DE2619014A1 - Information processing character recognition - uses estimated polynomials for weighting factor determination and coordinate reduction - Google Patents

Abstract

The character recognition method for information processing systems employs a scanner (1) and associated store (2) in which characteristic vectors for the raster composition are held. Individual characteristic values of the vectors are calculated (5) and undergo transformation (6) for coordinate reduction. These are stored (3). In a three-stage classifier calculator (7) the estimated polynomials for the reduced number of factors are computed and undergo squaring. The magnitude of the polynomial coefficients is used as an indicator for the order of importance of individual and combined picture elements (8, 9). The indicator is calculated from the sum of the squares of the individual weighting factors associated with the respective elements or combinations of elements. The selected values are stored (10).

Description

Procedure for machine drawing

detection by means of estimated value polynomials The invention relates to to a method for machine character recognition for the selection of picture elements and picture element combinations within a character window, used in polynomials, which are the arguments / class membership estimates to be provided with weighting coefficients determine where the specified, labeled according to their class Character patterns ("samples") are scanned, based on the scanning results Characteristic groups assigned to patterns are registered and the number of characteristics of these sets of characteristics is reduced with a computational transformation.

The character recognition process is known, cf. for example German Offenlegungsschriften 2 262 873 and 2 341 387, which consists in determining the respective class affiliation of the read character by means of class affiliation estimated values for characters that are read in the recognition engine in a character window divided into grid elements d, to determine the for all character classes k of the character set by means of the formula can be calculated, with the arguments x. can either be a single picture element in the grid of the nld window (linear term of the polynomial, where Xi = 1 if belonging to the symbol and x. = 0 if not belonging to the symbol) or the product of two such picture elements, which is also O or 1 (square member). The aik values are weighting coefficients.

When forming the terms of such polynomial classifiers, also higher potencies, i.e. Combinations of more than two picture elements are taken into account will. When creating a combination, an element is always combined with included himself. The coefficients aik can be determined by an optimization process on the basis of full learning samples marked with their class affiliation (adaptation of the recognition system), see "The adaptation of character recognition systems with the help of regression analysis "in" lektronisce Rechenanlagen "11 (1969) 5. 21 - 28.

However, the approach of the underlying polynomial structure presents difficulties. In the case of a quadratic classifier with around 200 picture elements, the number of possible pairs of features is 20,000, but for reasons of complexity and calculation time, no longer polvnom approaches than around 1200 can be allowed for the adaptation. If only 1200 elements are arbitrarily selected from, for example, about 20,000 possible elements, it must be expected that the performance of the classifier will be inappropriately restricted.

The object of the present invention is to create a feature selection method, the selection of the characters to be recognized from a given character set adapted so that the estimated value calculations in a simple manner, in particular only with binary additions (as with the German Offenlegungsschriften mentioned above) can be carried out.

It is already known - see the essay "On the problem of Merknialsreduzierung ei of character recognition "in 18 Scientific Reports AEG-Telefunken" 47 (1974), P. 100 - 110 -, for the purpose of reducing the number of characteristics according to their class marked predetermined character patterns (random samples) based on the Characteristic groups assigned to the individual patterns (characteristic vectors) to determine in which all the individual picture elements that can be scanned in the drawing window are taken into account, and then, associated with a coordinate transformation, in particular Major axis transformation, a (vector) coordinate "mutilation" by selection a smaller number of coordinates. The selection should be based on the requirements the size of the eigenvalues 2 i of the eigenvectors b i of the covariance matrix g which are based on the pattern regardless of the class calculated formula, where, if with {V}, the set of the aforementioned feature vectors is designated, from this the expected value and from this g is to be determined.

According to the invention, a method of the type mentioned in the Way carried out that 1) the sampling results are evaluated in an arithmetic unit that a) to the reduced number of characters for all character classes an estimate polynomial each using only these features and their combinations at least the power of 2 is determined, b) these polynomials are then converted into those, which all picture elements that can be scanned in the drawing window together with their combinations at least are based on the power of 2, c) the individual picture elements and picture element combinations one importance value each from the associated weighting coefficients of all Polynomials calculates that 2) a subset can be delimited from the importance values is made whose individual members are larger in amount than those of the Remainder, and that 3) those picture elements and picture element combinations which assigned to the individual members of the subset in a memory for registration be transmitted.

It is preferably provided that the importance values are the sum the squares of the individual weighting coefficients is determined, each to the same picture element or

belong to the same picture element combination.

Based on the drawings, an embodiment of the invention Procedure explained in more detail below.

Fig. 1 shows devices with which the inventive method is carried out, in a schematic representation, Figures 2 and 3 show diagrams to arithmetic operations.

