CN102446267A - Formula symbol recognizing method and device thereof - Google Patents
Formula symbol recognizing method and device thereof Download PDFInfo
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- CN102446267A CN102446267A CN2010102992164A CN201010299216A CN102446267A CN 102446267 A CN102446267 A CN 102446267A CN 2010102992164 A CN2010102992164 A CN 2010102992164A CN 201010299216 A CN201010299216 A CN 201010299216A CN 102446267 A CN102446267 A CN 102446267A
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Abstract
The invention belongs to the field of formula recognition and discloses a formula symbol recognizing method and device thereof. The method comprises the steps of: recognizing a formula symbol beta in a formula through character recognizing technology, giving a recognition candidate alpha corresponding to the formula symbol beta and giving a symbol similarity degree value of the recognition candidate alpha; calculating the linguistic probability of the recognition candidate alpha corresponding to the formula symbol beta on a formula structure g; and confirming the symbol recognition candidate alpha and /or the formula structure where the symbol recognition candidate alpha is according to the symbol similarity degree value and the linguistic probability. The device comprises a symbol recognition candidate confirming module, a similarity degree value confirming module and a linguistic probability calculating module and confirming module. According to the method and the device which are disclosed by the invention, similar symbols in mathematical formulas can be efficiently distinguished; fuzzy structures in the mathematical formulas can be distinguished; and the accuracy rate of recognizing the mathematical formulas is increased.
Description
Technical field
The present invention relates to formula identification field, particularly a kind of formula Symbol Recognition and device thereof.
Background technology
In mathematical formulae identification, not only there is a large amount of similar characters, also there is more fuzzy spatial relation.As shown in Figure 1, it is ' z ', ' Z ' etc. that symbol ' 2 ' possibly known by mistake, and it is that horizontal structure concerns that the structural relation of symbol ' 2 ' also possibly known by mistake except the superscript structural relation.Therefore, only use character recognition technologies to be difficult to identify effectively correct character, analyze the structural relation that also is difficult to confirm symbol through the locus.At present; What the probability statistics technical application of language model was maximum is the language probability between the statistics character; But this method can only distinguish similar character as ' 2 ' with ' Z ', the position relation between character ' 2 ' and the previous symbol can not distinguished is like superscript and level.
Summary of the invention
Technical matters to be solved by this invention provides a kind of formula Symbol Recognition and device thereof that improves the mathematical formulae recognition accuracy.
Provide a kind of formula Symbol Recognition to comprise according to an aspect of the present invention:
Formula symbols beta through in the character recognition technologies identification formula provides the corresponding identification candidate α of formula symbols beta, provides the symbol similarity degree value of said identification candidate α;
Calculate the corresponding language probability of said identification candidate α on formula structure g of said formula symbols beta;
Confirm the formula structure that Symbol recognition candidate α and/or said Symbol recognition candidate α belong to according to said symbol similarity degree value and said language probability.
According to another aspect of the present invention, provide a kind of formula Symbol recognition device to comprise:
Symbol recognition candidate α determination module, the formula symbols beta through in the character recognition technologies identification formula provides the corresponding identification candidate α of formula symbols beta;
Similarity degree value determination module provides the symbol similarity degree value of said identification candidate α;
Language probability calculation module is calculated the corresponding language probability of said identification candidate α on formula structure g of said formula symbols beta;
Determination module is confirmed the formula structure that Symbol recognition candidate α and/or said Symbol recognition candidate α belong to according to said symbol similarity degree value and said language probability.
According to formula Symbol Recognition provided by the invention and device thereof, not only can distinguish the similarity sign in the mathematical formulae effectively, can also distinguish the fuzzy structure in the mathematical formulae, improved the accuracy of mathematical formulae identification.
