CN104899607B - A kind of automatic classification method of traditional moire pattern - Google Patents
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Abstract
The present invention proposes a kind of Algorithms for Automatic Classification of traditional moire pattern.Mainly solve the problems, such as that moire pattern manual sort's efficiency is low, pre-processed by moire pattern, feature extraction, clustering processing realize that moire pattern is classified automatically.Implementation process is：(1) moire topography is pre-processed, including unified image size, removal ambient noise, refinement moire topography three steps of lines；(2) it is directed between moire topography and is mainly characterized by the shapes of lines, sub (SC) algorithm is described to extract the feature of moire topography using Shape context, passes through Shape context distance and obtain initial similarity between moire topography；(3) similarity matrix is optimized via improved neighbor relationships pass-algorithm；(4) input matrix using the similarity matrix after optimization as MEAP algorithms, MEAP clustering processings are carried out, realizes automatic classification.The cluster result display present invention is higher compared to SIFT MEAP and ED MEAP algorithm cluster accuracies, and Clustering Effect is more preferable.Moire pattern Algorithms for Automatic Classification simultaneously proposed by the invention, the cluster analysis for other traditional art patterns have good reference.
Description
Technical field
The invention belongs to cluster analysis, Image Classfication Technology field, is related to moire topography pretreatment, Shape context feature
Extraction, neighbor relationships transmission optimization similarity matrix.It is specifically a kind of to combine neighbor relationships transmission and Shape context spy
The automatic classification method of more subclass center neighbour's propagation algorithms cluster moire topography of sign.
Background technology
In Chinese tradition decorative patterns, moire is extremely abundant, the unique oriental art glamour of long history, sculpture style
A major class.Moire rheology is lively, and implied meaning is lucky, and the form of expression is various, the change of existing different monomers, there is all kinds of transfer again
Connect, continuous combining structure, be exactly important decorative element among all kinds of planes and stereo modelling since ancient times, even if to the present
My god, contemporary art is designed still has very big reference value with creating.Such as 2008 Beijing Olympic Games fire known to everybody
Single hook cirrus line that auspicious cloud grain pattern occurs as soon as decorative pattern, its moulding from Qin period is just employed on torch.Pushing away
Today of the outstanding traditional national cultures of Chong Hongyang, the research to traditional art form seem still to be important.Wherein, to tradition design
Pattern enters line search, collection, classification, analysis, the national wisdom that finds wherein to contain, the artistic language for meeting east aesthetic standards
Speech, it is all valuable that Modern Art Design vocabulary is either still enriched for academic research.
The original lira that the starting point of development of Chinese tradition moire can be traced back in Neolithic Age ancient painted pottery decorative pattern.And spring and autumn
Cloud thunder line on the Warring States Period bronze ware is considered as more clearly earliest shaping moire, rear to experienced cirrus line, cloud again
The procreation transition of the patterns such as gas line, stream moire, cloudlet line, the moire that complies with one's wishes, group's moire, folded moire, from initial simple abstract hair
Open up and intend shape and freehand brushwork, pattern is extremely rich and changeful, even the moire of same major class, with epoch, region, creator not
Together, also variform change.Because moire art form is extremely abundant, all kinds of patterns data are vast as the open sea, to do
This good research housekeeping relies solely on artificial lookup, arranges and sort out, and its efficiency is very low, therefore non-by introducing
The clustering method of supervision, the automatic classification of moire pattern is realized on the basis of pattern characteristics are studied undoubtedly has great meaning
Justice.
Frey in 2007 et al. proposes a kind of brand-new clustering algorithm based on cluster class center, i.e. AP on science
Clustering algorithm (Frey B J:《Clustering by passing messages between data points》[J]
.science,2007,315(5814):972-976.), and by the Euclidean distance pair between the algorithm combination different images pixel
Facial image has carried out cluster research, achieves Clustering Effect more more preferable than k-centers.AP is clustered and calculated by Frey et al. afterwards
Method combination SIFT feature is used for cluster analysis to Caltech101 images, it was demonstrated that using SIFT algorithms extraction characteristics of image knot
Closing AP algorithms progress image clustering has certain superiority (Dueck, Frey B J.《Non-metric Affinity
Propagation for Unsupervised Image Categorization》[C]//Proc of 11th
International Conference on IEEE Computer Vision.Toronto,Canada,2007:1-8).King
Prosperous et al. proposed MEAP clustering algorithms in 2013 on PAMI, and the Model Extension by AP algorithm single cluster classes center is more subclasses
The Clustering Model at center, and the cluster of facial image, Aaltech101 images and SceneClass13 is entered with reference to SIFT feature
Go research, improve clustering precision (the Wang C D of the more subclass images of algorithm process:《Multi-exemplar affinity
propagation》[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,
2013,35(9):2223-2237).At present, the research classified automatically to China's tradition moire pattern is still blank.
