JPH0789362B2 - Non-linear normalization method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of use] The present invention relates to a non-linear normal lower system for a two-dimensional figure.

[Conventional technology]

Pattern recognition methods, especially character recognition methods, are generally divided into two methods: an overlay method and a structure analysis method. Conventionally, the overlay method has been used for printed characters, and the structural analysis method has been used for handwritten characters. However, in recent researches on handwritten Chinese character recognition, the overlapping method has been widely used for handwritten Chinese characters for the following reasons.

(1) There are many types of characters and it is easy to automatically learn a dictionary. (2) The shape is complicated and the number of feature combinations diverges in the structural analysis method. Was introduced and the application range of the superposition method was expanded.

In the superposition method, a process of aligning (standardizing) the size and position of an unknown input pattern is usually performed prior to matching (matching) the unknown input pattern and the standard pattern. This is called normalization. In the superposition method, since the matching is performed on the assumption that the positions of the sample points are fixed, the normalization process for matching the positions of the sample points is particularly important.

Conventionally, normalization has been performed by using information on circumscribed polygons and information on moments such as the center of gravity so that the position, size, and inclination are constant. The conversion there is to convert the old coordinates to (X,
Y), and the new coordinates after conversion are (X ', Y'), Limited to the range represented by. This transformation is called an affine transformation, and the straight line in the old coordinates has the property that it becomes a straight line even in the new coordinates, and it is easy to handle mathematically. However, considering that the shape of handwritten characters is partially deformed, this linear conversion is not sufficient.

In order to overcome the limitation of such linear transformation, reference A (Yamada, Saito, Yamamoto “A method of nonlinear normalization”, IEICE Transactions D, J67-D, No. 11, 1984, 11 Month)
Proposes a normalization method by non-linear transformation that homogenizes the linear density. There, the number of vertical and horizontal lines at each point (the number of intersections with the black component) is used as the line density, so that the product of the number of lines and the sampling interval is constant.
The non-linear transformation function for resampling is determined independently for the X and Y axes. That is, the global characteristic of the number of lines in the vertical and horizontal directions is used as the line density, and
A laterally independent (one-dimensional) non-linear transformation is performed.
It is reported that such a non-linear transformation achieves effective use of the two-dimensional space and stabilization of the position of the sampling point, and that the recognition rate is improved experimentally.

[Problems to be solved by the invention]

However, some unnatural examples can be seen because the transformation is a one-dimensional transformation in which X and Y are independent of each other. A typical example thereof clearly appears in the "mouth" portion below the "word" in FIG. That is, FIG. 5 (a) is an input figure, and FIG. 5 (b).
Is a linear normalized figure by a conventional circumscribing quadrangle, FIG. 5 (c) is a non-linear normalized figure according to document A, FIG. 5 (d)
Is a non-linear normalized figure according to the present invention, and
The numbers 3, 5, 7, 9, 11, and 13 are attached, and those with the same number correspond to each other.

In contrast to the input image shown in FIG. 5 (a), in the non-linear conversion (c) according to Document A, the left "three" portion is abnormally narrowed. This is because the number of horizontal lines of "three" is 0 or 1, which is relatively small compared to the part of "mouth", so it is converted so that the part of "three" becomes smaller in the vertical direction. is there. However, in view of the purpose of performing non-linear conversion so as to make the original linear density uniform, it is necessary to carry out a modification in which the overall balance is maintained as shown in FIG. 5 (d). The unnatural conversion as shown in FIG. 5 (c) naturally hinders the improvement of the recognition performance.

