JPH01116892A - Non-linear normalizing system - Google Patents

Abstract

PURPOSE:To attain a natural non-linear normalization by two-dimensionally and locally extracting a line density in the normalization to an irregularly deformed pattern such as a hand written character. CONSTITUTION:A local line density function h(Xi, Yj) is obtained as the reciprocal of a line interval from two-dimensional pattern f(Xi, Yj), i=1-I, j=1-J sampled by a sampling interval delta and the sampling interval (deltai, epsilonj) of a new sampling point (X'i, Y'j) is determined so as to make the product of the line density h(Xi, Yi) and (deltai, epsilonj) constant. Then, a normalized sampled value in the new sampling point (X'i, Y'j) is obtained by resampling or recalculating from the two-dimensional pattern f(Xi, Yj). Thereby, a more natural normalized graphic can be obtained by locally changing the sampling interval and converting.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a nonlinear normalization method for two-dimensional figures.

(Prior Art) Techniques for pattern recognition, particularly character recognition, are generally divided into two types: superposition methods and structural analysis methods. Conventionally, the superposition method has been used for printed characters, and the structural analysis method has been used for handwritten characters. However, in recent research on handwritten kanji recognition, the superimposition method has come to be widely used even for handwritten kanji for the following reasons.

(1) There are many character types, and automatic learning of the dictionary is easy. (2) The shapes are complex, and the number of feature combinations diverges in structural analysis methods. (3) The idea of superposition method using higher-order features is The introduction of this method has expanded the scope of application of the superposition method.

In the superimposition method, prior to matching (matching) the unknown input cover pattern with the standard pattern, an 1A process is performed to align (standardize) the size and position of the unknown input cover pattern. This is called normalization.

In the superposition method, matching is performed on the assumption that the positions of sample points are fixed, so normalization processing to match the positions of sample points as much as possible is particularly important.

Conventionally, normalization uses information about circumscribed polygons, information about moments such as the center of gravity, and transforms so that the position, size, and inclination are constant. The transformation there is to change the old coordinates to (x
, y), and when the new coordinates after the transformation are (x', y'), it is limited to the range expressed by (1). This transformation is called an affine transformation, and has the property that a straight line in the old coordinates becomes a straight line in the new coordinates, and is easy to handle mathematically. However, considering that the shape of handwritten characters is partially deformed, this linear conversion alone is insufficient.

In order to overcome the limitations of such linear transformations, we have published literature A (Yamada, Saito, Yamamoto "A method of nonlinear normalization", Journal of the Institute of Electronics and Communication Engineers, Vol. J67-D, No. 11, 1984).
(November 2013) proposed a normalization method using nonlinear transformation to homogenize the linear density. In this method, the number of vertical and horizontal lines (the number of intersections with the black component) at each point is used as the line density, and X, so that the product of the number of lines and the sampling interval is constant, Nonlinear transformation functions for resampling are determined independently for each Y axis. That is, the global feature of the number of lines in the vertical and horizontal directions is used as the line density, and (one-dimensional) nonlinear transformation is performed independently in the vertical and horizontal directions. It has been reported that such nonlinear transformation makes effective use of the two-dimensional space and stabilizes the position of sample points, and that the recognition rate is improved experimentally.

(Problem to be solved by the invention) However, since the transformation is a one-dimensional transformation in which X and Y are mutually independent, there are some unnatural examples. ” clearly appears in the lower “mouth” part. In other words, FIG. 5(a) is the input shape, FIG. 5(b)
) is a conventional linear normalization figure using a circumscribed rectangle, and Figure 5 (
C) is the nonlinear normalization figure according to document A, and FIG. Items with the same number correspond to each other.

With respect to the input image shown in FIG. 5(a), in the nonlinear transformation (C) according to the document A, the "3" part on the left side is abnormally narrowed. This is because the number of horizontal lines in "three" is 0 or 1, which is relatively small compared to the "mouth" part, so the number of horizontal lines in "three" is relatively small compared to the "mouth" part.
It has been converted so that the 3" part is smaller.

However, in view of the purpose of nonlinear transformation to make the original linear density uniform, the transformation should be performed while maintaining the overall balance as shown in FIG. 5(d). Figure 5 (C)
Naturally, unnatural conversions such as this pose an obstacle to improving recognition performance.

This invention provides a method for natural nonlinear normalization by extracting two-dimensional and local line density in normalizing irregularly (nonlinear) deforming patterns such as handwritten characters. The purpose is to

(Means for Solving the Problems) The nonlinear normalization method according to the present invention provides a two-dimensional pattern f(Xi) sampled at a sampling interval γ.

