CN104200239A - Image feature fusion identification based signature authentic identification system and method - Google Patents
Image feature fusion identification based signature authentic identification system and method Download PDFInfo
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Abstract
The invention discloses an image feature fusion identification based signature authentic identification system and method. The signature authentic identification system is mainly composed of a signature image feature value database module, a signature image pre-processing module, a feature extraction and analysis module, a feature fusion module and a feature similarity measurement module. A scanner records a signature sample needing the authentic identification, and a feature processing module extracts feature parameters of the sample and records the feature parameters into a database; the signature image pre-processing module converts a signature image needing the authentic identification into a normalized binary image; the feature processing module processes and extracts corresponding characteristic parameters, and sends the feature value to the feature similarity measurement module after the feature vector infusion so as to finish matching and comparison with corresponding feature values in the database and output an identification result. The image feature fusion identification based signature authentic identification system and method can perform offline signature authentic identification, and the authentic identification result is steady and objective.
Description
Technical field
The present invention relates to a kind of signature identification system and method based on multi-features and image recognition, belong to Digital Image Processing and handwriting verification technical field.
Background technology
The develop rapidly of infotech brings great convenience to daily life, meanwhile to personal identification authenticate accurately, protection information safety become the current information age to need a key issue of solution badly.Handwritten signature is people's a kind of more stable behavioural characteristic, the certification that utilizes handwritten signature to carry out personal identification has non-infringement (or non-tactile property), is easy to obtain, easily makes the features such as people accepts, and is a kind of expression means of important personal identification.
Handwritten signature false distinguishing is under the jurisdiction of this technical field of handwriting verification, traditional handwriting verification based on artificial has exposed all drawbacks and defect in practical operation: as certifying agency lacks the mechanism that cooperatively interacts, appraiser recognition of qulifications standard is lack of standardization, identification level is uneven is difficult to ensure that correctness of identifying etc. all can cause negative effect to qualification result.Therefore utilize computer automation, normalized mode to process the field of the non-engineering of this script of handwriting verification, the development in this field is had to very large impetus.
At present signature false distinguishing can be divided into two kinds of online and off lines by the difference of practical manner, both has very wide application background, can play a significant role such as the field such as criminal investigation and court judgment of finance, insurance, police and judicial department.These technology have the features such as the impact that qualification is fast, efficiency is high, be not subject to civilian inspection personnel subjective factor.Very ripe and entered practical stage from the authentication detection technology of actual hand script Chinese input equipment signature, but off line signature stroke order, writing speed, the multidate informations such as pressure of wieling the pen because cannot get signer and write as Signature Verification time, undoubtedly can be larger in the difficulty of the qualification true and false, so the authenticate technology of off line signature is also not overripened at present, but also becomes study hotspot instantly.
Summary of the invention
The present invention is directed to the technology vacancy in the handwritten signature qualification of current social hot topic, proposed a kind of signature identification system and method based on multi-features and image recognition, attempt to improve the sign present situation of false distinguishing of off line.
Based on a signature identification system for multi-features identification, it is characterized in that, mainly comprise signature image database module, image pretreatment module, proper vector extraction module, proper vector Fusion Module and characteristic similarity metric module;
Also comprise image typing module and result output feedback module;
The pre-stored registered user's of signature image database module personal handwritten signature image, personal information, call these information in follow-up false distinguishing process and examine the true and false of signature image to be identified;
The signature image to be identified that image pretreatment module is entered system to typing carries out pre-service;
Proper vector extraction module carries out feature extraction to the signature image to be identified after pretreatment module is processed;
The feature that proper vector Fusion Module adopts characteristic layer Fusion Model to extract proper vector extraction module merges;
Characteristic similarity metric module: adopt Cosin method to calculate the similarity for the treatment of the signature image prestoring in false distinguishing signature image and database, by calculating the included angle cosine between the proper vector of correspondence image in proper vector that signature image to be identified extracts and database, judgement similarity between the two, as the judging basis of the qualification true and false.
The preprocessing process of described image pretreatment module comprises the step of gray processing processing, binary conversion treatment and size normalization processing.