Description of drawings
Fig. 1 is formula symbol X
2The symbol that middle subscript 2 possibly be identified and the synoptic diagram of structure;
Fig. 2 is the schematic flow sheet of a kind of formula Symbol Recognition of providing of the embodiment of the invention;
Fig. 3 is the schematic flow sheet that calculates the corresponding language probability of identification candidate α on formula structure g of said formula symbols beta in the method shown in Figure 2;
Fig. 4 is the schematic flow sheet of the language probability P (g) of computing formula structure g in corpus in the method shown in Figure 3;
Fig. 5 is the schematic flow sheet that the identification candidate α of computing formula structure g, formula symbols beta in the method shown in Figure 3 appears at the language probability P (g á) in the corpus simultaneously;
Fig. 6 confirms Symbol recognition candidate α according to symbol similarity degree value and language probability in the method shown in Figure 2;
Fig. 7 is the structured flowchart of a kind of formula Symbol recognition device of providing of the embodiment of the invention;
Fig. 8 is the structured flowchart of language probability calculation module in the device shown in Figure 7;
Fig. 9 is the structured flowchart of first computing module in the language probability calculation module shown in Figure 8;
Figure 10 is the structured flowchart of second computing module in the language probability calculation module shown in Figure 8;
Figure 11 is a determination module structured flowchart in the device shown in Figure 7;
The object of the invention, function and advantage will combine embodiment, further specify with reference to accompanying drawing.
Embodiment
As shown in Figure 2, a kind of formula Symbol Recognition that the embodiment of the invention provides can may further comprise the steps:
Step S1, through the formula symbols beta in the character recognition technologies identification formula, provide the corresponding identification candidate α of formula symbols beta, provide the symbol similarity degree value of identification candidate α.For example, to X
2In subscript 2 provide ' 2 ', the identification candidate of ' z ' and ' Z '; Can be to ' 2 ', ' z ' and ' Z ' provide symbol similarity degree value respectively; Symbol similarity degree value as ' 2 ' is 100, and the symbol similarity degree value of ' z ' is 50, and the symbol similarity degree value of ' Z ' is 30.
Step S2, the corresponding language probability of identification candidate α on formula structure g of computing formula symbols beta.This step will combine Fig. 3～flow process shown in Figure 5 to be elaborated.
Step S3, confirm the formula structure at Symbol recognition candidate α and/or said Symbol recognition candidate α place according to said symbol similarity degree value and language probability.This step will combine flow process shown in Figure 6 to be elaborated.
As shown in Figure 3, the corresponding language probability of identification candidate α on formula structure g of above-mentioned steps S2 computing formula symbols beta can comprise the steps: again
Step S21, the computing formula structure g language probability P (g) in corpus.This step will combine flow process shown in Figure 4 to be elaborated.
Wherein, corpus is to be used to collect the mathematical formulae language material.The mathematical formulae language material derives from mathematics handbook, mathematics textbook etc.Can mathematical formulae be preserved according to the LaTex form, and the formula language material of LaTex form is organized into the formula corpus according to the mode of " main symbol-structure-subordinate symbol ".In mathematical formulae, the formula symbol can comprise English alphabet, numeral, Greek alphabet, various operational symbol and operational character etc.Structural relation between symbol and the symbol mainly contains content, entry of a matrix element of radical exponent, the radical of denominator, the radical of molecule, the fraction of superscript, level, subscript, fraction etc.In the present embodiment, the mathematical formulae glossary of symbols can represent that the symbol in the glossary of symbols can represent that the formula structural relation set between symbol and the symbol representes that with G the structure among the formula structural relation collection G is represented with g with β with Ω.
For example, to
The LaTex form of formula (1) is: sqrt [3] frac{1}{x^3+1}}+y;
Formula (1) after putting in order according to " main symbol-structure-subordinate symbol " is: " radical sign radical exponent 3 ", " x in the radical sign radical sign, " " x subscript 3 "; " x horizontal score line ", " score line top 1 ", " score line below x "; " x subscript 3 ", " x level+", "+level 1 "; " radical sign level+", "+horizontal y ".
The said identification candidate α of step S22, computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously.This step will combine Fig. 4, flow process shown in Figure 5 to be elaborated.
