JPH06162199A - Method and device for fuzzy segment model preparation - Google Patents

Abstract

PURPOSE:To prepare the fuzzy segment model consisting of straight segment information which is made properly fuzzy corresponding to an input curve sample model which is made fuzzy. CONSTITUTION:A representative point selection part 2 selects two fuzzy representative points from the input curve sample model. A segment model preparation part 3 prepares a fuzzy segment model. The internal division fuzzy point arithmetic part 31 of the segment model preparation part 3 finds a set of internal division fuzzy points between the 1st and 2nd representative points and an end point arithmetic part 33 determines the end point of the fuzzy segment model so that the ratio of the length along the curve from the 1st to the 2nd representative point to the length from the 2nd representative point to the end point of the curve sample model along the curve of the sample model is equal to the ratio of the distance from the 1st to the 2nd representative point to the distance from the 2nd representative point to the end point of the fuzzy segment model; and an external division point arithmetic part 32 finds a set of externally divided fuzzy points between the 2nd representative point and the end point of the fuzzy segment model, thereby letting the set of internal division fuzzy points and the set of the external division fuzzy point be the fuzzy segment model.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pattern recognition system for recognizing characters / symbols input by handwriting, and in particular, inputting a handwriting curve as fuzzy curve information including input ambiguity information. , The input curve sample model in the pattern recognition system that discriminates the pattern of the input curve by comparing the curve sample model of the segment as a part of the input fuzzy curve information with the fuzzy expressed reference model as the reference pattern And a fuzzy line segment model generation method for generating a fuzzy line segment model as a reference model assuming that

[0002]

2. Description of the Related Art In recent years, a system called a pen computer or the like, that is, a computer system having a pen input tablet with a display as an input / output device has been receiving attention. Such a pen computer system
For example, it has a computer, a tablet with a display connected to this computer, and an input pen for input operation connected to this tablet. In this case, the tablet with a display serves both as a display device as an output device of the computer and as an input device for input to the computer. In a system using such a handwriting input and an application program operating in such a system, since the handwriting pen input information of the operator is recognized in the computer, the meaning of the direct line figure input data by the handwriting pen input is meant. Need to be recognized and discriminated in the computer. Input data from a pen on a tablet is generally given as a sequence of points sampled at equal time intervals, so spline interpolation processing is performed in order to interpolate this appropriately and to theoretically treat it as a continuous curve. Is used.

As a spline interpolation process for obtaining an interpolation curve from such a given point sequence, for example, a spline curve is passed through these points based on the coordinate information of each point given as a point sequence. It is general to find the control polygon of the spline curve by finding the coupling coefficient of the expressed basis function to find the interpolation curve. For example, in the case of a cubic spline curve, smoothly connecting each passing point to which an interpolation curve is given (for example, satisfying a so-called “C ² continuous” condition) 3
The spline curve of the form connected by the following Bezier curve is calculated.
Further, conventionally, in order to recognize and determine what kind of character / symbol, etc., the pattern information spline-interpolated in this way represents, it is necessary to match the input sample graphic with a reference graphic prepared in advance. By examining the degree, the input sample figure was recognized and judged as the character / symbol corresponding to the reference figure that best matches.

In such a conventional system, it is premised that the given point sequence is a fixed point sequence in the spline interpolation processing of the sample figure, and in reality, the given input point sequence is ambiguous. Considering the case where ambiguous points or improperly located points are included in the information of each point given as a sequence of points, although points or strictly incorrect points are often included. Absent.
Further, not only the sample graphic but also the reference graphic is processed as certain fixed information, and as a result, the information of the degree of these matching is also obtained as the fixed simple information. Therefore, in the above-described conventional system, the ambiguity is appropriately evaluated from the input point sequence that may include an ambiguous point or a point whose position is not exactly correct, such as handwriting input on a pen computer, etc. It is very difficult to perform recognition processing that matches the intent of.

On the other hand, the present inventors have previously proposed, as Japanese Patent Application No. 4-157573, appropriately evaluating and processing an ambiguous element from input information and performing pattern recognition according to the operator's intention. We have proposed a method and device for pattern recognition that can be performed. That is, this pattern recognition method and apparatus expresses a sample figure by a fuzzy spline curve including ambiguity information of an input sample figure, obtains a predetermined number of fuzzy-represented representative point information of this sample figure, and A predetermined number of fuzzy-represented representative point information about the figure is obtained by respectively corresponding to the representative points of the sample, and the section truth of the degree of matching between corresponding pairs of the representative point information of the sample and the representative point information of the reference The degree of matching of the entire figure curve is determined by obtaining the section truth value of the entire figure curve from the value.

As described above, inferring the figure intended by the handwriting input writer from the curve information of the input sample figure represented by the fuzzy spline curve including the ambiguity information, and discriminating / recognizing, the inference processing system Since the processing capacity is finite and enormous or infinite information cannot be processed instantaneously, the input fuzzy spline curve is divided into segments of an appropriate size by segmentation, and each segment is segmented. It is effective to make inferences.

[0007]

As described above, the curve information of the input sample figure represented by the fuzzy spline curve including the ambiguity information is divided into segments by the appropriate segmentation and compared with the reference figure to input. In order to discriminate and recognize sample figures, prepare multiple figure models for each unit figure that substantially correspond to partial figures for each segment as a reference figure model, and match those figure models with the input curve sample model for each segment. Will be determined. In this case, since the input curve sample model is fuzzy-represented curve information, if the reference figure model is also fuzzy-represented information, the fuzzy inference that effectively uses the ambiguity information can be used to determine the curve intended by the writer. It is considered that discrimination / recognition can be performed more appropriately.

However, in the past, since processing of such a spline curve represented by a fuzzy expression was not general, a reference figure model of a unit figure which has been fuzzified corresponding to a fuzzified input curve sample model, for example, There was no technology to generate a fuzzy line segment model. The present invention has been made in view of the above circumstances, and it is possible to generate a fuzzy line segment model including appropriately fuzzy straight line segment information, corresponding to a fuzzy input curve sample model. It is an object of the present invention to provide a fuzzy line segment model generation method and apparatus that enable the fuzzy line segment model generation.

[0009]

A method for generating a fuzzy line segment model according to the present invention inputs a handwritten curve as fuzzy curve information including input ambiguity information, and creates a segment as a part of the input fuzzy curve information. A fuzzy line as a reference model when it is assumed that the input curve sample model in pattern recognition that discriminates the pattern of the input curve by comparing the curve sample model with a fuzzy expressed reference model In generating the minute model,
Input two fuzzy points from the fuzzy spline curve that represents the input curve sample model.
And a fuzzy line segment satisfying the first and second fuzzy representative points is internally divided between the first and second fuzzy representative points. And a line segment constructing step for constructing a set of fuzzy points to obtain a fuzzy line segment model.

A fuzzy line segment model generation apparatus according to the present invention inputs a handwritten curve as fuzzy curve information including input ambiguity information, and uses a segment curve sample model as a part of the input fuzzy curve information as a reference pattern. Generate a fuzzy line segment model as a reference model assuming that the input curve sample model is a straight line segment in the pattern recognition system that discriminates the pattern of the input curve compared with the fuzzy representation reference model In the fuzzy line segment model generation device for, a representative point selecting means for selecting two appropriate fuzzy points from the fuzzy spline curve representing the input curve sample model as the first and second fuzzy representative points. , Meet the first and second fuzzy representative points And a line segment constructing means for constructing a fuzzy line segment as a fuzzy line segment model by constructing a fuzzy line segment as a set of internal and external fuzzy points between the first and second fuzzy representative points. It has a feature.

[0011]

The method and apparatus for generating a fuzzy line segment model of the present invention inputs a handwritten curve as fuzzy curve information including input ambiguity information, and references a curve sample model of a segment as a part of the input fuzzy curve information. Generate a fuzzy line segment model as a reference model when assuming that the input curve sample model in pattern recognition that discriminates the pattern of the input curve is a straight line segment compared with a reference model expressed as a fuzzy pattern At this time, two appropriate fuzzy points on the fuzzy spline curve representing the input curve sample model are selected as the first and second fuzzy representative points, and the fuzzy line segment satisfying these first and second fuzzy representative points is selected. Between these first and second fuzzy representative points Since internal division configured as a set of fuzzy point and the outer partial fuzzy points and fuzzy line model,
Corresponding to the fuzzified input curve sample model,
It is possible to generate a fuzzy line segment model including straight line segment information that is appropriately fuzzy.

[0012]

【Example】

<< Fuzzy Spline Interpolation >> Prior to the description of the embodiments of the present invention, first, basics for obtaining fuzzy spline curve information corresponding to these point sequences by interpolating and approximating point sequence data given as position information for each point. The basic principle. In this case, when a fuzzy point sequence in which the position of each point is ambiguous and has a certain spread is given, spline interpolation is performed while including this ambiguity information, and a smooth curve having a spread due to the ambiguity is generated. . For example, it is assumed that there is an ambiguity in the position information itself of the sample point sequence of the handwritten input figure, and this is expressed as a two-dimensional fuzzy point sequence (each point sequence represented as a two-dimensional fuzzy set). In this case, these fuzzy point sequences are interpolated under certain assumptions and expressed as continuous and ambiguity curves, that is, fuzzy spline curves. It is possible to save in a form that is easy to use.