The present invention provides a natural non-linear normalization method by extracting a two-dimensional and local line density in the normalization for a pattern deformed irregularly (non-linearly) such as a handwritten character. The purpose is to

[Means for solving problems]

The non-linear normalization method according to the present invention observes an external pattern at a constant sampling interval γ, converts it into an electric signal, and outputs a two-dimensional pattern f (Xi, Yj), i = as a set of sample values.
1 to I, j = 1 to J are obtained, and the two-dimensional pattern f (Xi, Y
j), at each two-dimensional point (Xi, Yj), the point (Xi, Yj
Find the line spacing in the X and Y directions around j),
The linear density function h (Xi, Yj) of the point (Xi, Yj) is obtained from the maximum value of the reciprocal of these line intervals, and a new sample point (X′i,
The sampling interval (δi, εj) of Y′j) is calculated as (X′i, Y′j)
The product of the linear density function h (Xi, Yj) and δi at is flat even if i is changed, and the product of the linear density function h (Xi, Yj) and εj changes j. Even if it is made to be flat, the normalized sample value at the new sample point (X'i, Y'j) is set to the sampling interval (δi, ε).
j), and re-observing them at non-uniform intervals, or recalculating from the two-dimensional pattern f (Xi, Yj).
The normalization pattern is obtained by executing.

[Action]

In the present invention, at each sampling point, the local line spacing in each of the X and Y directions is obtained, and the line density is calculated as the maximum value of the reciprocal of the line spacing in the vertical and horizontal directions. Resample or transform so that a certain relationship holds between.

〔Example〕

 First, the principle of the present invention will be described.

F (Xi, Xj), i = 1,2 …… I j = 1,2 …… J …………, which is obtained by converting the external information written on paper etc. into an electrical signal by an observation device such as a TV camera. (2) At this time, Xi and Yj are the X axis and Y defined on the external paper.
These are the coordinates of the i-th and j-th sample points on the axis, respectively, and the interval between the sample points is γ. In addition, the sample value f of each point is a binary figure of 0 when the external information is white and 1 when the external information is black. Here, 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, it is considered that (Xi−1 =) Xi−γ <x ≦ Xi, Xo = 0 (Yj−1 =) Yj−γ <y ≦ Yi, yo = 0. That is, the value on the continuous coordinate system other than the sample point is considered to be equal to the sample value of the sample point to which the coordinate belongs.

Here, the linear density ρ (i, j) at the point (Xi, Yj) is obtained by the following process. First, the right edge in the x direction Position L1, L2 and left edge The positions L3 and L4 of are detected. L1 and L3 are edges on the left side of the point (Xi, Xj), and L2 and L4 are edges on the right side (6th
Figure).

L1 = max {i '| i'<i, f (i ', j), ^ f (i' + 1, j) = 1} L2 = min {i '| i'≥i, f (i', j ), ^ F (i ′ + 1, j) = 1} L3 = max {i ′ | i ′ <i, ^ f (i′−1, j), f (i ′, j) = 1} L4 = min {I '| i'≥i, ^ f (i'-1, j), f (i', j) = 1} (4) where ^ f is the logical negation of f. Also, the corresponding i ′
If it does not exist, an indicator (indefinite) to that effect is included.

Next, the line spacing L _X in the x direction at the point (Xi, Yj) is calculated from L1, L2, L3, L4.

Fig. 6 shows this L _X , which is calculated by the black circle (X
i, Yj), the slanted line is the black background, the rest is the white background, and the dashed-dotted line is the center. The alphabet after the right side of the expression for L _X is the 6th
It corresponds to FIGS. w is the width of the input image, and in the case of (c), (b), and (f) in the above equation, 2w and 4w are used to make the value somewhat larger than the inside of the character line.
Is put in. (E) indicates that the outermost black background uses only the inner length.

Although the method of obtaining the line spacing L _X in the X direction at each point has been described above, L _y is similarly obtained in the Y direction.

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

Next, the projection of ρ (i, j) on the X and Y axes Ask for.

This projected function is also h _X (x) = h _X (Xi), xi−γ <x ≦ Xi h _y (y) = h _y (on the continuous coordinate system, as in the equation (3). Yi), Yi−γ <y ≦ Yj (8)

Then the sum of each function Ask for.