Proper vector extraction module comprises ratio feature extraction submodule, texture feature extraction submodule, elastic mesh feature extraction submodule, analyzes respectively and extract ratio feature, textural characteristics and the elastic mesh feature of signature image;
Ratio feature extraction submodule: the stroke length after the refinement of the each signature character of extraction signatory and the ratio of area occupied are as characteristic value data;
Texture feature extraction submodule: the textural characteristics that extracts font, word bit inclination, stroke direction, stroke and the radicals by which characters are arranged in traditional Chinese dictionaries collocation of reflection character;
Elastic mesh feature extraction submodule: utilize the netting twine of one group of imagination to carry out region division to signature image, the object pixel number between any two adjacent netting twines is equated; By font by horizontal, vertical, skim, after right-falling stroke four Directional Decompositions, extract horizontal, vertical, skim, right-falling stroke four direction proper vector value combines, and forms a complete font eigenvector.
Based on a signature false distinguishing method for multi-features identification, it is characterized in that: comprise the following steps:
Scanner completes the information acquisition to needing false distinguishing signature image;
Proper vector extraction module extracts the ratio feature, textural characteristics and the large feature of elastic mesh three that need false distinguishing signature image;
Proper vector Fusion Module is by the three large Fusion Features that extract;
Adopt Cosin method to calculate the similarity for the treatment of false distinguishing signature image and sample signature image, by calculating the included angle cosine between proper vector and the proper vector of sample correspondence image that signature image to be identified extracts, weigh similarity degree with cosine value, output false distinguishing result.
Comprise following detailed step: by needing false distinguishing signature image to use scanner to be input to the signature identification system that Fusion Features is identified, from database, recall the characteristic of its original signature image according to people information;
Picture pre-service to scanning obtains normalized bianry image, carries out feature detection and the analysis of bianry image;
Withdrawal ratio, texture and the large feature of elastic mesh three are carried out feature value vector simultaneously, then after three large features are merged and the characteristic of original signature image compare by vector angle Method of Cosine, draw false distinguishing result.
The extracting method of ratio feature is as eigenwert by ratio characteristic in compute signature bianry image, respectively the character of signature is carried out to rim detection one by one, (character quantity and rectangle frame quantity equate to obtain corresponding rectangle frame, rectangle frame number is at least greater than 1, otherwise typing again), calculate the size S of each character, then need are differentiated to signature image carries out font thinning processing, the pixel of each character is counted, as word length L; Data using the data of each character L/S as two bit vector groups, set up a Vector Groups, obtain ratio characteristic.
The extracting method of textural characteristics, by the extraction to signature image texture features, uses Gabor wave filter to extract texture features; Gabor function is measured in spatial domain and frequency field simultaneously, main target is that signature stroke has certain line thickness and direction, every width writing sample image extracts the feature of person's handwriting texture through each channel filtering, at sample image I (x, y) in, extract sampling point (X, Y), the feature that this some place extracts is by calculating the average of image after each path filter and standard deviation as feature composition characteristic vector, according to eigenwert position, through row feature value vector group, obtain n dimensional feature Value Data Vector Groups.
The extracting method of elastic mesh, by signature image elastic mesh eigenwert is extracted to comparison, adopts elastic mesh, utilizes bianry image, is expressed as black pixel in the time that institute's label taking will amount is 1, is expressed as white pixel point in the time that institute's label taking will amount is 0; Then by after horizontal, vertical font, slash, right-falling stroke four Directional Decompositions, extract transverse direction Chinese character subimage f
h(x, y), i grid internal characteristic of transverse direction uses eigenwert computing formula to calculate, the feature of other several directions in like manner, horizontal, vertical, skim, right-falling stroke four direction eigenwert combines, and forms a complete font proper vector.
The original database of signature false distinguishing Data Comparison work Main Basis, the construction method of database is the personal information that typing in advance needs detection signature, mainly comprises the storage of above three large characteristic data associated eigenvalue Vector Groups.
Signature identification system obtains the proper vector of three large modules by feature extraction analysis module, after using Feature Fusion that the eigenwert of three large modules is merged, be stored to database or backup and carry out similarity measurement work.
The beneficial effect that the present invention reaches:
The invention discloses a kind of signature identification system and method based on multi-features and image recognition, can carry out the false distinguishing of off line signature.By withdrawal ratio feature, textural characteristics, elastic mesh feature as three large main characteristic parameters, adopt Fusion Features model that the feature of extraction is merged, main parameters using proper vector included angle cosine as similarity measurement, completes signature false distinguishing work, and false distinguishing result is stable, objective.