The content of the invention
The present invention uses for reference Frey and Wang Changdong et al. achievement in research, proposes a kind of more subclasses based on neighbor relationships transmission
Center neighbour's propagation clustering algorithm (neighbor propagation based multi-exemplar affinity
Propagation, NP-MEAP), the automatic classification of moire pattern is realized with reference to SC feature extraction algorithms.The purpose of the present invention exists
In overcome moire topography manual sort very poorly efficient the shortcomings that, a kind of unsupervised moire topography automatic classification technology is designed.
Realizing the key problem in technology of the present invention is：Moire topography pretreatment, extract moire topography SC similarity matrixs, by changing
The NP algorithm optimizations similarity matrix that enters, finally classified automatically using MEAP propagation clustering algorithms.Implement step bag
Include as follows：
(1) moire topography pre-processes, and normalization moire topography size, removes ambient noise, the refinement of moire topography lines.
(1a) normalizes moire topography size, has so both facilitated being uniformly processed while will not changing image line for successive image
Bar distribution situation
(1b) removes ambient noise, while is also convenient for refining image using Mathematical Morphology Method.
(1c) moire topography lines refine, because the stripe shape of inhomogeneity moire topography is different, and similar moire topography
Stripe shape it is substantially similar, therefore be primarily upon moire topography stripe shape.
(2) the Shape context similarity matrix of moire topography is extracted
(2a) Shape context algorithm thinks that object in each image can be with equally distributed limited in graphic limit
The discrete point of number carrys out approximate description, so the borderline discrete point of moire topography need to be extracted.
(2b) calculates its Shape context for each discrete point.
(2c) calculates the Shape context difference between any two points in two width moire topographies.
(2d) calculates the tangent angular difference between any two points in two width moire topographies.
(2e) organically combines the Shape context difference between any two points in two width moire topographies and tangent angular difference.
(2f) calculates the Shape context distance value between any two width moire topography.
(3) improved neighbour's pass-algorithm (NP) optimization SscMatrix
(3a) calculates Shape context Distance matrix D.
(3b) calculates neighbor relationships and transmits threshold epsilon.
(3c) calculates the similarity matrix S between moire topography.
(3d) calculates neighbor relationships matrix N.
(3e) neighbor relationships pass-algorithm optimizes similarity matrix.
(4) input matrix using the similarity matrix after above-mentioned optimization as MEAP algorithms, by adjusting reference value, is obtained
Number of correctly classifying is obtained, realizes the automatic classification of moire topography.
The present invention is pre-processed to moire topography, suitable image characteristics extraction algorithm is have chosen, based on manifold
The thought of habit, similarity matrix is optimized using improved neighbor relationships pass-algorithm, finally using newest more subclasses
Center neighbour's propagation clustering algorithm realizes automatic classification, has filled up the blank that moire topography is classified automatically, while ensure that moire
The accuracy of classification of images.
The present invention has advantages below：
(1) by being pre-processed to moire topography, the influence of picture size, ambient noise, line weight is eliminated, is protected
It is unaffected to demonstrate,prove the accuracy classified automatically.
(2) its stripe shape is characterized mainly in that for moire topography, have chosen current superior shape facility and carry
Algorithm is taken, Shape context description ensures that cluster result is more satisfactory.
(3) present invention is further optimized such that algorithm using neighbor relationships pass-algorithm to Shape context similarity matrix
The automatic classification accuracy obtained is higher, realizes the automatic classification of moire topography.