With the above preparations, the normalized figure g intended by the present invention
(X'i, Y'j) can be expressed as follows.

g (X'i, Y'j), i = 1,2, ..., I j = 1,2, ... J δ (i) · h _x (X′i) = γ · C _x / I = Constant X′i−δ (i) = X′i−1 ε (j) · _hy (Y′j) = γ · C _y / J = Constant Y′j−ε (i) = Y′j−1 (10) That is, the i-th sample point X'i on the X axis is a place where the product of the sampling interval δ (i) and the characteristic value h _x (X'i) at that point becomes constant. Stipulated in.

The same applies to the Y axis (FIG. 4 (b)). The constants of γ · C _x / I and γ · C _y / J are set so that the number of sample points of the normalized figure is also I × J. Note that FIG. 4 (a) is a projection of the linear density on the X-axis and Y-axis, FIG. 4 (b) is a view showing the position of a new sampling point, and FIG. 4 (c) is normalized. It is a figure of a figure.

Normalized figure g (X'i, Y 'obtained by such resampling
In j), the lines are uniformly distributed, and the two-dimensional space is effectively used (Fig. 4 (c)). Therefore, when matching is performed by superposition, a stable result against deformation can be obtained.

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

Here, h is a function on the continuous coordinate system defined by the equation (8).

In this way, the normalized figure g (X'i,
The position (X'i, Y'j) of the sample point of Y'j) is: X'i = {x | dx (x) = i.Cx / I} Y'j = {y | dy (y) = j · Cy / J} (12) is calculated.

Next, an embodiment 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 a target image, 102 is a sampled 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,
107 is a normalized figure buffer, 110 is an observation device, 111 is a linear density calculation circuit, 112 is an X-axis conversion calculation circuit, 113 is a Y-axis conversion calculation circuit, 114 is a non-linear normalization circuit, and 121, 122, 123 and 124 are data buses.

Next, the operation will be described.

The target image 101 is observed / binarized through the observation device 110 and stored in the sampled figure buffer 102. In the linear density calculation circuit 111, the equation (5) is calculated using this sampled figure, then the equation (6) is calculated, and addition is performed in the X and Y directions as in the equation (7). , The result is respectively an X-axis projection buffer 103 and a Y-axis projection buffer 104.
Put in.

Next, in the X-axis conversion calculation circuit 112, the formula (11) is calculated with respect to the contents of the X-axis projection buffer 103, and I X-axis new values to be used in the calculation of the formula (12) are calculated. The coordinates of the coordinate points are put into the X-axis coefficient haffa 105. Here, since dx (x) is defined on the continuous coordinate system in the equations (11) and (12), it cannot be calculated as it is. So the actual calculation is By. i'indicates that the i-th sample point of the X-axis of the normalized figure is the i'-th sample point of the original sample figure. This i ′ is the i-th value of the X-axis coefficient buffer 105.
Second thought.

Similarly, with respect to the Y-axis, the Y-axis conversion calculation circuit 113 calculates the Y-axis projection buffer 104 according to the equation (11) (actually the same equation as the equation (13)). J Y-axis new sample coordinates are determined and stored in the Y-axis coefficient buffer 106.

Finally, the operation of the nonlinear normalization circuit 114 will be described.

First, the i-th content of the X-axis coefficient buffer 105 is i ′,
The j-th content of the Y-axis coefficient buffer 106 is j '.
At this time, the non-linear normalization circuit 114 uses the sampled figure buffer 1
The contents of the i-th position on the X-axis and the j-th position on the Y-axis are taken out from 02 and placed in the i-th position on the X-axis and the j-th position on the Y-axis of the normalized graphic buffer 107. This operation i = 1,2, ...
.., I, J = 1, 2, ..., J completes the normalized figure in the normalized figure buffer 107.