Brief description of the drawings
Fig. 1 is system module structural drawing.
Fig. 2 is characteristic layer Fusion Model figure.
Fig. 3 is system processing procedure figure.
Fig. 4 is that system identification is the surface chart of actual signature.
Fig. 5 is that system identification is the surface chart forging a signature.
Fig. 6 be database set up example (can according to information search raw data such as numbering, name, age, identification card numbers).
Fig. 7 is system test result statistical form.
Embodiment
Native system has adopted modular method for designing, whole system is mainly made up of signature image database module, image pretreatment module, proper vector extraction module, proper vector Fusion Module and this 5 modules of similarity measurement module, supplementary module has comprised image typing module and result output feedback module (as shown in Figure 1), and concrete scheme is as follows:
(1) the datumization information such as registered user's personal handwritten signature image, personal information (as name, sex, ID (identity number) card No. etc.) that signature image database module is pre-stored, as Fig. 6, in follow-up false distinguishing process, can call these information and examine the true and false of signature image to be identified;
(2) image pretreatment module mainly completes the signature image to be identified that typing is entered to system and carries out pretreated work, pretreated process has specifically comprised that gray processing processing, binary conversion treatment and size normalization process these concrete steps, the signature image after pre-service is used further to the processing of subsequent module;
(3) proper vector extraction module is that the false distinguishing signature image for the treatment of after pretreatment module is processed is carried out to the module of feature extraction, can be subdivided into again three submodules, three large features of signature image are analyzed respectively and extracted to modules: ratio feature, textural characteristics and elastic mesh feature.
1. ratio feature extraction submodule: the stroke length after the refinement of the each signature character of extraction signatory and the ratio of area occupied are as characteristic value data.
2. texture feature extraction submodule: textural characteristics can reflect font, word bit inclination, stroke direction, stroke and the radicals by which characters are arranged in traditional Chinese dictionaries of the character features that these are conventional, more stable, distinguishing ability is strong of arranging in pairs or groups, and this submodule uses Gabor wave filter to extract the textural characteristics of signature image.
3. elastic mesh feature extraction submodule: this module utilizes one group of imaginary netting twine to carry out region division to signature image, equates the object pixel number between any two adjacent netting twines.Normally by rectilinear(-al) grid in length and breadth.The feature that this submodule extracts can solve the problems such as the stroke position causing because of writing style difference in handwritten Chinese character is unstable, font local deformation well, and can effectively reflect the CONSTRUCTED SPECIFICATION of handwritten signature.
(4) proper vector Fusion Module: this module adopts characteristic layer Fusion Model (as shown in Figure 2) to merge three of said extracted large features.It is the intermediate level process that characteristic information extraction is comprehensively analyzed and processed from raw information that characteristic layer merges.The characteristic information extracting is abundant expression amount or the statistic that former data Layer merges raw information, and accordingly multi-source information is classified, collected and comprehensively, many feature extractions simultaneously can provide than the more clarification of objective information to be detected of single feature extraction, thereby increase feature space dimension.In brief, it is exactly the identification of combining of characteristic layer that characteristic layer merges, and can effectively improve the performance of false distinguishing.
(5) characteristic similarity metric module: this module adopts Cosin method to calculate the similarity for the treatment of the signature image prestoring in false distinguishing signature image and database.Included angle cosine similarity, also referred to as cosine similarity or cosine distance, is as the tolerance of weighing two interindividual variation sizes with the cosine value of two vector angles in vector space.Vector is the directed line segment in hyperspace, if two vectorial directions are consistent, mitre joint is bordering on zero, and these two vectors are just close so, and will determine that whether two vectorial directions are consistent, and this will use the angle of cosine law compute vector.Vectorial A (x in two-dimensional space
1, y
1) and vectorial B (x
2, y
2) included angle cosine formula:
By calculating the included angle cosine between the proper vector of correspondence image in proper vector that signature image to be identified extracts and database, can calculate similarity between the two, and then can be used as the judging basis of the qualification true and false.