In Fig. 1, 1 is an optical scanner of, for example, a character recognition machine, which e.g. contains a line of photodiodes and scrolling characters each in a character window that can be divided into e.g. 12x18 grid squares, each of which has one of the aforementioned picture elements results.

First there are character patterns of the character results to be read later numerically sampled stock and the sampling / (by the grid square number and associated "black" or "white" note) together with the identification of the respective Character class - stored in a memory 2. The totality of characteristics of the individual Pattern, namely "black" (= 1) or "white" (= O) descriptions of the individual (here 216) Raster elements, as is known, can be understood as feature vectors.

A memory 3 is derived from the content of the memory 2 the same amount of characteristic groups assigned to the individual patterns ~ entered, their respective number of features, m.a.W. Feature vector dimension, compared to that of the Memory 2 according to the procedure of the above-mentioned article on feature reduction is decreased. This is done by means of an arithmetic unit 4 in the way des already continues the aforementioned remaining after the reduction, Consider features and possible pairings of features. The calculation of the coefficients can be carried out according to the known procedure of square mean adaptation1 like it in the one mentioned at the beginning, which deals with the adaptation of character recognition systems Essay is indicated.

With the underlying reduced number of features of approx.

40 this calculation can be carried out with a reasonable amount of effort.

However, obtaining class membership estimates would be of value on this basis, apart from the transformation, require real multipliers, since the transformed characteristics are no longer simple binary 0 or 1.

Calculation method given above using the covariance matrix, the eigenvalues / | i is calculated from feature vectors bi and then by a selection device 5 the 40 largest eigenvalues, for example, picked out and with the associated eigenvectors bi in a transformation arithmetic unit 6 the set of feature vectors from memory 2 into the coordinate-reduced, e.g. 40-dimensional animal feature vectors mentioned is implemented in memory 3.

On the basis of the feature vectors obtained by the known method of the memory 3, which still refer to the given learning pattern, i.e. their characteristics - even if in incomplete form - are now reproduced in an arithmetic unit 7 (work stage a) a so-called.

"two-stage" classifier (because it is not directly related to the picture elements of the memory 2), namely the totality of the estimated value polynomials is calculated, the terms of which are then all calculated as indicated above The / obtained polynomial population is therefore converted in the arithmetic unit 7 (work stage b) into a "single-stage", namely once again directly related to all picture element features of the memory 2, i.e. a polynomial population whose polynomials each take into account all individual features and possible feature pairings there are around 20,000 members.

If the vector dimension of the feature populations in memory 2 is equal to n and the reduced vector dimension of the feature populations in memory 3 is equal to m, where mn, and the reduced (transformed) m-dimensional feature vector is denoted by «as in the article mentioned, W = (w1 w2 ..... wm) T, (3) and the inW fully quadratic polynomial approach with then, if m = 40 is provided, this has a total of 861 components. With this, the estimating equation is created in the computer stage 7a (cf. equation 5 of the above article) and the polynomial formation according to equation (5) with (4). Since both steps are clearly described, the system can be converted into an equivalent one-step system. Thus, in working stage b of arithmetic logic unit 7, there is a formed in the original features w and adapted in the quadratic mean, so that A ind. is the coefficient matrix of the estimation polynomials formed on the basis of the reduced sets of features, determined on the basis of the sampled patterns.

The fully quadratic classifier made up of these polynomials arises from the succession of two calculation stages, namely the transformation / Complete quaurall scner niassirator, where the approach is the amount of 23436 features and pairings of features.

The calculation method is as follows: If there are K character classes, the estimation vector has K components, namely the K scalar estimation functions already mentioned at the beginning according to equation (1), and accordingly the coefficient matrix Aind also breaks down into K column vectors (class-wise decomposition), i.e. and must therefore be able to be written as a square form in (1 WT) The difference between the two notations Eq. (9) and Eq. (Io) lies essentially in the arrangement of the coefficients of the polynomial. In equation (9) they are arranged in the form of a column vector, in equation (lo) in the form of a symmetrical matrix The conversion of the one-dimensional representation CLind, k into the two-dimensional Ak * takes place in two easily comprehensible steps.

The column vector aind, k is first written in sections in the lower half of a triangular matrix so that the first m + 1 terms are the first Column, the next m members form the second column and continue accordingly, until the last link from cLind, k into the main diagonal element of the (m + 1) -th column is registered. The resulting triangular matrix, Fig. 2, is then used in a second Step halved and one half added to the other after transposition.

