scrap of paper, otherwise makes a2=0, a3=0 and redirect execution step 5.7.；Together
Seasonal l=l2-l3, l '=a4-a3, wherein l is that the word of a line word is high, and l ' is the height in space between literal line, if some
There is no any complete row in row fragment, lead to not calculate l, l ', now with other row fragments for coming from same file
Average value replace；
If 5.6. a2＜ L-l-l ', wherein L are the height of a scrap of paper, a2, A2It is modified to a2=a2+ l+l ', a3=a3+
l+l′；If revised a3With uncorrected a4Meet condition a3+l′≤L∪a4=0, then a4It is modified to a4=a3+l′；Such as
Really revised a2With uncorrected a1Meet condition (0≤a2-N(l′+l)≤l)∪a1When=0, a1It is modified to a1=a2-R
(l '+l), wherein R are a constant and meet R ∈ { 1,2,3 }；Terminate characteristic vector pickup；
If 5.7. a1=0, a4=0, it means that there is no text information in a scrap of paper, the fragment from reconstructing restored
Removed in problem；Otherwise a is utilized1, a4, l, l ' is to a2, a3It is modified and terminates characteristic vector FCi=[a1, a2, a2, a4] carry
Take.
5.8. the characteristics of not having word according to a scrap of paper the first row top blank determines the first row and its spy of a scrap of paper
It is FC to levy vector1, the characteristic vector of the current row to be spliced of order is FCcInitial value is set as FCc=FC1。
If the 5.9. characteristic vector FC of certain row a scrap of paperiComponent and current characteristic vector FC to be splicedcMeet conditionOr(Represent the characteristic vector FC of current row to be splicedc's
Component a4,Represent the characteristic vector FC of certain row a scrap of paperiComponent a1；Represent the characteristic vector FC of current row to be splicedc
Component a3,Represent the characteristic vector FC of certain row a scrap of paperiComponent a2) when think row a scrap of paper i and current paper to be spliced
Piece is adjacent, completes the splicing to row a scrap of paper i, makes FCc=FCi, wherein δ is that random error tolerance can be set as 3.
Brief description of the drawings
Fig. 1：Floor projection process schematic；
Fig. 2：Test the restoration result of sample 1；
Fig. 3：Test the restoration result of sample 6；
Embodiment
The inventive method has used 10 groups of data tests (to be 10 pounds of Time New Roman comprising 5 parts of fonts, line-spacing is
The English a scrap of paper file of fixed 13 pounds, 5 parts of fonts are 10 pounds of Time New Roman, line-spacing for fixed 13 pounds and
Carry out the English a scrap of paper file of overstriking) precision and automaticity of method, 11 × 17 are included in each group of test data
A scrap of paper, i.e. file are crosscut 11, rip cutting 17, and the corresponding specification of picture of every fragment is 180 × 72 pixels.
According to step 1.1, binary-state threshold τ=200 in setting steps 2.1 carry out floor projection to each fragment,
Each fragment is changed into the one-dimensional vector that correspondence dimension is 180, represented in the calculation with this one-dimensional vector corresponding broken
Picture.
According to step 3.1, first fragment and corresponding one-dimensional vector d in every row fragment are found out1, d2... dmMake
The initial cluster center C for the K mean cluster algorithm being limited for seed point1...Cm, and complete cluster according to step 3.2-3.6.
In order to verify the precision of this method, this method is carried with basic K mean cluster algorithm and 2014 in a paper
The feature vector clusters algorithm gone out is compared, and result of the comparison see the table below：
Wherein FN, FP are illustrated respectively in assorting process receives the number with False Rejects by mistake, and the calculating of clustering precision is public
Formula is as follows：
Wherein TP, TN represent it is correct receive and correct rejection number, by it was found that clustering method precision in this method
Apparently higher than other two methods.
In order to verify the splicing precision of this method, in this method cluster process cluster mistake carry out manual correction (by
It is seldom in mistake, and vicious line number is seldom, therefore it is very limited to correct these wrong time spents).
According to step 1.3, the M in setting steps 4.2 is that longitudinal edge pixel gray value is 0 (i.e. should in the row fragment
Pixel is black) number average value, the parameter of ant group algorithm is α=1, β=0.5, ρ=0.5 in step 4.3, ant
Quantity is set to the solution of this traveling salesman problem of programming realization after the completion of 17, parameter setting.
According to step 1.4, realize the splicing of row fragment and calculate splicing precision, accuracy computation formula is as follows：
Result of calculation see the table below：
Precision to the test sample (test sample 1-5 font not overstrikings, test sample 6-10 overstrikings) of different fonts is carried out solely
Vertical sample t-test, as a result finds that font has a significant impact (93.4% ± 2% vs 88.6% ± 3.4%, p for splicing precision
=0.0038), the splicing result of test sample 1 and test sample 6 is shown in accompanying drawing.