Entity (together with the signature paper) vertical pendulum of signing when system practical operation is put in scanner below, require to take illumination moderate as far as possible, typing equipment pixel is relatively stable higher, pen, paper quality used is higher and unified, paper selects pure white without decorative pattern as far as possible, and pen is selected 0.5mm black signature pen (the refinement link of signature character can ensure the adaptability of system to different signature pens).Take and in chamber, at least use the LED lamp of 200W to provide light source for taking, in scanning process, there will not be the disturbing factors such as anti-light and shade, thereby improved the accuracy of system discriminatory analysis.After having scanned, image is reached to system and carry out discriminance analysis, after judgement, draw feedback.Main core process is extraction fusion and the compare of analysis of off line signature image eigenwert, aspect eigenwert extraction comparison, ratio feature, textural characteristics, elastic mesh feature are mainly extracted as three large main characteristic parameters, three large Fusion Features are drawn to proper vector group, use the main parameters of proper vector included angle cosine as similarity measurement, complete signature character value comparison work, differentiate the true or false of signature character.The signature relevant information of writing people of signature verification is through registration, and everyone of registration have an identification number, and the identity that only need declare according to person to be verified when checking recall corresponding reference signature characteristic value data and differentiate.
The idiographic flow of system algorithm of the present invention is as shown in Figure 3:
(1) in the time that the true and false of signature need be differentiated, utilize scanner to sample to target image, after analog to digital conversion, deposit in the image acquisition data storage area in this module.
(2) establishing the coloured image leaving in image acquisition data storage area is I
1, copy portion and deposit in data storage area and it is carried out to image gray processing to obtain gray level image I
2, and to I
2use medium filtering to remove noise, then use maximum variance between clusters (otsu algorithm) to I
2carry out Threshold segmentation, obtain target signature binary image I
3, finally to I
3carry out size normalization processing to obtain its normalized image I
4, coloured image I will sign
1, original signature gray level image I
2, target signature image I after binary conversion treatment
3, normalized image I
4all temporarily be stored in data storage area for subsequent treatment.
(3) by the bianry image I of size normalization
4the size of middle Chinese character extracts as characteristic ratio characteristic, first determine that the left and right side frame of each word in every row calculates the intersection point of perspective view hist (i) and horizontal ordinate, the row coordinate that records these intersection point places is respectively d1, d2 and d3, store successively by array, respectively the black picture element between d1 and d2, d2 and d3 is added up, if and be greater than zero, can think d1 and d2, d2 and d3 be respectively signature first character and second word, etc. two words and triliteral left and right side frame.Default two indexed variable jug1=0 and jug2=0, pass through sequential query from top to bottom to each character in every row again.Search for the first time black picture element and put jug1=1, now can determine that the row at upper side frame place is ordinate according to this black pixel point.Then by sequential query from bottom to top, search for for the first time black pixel point juxtaposition jug2=1, the row that obtains lower frame place is ordinate.Thereby determine the upper and lower side frame of each word.After determining frame, calculate the size S of each character.Again need are differentiated to signature picture carries out font thinning processing, counts the pixel of each character, as word length L.Data using the data of each character L/S as two bit vector groups, set up a Vector Groups, thereby obtain ratio characteristic.
(4) extraction of texture features, uses Gabor wave filter to extract texture features, has excellent performance aspect the frequency of Gabor conversion regional area in analysing digital image and directional information, and it can accomplish the localization of time-domain signal and frequency-region signal.Gabor function can be measured in spatial domain and frequency field simultaneously, and is all local conversion in these two kinds of territories, has obvious directional selectivity and frequency characteristic.Because signature stroke has certain line thickness and direction, first start with from the statistical information of signature image, every width writing sample image extracts the feature of person's handwriting texture through each channel filtering, at sample image I (x, y) in, extract sampling point (X, Y) characteristic Z of, extracting at this some place is:
Wherein, the size that w is filtering window, h (x, y, f
0, θ
k, σ
x, σ
y) for removing DC component postfilter core function:
Wherein f
0with θ
kbe respectively frequency and the direction parameter of wave function, σ
xand σ
ybe respectively the standard deviation of Gaussian envelope in x direction and y direction.Extract abundant sampling point at I (x, y), all sampling points can be used (X, Y, f by formula Z=
0, θ
k, σ
x, σ
y) extraction feature.
Calculate the average of image after each path filter and standard deviation as feature composition characteristic vector, here the proper vector value obtaining still distributes as the pixel on image, and we are according to eigenwert position, through row feature value vector group, obtain n dimensional feature Value Data Vector Groups.