Brief description of the drawings
Fig. 1 is the implementation process figure of the present invention；
Fig. 2 is MEAP Clustering Model；
Fig. 3 is part moire topography example；
Fig. 4 is the moire topography example after size normalization；
Fig. 5 is the moire topography after binaryzation；
Fig. 6 is the moire topography after refinement；
Fig. 7 is that discrete point schematic diagram is extracted on moire topography lines；
Fig. 8 is the vectorial schematic diagram that certain point is put to other in moire topography；
Fig. 9 is six kinds of cirrus print image exemplary plots；
Figure 10 is NP-MEAP and SIFT-MEAP, ED-MEAP moire topography clustering precision contrast schematic diagram；
Figure 11 is NP-MEAP algorithms in moire topography upper part cluster result schematic diagram；
Embodiment
First, basic theory introduction
The center of subclass more than 1. neighbour's propagation clustering algorithm
MEAP algorithms are a clustering algorithms for possessing two-layer structure, and the algorithm as shown in Figure 2 divides all data objects
The most suitable subclass center of dispensing, most suitable super cluster class center is distributed at each subclass center, so as to which implementation model is more
The purpose of subclass problem.
It is similar with AP algorithms, MEAP algorithms be each data object establish with the similarity information s of other data objects (i,
And Connected degree information l (i, j) j).Algorithm is that parameter p=s (k, k) and pp=l (k, k) value are inclined in the setting of each data object,
P is bigger as the subclass center of candidate and the possibility of super cluster centre with the pp values corresponding data object of bigger expression, obtains
The cluster numbers arrived are more, generally set intermediate values of the p with pp values for similarity matrix and Connected degree matrix respectively.MEAP algorithms
Core procedure is the alternating renewal process of 47 formula of class, and more new formula is as follows：
The concrete meaning of relevant parameter can be found in document multi-exemplar affinity in above-mentioned formula
Propagation, all new variables are initialized as 0.In whole iteration renewal process, each data object is carried out MEAP algorithms
Competition automatically produces corresponding subclass center and super cluster class center, and other data objects are distributed to nearest subclass center,
Subclass center is combined together to form final cluster result by super cluster class center.
2nd, the present invention is a kind of traditional moire topography automatic classification method
Reference picture 1, specific implementation process of the invention comprise the following steps：
Step 1. moire topography pre-processes
Fig. 3 is multiple moire pattern examples, the different moire patterns as can be seen from Figure 3 gathered from various data
Size dimension is different, and the thickness of lines differs, while the moire topography of part collection includes gray background noise.Therefore need
Moire topography is pre-processed, to obtain more accurate clustering precision.
(1.1) size of moire topography is different, first by the size of all image normalizations to 85*45, so both
Facilitate being uniformly processed while image lines distribution situation will not being changed for successive image.The moire pattern normalized to after 85*45
As shown in Figure 4.
(1.2) the problem of including ambient noise for moire topography, binary conversion treatment is carried out to image and eliminates ambient noise,
It is also convenient for refining image using Mathematical Morphology Method simultaneously.Using Da-Jin algorithm calculate binary-state threshold, binaryzation it
Moire topography afterwards is as shown in Figure 5.
(1.3) because the stripe shape of inhomogeneity moire topography is different, and the basic phase of stripe shape of similar moire topography
Seemingly, therefore present invention is primarily concerned with moire pattern stripe shape.The different thicknesses of lines and the classification of moire pattern are simultaneously uncorrelated,
The accuracy of cluster may be influenceed on the contrary, therefore uses the method for mathematical morphology that lines are refine to the width of a pixel.Carefully
Moire topography after change is as shown in Figure 6.
Step 2. calculates the Shape context similarity matrix of moire pattern image set
(2.1) SC algorithms think object in each image can with a limited number of discrete point come approximate description, and this
A little discrete points simultaneously need not be the key points such as the flex point in figure, extreme point, but equally distributed discrete point in graphic limit
.Fig. 7 is is extracted discrete point schematic diagram after pretreatment on moire topography lines, the small figure corresponding diagrams 6 of a in wherein Fig. 7
In small figure among upper row, upper row's small figure in the rightmost side in the small figure corresponding diagrams 6 of b in Fig. 7.It can be seen from figure 7 that moire topography lines
On discrete point corresponding moire pattern stripe shape can be described accurately, and the boundary point extracted is more, right
The approximate description of pattern is more accurate.But extraction boundary point it is excessive when, then the run time of algorithm can be caused long, generally choosing
100-150 boundary point is taken more accurately to describe stripe shape, the present invention is retouched using n=100 boundary discrete method point
State stripe shape.
Some point in two small figures in Fig. 7 is marked with small square frame.To profile point set p={ p in Fig. 71,p2,...,
pn, for some discrete point in n=100, consider to arrive the vector of other n-1 point from this point, this n-1 vector can
More accurately to describe the shape information of the moire topography.The discrete point that is marked in Fig. 7 is illustrated in figure 8 to other institutes a little
Vector diagram.