In view of this method very high clustering precision, attempts to solve the transverse and longitudinal chopping of two files in the test process of this method
Scraps of paper Problems of Reconstruction (i.e. fragment is from two different files).We use tricks at arbitrarily two files of selection in 10 files
Calculation machine, which is ground into 11*17 specification, i.e. problem, 374 fragments, the corresponding picture specification of fragment and as above.It is such
Experiment has carried out 10 groups altogether, and cluster result is as follows：
From result, this method can reach in the transverse and longitudinal chopping scraps of paper Problems of Reconstruction for solving two files in some cases
Precision shredding scraps of paper Problems of Reconstruction with conventional transverse and longitudinal, for example, will test sample 1 and test sample 6, and test sample 2
When being combined with test sample 9.
Claims (5)
1. the transverse and longitudinal based on floor projection and seed point constraint K mean cluster shreds scraps of paper method for reconstructing, it is characterised in that including
Following steps：
1.1. floor projection is carried out to each fragment, each fragment is converted into an one-dimensional signal；
1.2. according to the one-dimensional signal of fragment, the K mean cluster algorithm being limited using seed point realizes that the branch of fragment clusters；
1.3. each row is ranked up, Bonding Problem in row of tiles is converted into traveling salesman problem, solved using ant colony method
This traveling salesman problem；
1.4. the characteristic vector FC- [a of row fragment are used1, a2, a3, a4] carry out the splicing that row fragment is realized in matching.
2. according to the method described in claim 1, it is characterised in that：Described step 1.1 includes：
2.1. the image of each a scrap of paper is carried out binary conversion treatment, two-value is turned to when the gray value of pixel is more than threshold value
1, two-value turns to 0 when gray value is less than threshold value；
2.2. it is the number of the pixel of black, the following institute of mathematic(al) representation of the process during from left to right accumulated image is per a line
Show：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>N</mi>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
Wherein f (y) represents the number of image pixel of black in y rows；I (x, y) represents ashes of the image I at point (x, y) place
Angle value, when the point is black, the gray value of the point is 0, and when the point is white, the gray value of the point is 1；N represents fragmentation pattern
The horizontal resolution of picture；
2.3. step 2.2. is passed through, fragmentation pattern is converted into an one-dimensional vector d for having m to tie up as ii, wherein m represent fragmentation pattern as
Vertical resolution.
3. according to the method described in claim 1, it is characterised in that：Described step 1.2 includes：
3.1. it is the first fragment and one that this white feature determines every a line according to the left part of first fragment in often row fragment
Dimensional signal CVF1...CVFt, it is that this white feature is determined per a line most according to the right part of last fragment in every row fragment
Latter fragment and its one-dimensional signal CVL1...CVLt, wherein t represents the pulverized line number of fragment；
3.2. the corresponding one-dimensional signal CVF of the first fragment of every row1...CVFtAs cluster centre initial in clustering algorithm to
Measure C1...Ct；
3.3. the one-dimensional vector d of each fragment is calculated using Euclidean distance calculation formulaiTo all kinds of center C1...CtDistance,
The mathematical expression form of the step is as follows：
disted(di, Cj)=| | di-Cj||2
Wherein disted(di, Cj) represent fragment i one-dimensional vector diWith cluster centre CjThe distance between；
3.4. fragment i is clustered in from the corresponding classifications of cluster centre j minimum with a distance from it；
3.5. the cluster result in 3.4 steps recalculates cluster centre, and calculation formula is as follows：
<mrow>
<msubsup>
<mi>C</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mo>|</mo>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
</mfrac>
<msub>
<mi>&Sigma;</mi>
<mrow>
<mi>d</mi>
<mo>&Element;</mo>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<mi>d</mi>
</mrow>
Wherein | Ci| represent to be clustered into the number of i fragment, C 'iCluster centre C after expression is updatedi, d represents to be clustered
To cluster centre CiThe one-dimensional vector of the fragment of corresponding class；
3.6. iterative step 3.3.-3.5. until in each class fragment no longer change；
3.7. cluster result is returned.