(5) elastic mesh eigenwert is extracted comparison, is mainly that imaginary netting twine is cut apart font image region here, is the font image housing that proportion of utilization characteristic draws here, carries out the vertical division of certain interval and laterally divides.If grid vertical direction and horizontal direction are equally distributed in figure, so we are called again fixed mesh, if grid vertical direction and horizontal direction right and wrong are equally distributed, we are called again elastic mesh.Adopt elastic mesh here, can tolerate the problems such as signature style difference, local self distortion.We utilize normalization bianry image I
4, work as I
4be expressed as black pixel, I at=1 o'clock
4be expressed as white pixel point at=0 o'clock.Then by after font four Directional Decompositions, we extract transverse direction Chinese character subimage f
h(x, y), the bianry image that wherein f (x, y) is Chinese character, i grid internal characteristic of transverse direction is:
In like manner, " horizontal, vertical, skim, right-falling stroke " four direction eigenwert combines the feature of other several directions, forms a complete font eigenvector.Here the proper vector value obtaining still distributes as the pixel on image, and we through row feature value vector group, also obtain n dimensional feature Value Data Vector Groups according to eigenwert position.
(6), through the extraction of above-mentioned ratio feature, Gabor feature and elastic mesh feature, obtain respectively representing the l dimensional vector F of its feature
1, d dimensional vector F
2and x dimensional vector F
3, wherein F
1={ F
s1, F
s2..., F
sl, F
2={ F
g1, F
g2..., F
gd, F
3={ F
e1, F
e2..., F
ex, then respectively to F
1, F
2and F
3be F according to minimax principle normalization proper vector
1', F '
2and F '
3?
Finally, the above-mentioned three kinds of features after normalization are weighted to cascade and merge,
W in formula
1, w
2and w
3for experience weights, obtain by experiment, and w
1+ w
2+ w
3=1.
(7) vector angle cosine similarity measurement, the fusion feature vector of establishing the signature image to be identified being obtained by above-mentioned steps can be expressed as F=(x
11, x
12..., x
1n), in database, the proper vector of corresponding signature image is G=(x
21, x
22..., x
2n).For these two n-dimensional vectors, can weigh the similarity degree between them by the concept that is similar to included angle cosine, that is:
Included angle cosine span is [1,1], and two vectorial angles of the larger expression of included angle cosine are less, and the angle of less expression two vectors of included angle cosine is larger.In the time that two vectorial directions overlap, included angle cosine is got maximal value 1, when the completely contrary included angle cosine of two vectorial directions is got minimum value-1.The included angle cosine value between image feature vector corresponding in false distinguishing signature image and database is treated in calculating, it is made comparisons with the empirical value T being drawn by experiment in advance, if be greater than the signature (feedback interface as shown in Figure 4) that this threshold value is accredited as same people, if be less than this threshold value, be accredited as the signature (feedback interface as shown in Figure 5) that others forges.
Finally, we utilize existing data sample and instrument to test the performance of system, and test result as shown in Figure 7, has completed the task of the qualification signature true and false substantially.
The present invention can summarize with other the concrete form without prejudice to spirit of the present invention and principal character, therefore, above-mentioned embodiment of the present invention all can only think explanation of the present invention can not limit the present invention, any change in the implication suitable with claim of the present invention and scope, all should think to be included in the scope of claims.
Claims (8)
1. the signature identification system based on multi-features identification, is characterized in that, mainly comprises signature image database module, image pretreatment module, proper vector extraction module, proper vector Fusion Module and characteristic similarity metric module;
Also comprise image typing module and result output feedback module;
The pre-stored registered user's of signature image database module personal handwritten signature image, personal information, call these information in follow-up false distinguishing process and examine the true and false of signature image to be identified;
The signature image to be identified that image pretreatment module is entered system to typing carries out pre-service;
Proper vector extraction module carries out feature extraction to the signature image to be identified after pretreatment module is processed;
Proper vector Fusion Module: the feature that adopts characteristic layer Fusion Model to extract proper vector extraction module merges; Characteristic layer merges the identification of combining that characteristic information extraction is comprehensively analyzed and processed from raw information;
Characteristic similarity metric module: adopt Cosin method to calculate the similarity for the treatment of the signature image prestoring in false distinguishing signature image and database, by calculating the included angle cosine between the proper vector of correspondence image in proper vector that signature image to be identified extracts and database, judgement similarity between the two, as the judging basis of the qualification true and false.