The ambiguity of the position information of the point sequence means the inaccuracy or ambiguity of the actually drawn and sampled data with respect to the conceptual position information of the figure which the operator intends to draw. That is. Generally speaking,
It is considered that the positional information of the sample points of the curve of the portion that the operator carefully draws has high fidelity to the figure that the operator intends to draw, and contains few ambiguous elements. On the other hand, the position information of the sample points of the curve of the portion roughly drawn by the operator is considered to be information including many ambiguous elements with respect to the figure that the operator intends to draw. Therefore, considering such a property, if appropriate ambiguity is added to the position information of each sampling point, a fuzzy spline curve is generated by the fuzzy spline interpolation method, and it is held in the computer, As the input curve information, the ambiguity information according to how to draw each part of the line figure is held together with the shape of the input line figure itself.

Regarding the method of adding the ambiguity information described above, for example, it is conceivable to use the acceleration of the pen or the writing pressure information at the time of handwriting input. Generally, it may be set so that a lot of ambiguity is included in proportion to the acceleration. As described above, if the ambiguity information in the input line figure and each part thereof is simultaneously stored as fuzzy spline curve information inside the computer, for example, elliptical data intentionally drawn carefully and circles drawn roughly Data that has become an ellipse will be retained in a form that can be distinguished in the computer. In this way, the fuzzy spline curve information once held in the computer can be used as a material for inferring and recognizing the line figure intended by the operator from the sampling data of the handwritten input line figure. It should be possible. The principle of the above fuzzy spline interpolation will be described more specifically.

In fuzzy spline interpolation, first, consider a fuzzy vector having a conical membership function in order to represent a vector on a two-dimensional plane containing ambiguity,
The operation of the fuzzy vector is defined based on the extension principle. Next, a fuzzy spline curve, which is an extension of a normal spline curve, is constructed by expressing the vertices of the control polygon of the spline curve by fuzzy vectors. Furthermore, the fuzzy spline curve is used to interpolate a fuzzy point sequence on a plane including ambiguity while including ambiguity information. <Cone-shaped fuzzy vector and its operation> Consider a fuzzy vector having a conical membership function, and define the sum operation of the fuzzy vectors and the multiplication of the fuzzy vector and the crisp scalar quantity.

First, the membership function of the conical fuzzy vector and its notation will be examined. To represent an ambiguous two-dimensional vector on a plane, consider a fuzzy vector characterized by a conical membership function as shown in FIG. Here, the first fuzzy vector having the conical membership function is expressed by the mathematical expression 1 using the vector a representing the position of the apex of the cone and the radius r _a of the base circle of the cone.

[0017]

[Equation 1]

The first expressed by the equation 1 at this time
The fuzzy vector membership function of is given by equation 2 for any variable vector v on the plane (note that
The operator "∨" in Equation 2 takes the larger max
(Maximum value) represents the calculation).

[0019]

[Equation 2]

The conical fuzzy vector shown in the equations 1 and 2 is a direct extension of the symmetrical triangular fuzzy number which is a fuzzy model of the scalar quantity. Next, we consider the sum operation of conical fuzzy vectors and the operation of conical fuzzy vectors and crisp scalars. Consider a second fuzzy vector as shown in Equation 3.

[0021]

[Equation 3]

By applying the extension principle, the first
It is derived that the sum of the fuzzy vector of and the second fuzzy vector is expressed by the equation 4.

[0023]

[Equation 4]

Similarly, the result of multiplying the first fuzzy vector by the crisp scalar quantity k is expressed by equation 5.

[0025]

[Equation 5]

Therefore, the linear combination of fuzzy vectors as shown in equation 6 is also represented by the same type of fuzzy vector as shown in equation 7.

[0027]

[Equation 6]

[0028]

[Equation 7]

<Fuzzy Spline Curve> Nodal series u
_{If the} normalized B-spline function of order n defined by _i−1 , ..., U _{i + n} is N _i ⁿ (u), the interval on the parameter space: [u _n-1 , u _{n + L- The} arbitrary n-th order spline curve s ⁿ (u) whose domain is [ ₁ ] is expressed by Equation 8.

[0030]

[Equation 8]

Here, the position vectors d ₀ , ..., d _{L + n-1}
Represents the vertices of the control polygon, and the points on the spline curve are given as a linear combination of the vertices of the control polygon. Therefore, the fuzzy spline curve is defined by expanding the position vector representing the apex of the control polygon of Expression 8 to the fuzzy position vector based on the fuzzy vector described above. That is, by giving the equation 9 as the vertices of the fuzzy control polygon, the nth-order fuzzy spline curve is defined as an extension of the equation 8 like the equation 10.

[0032]

[Equation 9]

[0033]

[Equation 10]

Equation 10 shows that the point on the fuzzy spline curve corresponding to the parameter value u is a linear combination of fuzzy position vectors. Therefore, by applying the above-described calculation rule of the fuzzy vector sum calculation and the multiplication by the crisp scalar quantity, this point can be expressed by Expression 11, and it is understood that it is evaluated as a conical fuzzy position vector.

[0035]

[Equation 11]

<Interpolation of Fuzzy Point Sequence by Fuzzy Spline Curve> When a fuzzy point sequence such as equation (12) is given by a fuzzy position vector on the figure plane, the control polygon of the fuzzy spline curve that passes through these is It is obtained by solving the linear system expressed by the equation 13.

[0037]

[Equation 12]

[0038]

[Equation 13]

However, m = L + n-1, and s _i
Is the value of the parameter u corresponding to the fuzzy point sequence of the equation 12, the equations 14, 15 and 16 are obtained.

[0040]

[Equation 14]

[0041]

[Equation 15]

[0042]

[Equation 16]

As described above, in order to obtain the control polygon of the fuzzy spline curve, the linear system represented by the equation 13 may be solved for the equation 14. Equation 13 is actually a triple linear system regarding the x-axis element, the y-axis element of the apex of the cone of the fuzzy vector, and the radius of the base circle of the cone. Therefore, by solving these three linear systems, fuzzy The control polygon of the spline curve is sought.
A specific example of the above fuzzy spline interpolation will be described. 4 to 6 show examples of interpolating a fuzzy point sequence given in the graphic space with a cubic fuzzy spline curve. The circles in FIGS. 4 to 6 are the bottom circles of the conical fuzzy vector. (1) The fuzzy point sequence of equation 17 having a conical membership function is given as shown in FIG.

[0044]

[Equation 17]

At this time, the points actually sampled are used as the vertices of the cone, and the ambiguity is given as the radius of the base circle. The ambiguity is given based on information such as acceleration. (2) By the method that extends the normal spline interpolation method,
Find the fuzzy control polygon of Eq. This fuzzy control polygon is shown in FIG.

[0046]

[Equation 18]

(3) Interpolation / evaluation is performed on the fuzzy control polygon of Eq. 18 by a method obtained by expanding an ordinary de Boer's algorithm, and a fuzzy curve as shown in FIG. 6 is obtained with desired fineness. To generate.

<< Fuzzy segmentation of handwritten curve >> Whatever the writer should write from the handwritten input data of a line figure which is considered to include ambiguity input from a tablet or the like by applying the above-mentioned fuzzy spline curve interpolation In inferring whether or not it is necessary to divide the input data into segments of a certain size. In this case, since the handwritten line figure is basically drawn with the stroke intended by the writer, it is considered effective to divide the input data by the stroke of the handwriting input.
Therefore, the principle of segmentation by dividing handwritten strokes from a fuzzy spline curve will be described.

In order to find out what the writer intended to write, in segmentation, the strokes of the input line figure are detected and the stroke delimiters are detected. In the handwriting input, the input speed becomes slower at the stroke delimiter, and it appears as a corner or a stop point in a line figure. Therefore, it is considered that stroke delimiters can be extracted by checking whether or not a certain point is stopped, and if a certain point is fuzzy evaluated whether or not it is stopped for a certain period of time,
Fuzzy segmentation can be performed by separating strokes. <Fuzzy Spline Interpolation of Sample Points> The input point sequence p _i sampled at constant time intervals does not always have accurate position information that accurately reflects the intention of the writer of the curve. Generally, the coarser the curve, the more ambiguous the position information. From this viewpoint, each sample point is considered to have a position ambiguity proportional to the handwriting acceleration at that point. This can be expressed by using the fuzzy vector of Equation 19 to indicate each sample point p _i .

[0050]

[Formula 19]

Here, r _pi is set in proportion to the acceleration at the sample point p _i . A sample point sequence represented by such a fuzzy vector can be interpolated by the above-described method to obtain a fuzzy spline curve. <Evaluation of Termination by Interval Truth Value> By using the equation 11, the spline curve is evaluated at a constant time interval shorter than the original sampling interval. As a result, the finer fuzzy sequence of points, Formula 20, is obtained.