Yj), i = 1 ~ I, j = x ~ J to find the local line density function h (Xi, Yj) as the reciprocal of the line spacing, and Sampling interval (
δi, εj) as the linear density h at (Xi, Yj)
means for determining the product of (Xi, Yj) and (δi, εj) to be constant; and means for determining the new sample point (x'i, Y'j);
), or by recalculating from the two-dimensional pattern f (Xi, Yj).

(Operation) In this invention, the local line spacing is determined in each of the X and Y directions at each sample point, and the line density is calculated as the maximum value of the reciprocal of the line spacing in the vertical and horizontal directions. Re-sample or transform so that a certain relationship with the sampling interval is established.

〔Example】

First, the principle of this invention will be explained.

The binary figure sampled at the sampling interval γ is expressed as f (Xi, Y
j), i = 1.2...... Engineering j = t, 2...
...J ...... (2). (Xi, Yj) are the coordinates of the first and j-th sample points on the X-axis and Y-axis, respectively. Also, change this to f
Also expressed as (i, j). Here, the points other than the sample points of the original figure to be sampled, that is, the values on the continuous coordinate system, are f (x, y) = f (Xi, yj)
...” (3) However, (Xi-1=)Xi-y<x≦Xi, Xo=0(Yj-
1=)Yj−γ, y≦Yj, and yo=0.

That is, values on the continuous coordinate system other than sample points are considered to be equal to the sample value of the sample point to which the coordinates belong.

Here, the linear density ρ(t, j) at the point (Xi, Yj)
is obtained using the following process. First, the right edge in the X direction (-shi)
positions Ll, L2 and left edge (J) position L3. L
4 is detected. Ll and L3 are edges that exist on the left side of the point (xi, Yj), and L2 and L4 are edges that exist on the right side (FIG. 6).

Ll-max(i'li'<i,f(i'
, j), "f(i' +1.j)-1) L2-min
(i'li' ≧i, f(i', j),
”f(i' +1.j)-1)L3-max (i'
l i'< i f(i' −1, J), f(
i', j)-1) L4=min(i'If'≧i
, 'f(i'-1,j), f(i',j)-1
)...(4) However, -f is the logical negation of f. Also, the corresponding i
′ is missing, the indicator to that effect (indeterminate) is missing.

Next, Ll, L2. L3. From L4, point (Xi.

The line spacing L8 in the X direction at Yj) is calculated.

[(L2-L1+L4-L3)/2Other (a
) (d)... (5) Figure 6 shows this L8, and the black circle is the required (
Xl, YJ)% The diagonal line represents the black background, the rest represents the white background, and the dashed dotted line represents the center. The alphabet after the right side of the equation for Lx corresponds to FIGS. 6(a) to (f). W is the width of the input image, and in the cases of (C), (b), and (f) in the above equations, 2W and 4W are included to make the value somewhat larger than that inside the character line. (e) shows that only the inner length is used for the outermost black background.

The method for determining the line spacing LX in the X direction at each point has been described above, but the method for determining the line spacing LX in the Y direction is similarly performed.

Next, the linear density ρ is obtained from L, ,L, basically as the maximum value of the reciprocal.

・・・・・・(6) Next, the projection of ρ(i, j) onto the X and Y axes is determined.

This projected function is also expressed as hX(x) = hx(X i ), X i-y<
x≦X1hy(y) −hy(Yi), Y
Consider the following: J-γkuy≦Yj...-(8).

Next, the sum of each function ■ seek.

Under the above preparation, the normalization figure g intended by this invention
(X' t, y' j) can be expressed as follows.

g (X' i, Y' j), 1==l, 2.・・・
..., Ij=t, 2.・・・・・・J δ(i) ・hX(x' t)=γ・Cx/I=Constant X' Constant X-δ(i)=X'i-1 ε(j)・hy(Y' j) = γ・C, /J = constant Y'
j-ε(i)=Y'j-1 ...'-(to) In other words, the i-th sampling point x'i on the X axis is the sampling interval δ(i) and the Characteristic value, (X'
It is determined where the product with i) is constant.

The same applies to the Y axis (FIG. 4(b)).

Note that the reason why the constants are set to γ·C, /I and γ·C, /J is that the number of sample points of the normalized figure is also set to IXJ.

In addition, Fig. 4(a) is a diagram showing the projection of the linear density onto the X-axis and Y-axis, Fig. 4(b) is a diagram showing the position of the new sample point, and Fig. 4(C) is a diagram showing the normalized FIG.

The normalized figure g(X′i, Y′
In j), the lines are distributed homogeneously, and the two-dimensional space is effectively utilized (FIG. 4(C)). For this reason, when matching by superimposition is performed, a result that is stable against deformation can be obtained.

The above is the principle of the present invention. In order to perform the resampling expressed by equation (10), first, the cumulative function of h is defined as follows.

dx (x) = f hx (u)/y dud
y (y) = f hy (v)/y dv...
(11) Here, h is a function on the continuous coordinate system defined by equation (8).