2. the signature identification system based on multi-features identification according to claim 1, is characterized in that: the preprocessing process of described image pretreatment module comprises the step of gray processing processing, binary conversion treatment and size normalization processing.
3. the signature identification system based on multi-features identification according to claim 1, it is characterized in that: proper vector extraction module comprises ratio feature extraction submodule, texture feature extraction submodule, elastic mesh feature extraction submodule, analyze respectively and extract ratio feature, textural characteristics and the elastic mesh feature of signature image;
Ratio feature extraction submodule: the stroke length after the refinement of the each signature character of extraction signatory and the ratio of area occupied are as characteristic value data;
Texture feature extraction submodule: the textural characteristics that extracts font, word bit inclination, stroke direction, stroke and the radicals by which characters are arranged in traditional Chinese dictionaries collocation of reflection character;
Elastic mesh feature extraction submodule: utilize the netting twine of one group of imagination to carry out region division to signature image, the object pixel number between any two adjacent netting twines is equated; By font by horizontal, vertical, skim, after right-falling stroke four Directional Decompositions, extract horizontal, vertical, skim, right-falling stroke four direction proper vector value combines, and forms a complete font eigenvector.
4. the signature false distinguishing method based on multi-features identification, is characterized in that: comprise the following steps:
Scanner completes the information acquisition to needing false distinguishing signature image;
Proper vector extraction module extracts the ratio, texture and the large feature of elastic mesh three that need false distinguishing signature image;
Proper vector Fusion Module is by the three large Fusion Features that extract;
Adopt Cosin method to calculate the similarity for the treatment of false distinguishing signature image and sample signature image, by calculating the included angle cosine between proper vector and the proper vector of sample correspondence image that signature image to be identified extracts, weigh similarity degree with cosine value, output false distinguishing result.
5. the signature false distinguishing method based on multi-features identification according to claim 4, it is characterized in that: comprise following detailed step: by needing false distinguishing signature image to use scanner to be input to the signature identification system that Fusion Features is identified, from database, recall the characteristic of its original signature image according to people information;
Picture pre-service to scanning obtains normalized bianry image, carries out feature detection and the analysis of bianry image;
Withdrawal ratio, texture and the large feature of elastic mesh three are carried out feature value vector simultaneously, then after three large features are merged and the characteristic of original signature image compare by vector angle Method of Cosine, draw false distinguishing result.
6. according to the signature false distinguishing method based on multi-features identification described in claim 4 or 5, it is characterized in that: the extracting method of ratio feature is as eigenwert by ratio characteristic in compute signature bianry image, respectively the character of signature is carried out to rim detection one by one, obtain corresponding rectangle frame, calculate the size S of each character, again need are differentiated to signature image carries out font thinning processing, counts the pixel of each character, as word length L; Data using the data of each character L/S as two bit vector groups, set up a Vector Groups, obtain ratio characteristic.
7. according to the signature false distinguishing method based on multi-features identification described in claim 4 or 5, it is characterized in that: the extracting method of textural characteristics, by the extraction to signature image texture features, uses Gabor wave filter to extract texture features; Gabor function is measured in spatial domain and frequency field simultaneously, main target is that signature stroke has certain line thickness and direction, every width writing sample image extracts the feature of person's handwriting texture through each channel filtering, at sample image I (x, y) in, extract sampling point (X, Y), the feature that this some place extracts is by calculating the average of image after each path filter and standard deviation as feature composition characteristic vector, according to eigenwert position, through row feature value vector group, obtain n dimensional feature Value Data Vector Groups.
8. according to the signature false distinguishing method based on multi-features identification described in claim 4 or 5, it is characterized in that: the extracting method of elastic mesh, by signature image elastic mesh eigenwert is extracted to comparison, adopt elastic mesh, utilize bianry image, in the time that institute's label taking will amount is 1, be expressed as black pixel, in the time that institute's label taking will amount is 0, be expressed as white pixel point; Then by after horizontal, vertical font, slash, right-falling stroke four Directional Decompositions, extract transverse direction Chinese character subimage f
h(x, y), i grid internal characteristic of transverse direction uses eigenwert computing formula to calculate, the feature of other several directions in like manner, horizontal, vertical, skim, right-falling stroke four direction eigenwert combines, and forms a complete font proper vector.
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