[0052]

[Equation 20]

The degree of termination at each fuzzy point in the equation 20 is evaluated by the interval truth value [N _i , P _i ] based on the inevitability measure N _i and the possibility measure P _{i shown} in the equations 21 and 22 (note that , The operator “∨” in Equation 21 represents the max (maximum value) operation that takes the larger one, and Equation 2
The operator “∧” in 2 represents a min (minimum value) operation that takes the smaller one, and “in” in Equation 21
"f" indicates an operation that takes a lower limit, and the operator "sup" in the equation 22 shows an operation that takes an upper limit).

[0054]

[Equation 21]

[0055]

[Equation 22]

Here, the inevitability measure N _i and the possibility measure P _i shown in the equations 21 and 22 are defined as the inevitability and the possibility that the proposition shown in the equation 23 holds for the fuzzy points. If we choose an appropriate integer for k, the proposition above is that "the position on the curve at time i is
It is the same as the position on the curve a minute time before (k hours). "

[0057]

[Equation 23]

<Fuzzy Segmentation> A method is proposed in which a handwritten curve is divided into segments corresponding to strokes intended by the writer by using interval truth values for evaluating the degree of stopping at each point. This approach provides accurate segmentation if the curves are carefully written. On the other hand, if the curve is coarsely written, the ambiguity of segmentation is detected. [Labeling to evaluation fuzzy points] Interval truth value [N _i ,
P _i ] is compared with an arbitrary threshold α ∈ [0, 1] and quantized, and as shown in FIG. 7, “1 (true)”, “? (Unknown)” or “0 (false)”. To be labeled.

[Grouping of evaluation fuzzy points] Next,
All fuzzy points labeled “?” Or “1” as in FIG. 7 are separated from the fuzzy points labeled “0” and grouped into Gj. Each group Gj
Is estimated to correspond to a candidate for a stopping point, or a break point for the two segments joined. Fuzzy Extraction of Breakpoints Each group Gj itself is labeled "1" if it contains at least one fuzzy point labeled "1", otherwise "0". Is labeled ". Now
As shown in FIG. 7, by selecting one fuzzy point for each group Gj, the break points that inherit the label from those mother groups are extracted as shown in Expression 24.

[0060]

[Equation 24]

The breakpoints labeled "1" are treated as automatically extracted accurate breakpoints. On the other hand, breakpoints labeled with "?" Are still questionable and are presented to the curve writer as a mere breakpoint candidate for direct judgment. According to such a principle, the fuzzy spline curve information including the ambiguity information by the handwriting operation can be effectively used to divide the fuzzy spline curve information into appropriate segments according to the strokes, which can be used for recognition processing.

<< Fuzzy Recognition Algorithm of Handwriting Curve >> Here, the fuzzy recognition algorithm of the handwriting curve in the fuzzy recognition system of the handwriting curve to which the embodiment of the present invention is applied will be described in detail. This system directly creates a curve with the geometrical meaning desired by the writer in a computer by handwriting the curve with a stylus pen on an input device such as a pen computer that has an integrated tablet and display. It realizes a typical figure input human interface. More specifically, this is a "line segment", a "circle",
"Arc", "Ellipse", "Elliptic arc", "Closed free curve",
It realizes a human interface that allows you to write 7 types of curve classes of "Open Free Curve" by handwriting and input them into a computer. It is possible to realize a more direct and natural graphic input interface that does not rely on physical operation.

As a matter of course, a "deviation" occurs between the position information of the curve that is manually input and observed and that of the ideal curve that the writer originally intended to write. Therefore, the position information of the input / observed curve sample cannot be definitely treated. In this system, the input curve sample is represented by a fuzzy spline curve, and the ambiguity of the observed position information is retained as information, and the writer's intended ideal curve is inferred while considering the ambiguity of the handwritten curve. Give a method to realize.

Here, the ambiguity information of the input curve sample is set and inferred / recognized based on the politeness adjustment of the curve, so that the human being can naturally adjust the curving shape and the politeness. A human interface that can write the curve class intended for is realized. According to the present system, the more carefully written, the more flexible the curve class will be, and the more coarsely written, the more simple the curve class will be. Therefore, when a writer wants to write a simple class of curves, he / she expresses shapes symbolically by writing the curves appropriately coarsely, and conversely when he / she wants to intentionally write more complicated shapes, the actual writing is done. It can be expressed by carefully writing that the shape in which it is intended is intentional.

For example, if a circle is appropriately written, a curve can be input so that it can be recognized as a true circle even if the shape is slightly distorted, or if it is carefully written, a free curve slightly deviated from the true circle. It is possible to intentionally input. In addition, this method realizes inference based on information that originally contains ambiguity.
That is, the "inferred curve class" and the "recognized curve shape" themselves are obtained as a fuzzy expression including ambiguity that reflects the ambiguity of the input curve sample. Such a fuzzy expression can convey information for final curve class determination and curve shape determination to the writer's human being and higher-level inference systems without excess or deficiency. For this reason, it is possible to realize a natural and efficient next candidate selection operation by a human, and to realize a higher-level inference system that makes a judgment in combination with other information.

<Flow of Algorithm> In this algorithm, for example, a handwritten curve input from a tablet is represented by a fuzzy spline curve by the above-mentioned fuzzy spline interpolation, and this is used as a clue by a fuzzy segmentation described above for each basic curve. It is assumed that it has been segmented into. At this time, in this method, the individual basic curve segments are “line segment”, “circle”, “arc”, “ellipse”, “elliptic arc”,
A means for fuzzy inference as to which of the seven curve classes "closed free curve" and "open free curve" is given is provided, and the basic curve sequence determined interactively is output as CAD data. Realize that. The conceptual structure of the entire process is as shown in FIG.

First, when a sample data point sequence of a handwritten curve is input from the tablet (curve sample data input M1), this sample data point sequence is fuzzy based on acceleration or the like, and the obtained fuzzy sample data is obtained. By performing fuzzy spline interpolation on the point sequence, a fuzzy spline curve representation of the input curve is obtained (fuzzy spline interpolation M2). Next, the entire fuzzy spline curve is divided into parts, such as line segments, circles, and ellipses, which should correspond to the basic curve, by relying on the stroke breaks. This division is executed by a fuzzy segmentation method considering the ambiguity of the input curve, and finally the division points are interactively determined (fuzzy segmentation M3). When the above pre-processing is completed, the curve class of each divided basic curve segment is fuzzy inferred (processing M4 for each fuzzy curve segment). This is done as follows.

First, the possibility that the basic curve segment is a "line segment", "an arc (including a circle)", and "an elliptic arc (including an ellipse)" is fuzzy determined (curve class possibility evaluation M9). . This is realized by hypothesis verification. That is, a curve reference model for each curve class is constructed based on a few representative points of a basic curve segment represented as a part of a fuzzy spline curve (line segment reference model configuration M
6, arc reference model configuration M7, elliptical arc reference model configuration M8). Next, a curve sample model of the basic curve segment is constructed from the original fuzzy spline curve (curve sample model configuration M5). At this time, by performing a fuzzy evaluation of how much the curve sample model may actually match the assumed curve reference model for each curve class over the entire basic curve segment, The curve class of is calculated fuzzy.

On the other hand, the possibility that the basic curve segment is a closed curve is obtained in a fuzzy manner by using the start and end points of the basic curve segment obtained as fuzzy points on the fuzzy spline curve (closed figure possibility evaluation M1.
0). When the possibility of each curve class and the possibility of a closed curve are obtained, fuzzy inference with these possibilities as input is performed to recognize the curve class intended by the writer in a fuzzy manner (fuzzy inference for curve recognition). M11). At this time, the recognition result of the curve class is "line segment", "circle", "arc",
It is obtained as a discrete fuzzy set whose domain is a set having seven curve classes of "ellipse", "elliptic arc", "closed free curve" and "open free curve". Further here,
Based on this fuzzy inference result, one curve class is decided by interactive processing with the writer. Since this interactive processing is performed based on the fuzzy inference result, it is efficiently executed according to the ambiguity of the written curve.

When the curve class is determined, the recognition curve is obtained as the corresponding curve reference model.
However, since this curve reference model itself is a fuzzy expression, its representative part is extracted as a normal curve according to the application (representative curve extraction M12). When the above processing is completed for all the basic curve segments and the representative curves of the respective segments are obtained, these representative curves are connected according to the application (representative curve connection M1).
3). This is a process because even if the entire curve is drawn with a single stroke, the recognized curve segments are not necessarily obtained as being connected. Finally, the expression form of each recognized representative curve is converted into a parameter form that can be easily used in normal CAD (parameter conversion M14) and output. This is because the internal representation of the recognized curve segment is obtained as a B-spline curve or a rational Bezier curve. For example, a “circle” represented by a rational Bezier curve is converted into a parameter representation such as “center” and “radius”. Convert.

<Curve Sample Model and Its FMPS> Among the input curve samples, a model showing the shape of the basic curve segment of interest is constructed as a curve sample model. Further, a fuzzy matching point set (hereinafter abbreviated as "FMPS") is extracted from this curve sample model. This FMPS represents the overall shape of the curve by, for example, about 10 fuzzy points, and is used for verification of the degree of agreement with a reference model described later.