(2.2) each point can originate in the point with n-1 and terminate at the vector of remaining point to describe, each in Fig. 8
The vector description that moire lines are tieed up by n n-1, it is hereby achieved that every width moire topography is than more rich feature Description Matrix.
But all calculate all these vectors to describe moire topography, amount of calculation can be very big and unrealistic.For shape
For, only just know that and calculate on moire topography outline all discrete points relative to the position relationship of the point.Cause
Rectangular coordinate system where moire lines is transformed under log-polar system by this, using discrete point to be calculated as log-polar
It is round dot, by polar coordinate system, the π from 0 to 2 is equally divided into 12 parts on direction, leads on radius since polar coordinates round dot out to 2r
Cross the conversion of log space function and be divided into 5 parts, wherein r is the average value of data set Euclidean distance, so whole polar coordinate system just by
It is divided into 60 parts (bin).The profile point for calculating moire topography is scattering into discrete points in each bin, formed one 60 dimension to
Amount, the vector of this 60 dimension are referred to as the log-polar histogram of the Shape context, i.e. discrete point of corresponding discrete point.Calculate straight
Square figure formula is as follows：
hi(k)=# { q ≠ pi:(q-pi)∈bin(k)}
Wherein k represents k-th of bin in polar coordinate system, and value is 1 to 60, piFor the moire topography of histogram to be calculated
Boundary point, q are except piOther n-1 boundary point outside point, q-piFor the number of boundary point in k-th of bin.
(2.3) the Shape context difference in two width moire topographies between any two points is calculated, in moire topography P
One boundary point piWith boundary point q in moire topography Qj, useThe Shape context difference for marking the two to put,
SoCalculation formula it is as follows, wherein hiAnd h (k)j(k) p is represented respectivelyiWith qjBorder in k-th of bin in histogram
The number of point.
(2.4) the tangent angular difference in two width moire topographies between any two points is calculated.Shape context diversity ratio is preferable
The overall difference for capturing different moires discrete point in shape, in order that difference between moire shape discrete point is more accurate
Really, the tangent angular difference of discrete point is added, formula is as follows, wherein θiWith θjRespectively piWith qjTangent angle at point.
(2.5) by the Shape context difference between any two points in two width moire topographies and the organic knot of tangent angular difference
Close, it is possible to more accurately measure the Shape context distance between any two point on different moire topographies.Formula is as follows：
(2.6) the Shape context distance between two width moire topographies is calculated.By above-mentioned formula by calculating moire topography P
In Arbitrary Boundaries point piWith Arbitrary Boundaries point q in moire topography QjBetween Shape context distance, obtain a n*n (n=
100) distance matrix, by distance matrix, laterally and longitudinally the average value of minimum value sums to obtain the shape between two width moire topographies
Shape context distance value.Calculation formula is as follows：
Above-mentioned formula income value is smaller, and difference is smaller between two images, and similitude is bigger, on the contrary then similitude is smaller.
The value is negated as the Shape context similarity measurement between two images, is designated as Ssc(P, Q)=- Dsc(P, Q), calculate
Shape context similarity measurement between all images tries to achieve the similarity matrix S of moire pattern image setsc。
Improved neighbour's pass-algorithm (NP) optimization S of step 3.scMatrix
(3.1) Shape context Distance matrix D=[d is calculatedij]n×n, the matrix is for initializing neighbour described below
Relational matrix N, the element d in matrixijFor moire topography i and j Shape context distance, the value takes opposite number to be used for more recently
Similarity matrix S after adjacent relation transmission success.
(3.2) neighbor relationships are calculated and transmit threshold value, note moire topography xiDistance with its k-th of Neighbor Points is dik, take institute
There are moire topography and the average value of its k-th of nearest neighbor distance to weaken noise data to a certain extent as threshold value, the threshold value
Influence, while choose different k values for different data set and can make it that neighbor relationships transmission is more accurate.New threshold formula
It is defined as follows：
(3.3) similarity matrix between moire topography, similarity matrix S=[s are calculatedij]n×n, the i-th row jth in matrix
Column element sijCalculation formula be defined as follows：
dijFor Shape context distance, amplify the distance between all moires here by exponential transform, main purpose is
Amplification is positioned at the distance between moire topography in different manifolds, so as to reduce its similarity.