[Modification 1] In the above embodiment, the already sampled graphic (sampled graphic buffer 102 in FIG. 1) was used in the non-linear normalization, but the non-linear normalization from the observation apparatus 110 in FIG. As indicated by a broken line to the conversion circuit 114, the observation device 110 can perform re-observation while performing non-linear conversion using the conversion coefficients obtained in the X-axis coefficient buffer 105 and the Y-axis coefficient buffer 106 of the embodiment. When this method is compared with the embodiment, a finer normalized figure is obtained. Further, in FIG. 1, the sampled figure buffer 102 and the normalized figure buffer 107 can be shared.

[Modification 2] In the above-described embodiment, after the linear density is obtained at each point, the projection to the X and Y axes is taken and the re-sampling point is obtained as a one-dimensional conversion function of the X and Y axes. As a result, in FIG. 4, the mesh divisions are non-equidistant, but the dividing line is a straight line.

On the other hand, in order to perform a more two-dimensional conversion, the projection is not taken and the two-dimensional density function itself can be used to perform the two-dimensional conversion. There, the resulting mesh is non-equidistant and at the same time the dividing lines are curves (actually polygonal). The example is shown below.

In equation (6), after obtaining the linear density ρ (i, j) at each point, Ask for. This is the linear density divided into 2 × 2 and added. Then, the nonlinear transformation (Xi, Yj) → (X'i,
Perform Y'j) as follows.

When Yj ≤ YJ / 4 When Yj ≧ Y 3J / 4 When YJ / 4 <Yj <Y 3J / 4 X'i = X '(i, j) = (Y3J / 4-Yj) X' (i, J / 4) / YJ / 2 + (Yj-YJ /4).X'(i,3J/4)/YJ/2 (15) Y direction conversion Yj → Y'j = Y '(i, j) is also obtained in the same manner as in the X direction.

Conversion (Xi, Yj) by the above X '(i, j) and Y' (i, j)
→ Perform (X'i, Y'j). Where X ′, Y ′ are points (i,
For each j), that is, the point obtained in two dimensions is the first (1
This is a difference from the embodiment based on the expressions (0), (12), and (13).

FIG. 2 shows an example of spatial distortion due to nonlinear conversion in the case of h11: h21: h21: h22 = 1: 3: 4: 2. It should be noted that "aiueo" indicates the corresponding area.

In this example, the conversion is calculated by 2 × 2 division, but more precise conversion can be performed by repeatedly applying this method hierarchically to a 1/4 area.

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

In FIG. 3, 201 is a target image, 202 is a sampled figure buffer, 203 is a linear density buffer, 204 is a normalized figure buffer, 210 is an observation device, 211 is a linear density calculation circuit, 212
Is a non-linear normalization circuit, and 221, 222, 223 and 224 are data buses.

Comparing FIG. 3 with the embodiment of FIG. 1, the output of the linear density calculation circuit 111 or 211 is a buffer independent of X and Y in the above embodiment, whereas in the modification 2, the linear density buffer is 20
3 is two-dimensional. Therefore, the input to the nonlinear normalization circuit 212 is also changed to two-dimensional information. As in the case of the embodiment, more precise normalization by re-observation is possible as indicated by the broken line in FIG.

[Modification 3] It is possible to use the method of modification 2 for 2 × 2 coarse division and then use the method of projection described in the embodiment for squares divided into 4 × 4. It is possible.

In this case, the modification 2 is applied to the global two-dimensional deformation.
The two-dimensional deformation is performed and the local deformation is absorbed by using the projection method whose processing is simple.

FIGS. 5 (a), (b), (c) and (d) show a figure normalized by the method shown in the embodiment of the present invention as described above and a conventional normalized figure. Are compared. From this figure, it is understood that a more natural normalized figure is obtained according to the present invention as compared with the conventional non-linear normalization method.

The effect of this method has been confirmed by handwriting recognition experiments. The results are shown in the table below.

Experimental condition Experimental data: ETL8 Handwriting Educational Kanji Database by the Institute of Electro-Communications
(956 character type 160 data sets) Of the total 956 x 160 characters, the odd numbered data set was used to create the dictionary and data set 2 and
The evaluation was made at 34.