By the fuzzy segmentation method described above, the fuzzy start point [q] _s and the fuzzy end point [q] _{e of} one basic curve segment represent two original fuzzy spline curves representing the entire input curve. Obtained as fuzzy points [q] _i and [q] _{i + k} , respectively. (Fuzzy points are indicated by adding a tilde "~" over the letters in mathematical formulas, drawings, etc., but may be indicated by adding a tilde over the letters in the description text. Since it is impossible, for convenience of explanation, the fuzzy points are indicated by enclosing them with "[" and "]" instead of adding a tilde.) Therefore, the curve sample model of the basic curve segment of interest is starting [q] fuzzy end point from the parameter values u _i giving _i [q] _{i + k} giving the parameter value u _{i + k} until the parameter value sections [u _i, u i _{+ k]}
It is already given as the fuzzy spline curve corresponding to.

Next, this curve sample model is evaluated with n _fmps fuzzy points which are the number determined so as to be equidistant in distance along the curve, and the obtained n _fmps fuzzy points are evaluated. A set, that is, the equation (25) is the FMPS of the curve sample model.

[0074]

[Equation 25]

9 (a) and (b) to FIG. 11 (a) and
Examples of the curve sample model and FMPS are shown in (b) (n _fmps = 5 for simplicity in these illustrations).
However, actually, it is desirable to set n _fmps to about 10 or more so as to _show the characteristics of the entire basic curve segment). However, it is difficult to exactly determine the points at which the fuzzy spline curve is divided into equidistant intervals. Therefore, based on the polygon formed by the vertices of the membership function of the evaluation points [q] _i , ..., [q] _{i + k} on the original fuzzy spline curve, the points are divided approximately equidistantly. The FMPS is obtained by finding the corresponding parameter values and re-evaluating the fuzzy points on the fuzzy spline curve at these parameter values.

<Reference Model for Each Curve Class and Its FMPS> Regarding the curve sample model of each basic curve segment extracted by the above-mentioned fuzzy segmentation method, it is a “line segment” or “arc (including a circle). , And “elliptic arc (including ellipse)”, a hypothesis of what kind of shape the curve can be made is assumed. Here, this is called a reference model for each curve class. This reference model is constructed as a fuzzy rational Bezier curve based on some representative fuzzy points in the curve sample model. A fuzzy rational Bezier curve is a definition of an ordinary rational Bezier curve which is a curve that can express "line segment", "arc" and "elliptic arc" in a fuzzy extension. The model becomes a fuzzy curve.

Next, similar to the above-mentioned curve sample model, the overall shape of the reference model constructed as a fuzzy rational Bezier curve is represented by a set of 10 fuzzy points, and the FMPS as shown in Eq. Make up.

[0078]

[Equation 26]

The FMPS of this reference model will be used later to verify the degree of agreement with the curve sample model. <Construction Method of Line Segment Reference Model> As such a reference model for each curve class, a construction method of the line segment reference model according to the present invention will be described first.
Assuming that the curve sample model of the basic curve segment of interest is a line segment, the reference model selects two fuzzy representative points from the curve sample model,
A fuzzy line segment that satisfies these is constructed. Next, from this fuzzy line segment, the FMPS of the line segment reference model
To extract.

Fuzzy Representative Point Since a straight line is determined by two points, basically two arbitrary fuzzy points are selected from the curve sample model and these are used as fuzzy representative points for constructing a line segment reference model. do it. However, so that the fuzzy representative points represent the general outline of the curve sample model,
It is desirable to select these so that they are not too close together. In the following, the starting point [q] _s of the curve sample model is defined as one of the fuzzy representative points [a] ₀ ,
When an arbitrary fuzzy point on the curve sample model is set as the other fuzzy representative point [a] ₁ , that is, for a curve sample model as shown in FIG. 9 (a),
As shown in FIG. 12, fuzzy representative points [a] ₀ and [a] ₁
The case of setting will be described.

It can be easily understood that the line segment reference model can be constructed by the same method even in the generalized case where any two points on the curve sample model are selected as fuzzy representative points. In the experiment, good results were obtained by selecting the starting point [q] _s of the curve sample model as [a] _{0 and} the end point [q] _e of the curve sample model as [a] ₁ . Line segment reference model The line segment reference model is constructed as a fuzzy line segment that satisfies the selected fuzzy representative points [a] ₀ and [a] ₁ . This fuzzy line segment is a fuzzy point [a]
It can be defined as a set of internal and external fuzzy points of ₀ and [a] ₁ (this definition is defined as a special case of Bezier curve as well as the reference model of circular arc and elliptic arc described later). It is equivalent to that, but in the case of a line segment is easy, so I will not treat it as a Bezier curve here).

For example, for the fuzzy representative points selected as shown in FIG. 12, a line segment reference model as shown in FIG. 13 is constructed. Here, the end point [q] _e ^Line of the line segment reference model is the length along the curve from [a] ₀ to [a] ₁ of the curve sample model and [a] ₁ to [q]
The ratio to the length along the curve to _e is the ratio of the distance from [a] ₀ to [a] ₁ on the line segment reference model to the distance from [a] ₁ to [q] _e ^Line Set to match. Here, the internal division fuzzy point and the external division fuzzy point are obtained as follows. Let R be the vector v, using the vector length R _v and the angle θ _v of the vector from the x-axis
If we express it as _v exp (jθ _v ), where j is an imaginary unit, then the α-level sets of arbitrary conical fuzzy vectors [a] and [b] such as Equations 1 and 3 are 27 and the number 28.

[0083]

[Equation 27]

[0084]

[Equation 28]

Here, based on the extension principle, the α-level set of [a] + [b] which is the calculation result of [a] and [b] becomes the calculation result of each α-level set. , Number 29 is obtained. Therefore, from this result, the sum of the fuzzy vectors is given by Equation 30.

[0086]

[Equation 29]

[0087]

[Equation 30]

Further, since the formula 31 holds for a certain positive real number k, the formula 32 is obtained.

[0089]

[Equation 31]

[0090]

[Equation 32]

On the other hand, for a certain negative real number k,
Since Expression 33 is established, Expression 34 is obtained.

[0092]

[Expression 33]

[0093]

[Equation 34]

Therefore, by combining the equations 32 and 34, the equation 35 is obtained for an arbitrary real number k.

[0095]

[Equation 35]

Now, assuming that [a] and [b] are fuzzy points, a fuzzy point [p] that internally or externally divides them into α: β can be defined as the equation 36. Here, when α and β are both positive, the internal division point is obtained, and when either α or β is negative, the external division point is obtained. Further, α + β is always a positive number.

[0097]

[Equation 36]

If the results of Eq. 30 and Eq. 35 are used for Eq. 36, the inner dividing point and the outer dividing point are finally obtained by Eq.

[0099]

[Equation 37]

This is shown in FIGS. 14 and 15, for example. Now, first, [p] and [b] are given, and [a] is determined so that [p] is a point that internally divides [a] and [b] into α: β. In such cases, caution is required. In this case, [a] is
And not the number 39.

[0101]

[Equation 38]

[0102]

[Formula 39]

FMPS An n _fmps number of fuzzy points are obtained on the line segment reference model so as to divide the line segment reference model at equidistant intervals, and the result is used as the FMPS of the line segment reference model. Such FMPS can be easily obtained by the operation of obtaining the internal division fuzzy points and the external division fuzzy points of [a] ₀ and [a] ₁ . For example, from the line segment reference model as shown in FIG. 13, the FMPS of Formula 40 as shown in FIG. 16 is obtained.

[0104]

[Formula 40]

<Construction Method of Circular Arc Reference Model> Next, assuming that the curve sample model of the basic curve segment of interest is an arc (including a circle), the reference model is three fuzzy representatives from the curve sample model. Select points and construct them as fuzzy arcs that satisfy them. Next, the FMPS of the circular arc reference model is extracted from this fuzzy circular arc. Representation of a quadratic rational Bezier curve of an arc An arc is a type of conic curve and can be represented by a quadratic rational Bezier curve. FIG. 17 shows an example of an arc represented by a quadratic rational Bezier curve. B ₀ to f in the figure
The arc of the portion that passes through to b ₂ is a Bezier polygon b ₀
It can be represented as a part of the parameter value interval [0, 1] of the quadratic rational Bezier curve given by the equation 41 by b ₁ b ₂ and a certain weight w.

[0106]

[Formula 41]

[0107] The b arc portion extending in b ₀ through the other end of the ₂ to f are secondary rational given by the number 42 by the weight -w where the sign and Bezier polygon b ₂ b ₁ b ₀ in the opposite It can be represented as a part of the parameter value section [0, 1] of the type Bezier curve. However, B _i ² (t) is a quadratic Bernstein polynomial.

[0108]

[Equation 42]

[0109] At this time, necessary and sufficient condition for these curves are arcs line b ₁ m line segment b ₀ b ₂ vertical 2
That is, the lines are bisectors, and the relationship shown in Formula 43 is established between the weight w and the lengths l and h shown in the figure.