(3.4) neighbor relationships matrix N is calculated, if the element d in Distance matrix DijThreshold epsilon is transmitted less than neighbor relationships,
It is considered that data object xiWith xjNeighbour each other, it is expressed as (xi,xj) ∈ R, thus define the neighbour for trying to achieve all moire topographies
Relational matrix.I.e. as data object xiWith xjEach other during neighbour, then corresponding element n in matrixijValue be 1, otherwise value
For 0, diagonal entry 0.
(3.5) neighbor relationships transmission optimization similarity matrix, i.e., if nij=0, and nik=1, nkj=1, then n is setij
=1, nji=1, while update sij=sji=-min (dik,dkj)。
The similarity matrix after above-mentioned optimization is run algorithm by step 4., passes through tune
Whole reference value, correctly classification number is obtained, realizes the automatic classification of moire topography.
The effect of the present invention can be further illustrated by following experiment.
1. simulated conditions
The cirrus line for resulting from Qin period is expanded the group that circumnutates for becoming different structure of moving out by Yun Leiwen abstract hook scroll
Close.Cirrus line is widely used in the incrustation of various implements moulding from period in Spring and Autumn and Warring States to Qin Han dynasty, bronze ware, lacquerware,
The cirrus line of various moulding can be seen in beautiful decorations, the embroidery of eaves tile tile carving, picture-weaving in silk etc..Cirrus line sculpture style species is enriched,
Decorative effect is various, and consequence is suffered from decorative art developing history and Contemporary Design application field.
Here sample patterns of the moire pattern as test the inventive method are rolled up from Qin period.Data set includes 6
230 width moire patterns of type.It is respectively single hook formula cirrus line, cohesive type cirrus according to the difference of cirrus line curve shape
Line, divergence expression cirrus line, composite type cirrus line, such as S-shaped cirrus line, Italian type cirrus line.Fig. 9 is the exemplary plot of this 6 kinds of cirrus lines
Case.
In order to verify that the present invention puies forward the feasibility and validity of algorithm, the present invention is transmitted special with SC based on neighbour
The MEAP algorithms (NP-MEAP) of sign are with the MEAP algorithms (SIFT-MEAP) based on SIFT feature and based on Euclidean distance
MEAP algorithms (ED-MEAP) are compared.Whole experiment process, the initial value for setting the p and pp of algorithm are similarity matrix
Intermediate value, damped coefficient lam=0.9, convergent iterations number convits=50, maximum cycle maxits=1000, γ=3.
It is as follows to test running environment：Processor is Core (TM) i5-3470, dominant frequency 3.2GHz, internal memory 4GB, hard disk 500GB, operation system
It is Matlab R2013a to unite as the bit manipulation system of 7 Ultimates of Windows 64, programming language.The present invention is using conventional cluster
Evaluation of result index NMI indexs and FMI indexs.
The calculation formula for standardizing co-information NMI indexs is as follows：
The class label of wherein π cluster classes obtained by clustering algorithm, the class label that ζ truly classifies for data set, ni(h) cluster is represented
Class l and data object in true classification h number.H (π) is cluster class label π Shannon entropy, and H (ζ) is true tag along sort ζ's
Shannon entropy, niWith n(j)Respectively cluster class i and sample point in true classification j number.NMI value is bigger, illustrate cluster result with
Truly classify closer.
The calculation formula of FMI (Fowlkes-Mallows Index) index is as follows：
If the cluster result of clustering algorithm C={ c1,c2,...,cmRepresent, the true classification P={ p of data set1,
p2,...,plRepresent.xiAnd xjFor any two data object in data set.Wherein a is xiAnd xjOne is belonged in C and P
The number of cluster；B is xiAnd xjBelong to same cluster in C, and belong to the number of different clusters in P；C is xiAnd xjBelonged in C
Different clusters, and belong to the number of same cluster in P；D is xiAnd xjIn the number of C clusters different from being belonged in P, a+b+c+d here
=n (n-1)/2.It can thus be appreciated that FMI spans are [0,1], and value is bigger, and algorithm cluster accuracy rate is higher.