In this way, the normalized sampling figure g(x′i
, Y'j), the position (X'i, Y'j) of the sample point is as follows:
=(yldy(y)=J −Cy/J)・・・・・・−
(12) It is calculated as follows.

Next, embodiments of the present invention will be described.

FIG. 1 shows a block diagram of an embodiment of the present invention. In this figure, 101 is the target image, 102 is the sampling figure buffer, 103 is the X-axis projection buffer, and 104 is the Y-axis projection buffer.
Axis projection buffer, 105 is an X-axis coefficient buffer, 106 is a Y-axis coefficient buffer, 107 is a normalized figure buffer, 1
10 is an observation device, 111 is a linear density calculation circuit, and 112 is an X
An axis conversion calculation circuit, 113 a Y-axis conversion calculation circuit, 114 a nonlinear normal circuit, 121, 122, 123, and 124 a data bus.

Next, the operation will be explained.

The target image 101 is observed and observed through the observation device 110.
It is binarized and stored in a sampled graphic buffer 1.2. The linear density calculation circuit 111 uses this sampling figure to calculate equation (5), then calculates equation (6), and then calculates equation (7) and << in the X and Y directions. The addition is performed and the results are placed in the X-axis projection buffer 103 and Y-axis projection buffer 104, respectively.

Next, in the X-axis conversion calculation circuit 112, by calculating equation (11) on the contents of the X-axis line density buffer 103, one new The coordinates of the coordinate points are entered into the X-axis body number buffer 105. Here, in equations (11) and (12), dx (x) is defined on a continuous coordinate system, so it cannot be calculated as is. Therefore, the actual calculation is performed as follows. i' indicates that the i-th sample point on the X axis of the normalized figure is the i'-th sample point of the original sample figure. This i' is stored in the i-th position of the X-axis body number buffer 105.

Similarly, regarding the Y-axis, the Y-axis conversion calculation circuit 113 calculates the (11th)
Five Y-axis new sample coordinates are obtained by performing calculations according to the formula (actually, a formula similar to formula (13)) and are stored in the Y-axis coefficient buffer 106.

Finally, the operation of the nonlinear expansion/contraction circuit 114 will be explained.

First, the i-th content of the X-axis coefficient buffer 105 is
, the j-th content of the Y-axis coefficient buffer 106 is j'. At this time, the nonlinear expansion/contraction circuit 114 takes out the i'-th content on the X axis and the j'-th content on the Y axis from the sampling figure buffer 102,
Put it in the i-th position on the axis and the j-th position on the Y-axis. This operation
=1.2. ...e, I, J=1.2. ...-,
Normalized figure buffer 107 by performing for J
The normalized figure of is completed.

[Modification 1] In the above embodiment, the already sampled figure (sampled figure buffer 102 in FIG. 1) was used during nonlinear normalization. conversion circuit 1
As shown by the broken line to 14, re-observation from the observation device 110 can be performed while performing nonlinear conversion using the conversion coefficients obtained for the X-axis coefficient buffer 105 and the Y-axis coefficient buffer 1106 of the embodiment. Comparing this method with the example, a more fine-grained normalized figure can be obtained. Another feature of FIG. 1 is that the sampled graphic buffer 102 and the normalized graphic buffer 107 can be used in common.

[Modification 1 Example 2] In the above example, after determining the linear density at each point, the projection to the X and Y axes is taken and the resampling point is determined as a one-dimensional transformation function of the X and Y axes. . As a result, although the mesh divisions in FIG. 4 are at non-uniform intervals, the division lines are characterized by straight lines.

On the other hand, in order to achieve a more two-dimensional transformation, a two-dimensional transformation can be performed without taking the projection and using the two-dimensional density function itself. There, the resulting mesh is non-uniformly spaced and at the same time the dividing line is a curve (actually a broken line).

An example is shown below.

In Equation (6), after finding the linear density ρ(t, j) at each point, find: This is obtained by dividing the linear density into 2×2 and adding them. Then, nonlinear transformation (Xi) is performed.

Yj)→(X' i, Y' j) is performed as follows.

■When Yj≦YJ/4 x′ i=X′ (i, j) / (hl+h21).

XI/2　＜X　i　＜XI ■When Yj≧Y3J/4 X' i=X' (i, j) / (h12+h22).

XI/2 <X i <XI ■YJ/4 <Y j <Y3J/4 when X' 1
==X' (i, j) = (Y3J/4-Yj) ・X'(i, J/4)/Y
J/2 + (Y j -YJ/4) ・X
'(i, 3J/4) /YJ/2 (15) Transformation in the Y direction Yj-4y'j=Y' (i, j) is also obtained in the same way as in the X direction.

By the above X' (i, jL Y' (i, j),
Perform the transformation (Xi, Yj)-+ (X' t, Y' j). Here, X' and Y' are determined for each point (t, j), that is, the point (10) is determined two-dimensionally.