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

Nonlinear normalization 1: The method described in the above-mentioned document A.

Non-Linear Normalization 2: Normalization according to an embodiment of the present invention.

〔The invention's effect〕

As described in detail above, according to the present invention, a two-dimensional pattern f (Xi, Yj), i = as a set of sample values is obtained by observing an external pattern at a constant sampling interval γ and converting it into an electric signal.
1 to I, j = 1 to J are obtained, and the two-dimensional pattern f (Xi, Y
j), at each two-dimensional point (Xi, Yj), the point (Xi, Yj
Find the line spacing in the X and Y directions around j),
The linear density function h (Xi, Yj) of the point (Xi, Yj) is obtained from the maximum value of the reciprocal of these line intervals, and a new sample point (X′i,
The sampling interval (δi, εj) of Y′j) is calculated as (X′i, Y′j)
The product of the linear density function h (Xi, Yj) and δi at is flat even if i is changed, and the product of the linear density function h (Xi, Yj) and εj changes j. Even if it is made to be flat, the normalized sample value at the new sample point (X'i, Y'j) is set to the sampling interval (δi, ε).
j), and re-observe at non-uniform intervals, or recalculate from the two-dimensional pattern f (Xi, Yj), and normalize by executing ~ in the order of ~. Since the pattern is obtained, it is possible to obtain a more natural normalized figure while converting while partially changing the sampling interval. Therefore, there is an advantage that the superposition method can be effectively used even for a partially converted pattern such as a handwritten character.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 2 is a diagram showing a state of change of divisional cells during two-dimensional conversion in a modification of the present invention, and FIG. 3 is a modification thereof. FIG. 4 (a), (b), (c) is a block diagram for realizing
Is a diagram showing a processing process according to the embodiment, FIG. 5 (a),
(B), (c) and (d) are diagrams showing figures normalized by the embodiment of the present invention and figures normalized by the conventional method, and FIG. 6 shows the definition of the line spacing in the X direction. It is a figure. In the figure, 101 is an image, 102 is a sampled figure buffer, and 103 is X.
Axis projection buffer, 104 Y axis projection buffer, 105 X axis coefficient buffer, 106 Y axis coefficient buffer, 107 normalized figure buffer, 108 normalized figure buffer, 110 observation device, 111 line density Calculation circuit, 112 is an X-axis conversion calculation circuit, 11
3 is a Y-axis conversion calculation circuit, 114 is a non-linear normalization circuit, 121, 12
2,123,124 are data buses.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-60-251482 (JP, A) Transactions of the Institute of Electronics and Communication Engineers, Vol. 67-D, No. 11, (1984-11), P. 1379-1383

Claims (1)

[Claims] 1. A two-dimensional pattern f (Xi, Yj), i = 1 to I, j = 1 as a set of sampled values obtained by observing an external pattern at a constant sampling interval γ and converting it into an electric signal. .. J, and two-dimensional points (Xi, Yj) from the two-dimensional pattern f (Xi, Yj).
Yj), the line spacing in the X direction and the line spacing in the Y direction around the point (Xi, Yj) are obtained, and the linear density function h (Xi, Yi) of the point (Xi, Yj) is calculated from the maximum value of the reciprocal of these line spacings. , Yj)
Sampling interval (δi, εj) of new sampling point (X'i, Y'j)
Is the linear density function h (Xi, Yj) in (X'i, Y'j)
And the product of the value of the linear density function h (Xi, Yj) and εj are set to be flat even if j is changed. Normalized sample values at new sample points (X'i, Y'j) are re-observed at non-uniform intervals based on the sampling intervals (δi, εj), or two-dimensional Pattern f
Non-linear normalization characterized in that a normalization pattern with uniform line intervals is obtained by recalculating from (Xi, Yj) and executing ,,,,, in the order of to. Method.