[0110]

[Equation 43]

Now, the calculation of the weight of the circle will be described.
When the circle is given by the quadratic rational Bezier curve as shown in FIG. 18, the weight w is given by

[0112]

[Equation 44]

In this figure, since of b ₀ m and oa b ₀ f, the _equation 45 is established.

[0114]

[Equation 45]

Further, since the triangle ab ₀ f is an isosceles triangle, the formula 46 is obtained.

[0116]

[Equation 46]

Therefore, from the equations 44 to 46, the weight w
Is calculated by Equation 47.

[0118]

[Equation 47]

Fuzzy representative point According to the above-mentioned property, two points b ₀ and b _{2 on} the circumference, and a perpendicular bisector of the line segment b ₀ b ₂ formed by these two points and the circumference 1 Given two intersection points f, a circle passing through these three points can be obtained as a quadratic rational Bezier curve. Therefore, three fuzzy points having the same relationship as these may be selected from the curve sample model and used as the fuzzy representative points for constructing the arc reference model. That is, two arbitrary fuzzy points [a] ₀ and [a] ₁ are selected from the curve sample model, and then the 2
A perpendicular bisector for the line segment connecting the vertices of the membership function of the fuzzy points is obtained. Further, of the fuzzy points in the portion from [a] ₀ to [a] ₁ of the curve sample model, the fuzzy point [f] on this vertical bisector is obtained, and this is used as the third fuzzy representative point.

Here, in order for the fuzzy representative points to represent the general outline of the curve sample model, it is desirable to select them so that they are not too close to each other. Below is one of the fuzzy representative points
[A] ₀ as the starting point [q] of the curve sample model
_{When s} is set as a second fuzzy representative point [a] _{1 and} an arbitrary fuzzy point on the curve sample model is set, that is, for a curve sample model as shown in FIG. A case where the fuzzy representative points [a] ₀ and [a] ₁ and [f] are obtained will be described.

Even in the generalized case where any two points on the curve sample model are selected as the fuzzy representative points [a] ₀ and [a] ₁ , the arc reference model can be constructed by the same method. It is omitted here. By the way, in the experiment, as [a] ₀ , [q] _s ,
Good results have been obtained by selecting the fuzzy point having the longest linear distance from [q] _s in the latter half of the curve sample model as [a] ₁ . Circular Reference Model The circular reference model is constructed as a fuzzy circular arc that satisfies three fuzzy representative points. Here, the fuzzy arc is the vertex b of the Bezier polygon in the equations 41 and 42.
_{Let i} (i = 1, 2, 3) be a fuzzy point [b] _i (i = 1, 1
It is defined as in Eqs. 48 and 49 by expanding to 2, 3).

[0122]

[Equation 48]

[0123]

[Equation 49]

At this time, the fuzzy Bezier polygon [b] _{i is set} so that this fuzzy circular arc satisfies the given three fuzzy representative points [a] ₀ , [a] ₁ and [f].
(I = 1, 2, 3) and the weight w are defined, and this is used as a reference model of an arc. The procedure is as follows. First, as shown in FIG. 19, two fuzzy representative points [a] ₀
Let [a] ₁ and [a] ₁ be [b] ₀ and [b] ₂ , respectively. Next, the fuzzy midpoint [m] of [a] ₀ and [a] ₁ is calculated by the _equation 50.

[0125]

[Equation 50]

Here, the distance between the vertices of the membership functions of [a] ₀ and [m] is set to 1, and the distance between the vertices of the membership functions of [f] and [m] is set to h. The weight w is calculated by 43. Finally, [b] ₁ is calculated by the equation 51 so that [f] becomes a fuzzy point that internally divides [b] ₁ and [m] into 1: w.

[0127]

[Equation 51]

By constructing the circular arc reference model as described above, for example, the circular arc reference model satisfying the fuzzy representative points as shown in FIG. 19 can be obtained as shown in FIG. However, here, the end point [q] _e ^Circle of the arc reference model is the length along the curve from [a] ₀ to [a] ₁ of the curve sample model and [a] ₁ to [q] _e.
Along the curve from [b] ₀ to [b] ₂ on the arc reference model and along the curve from [b] ₂ to [q] _e ^Circle Determine to match length ratio. On the FMPS circular arc reference model, n _fmps fuzzy points are obtained so as to be divided at equal distances along a curve,
FMPS of the circular arc reference model, that is, Equation 52. For example, the FMPS shown in FIG. 21 is obtained from the circular arc reference model shown in FIG.

[0129]

[Equation 52]

Here, it is difficult to divide the fuzzy rational Bezier curve along the curve exactly at equal intervals. Therefore, first, the circular arc reference model is evaluated at an appropriate number of points so as to be evenly spaced on the parameter t, and the approximate polygon of the circular arc is constructed. Next, the relationship between the parameter and the distance along the curve on the circular arc is approximately obtained from this as a line graph, and the parameter value corresponding to the points at which the distance on the curve is divided into equal intervals is approximately obtained. The FMPS is approximately obtained by re-evaluating the arc reference model with the finally obtained parameter values.

<Construction Method of Elliptical Arc Reference Model> When the curve sample model of the basic curve segment of interest is assumed to be an elliptic arc (including an ellipse), the reference model is three fuzzy representative points and 1 from the curve sample model. Select two auxiliary points and construct them as a fuzzy elliptic arc satisfying them. Next, the FMPS of the elliptic arc reference model is extracted from this fuzzy elliptic arc. Representation of quadratic rational Bezier curve of elliptic arc Elliptic arc is a kind of conic curve and can be represented by quadratic rational Bezier curve. FIG. 22 shows an example of an elliptic arc represented by a quadratic rational Bezier curve. The elliptic arc of the part from b ₀ to f through b ₂ in the figure is a quadratic rational type given by the number 53 by Bezier polygon b ₀ b ₁ b _{2 and a} certain weight w (1>w> -1). It can be represented as a part of the parameter value section [0, 1] of the Bezier curve.

[0132]

[Equation 53]

Also b₂Through the other side of f to b₀To
The elliptic arc of the part is the Bezier polygon b ₂b₁b₀And sign
The quadratic rational given by the equation 54 by the inverted weight −w
As a part of the parameter value interval [0, 1] of the type Bezier curve
Can be represented. However, B_i ²(t) is the quadratic
It is assumed to be an Ernstein polynomial

[0134]

[Equation 54]

At this time, if the midpoint of the line segment b ₀ b ₂ is m, the intersection f of the line segment b ₁ m and the elliptic arc is farthest from the line segment b ₀ b ₂ among the points on the elliptic arc. To give a point. Also,
As shown in FIG. 23, another auxiliary point p is arbitrarily set on the elliptic arc.
And the leg of the line segment drawn from the point p on the straight line fm so as to be parallel to the line segment b ₀ b ₂ is t, the distance c in the figure,
The relationship of Expression 55 is established between the internal division ratio α: β of the line segment fm based on d and the point t and the weight w.

[0136]

[Equation 55]

Here, the method of calculating the weight of the ellipse by the auxiliary points will be described. It is assumed that the auxiliary point p is on an elliptic arc as shown in FIG. Then, the weight w becomes the expression 56, and if the expression 56 is squared, the expression 57 is obtained.

[0138]

[Equation 56]

[0139]

[Equation 57]

On the other hand, since the equation (58) is obtained from FIG. 24, the equation (59) is obtained.

[0141]

[Equation 58]

[0142]

[Equation 59]

Further, since the expression 60 is obtained, the expression 61 is obtained. Further, since the number is the number 62, the number 63 is obtained.

[0144]

[Equation 60]

[0145]

[Equation 61]

[0146]

[Equation 62]

[0147]

[Equation 63]

Here, by substituting the equation 61 into the equation 63 and rearranging it, the equation 64 is obtained, and by substituting the equation 59 and rearranging, the equation 65 is obtained.

[0149]

[Equation 64]

[0150]

[Equation 65]

Here, the value of both sides of the equation 65 is set to P and the equation 6 is obtained.
If we use 6 and number 67, we get number 68 and number 69,
The number 70 is obtained.

[0152]

[Equation 66]

[0153]

[Equation 67]

[0154]

[Equation 68]

[0155]

[Equation 69]

[0156]

[Equation 70]

Further, paying attention to the equation 59, the equation 71 is obtained.

[0158]

[Equation 71]

Now, the numbers 68, 69 and 71
By substituting the result of (1) into (57) and rearranging, (72) is obtained.

[0160]

[Equation 72]

Since A and B are given as the equations 66 and 67, the equation 73 is obtained by substituting these into the equation 72 and rearranging them.

[0162]

[Equation 73]

In the case of an ellipse, -1 <w <1, so that w ≠ -1. Therefore, the formula 74 is obtained.

[0164]

[Equation 74]

If Equation 74 is solved for w, the weight is Equation 75.
Required by.