This is different from the embodiments based on equations (12) and (13).

Figure 2 shows hll: h21: h21: h22 1
An example of spatial distortion due to nonlinear transformation in the case of :3:4:2 is shown. Note that iweo... indicates a corresponding area.

Note that in this example, the conversion is obtained by 2×2 division, but more precise conversion is possible by repeatedly applying this method to the 1/4 area in a hierarchical manner.

FIG. 3 shows a circuit configuration for realizing the above method.

In FIG. 3, 201 is the target image, 202 is the sampling figure buffer, 203 is the linear density buffer, and 204
210 is a normalization figure buffer, 210 is an observation device, 211 is a linear density calculation circuit, 212 is a nonlinear normalization circuit, 221,
222 and 223 indicate data buses.

Comparing FIG. 3 with the embodiment shown in FIG. 1, it is found that the output of the linear density calculation circuit 111 or 211 is
In contrast to the independent buffer, the second modification has a two-dimensional buffer 203. Therefore, the input to the nonlinear normalization circuit 212 has also changed to two-dimensional information. As shown in the broken line in FIG. 3, more precise normalization is possible through re-observation, as in the case of the embodiment.

[Modification 3] After using the method of Modification 2 for the 2×2 rough division, the projection method described in the embodiment can be used for the 4×4 grid. It is possible.

In this case, for global two-dimensional deformation, modification example 2
A two-dimensional deformation is performed, and a projection method with simple processing is used to absorb the local deformation.

FIGS. 5(a), (b), (C), and (d) show figures normalized by the method shown in the embodiment of the present invention as described above, and conventional normalized figures. This is a comparison. From this figure, it can be seen that according to the present invention, a more natural normalized figure is obtained compared to the conventional nonlinear normalization method.

The effectiveness of this method has also been confirmed through handwritten character recognition experiments. The results are shown in the table below.

Experimental conditions Experimental data: Densoken handwriting education kanji database ETL
8 (160 data sets of 956 character types) Out of a total of 956 x 160 characters, the odd numbered data sets were used to create dictionaries and calligraphy, and data sets 2 and 34 were evaluated.

Linear normalization: Normalize the circumscribed rectangle of a character to a square.

Nonlinear normalization 1: The method described in Document A mentioned above.

Nonlinear Normalization 2: Normalization according to an embodiment of the invention.

〔Effect of the invention〕

As described in detail above, the present invention provides a two-dimensional pattern f (Xi) sampled at a sampling interval δ.

Yj), i = 1 ~ I, j = 1 ~ J to find the local line density function h (Xi, Yj) as the reciprocal of the line spacing, and the new sampling point (X'i, Y'j). Sampling interval (
δi, εj) as the linear density h (X
means for determining the product of i, Yj) and (δi, εj) to be constant; and resampling and obtaining the normalized sample value at the new sampling point (X'i, Y'j). mosquito,
Alternatively, since there is a means to recalculate and obtain from the two-dimensional pattern f (Xi, Yj), a more natural normalized figure can be obtained while performing conversion while partially changing the sampling interval. Therefore, there is an advantage that the superposition method can be effectively used even for partially converted patterns such as handwritten characters.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 2 is a diagram showing how the dividing grid changes during two-dimensional transformation in a modified example of the present invention, and FIG. 3 is a diagram showing this modified example. Block diagram for realizing this, Figure 4 (a), (b), (C)
Figures 5(a) and 5(b) are diagrams showing the processing process according to the embodiment.
), (c). (d) is a diagram showing a figure normalized by the embodiment of the present invention and a figure normalized by the conventional method, and FIG. 6 is a diagram showing the definition of the line spacing in the X direction. In the figure, 101. is an image, 102 is a sampling figure buffer,
103 is an X-axis projection buffer, 104 is a Y-axis projection buffer, 105 is an X-axis coefficient buffer, 106 is a Y-axis coefficient buffer, 108 is a normalization figure buffer, 110 is an observation device, 111 is a linear density calculation circuit, 112 is an An X-axis conversion calculation circuit, 113 a Y-axis conversion calculation circuit, 114 a nonlinear normalization circuit, and 121.122, 123.124 data buses. Figure 2 2゛1 (a) Figure 4 (b) (C) Figure 5

Claims (1)

[Claims] Two-dimensional pattern f(Xi,
Yj), i=1~I, j=1~J to find the local line density function h(Xi, Yj) as the reciprocal of the line spacing, and Sampling interval (δi
, εj) as the linear density h(Xi, Yj) at (Xi, Yj)
, Yj) and (δi, εj) to be constant, and determining the normalized sample value at the new sampling point (X'i, Y'j) by resampling. , or a means for recalculating from the two-dimensional pattern f(Xi, Yj).