Based on the MEAP algorithms of moire topography SIFT feature after moire topography pretreatment, by the moire of a pixel wide
Lines are suitably expanded, to ensure to enable SIFT algorithms more effectively to extract suitably in the case that stripe shape is constant
SIFT feature.MEAP algorithms based on Euclidean distance are after moire topography pretreatment, equally by the moire line of a pixel wide
Bar is suitably expanded, while the image pixel gray level value that image is returned to before binaryzation, ensures that Euclidean distance can be more with this
Add the distance reflected exactly between moire topography.MEAP algorithms based on Shape context and neighbor relationships transmission extract discrete
Point has certain randomness, thus the discrete point detected every time has certain difference, so that algorithm once runs institute
The Shape context distance obtained has certain fluctuation, therefore Shape context algorithm is run 20 times, takes 20 Shape contexts
Distance and the input as neighbor relationships pass-algorithm, optimize similarity matrix, so as to ensure the stability of algorithm.
2. simulation result
The inventive method (NP-MEAP) is compared with ED_MEAP and SIFT_MEAP methods.
Figure 10 is NP-MEAP and SIFT-MEAP, ED-MEAP moire topography clustering precision contrast schematic diagram, can from figure
To see, the clustering precision of two kinds of algorithms of SIFT-MEAP and ED-MEAP is essentially identical, all can only achieve 40% or so cluster
Accuracy, it can thus be appreciated that the moire topography characteristic matching number based on SIFT extractions is similar to the moire topography based on negative Euclidean distance
Spend the similarity that can not all reflect well between moire topography.And the cluster accuracy for reviewing NP-MEAP can reach 80% with
On.For sufficiently complex moire pattern clustering problem, such precision is pretty good, can largely mitigate
The working strength and efficiency of manual sort.This also illustrates by the optimization of neighbor relationships pass-algorithm based in shape simultaneously
The similarity that the similarity matrix of following traits can preferably reflect between moire topography, thus Clustering Effect is more preferable.
Figure 11 is NP-MEAP algorithms cluster result schematic diagram on moire topography, wherein each round rectangle represents one
Cluster class, by the image of middle mistake cluster that the moire topography of grid mark is corresponding cluster class in each round rectangle.
Claims (3)
1. a kind of automatic classification method of traditional moire pattern, comprises the following steps：
(1) moire topography pre-processes, and normalization moire topography size, removes ambient noise, the refinement of moire topography lines：
(1a) normalizes moire topography size, has so both facilitated being uniformly processed while will not changing image lines point for successive image
Cloth situation；
(1b) removes ambient noise, while is also convenient for refining image using Mathematical Morphology Method；
(1c) moire topography lines refine, because the stripe shape of inhomogeneity moire topography is different, and the line of similar moire topography
Strip is substantially similar, therefore is primarily upon moire topography stripe shape；
(2) the Shape context similarity matrix of moire topography is extracted：
(2a) Shape context algorithm thinks that the object in each image can use equally distributed finite population in graphic limit
Discrete point carry out approximate description, so extraction borderline 100 discrete points of moire topography carry out approximate description moire topography lines
Profile；
(2b) calculates its Shape context for each discrete point, and the rectangular coordinate system where moire lines is transformed into logarithm pole
Under coordinate system, using discrete point to be calculated as log-polar system round dot, by polar coordinate system on direction from 0 to 2 π is equally divided into
12 parts, it is divided into 5 parts by the conversion of log space function out to 2r since polar coordinates round dot on radius, wherein r is data set
The average value of Euclidean distance, so whole polar coordinate system are divided into 60 parts (bin), and the profile point for calculating moire topography is scattering into
Discrete points in each bins, the vector of one 60 dimension is formed, the vector of this 60 dimension is referred to as to correspond to discrete point in shape
Hereafter, i.e., the log-polar histogram of discrete point, calculating histogram formula are as follows：
hi(k)=# { q ≠ pi:(q-pi) ∈ bin (k),
Wherein k represents k-th of bin in polar coordinate system, and value is 1 to 60, piFor the border of the moire topography of histogram to be calculated
Point, q are except piOther n-1 boundary point outside point, q-piFor the number of boundary point in k-th of bin；
(2c) calculates the Shape context difference between any two points in two width moire topographies, for one in moire topography P
Boundary point piWith boundary point q in moire topography Qj, useThe Shape context difference for marking the two to put, thenCalculation formula it is as follows, wherein hiAnd h (k)j(k) p is represented respectivelyiWith qjBoundary point in k-th of bin in histogram
Number：
<mrow>
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<mi>j</mi>
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</mrow>
</msubsup>
<mo>=</mo>
<mi>C</mi>
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<mi>p</mi>
<mi>i</mi>
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<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<mfrac>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>h</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>h</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