[0166]

[Equation 75]

The above equation 55 holds even when the auxiliary point p is located outside the Bezier polygon b ₀ b ₁ b ₂ as shown in FIG. 25, but in this case β becomes negative. To do. Fuzzy representative point According to the above property, two points b ₀ and b on the elliptic arc
_{If 2} and a point f farthest from the line segment b ₀ b ₂ are given, an ellipse passing through these three points is obtained as a quadratic rational Bezier curve by giving appropriate weights.
Therefore, three fuzzy points having the same relationship as these may be selected from the curve sample model and used as fuzzy representative points for constructing the elliptic arc reference model. That is, any 2 from the curve sample model
Two fuzzy points [a] ₀ and [a] ₁ are selected, and then, among the fuzzy points in the portion from [a] ₀ to [a] ₁ of the curve sample model, the values of [a] ₀ and [a] ₁ A fuzzy point [f] that is farthest from the straight line connecting the vertices of the membership function is obtained, and this is used as the third fuzzy representative point.

Here, in order for the fuzzy representative points to represent the general outline of the curve sample model, it is desirable that they are not very close to each other. In the following, the starting point [q] _s of the curve sample model is set as one of the fuzzy representative points [a] ₀ ,
When setting an arbitrary fuzzy point on the curve sample model as the second fuzzy representative point [a] ₁ ,
For example, a case where fuzzy representative points [a] ₀ and [a] ₁ and [f] are obtained as shown in FIG. 26 for a curve sample model as shown in FIG. 11A will be described.

It is possible to construct an elliptic arc reference model by a similar method even in the generalized case where any two points on the curve sample model are selected as fuzzy representative points [a] ₀ and [a] _1. It is omitted here. By the way, in the experiment, as [a] ₀ , [q] _s ,
Good results have been obtained by selecting the fuzzy point having the longest linear distance from [q] _s in the latter half of the curve sample model as [a] ₁ . An example of selecting the fuzzy representative points in this way is shown in FIGS. 27 and 28. Elliptic arc reference model The elliptic arc reference model is constructed as a fuzzy elliptic arc satisfying three fuzzy representative points. Here, in the fuzzy elliptic arc, the vertices b _i (i = 1, 2, 3) of the Bezier polygon in the equations 53 and 54 are fuzzy points [b] _i (i =
76, 77 by expanding to 1, 2, 3)
Define as follows.

[0170]

[Equation 76]

[0171]

[Equation 77]

At this time, the fuzzy Bezier polygon [b] _{i is set} so that the fuzzy elliptic arc satisfies the given three fuzzy representative points [a] ₀ , [a] ₁ and [f].
(I = 1, 2, 3) and a weight w are defined, and this is used as a reference model of an elliptic arc. The procedure is as follows. First, as shown in FIG. 26, two fuzzy representative points [a] ₀ and [a] ₁ are directly set as [b] ₀ and [b] ₂ . Next, the fuzzy midpoint [m] of [a] ₀ and [a] ₁ is calculated by the formula 78.

[0173]

[Equation 78]

Here, one auxiliary point p is set on the curve sample model, and [f] is set so as to be parallel to the straight line connecting the vertices of the membership functions of [b] ₀ and [b] ₂ from the point p.
And a foot t of a line segment drawn on a straight line connecting the vertices of the membership functions of [m] are obtained.
After obtaining the values corresponding to d, α and β, the weight w is calculated by the equation 55. Finally, [f] is [b] ₁ and [m]
[B] ₁ so that the fuzzy point is internally divided into 1: w
Is calculated as the equation 79.

[0175]

[Equation 79]

By constructing the elliptic arc reference model in this way, an elliptic arc reference model satisfying the fuzzy representative points as shown in FIG. 26 can be obtained as shown in FIG. Here, the end point [q] _e ^Ellipse of the elliptic arc reference model is the length along the curve from [a] ₀ to [a] ₁ of the curve sample model and [a] ₁ to [q].
The ratio of the length along the curve to _e is the length along the curve from [b] ₀ to [b] ₂ and the curve from [b] ₂ to [q] _e ^Ellipse on the elliptic arc reference model. The length ratio should be the same.

Here, as the auxiliary point p, basically, a point on an arbitrary curve sample model distant from the three fuzzy representative points to some extent may be selected. However, depending on how the auxiliary point is taken, an elliptic arc reference model is used. In some cases, the deviation of the original curve sample model may become partly large. Therefore, in the experiment, as shown in FIG. 30, three auxiliary points p ₀ , p ₁ , and p ₂ are selected, and three kinds of elliptic arc reference models are constructed for each auxiliary point, which will be described later. Good results have been obtained by adopting the elliptic arc reference model, which has the highest possibility in the evaluation of the potential curve classes, as the final elliptic arc reference model. These three auxiliary points p
₀ , p ₁ and p ₂ are line segments connecting the vertices of the membership functions [a] ₀ and [f], line segments connecting the vertices of the membership functions [f] and [a] ₁ , respectively. a] ₁ and [a] ₀
The farthest point from the line segment connecting the vertices of is selected.

FMPS On the elliptic arc reference model, n _fmps fuzzy points are obtained so as to be divided at equal distances along the curve, and the result is _{FMPS of} the elliptic arc reference model, that is, Equation 80. For example, the FMPS shown in FIG. 31 is obtained from the elliptic arc reference model shown in FIG.

[0179]

[Equation 80]

Here, it is difficult to divide the fuzzy rational Bezier curve along the curve exactly at equal intervals. Therefore, first, the elliptic arc reference model is evaluated with an appropriate number of points so as to be evenly spaced on the parameter t, and an approximate polygon of the elliptic arc is constructed. Next, the relationship between the parameter and the distance along the curve on the elliptic arc is approximately obtained from this as a line graph, and the parameter value corresponding to the points at which the distance on the curve is divided into equal intervals is approximately obtained.
The FMPS is approximately obtained by re-evaluating the elliptic arc reference model with the finally obtained parameter values.

<Possibility Verification for Each Curve Class> As described above, the curve sample model of the basic curve segment of interest is obtained, and the curve sample model is further divided into “line segments”, “arcs” and “elliptic arcs”. Assuming that there is a curve model, the line segment reference model,
Obtained as "Arc Reference Model" and "Elliptic Reference Model". However, here these reference models are hypothetical models that are constructed to satisfy at most a few fuzzy representative points of the curve sample model, and in fact, to what extent these hypotheses are over the basic curve segment. , It is necessary to verify that it matches the original curve sample model.

In the present method, the verification of the matching degree between the fuzzy curves is performed by the FMPS of the curve sample model described above.
(Equation 25) is replaced with the matching degree of the FMPS (Equation 26) of the reference model for each curve class described above, and this is evaluated by the possibility measure which is a kind of fuzzy measure. That is, one curve sample model is a curve class C.
lass (ε {Line, Circle, Ellips
e}) is a potential P ^Class is defined as the number 81.

[0183]

[Equation 81]

Here, the two left and right terms connected by the operator ∧ indicating the min operation taking the smaller one represent the conical membership functions of [s] _i and [r] _i ^Class , respectively. The part of the number 82 in the number 81 may be the possibility of the proposition that "the i-th fuzzy matching point [s] _{i of the} sample model is the i-th fuzzy matching point [r] _i ^Class of the reference model". It has been obtained by a measure.

[0185]

[Equation 82]

Since Equation 81 is a possibility that AND (logical product) of such possibilities at all fuzzy matching points is taken, P ^Class is "F of sample model".
It means that the MPS is the FMPS of the reference model. ” The expression 82 can be easily obtained from the cross section obtained by cutting the membership functions of [s] _i and [r] _i ^{Class with} a line connecting their vertices as shown in FIG.
^Class is easily required. If such P ^Class is obtained for each of “line segment”, “arc”, and “elliptic arc”, the possibility P ^Line , P ^Circle , P for each curve class is obtained.
^Ellipse is required.

In FIG. 33, the FMPS of the curve sample model of FIG. 9A is the FMPS of the line segment reference model of FIG.
FIG. 34 shows the state of verifying the possibility that
The verification of the possibility that the FMPS of the curve sample model of (a) becomes the FMPS of the arc reference model of FIG. 21 is further shown in FIG. 35. The FMPS of the curve sample model of FIG. 11 (a) is the elliptic arc reference model of FIG. FM
The following shows how to verify the possibility of PS.

<Possibility of ^Closed Curve> In order to evaluate whether or not the curve sample model of the basic curve segment of interest described above is a closed curve, the possibility that the curve is closed P ^Closed is a kind of fuzzy measure. It is defined as the number 83 using a certain possibility measure.

[0189]

[Equation 83]

Here, μ _qs (v) and μ _qe (v) represent conical membership functions of q _s and q _e , respectively, and ∧ is a min operation that takes the smaller one. Here, the operator ∧ that indicates the min operation that takes the smaller one
The two left and right terms connected with each other represent the conical membership functions of [q] _s and [q] _e , respectively. The expression 83 represents the possibility of the proposition that "the end point [q] _e is the start point [q] _s ", and its value is shown in FIG.
As shown in FIG. 6, the membership functions of [q] _s and [q] _e can be easily obtained from the cross section taken along the line connecting the vertices.