Step S23, according to said P (g), P (g á) calculate the formula symbols beta that structure fomula g is arranged the language probability P (á | g), said P (á | g)=P (g á)/P (g).
As shown in Figure 4, the language probability P (g) of step S21 computing formula structure g in corpus can comprise the steps: again
The number of times f (g) that formula structure g occurs in step S211, the statistics corpus.
The total degree S (G) that all formula structures occur in step S212, the said corpus of calculating,
The language probability P (g) of step S213, computing formula structure g, said P (g)=f (g)/S (Ω).
Table 1 is the number of times that various formula structures occur in the corpus, wherein first classifies the formula structure type that exists in the formula as; Second classifies the number of times that corresponding formula structure occurs in the corpus as, and the total degree that all formula structures occur is 2867658; The 3rd classify various formula structures as the language probability be the total degree that number of times/all formula structures occur that various formula structures occur.
The language probability of various formula structures in table 1 corpus
As shown in Figure 5, the language probability P (g á) that the said identification candidate α of step S22 computing formula structure g, formula symbols beta appears in the corpus simultaneously can comprise the steps: again
The number of times f (g á) that the identification candidate α of formula structure g, formula symbols beta occurs simultaneously in step S221, the statistics corpus;
Step S222, calculate the total degree S (G Ω) that formula structures all in the corpus and all formula symbols occur,
Step S223, according to f (g á), the identification candidate α of S (G Ω) computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously, P (g á)=f (g á)/S (G Ω).
The number of times that table 2 occurs for various formula structures in the corpus and formula symbol simultaneously; Wherein first classify formula structure and formula symbol in the formula as combination; Second classifies the number of times that counter structure and corresponding symbol occur in the corpus as; The total degree that all structures, symbol occur be 4875018, the three classify formula structure, formula symbol as associating language probability be number of times/all structures of occurring simultaneously of formula structure, formula symbol, the total degree that all symbols occur.The associating language probability of formula structure, formula symbol has not only reflected the language difference between the similar formula character, has also reflected the language probability difference between the different formulas structure.
The language probability that formula structure, formula symbol occur simultaneously in table 2 corpus
After the said identification candidate α that draws language probability P (g) and the formula structure g of formula structure g in corpus, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously; Can obtain the formula symbols beta of structure fomula g the language probability P (á | g), P (á | g)=P (g á)/P (g).
Table 3 is the language probability that the symbol of formula structure is arranged, and first classifies all the formula symbols under all formula structures as, and second classifies the language probability of this formula symbol when certain formula structure exists as.
Table 3 has the language probability of the symbol of formula structure
| The formula symbol | the formula structure | The language probability that the formula formula-symbol is arranged |
| The x| level | 0.0672 |
| The b| level, | 0.0128 |
| The 2| subscript | 0.0134 |
| The z| subscript | 0.0001 |
| ... | |
| In the x| radical sign | 0.008 |
Draw the symbol similar value of discerning candidate α and discerning candidate α behind the language probability on the formula structure g; So just can confirm Symbol recognition candidate α, step S3 as shown in Figure 6 confirms that according to said symbol similarity degree value and language probability Symbol recognition candidate α can comprise the steps: again
As shown in Figure 7, the embodiment of the invention also provides a kind of formula Symbol recognition device can comprise Symbol recognition candidate determination module 1, similarity degree value determination module 2, language probability calculation module 3 and determination module 4.Wherein, Symbol recognition candidate's determination module 1 provides the corresponding identification candidate α of formula symbols beta through the formula symbols beta in the character recognition technologies identification formula.Similarity degree value determination module 2 provides the symbol similarity degree value of said identification candidate α.Language probability calculation module 3 is calculated the corresponding language probability of said identification candidate α on formula structure g of said formula symbols beta.Determination module 4 is confirmed the formula structure at Symbol recognition candidate α and/or said Symbol recognition candidate α place according to symbol similarity degree value and said language probability.