4. according to the method described in claim 1, it is characterised in that：Described step 1.3 includes：
4.1. each class in cluster branch result is all individually handled, and a scrap of paper of every row is abstracted into the summit in graph theory, broken
Matching degree between piece matrix of edge is abstracted into the distance between summit；
4.2. summit i is calculated to summit j apart from d using formulam(i, j), i.e. a scrap of paper i right hand edge and a scrap of paper the j left side
Edge；Calculate the distance between any summit and obtain a complete weighted graph；
<mrow>
<msub>
<mi>d</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
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<mo>=</mo>
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<mn>1</mn>
<mo>+</mo>
<mi>p</mi>
</mrow>
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<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>|</mo>
<msub>
<mo>|</mo>
<mn>2</mn>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
<msqrt>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>u</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mo>|</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mi>u</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>j</mi>
<mi>u</mi>
</mrow>
</msub>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
Wherein p is a penalty coefficient, and penalty coefficient is defined as follows：
<mrow>
<mi>p</mi>
<mo>=</mo>
<mfrac>
<mi>T</mi>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>u</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</msubsup>
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<mrow>
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<mo>+</mo>
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<mo>=</mo>
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</mrow>
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</msubsup>
<msub>
<mi>x</mi>
<mrow>
<mi>j</mi>
<mi>u</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
Wherein xiRepresent the vector corresponding to the right hand edge of a scrap of paper i images；xjRepresent that the left hand edge of a scrap of paper j images is corresponding
Vector；xjuRepresent vector xiCorresponding gray value, x at the u of positionjuWith xiuIt is similar；T is a constant, wherein true by experiment
It is fixed, found through overtesting, be 0 (i.e. the pixel is black) when M is arranged to longitudinal edge pixel gray value in the row fragment
Number average value when splicing precision it is higher；
4.3. ant colony method result of calculation is used, the parameter of ant colony method is set to α=1, β=5, ρ=0.5, (wherein α is represented and opened
The factor is sent out, β is represented from the inspiration amount factor, ρ representative informations element residual coefficients) the ant quantity in ant colony method is set to a scrap of paper
Quantity；
4.4. the result for fragment of going on a journey is rebuild according to ant colony result of calculation.
5. according to the method described in claim 1, it is characterised in that：Described step 1.4 includes：
If being 5.1. white at the top of row a scrap of paper, incomplete literal line is not present in row fragment top, order row is broken
Piece i characteristic vector FCiOne-component a1=0；
If 5.2. the top the first row word of row a scrap of paper is complete, a is made1=0, the i.e. coboundary of the style of writing word and row
The coboundary of a scrap of paper is overlapping；Otherwise a is made1=l1, wherein l1It is the bottom of incomplete literal line at the top of row fragment in a scrap of paper
Position；
If 5.3. the bottom of row a scrap of paper is white, incomplete literal line is not present in the bottom of the row fragment, makes a4=0；
If 5.4. bottom last column word of row a scrap of paper is complete, a is made4=0, the i.e. coboundary of the style of writing word with
The lower boundary of row a scrap of paper is overlapping；Otherwise a is made4=l4, wherein l4It is the top of the imperfect literal line in row fragment bottom in a scrap of paper
In position；
If 5.5. making a comprising the word that any a line is complete in row a scrap of paper2=l2, a3=l3, wherein l2It is closest to row
Position of the coboundary of the complete word of that row of a scrap of paper bottom in a scrap of paper, l3It is closest to that row of a scrap of paper bottom
Position of the lower boundary of complete word in a scrap of paper, otherwise makes a2=0, a3=0 and redirect execution step 5.7.；With season l
=l2-l3, l '=a4-a3, wherein l is that the word of a line word is high, and l ' is the height in space between literal line, if some row is broken
There is no any complete row in piece, lead to not calculate l, l ', now putting down with other row fragments for coming from same file
Average is replaced；
If 5.6. a3＜ L-l-l ', wherein L are the height of a scrap of paper, a2, a3It is modified to a2=a2+ l+l ', a3=a3+l+l′；
If revised a3With uncorrected a4Meet condition a3+l′≤L∪a4=0, then a4It is modified to a4=a3+l′；If repaiied
A after just2With uncorrected a1Meet condition (0≤a2-N(l′+l)≤l)∪a1When=0, a1It is modified to a1=a2-R(l′+
L), wherein R is a constant and meets R ∈ { 1,2,3 }；Terminate characteristic vector pickup；
If 5.7. a1=0, a4=0, it means that there is no text information in a scrap of paper, the fragment from reconstructing restored problem
It is middle to remove；Otherwise a is utilized1, a4, l, l ' is to a2, a3It is modified and terminates characteristic vector FC1=[a1, a2, a3, a4] extract；
5.8. the characteristics of word not being had according to a scrap of paper the first row top blank determine the first row and its feature of a scrap of paper to
Measure as FC1, the characteristic vector of the current row to be spliced of order is FCCInitial value is set as FCC=FC1；
If the 5.9. characteristic vector FC of certain row a scrap of paperiComponent and current characteristic vector FC to be splicedCMeet conditionOrWhen think that row a scrap of paper i is adjacent with the current scraps of paper to be spliced, whereinTable
Show the characteristic vector FC of current row to be splicedCComponent a4,Represent the characteristic vector FC of certain row a scrap of paperiComponent a1；Table
Show the characteristic vector FC of current row to be splicedCComponent a3,Represent the characteristic vector FC of certain row a scrap of paperiComponent a2；Complete
Splicing to row a scrap of paper i, makes FCC=FCi, wherein δ is that random error tolerance is set as 3.
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