<Fuzzy Inference of Curve Class> Possibility of a line segment P ^Line obtained as described above, arc (including circle)
From the possibility P ^Circle and the possibility P ^Ellipse of the elliptic arc (including the ellipse) and the possibility P ^{Closed of the} closed curve, the curve sample model of the basic curve segment of interest is “line segment”, “circle”, “arc”. , Ellipse, “elliptic arc”, “closed free curve”, and “open free curve” are obtained by fuzzy reasoning. The curve classes “line segment”, “arc”, “elliptical arc”, and “free curve” have a higher degree of freedom in this order, and have an inclusive relationship as shown in FIG. Therefore, it is general that the relationship of Expression 84 is established between the possibilities obtained separately for each curve class with respect to the same curve sample model.

[0192]

[Equation 84]

Therefore, the probability P for each curve class
It is meaningless to simply infer the intended curve from the magnitude relation of ^Class , and each P ^Class ( ^Class ∈ {Li
It is necessary to infer the curve class from the interrelationship of ne, Circle, Ellipse}). In other words, if the probability of a simple curve class with a low degree of freedom is high enough, it is necessary to infer that a simple curve class is selected even if it is slightly lower than the probability of a curve with a high degree of freedom. On the other hand, each curve class can be subdivided depending on whether the curve is a closed curve. For example, "elliptic arc"
And "ellipse" can be subdivided into different curve classes. As the "ellipse" can be regarded as a special case of "elliptic arc", the open curve includes the closed curve as a special case, and the open curve can be considered as a curve having a higher degree of freedom than the closed curve. .

Combining the above facts, the curve class which the writer of the curve may have intended is obtained by fuzzy inference using the inference rules of FIG. For example, the first rule in FIG. 38 is "if there is a possibility of a line segment, it is a line segment", and the fourth rule is "there is no possibility of line segment, no possibility of arc, and possibility of elliptic arc". Yes, it is an ellipse if it may be closed ", the 7th rule is" no possibility of a line segment, no possibility of an arc, no possibility of an elliptic arc, no possibility of being closed If it is an open free curve ", the rule is shown. Note that this inference is performed as a fuzzy inference, so that all seven rules are evaluated in parallel, rather than applying any one of the inference rules in FIG. Further, as a result, the obtained curve class is obtained as a discrete fuzzy set having the domain of equation (85).

[0195]

[Equation 85]

More specifically, each grade value of the inference result [C] _I of the curve class according to the inference rule of FIG. 38 can be obtained as shown in Eqs. 86 to 92.

[0197]

[Equation 86]

[0198]

[Equation 87]

[0199]

[Equation 88]

[0200]

[Equation 89]

[0201]

[Equation 90]

[0202]

[Formula 91]

[0203]

[Equation 92]

FIGS. 39 (a) and 39 (b) show an example of a curve sample model and a fuzzy curve class [C] _I inferred thereto. In this example, the grade of "elliptic arc (EA)" (Equation 90) is the highest, but the grades of other curve classes are also quite high, and the inferred curve class is rather ambiguous. . This is because the inference result by this method can reflect the roughness of writing and the ambiguity of the shape of the input curve sample model itself. On the other hand, when the curve sample model is written more carefully or the shape is characteristic, a definite inference result with less ambiguity is obtained.

The inferred fuzzy curve class [C] _I is presented to the writer so that the final curve class can be efficiently selected interactively. The curve class is determined as one by passing it as one input information. In the experimental system, an efficient human interface is realized by sequentially presenting on the screen from the highest grade curve class until the writer accepts. When the curve class is uniquely determined, the reference model corresponding to the curve class is adopted as the recognition curve. However, when it is determined that the curve is a free curve, the curve sample model is directly used as the recognition curve. All the curves recognized at this stage are obtained as fuzzy curves.

<Calculation of recognition curve representative value (representative curve)> The recognition curves obtained as described above are all fuzzy curves and are not suitable for being displayed on the screen or used for a normal CAD system. A normal (non-fuzzy) curve is calculated by extracting the portion where the grade of the fuzzy curve obtained is 1 as a representative value (representative curve) of the recognition curve. In the case of line segment When the recognition curve class is a line segment, a line segment reference model as shown in FIG. 13 becomes the recognition curve. Therefore,
The vertex of the membership function of [q] _s ^Line and [q] _e ^Line
The line segment connecting the vertices of the membership function of is the representative value of the recognition curve.

In the case of a circle When the recognition curve class is a circle, an arc reference model as shown in FIG. 20 becomes a recognition curve. In this case, if the normal Bezier polygon b ₀ b ₁ b ₂ is constituted by the vertices of the membership functions of the obtained fuzzy Bezier polygon [b] ₀ [b] ₁ [b] ₂ , then Equation 41 and the number By 42, a circle that is a representative value of the recognition curve is obtained in the form of a rational Bezier curve. Here, the domain of the parameter t is set to [0, 1] in both equations regardless of the position of the end point [q] _e ^Circle so as to form a closed circle.

In the case of an arc When the recognition curve class is an arc, as in the case of a circle, as shown in FIG.
An arc reference model such as 0 becomes the recognition curve.
Therefore, the obtained fuzzy Bezier polygon [b]
_{If the} normal Bezier polygon b ₀ b ₁ b ₂ is constructed by the vertices of the membership functions of ₀ [b] ₁ [b] ₂ , the recognition curve is represented by the _equations 41 and 42 in the form of a rational Bezier curve. A value arc is obtained. However, the domain of the parameter t in the equation 42 is limited to the range from 0 to the parameter value giving [q] _e ^Circle .

Case of Ellipse When the recognition curve class is an ellipse, an elliptic arc reference model as shown in FIG. 29 becomes the recognition curve. In this case, the obtained fuzzy Bezier polygon [b] ₀ [b] ₁ [b] ₂
If the normal Bezier polygon b ₀ b ₁ b ₂ is constructed by the vertices of the membership functions of
4 gives an ellipse that is a representative value of the recognition curve in the form of a rational Bezier curve. Here, the domain of the parameter t is set to [0, 1] in both equations so as to form a closed ellipse regardless of the position of the end point [q] _e ^Ellipse .

Case of Elliptic Arc When the recognition curve class is an elliptic arc, an elliptic arc reference model as shown in FIG. 29 becomes the recognition curve as in the case of an ellipse. Therefore, if the normal Bezier polygon b ₀ b ₁ b ₂ is constructed by the vertices of the respective membership functions of the fuzzy Bezier polygon [b] ₀ [b] ₁ [b] _{2 obtained} , An elliptic arc that is a representative value of the recognition curve is obtained in the form of a rational Bezier curve. However, the domain of the parameter t in Equation 54 is 0 to [q] _e
^It is limited to the range up to the parameter value that gives ^Ellipse .

Case of Closed Free Curve When the recognition curve class is a closed free curve, an appropriate number of fuzzy points on the curve sample model are obtained, and a closed B-spline curve passing through the vertices of these membership functions is obtained. , Which is the representative value of the recognition curve. In the case of open free curve When the recognition curve class is open free curve, an appropriate number of fuzzy points on the curve sample model are obtained, open B spline curves passing through the vertices of these membership functions are obtained, and Use the representative value of the recognition curve.

<Recognition Curve Representative Value (Representative Curve) Connection Processing> By performing the above-described processing for all the basic curve segments, the entire curve initially input is made up of several representative curves. Recognized as a set. However, here, although the original input curve is drawn with one stroke, the recognized representative curves are not always obtained as being connected to each other, and are obtained as shown in FIG. 40, for example. Therefore, if it is necessary to recognize these as connected, a connection process by post-processing is required. Note that it is necessary to save the curve class of the recognized curves here, and the affine transformations of the curves that can be used in the connection process are limited to translation, rotation and scaling. Therefore, the following connection processing is performed.

First, as shown in FIG. 41, the second and subsequent representative curves are moved in parallel so that the start and end points of the representative curve of each curve segment match. At this point, the end point of the last representative curve (p ′ ^e _{4 in} FIG. 41) may accumulate the deviation due to the parallel movement, and the deviation from the original point (p ^e _{4 in} FIG. 40) may increase. . Therefore, in order not to change the global shape as much as possible, the start point of the first representative curve (see FIG.
Then, the connection point farthest from p ′ ^s ₁ ) (p ′ ^s _{3 in} FIG. 41) is obtained, and the representative curve after this point is rotated and enlarged / reduced about this point, and the final representative curve Convert so that the end point matches the position of the original end point (Fig. 4
2).

Since the representative curve obtained previously is expressed as a rational Bezier curve or a B-spline curve, affine transformations such as translation, rotation, and enlargement / reduction necessary for connection processing are performed by Bezier polygons or control. It is easily realized by the affine transformation of polygons. If the recognized / selected representative curve is valid, the connection process shown in FIG.
Good connection processing is performed as shown in (a) and (b) to FIGS. 45 (a) and (b).