As shown in Figure 8, language probability calculation module 3 can comprise that again first computing module 31, second computing module 32 and the 3rd calculate module 33.Wherein, the language probability P (g) of first computing module, 31 computing formula structure g in corpus.The said identification candidate α of second computing module, 32 computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously.The 3rd calculate module 33 according to said P (g), P (g á) calculate the formula symbols beta that structure fomula g is arranged the language probability P (á | g), said P (á | g)=P (g á)/P (g).
As shown in Figure 9, first computing module 31 can comprise first statistic unit 311 and first computing unit 312 again.Wherein, the number of times f (g) that formula structure g occurs in the said corpus of first statistic unit, 311 statistics.First computing unit 312 calculates the total degree
of formula structure appearance all in the said corpus and the language probability P (g) of computing formula structure g, said P (g)=f (g)/S (Ω); Said Ω representes the mathematical formulae glossary of symbols, said G formula structure collection.
Shown in figure 10, second computing module 32 can comprise second statistic unit 321 and second computing unit 322 again.Wherein, the number of times f (g á) that the said identification candidate α of formula structure g, formula symbols beta occurs simultaneously in second statistic unit, the 321 statistics corpus.Second computing unit 322 calculates total degree
that formula structures all in the said corpus and all formula symbols occur and according to said f (g á); The identification candidate α of S (G Ω) computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously, said P (g á)=f (g á)/S (G Ω).
Shown in figure 11, determination module 4 can comprise the 4th computing unit 41 and processing unit 42 again.The similarity degree value of the identification candidate α that wherein, the 4th computing unit 41 is corresponding with the formula symbols beta and language probability P (á | g) carry out weighted.Processing unit 42 is confirmed the formula structure at Symbol recognition candidate α and/or said Symbol recognition candidate α place according to weighted result's size.
Formula Symbol Recognition that the embodiment of the invention proposes and device thereof be through compiling corpus, the associating language probability calculation of language probability calculation, mathematical formulae structure and the formula symbol of mathematical formulae structure, the language probability calculation of the mathematical formulae symbol of structural relation being arranged, and realized having in the mathematical formulae language method for calculating probability of the formula symbol of structural relation.Formula Symbol Recognition that the embodiment of the invention proposes and device thereof not only can be distinguished the similarity sign in the mathematical formulae effectively, can also distinguish the fuzzy structure in the mathematical formulae, have greatly improved the accuracy of mathematical formulae identification.Wherein, the formula Symbol Recognition can also be as an ingredient of computer applied algorithm, and operation is discerned in the relevant algorithm or program with mathematical formulae, also may operate in other similar pattern recognition programs like form identification, polar plot identification etc.
The foregoing description is a preferred implementation of the present invention; But embodiment of the present invention is not restricted to the described embodiments; Other any do not deviate from change, the modification done under spirit of the present invention and the principle, substitutes, combination, simplify; All should be the substitute mode of equivalence, be included within protection scope of the present invention.
Claims (10)
1. a formula Symbol Recognition is characterized in that, comprising:
Formula symbols beta through in the character recognition technologies identification formula provides the corresponding identification candidate α of formula symbols beta, provides the symbol similarity degree value of said identification candidate α;
Calculate the corresponding language probability of said identification candidate α on formula structure g of said formula symbols beta;
Confirm the formula structure that Symbol recognition candidate α and/or said Symbol recognition candidate α belong to according to said symbol similarity degree value and said language probability.
2. method according to claim 1 is characterized in that, the corresponding language probability of said identification candidate α on formula structure g of the said formula symbols beta of said calculating comprises:
The language probability P (g) of computing formula structure g in corpus; Said corpus is to put various mathematical formulaes in order form formula corpus according to the mode of " main symbol-formula structure-subordinate symbol ";
The said identification candidate α of computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously;
According to said P (g), P (g á) calculate the formula symbols beta that structure fomula g is arranged the language probability P (g á | g), said P (á | g)=P (g á)/P (g).