Each of the K scalar estimation functions dk (V) from the estimation vector d = (d1 d2 ... dK) T (8) is a fully quadratic polynomial in AN according to equations (4) and (5) .t6) by a linear transformation from the vector y of the directly measured character features. Therefore, the vector (1 wT) used in Eq. (10) can be expressed by To simplify the notation, the matrix of this linear mapping is abbreviated as Thus, Eq. (12) can be written as If the notation of Eq. (14) into the equation of the quadratic form, Eq. (10), then the scalar estimator belonging to class k results as a quadratic form in (1 VT) The again symmetrical matrix of this square shape is It contains all the coefficients of the fully quadratic polynomial in the directly measured character features in a two-dimensional arrangement. This type of representation can be transferred back to the stretched form, The components of the transformation matrix 8 contained in the expression according to equation (13), cf. equation (6), taken from the transformation stage 6 when the calculation is made.

Lu note that the character features v. binary variable are, and therefore the coefficients of the purely quadratic terms with those of the linear ones need to be summarized. Apart from this peculiarity, however, are essentially only to undo the operations that aind, k from the stretched form in have transferred the matrix representation Ak *.

Fig. 3a, b, c The necessary operations take place in three Sub-steps, see / In the first step, all elements of the upper triangular matrix from Ck * the symmetrically corresponding elements of the lower triangular matrix slammed. Since Ck * is symmetrical, this boils down to the values in the Positions of the lower triangular matrix - but without the main diagonal - to be doubled. In the second step, the values of all main diagonal elements are excluded of the first main diagonal element in the corresponding positions of the first Column added into it. This unites the coefficients in polynomial terms v2i with the coefficients for the linear polynomial terms vi. By 1 1 of these measures have the upper triangular matrix and main diagonal in the originally given number scheme - but not the first main diagonal element - emptied. What is left is one lower triangular matrix without main diagonal - apart from the first main diagonal element. In a third processing step, the column vectors finally become this Transfer residual schemes one after the other into the column vector Q equ k.

The first n + 1 elements of result from the first column aäqu, k, from the second column the next n-1 elements, until finally the one Element of the penultimate column becomes the last link in.

equ, k The coefficient vector 0Lä.qu, k created in this way is a column vector from the coefficient matrix Aäqu of a fully quadratic classifier with a direct polynomial approach which produces exactly the same estimates as the fully quadratic classifier with indirect polynomial approach that was used as a starting point, with The coefficient matrix 1A .. of this classifier is obtained by applying the operations described in succession to the K column vectors of the coefficient matrix A in equation (7). The coefficients calculated in this way are again referred to below as aik.

Once the total estimated polynomial population has been determined, the arithmetic logic unit 7, arithmetic stage c, compiles the coefficients aik from all polynomials and squares them individually, each belonging to the same picture element or the same picture element pairing, and these respective squares belonging to the same picture element or the same picture element pair are each added together to form a sum Si, where The amounts of the polynomial coefficients are now used as indicators for the importance of the associated polynomial members. For this purpose, the sizes of the amounts S. - in which the coefficients, because squared, are always positively accumulated (you could also accumulate the absolute amounts of the respective aik instead) - are assessed by compiling them in descending order, see above that a subset of, for example, N Si values can be delimited, all of which are greater than those of the remainder.

The associated picture element or picture element pair is also for each 5 stored in evaluation level 8.

To estimate polynomials each with N terms1 e.g. as mentioned at the beginning 1,200 links, for a final adaptation based on the given pattern One-level classifications of characters of the font will eventually be gained by a selection device 9 those picture elements or picture element pairs selected and fed to a memory 10 for registration, the N largest Si values belong, for example, by serial feeding in the above-mentioned order can be carried out with counting by a counter of the selection device.

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Claims (2)

P a t e n t a n 5 p r ü c h e Process for machine character recognition for the selection of picture elements and picture element combinations within a drawing window, which serve as arguments to be provided with weighting coefficients in polynomials, determine which estimated class membership values for the character pattern ("samples") are scanned, on the basis of the scanning results associated with the patterns feature populations are registered and the number of features of these sets of features with a computational transformation is reduced, characterized in that i) the Sampling results are evaluated in an arithmetic unit (7), which a) to the reduced Number of features for all character classes each using an estimator polynomial only these features and their combinations are determined at least to the power of 2, b) these polynomials are then converted into those that can all be scanned in the drawing window Image elements and their combinations are based on at least the power of 2, c) an importance value for each of the individual picture elements and picture element combinations calculated from the associated weighting coefficients of all polynomials that 2) a subset is made delimitable from the importance values, the individual Members are larger in amount than the remaining amount (evaluation level 8), and that 3) those picture elements and picture element combinations which make up the individual Members of the subset are assigned to a memory (10) for registration transmitted (selection level 9). 2. The method according to claim 1, characterized in that the importance values the sums of the squares of the individual weighting coefficients are determined, which each belong to the same picture element or the same picture element combination.