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<mn>2</mn>
</msup>
<mrow>
<msub>
<mi>h</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
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</mrow>
<mo>+</mo>
<msub>
<mi>h</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
(2d) calculates the tangent angular difference between any two points in two width moire topographies, in order that difference between moire shape more
Add the tangent angular difference of accurate addition profile point, formula is as follows, wherein θiWith θjRespectively piWith qjTangent angle at point：
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<msubsup>
<mi>C</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
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<mi>t</mi>
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<mi>n</mi>
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<mo>=</mo>
<mn>0.5</mn>
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<mn>1</mn>
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<mi>&theta;</mi>
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<mi>&theta;</mi>
<mi>j</mi>
</msub>
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</mrow>
<mo>;</mo>
</mrow>
(2e) organically combines the Shape context difference between any two points in two width moire topographies and tangent angular difference, can be with
It is as follows more accurately to measure the Shape context distance between any two point, formula on different moire topographies：
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<mrow>
<mi>i</mi>
<mi>j</mi>
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<mo>=</mo>
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<mi>&beta;</mi>
<mo>)</mo>
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<mrow>
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<mo>+</mo>
<msubsup>
<mi>&beta;C</mi>
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<mi>a</mi>
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<mo>,</mo>
<mi>&beta;</mi>
<mo>=</mo>
<mn>0.1</mn>
<mo>;</mo>
</mrow>
The Shape context that the Shape context distance that (2f) is calculated between any two width moire topography obtains moire topography is similar
Matrix is spent, by calculating the Arbitrary Boundaries point p in moire topography PiWith Arbitrary Boundaries point q in moire topography QjBetween in shape
Hereafter distance, obtain the distance matrix of a n*n (n=100), by distance matrix laterally and longitudinally minimum value average value sum
The Shape context distance value between two width moire topographies is obtained, calculation formula is as follows：
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(3) improved neighbour's pass-algorithm (NP) optimization SscMatrix：
(3a) calculates Shape context Distance matrix D=[dij]n×n, the element d in matrixijFor moire topography i and j in shape
Hereafter distance, the value take opposite number to be used to update the similarity matrix S after neighbor relationships transmission success；
(3b) calculates neighbor relationships and transmits threshold epsilon, note moire topography xiDistance with its k-th of Neighbor Points is dik, take all clouds
The average value of print image and its k-th of nearest neighbor distance is defined as follows as threshold value, threshold formula：
<mrow>
<mi>&epsiv;</mi>
<mo>=</mo>
<mi>m</mi>
<mi>e</mi>
<mi>a</mi>
<mi>n</mi>
<mrow>
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<mrow>
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<mo>=</mo>
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</mrow>
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</munderover>
<msub>
<mi>d</mi>
<mrow>
<mi>i</mi>
<mi>k</mi>
</mrow>
</msub>
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</mrow>
<mo>;</mo>
</mrow>
(3c) calculates the similarity matrix S, similarity matrix S=[s between moire topographyij]n×n, the i-th row jth row member in matrix
Plain sijCalculation formula be defined as follows：
sij=-dij γ,
Wherein dijFor Shape context distance, amplify the distance between all moires here by exponential transform, main purpose is
Amplification is positioned at the distance between moire topography in different manifolds, so as to reduce its similarity；
(3d) calculates neighbor relationships matrix N, if the element d in Distance matrix DijThreshold epsilon is transmitted less than neighbor relationships, then is recognized
For data object xiWith xjNeighbour each other, corresponding matrix element nijValue be set to 1, otherwise value be 0, diagonal entry 0；
(3e) neighbor relationships pass-algorithm optimizes similarity matrix, i.e., if nij=0, and nik=1, nkj=1, then n is setij
=1, nji=1, while update sij=sji=-min (dik,dkj)；
(4) input matrix using the similarity matrix after above-mentioned optimization as MEAP algorithms, by adjusting reference value, obtain just
True classification number, realize the automatic classification of moire topography.
2. the automatic classification method of traditional moire pattern according to claim 1, wherein step (1a) enter according to the following procedure
OK：Moire topography binary-state threshold is calculated using Da-Jin algorithm, pixel is more than the threshold value in moire topography, the pixel value at the point
0 is set to, is otherwise set to 1.
3. the automatic classification method of traditional moire pattern according to claim 1, wherein step (1b) enter according to the following procedure
OK：By image thinning it is a pixel moire lines by Mathematical Morphology Method.
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