3. method according to claim 2 is characterized in that, the language probability P (g) of said computing formula structure g in corpus comprising:
Add up the number of times f (g) that formula structure g occurs in the said corpus;
Calculate the total degree S (G) that formula structures all in the said corpus occurs,
The language probability P (g) of computing formula structure g, said P (g)=f (g)/S (Ω); Said Ω representes the mathematical formulae glossary of symbols, said G formula structure collection.
4. method according to claim 3 is characterized in that, the language probability P (g á) that the said identification candidate α of said computing formula structure g, formula symbols beta appears in the corpus simultaneously comprising:
The number of times f (g á) that the said identification candidate α of formula structure g, formula symbols beta occurs simultaneously in the statistics corpus;
Calculate the total degree S (G Ω) that formula structures all in the said corpus and all formula symbols occur,
According to said f (g á), the identification candidate α of S (G Ω) computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously, said P (g á)=f (g á)/S (G Ω).
5. according to each described method of claim 2 to 4, it is characterized in that, confirm that according to said symbol similarity degree value and said language probability Symbol recognition candidate α comprises:
With said symbol similarity degree value and said language probability P (á | g) carry out weighted;
Confirm the formula structure at Symbol recognition candidate α and/or said Symbol recognition candidate α place according to said weighted result's size.
6. a formula Symbol recognition device is characterized in that, comprising:
Symbol recognition candidate's determination module, the formula symbols beta through in the character recognition technologies identification formula provides the corresponding identification candidate α of formula symbols beta;
Similarity degree value determination module provides the symbol similarity degree value of said identification candidate α;
Language probability calculation module is calculated the corresponding language probability of said identification candidate α on formula structure g of said formula symbols beta;
Determination module is confirmed the formula structure that Symbol recognition candidate α and/or said Symbol recognition candidate α belong to according to said symbol similarity degree value and said language probability.
7. device according to claim 6 is characterized in that, said language probability calculation module comprises:
First computing module, the computing formula structure g language probability P (g) in corpus; Said corpus is to put various mathematical formulaes in order form formula corpus according to the mode of " main symbol-formula structure-subordinate symbol ";
Second computing module, the said identification candidate α of computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously;
The 3rd calculates module, according to said P (g), P (g á) calculate the formula symbols beta that structure fomula g is arranged the language probability P (á | g), said P (á | g)=P (g á)/P (g).
8. device according to claim 7 is characterized in that, said first computing module comprises:
First statistic unit is added up the number of times f (g) that formula structure g occurs in the said corpus;
First computing unit; Calculate the total degree
of formula structure appearance all in the said corpus and the language probability P (g) of computing formula structure g, said P (g)=f (g)/S (Ω); Said Ω representes the mathematical formulae glossary of symbols, said G representation formula structure collection.
9. device according to claim 8 is characterized in that, said second computing module comprises:
Second statistic unit, the number of times f (g á) that the said identification candidate α of formula structure g, formula symbols beta occurs simultaneously in the statistics corpus;
Second computing unit; Calculate total degree
that formula structures all in the said corpus and all formula symbol occur and according to said f (g á); The identification candidate α of S (G Ω) computing formula structure g, formula symbols beta appears at the language probability P (g á) in the corpus simultaneously, said P (g á)=f (g á)/S (G Ω).
10. according to each described device of claim 7 to 9, it is characterized in that said determination module comprises:
The 4th computing unit, with said symbol similarity degree value and said language probability P (á | g) carry out weighted;
Processing unit is confirmed the formula structure that Symbol recognition candidate α and/or said Symbol recognition candidate α belong to according to said weighted result's size.
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| CN106611148A (en) * | 2015-10-21 | 2017-05-03 | 北京百度网讯科技有限公司 | Image-based offline formula identification method and apparatus |
| CN110728321A (en) * | 2019-10-11 | 2020-01-24 | 北京一起教育信息咨询有限责任公司 | Training method and device for recognizing fractional image, and recognition method and device |
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| CN106611148B (en) * | 2015-10-21 | 2020-04-24 | 北京百度网讯科技有限公司 | Image-based offline formula identification method and device |
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