<Parameter conversion of recognition curve representative value (representative curve)> Among the representative curves obtained above, “circle”, “arc”, “ellipse” and “ellipse arc” are expressed as rational Bezier curves. , This is not a common representation format of a normal CAD system. Therefore, it is necessary to convert the output result of this method into a general parameter expression for use in a normal CAD system. For circles and arcs For circles, use the center and radius. For arcs, use the center, radius, start point, and end point. Here, since the start point and the end point of the arc have already been obtained, the center and the radius may be obtained. Center o, as shown in FIG. 46, through the b ₀ b ₀ b
Determined as an intersection of a perpendicular b ₂ b ₁ through ₁ of the perpendicular line and b _2. Once the center o is found, the radius is found as the distance between b ₀ and o.

In the case of ellipse and elliptic arc: In the case of an ellipse, the center, the major axis, the minor axis, the inclination angle of the major axis with respect to the horizontal axis (x axis), and in the case of an elliptic arc, the center, major axis, minor axis, the major axis of the major axis. It is expressed by the tilt angle with respect to, the start point, and the end point. Here, since the start point and the end point of the elliptic arc have already been obtained, the center, the major axis, the minor axis, and the tilt angle of the major axis may be determined. First, if an implicit function expression of an ellipse such as Expression 93 is obtained from the Bezier polygon b ₀ b ₁ b ₂ and the weight w,
The following results can be obtained.

[0217]

[Equation 93]

From the implicit function expression of Expression 93, the center o of the ellipse o =
(X ₀ , y ₀ ) is obtained by the equations 94 and 95.

[0219]

[Equation 94]

[0220]

[Formula 95]

In order to obtain the major axis and the minor axis, first, two solutions of the quadratic equation of t as shown in Expression 96 are obtained, and the smaller solution is t _a and the larger solution is t _b .

[0222]

[Equation 96]

Next, if Expression 97 is obtained, the major axis (major axis length) d _l and the minor axis (minor axis length) d _s can be calculated by Equations 98 and 99.

[0224]

[Numerical Expression 97]

[0225]

[Equation 98]

[0226]

[Numerical expression 99]

To obtain the inclination θ of the long axis, first,
Is obtained such that 0 ≦ θ ′ <(π / 2).

[0228]

[Equation 100]

Then, θ becomes equation 101 according to the sign of h, and is obtained so that 0 ≦ θ <π. The parameters of the above ellipse are shown in FIG.

<Example of Recognition Experiment> FIGS. 48 (a) and (b) to FIGS. 51 (a) and (b) show some curve sample models consisting of one curve segment and some of the fuzzy curve classes inferred from them. For example: Figure 48 (a) and
(b) is an example of symbolically inputting a circular arc by rough writing, and FIGS. 49 (a) and (b) are examples of inputting an elliptical arc with a medium roughness, FIG. 50 (a). 51A and 51B show inference results of the fuzzy curve class in an example in which a free-form curve is input by careful writing, and FIGS. 51A and 51B show examples in which writing and shape are delicate. It is understood from the examples of FIGS. 48 to 50 that the curve classes can be sorted based on the roughness and the shape of the writing method. In addition, FIG.
From the example, it can be seen that when the writing style and the shape are subtle and the judgment cannot be made, the information that it is ambiguous is output as an ambiguous fuzzy curve class in which the grades of all curve classes are high.

Also, FIGS. 52 (a), 52 (b) and 53 (a)
, (B) show examples of recognition of input curves consisting of multiple curve segments. (A) and (b) in each figure are respectively the representative curve corresponding to the input curve that was fuzzy splined and the highest grade obtained curve class in the fuzzy curve class inferred by each curve segment. Is subjected to the connection processing as described above.

<< Embodiment of the Invention >> An embodiment of the present invention based on the above principle will be described below with reference to the drawings. Figure 1
FIG. 2 shows a schematic configuration of a fuzzy line segment model generation device according to an embodiment of the present invention which is applied to the system described above. The fuzzy line segment model generation device of this embodiment is shown in FIG.
A fuzzy line segment model as a reference model used in the line segment reference model configuration M6 in the processing of the pattern recognition system shown in FIG. 2 and assuming that the input curve sample model segmented by fuzzy spline interpolation is a straight line segment. To generate a curve class for curve recognition.

The fuzzy line segment model generation apparatus shown in FIG. 1 comprises a sample model generation unit 1, a representative point selection unit 2, a line segment model generation unit 3 and a line segment model FMPS extraction unit 4. It should be noted that this device typically includes a CPU (central processing unit) and is configured to function as a predetermined function mainly by software. Of course, part or all of this device may be configured by hardware corresponding to each functional element. The sample model generation unit 1 uses the fuzzy spline interpolation to input curve information input as fuzzy point sequence information including ambiguity information,
A fuzzy sample model of the input curve is generated by making a continuous fuzzy spline curve and segmenting it by fuzzy segmentation. Representative point selection unit 2
Are selected as two fuzzy representative points from the input curve sample model expressed as a fuzzy spline curve, and set as the first and second fuzzy representative points, respectively.

The line segment model generating section 3 includes an internal segment fuzzy point arithmetic section 31, an external segment fuzzy point arithmetic section 32, and an end point arithmetic section 33.
And a line segment constructing unit 34, and a fuzzy line segment satisfying the first and second fuzzy representative points selected by the representative point selecting unit 2 is generated as a fuzzy line segment model. The internally-divided fuzzy point calculation unit 31 determines whether the first fuzzy representative point and the second fuzzy representative point selected by the representative point selection unit 2 are between the first and second fuzzy representative points. Find the set of min fuzzy points. The end point calculation unit 33 determines the length of the curve sample model from the first fuzzy representative point to the second fuzzy representative point along the curve of the sample model and the second fuzzy representative point to the end point of the curve sample model. To the length along the curve of the sample model to the distance from the first fuzzy representative point to the second fuzzy representative point on the fuzzy line segment model and the second fuzzy representative point from The end point of the fuzzy line segment model is determined so as to match the ratio to the distance to the end point of the fuzzy line segment model.

The outer-division fuzzy point calculation unit 32 determines whether the first fuzzy line segment model between the second fuzzy representative point selected by the representative point selection unit 2 and the end point of the fuzzy line segment model calculated by the end point calculation unit 33. And a set of external fuzzy points between the second fuzzy representative points. The line segment construction unit 34 is obtained by the set of internal division fuzzy points between the first and second fuzzy representative points obtained by the internal division fuzzy point calculation unit 31 and the external division fuzzy point calculation unit 32. A fuzzy line segment model is constituted by the set of outer-segment fuzzy points between the second fuzzy representative point and the end point of the fuzzy line segment model. FMPS extraction unit 4
Is divided into n on the line segment reference model obtained by the line segment model generation unit 3 at equal distance intervals.
_{The fmps} fuzzy points are obtained and used as the FMPS of the line segment reference model. As described above, such FMPS can be obtained by the operation of obtaining the internally and externally fuzzy points of the first fuzzy representative point and the second fuzzy point.

Next, the operation of the fuzzy line segment model generating apparatus of the present embodiment having the configuration shown in FIG. 1 will be described in detail. FIG. 2 shows a flowchart of the processing operation of the fuzzy line segment model generation device of this embodiment. In FIG. 2, when the system starts, first, the input curve information based on the handwritten curve information input as fuzzy point sequence information including ambiguity information by the tablet device is continuously processed by the sample model generation unit 1 by fuzzy spline interpolation. The fuzzy sample model of the input curve, which is a fuzzy spline curve, is further segmented by fuzzy segmentation and is taken into the system (step S1).

Next, from the input curve sample model represented as the fuzzy spline curve fetched in step S1, the representative point selecting unit 2 makes the first
And two appropriate fuzzy points are selected as the second fuzzy representative points (step S2). Next, the first and second fuzzy representative points are determined by the line segment model generation unit 3 including the internal division fuzzy point calculation unit 31, the external division fuzzy point calculation unit 32, the end point calculation unit 33, and the line segment configuration unit 34. A satisfying fuzzy line segment is generated as a fuzzy line segment model (step S3).

In this step S3, the internal division fuzzy point calculation unit 31 determines between the first fuzzy representative point and the second fuzzy representative point between the first fuzzy representative point and the second fuzzy representative point. A set of internally-divided fuzzy points is obtained, and the end point calculation unit 33 determines the length along the curve of the curve sample model from the first fuzzy representative point to the second fuzzy representative point and the second fuzzy representative point. The ratio of the length from the fuzzy representative point to the end point of the curve sample model along the curve of the sample model is the distance from the first fuzzy representative point to the second fuzzy representative point on the fuzzy line segment model. And the distance from the second fuzzy representative point to the end point of the fuzzy line segment model, the end point of the fuzzy line segment model is obtained. The outer partial fuzzy point calculation unit 32,
A set of externally divided fuzzy points between the first and second fuzzy representative points is obtained between the second fuzzy representative point and the end point of the fuzzy line segment model.

Further, in this step S3, the line segment constructing section 34 causes the set of internally divided fuzzy points between the first and second fuzzy representative points and the second set of fuzzy points.
A fuzzy line segment model is constituted by the set of outer-segment fuzzy points between the fuzzy representative point of and the end point of the fuzzy line segment model. Next, on the line segment reference model obtained in step S3, n _fmps fuzzy points are obtained so as to divide the line segment reference model at equidistant intervals, and set as FMPS of the line segment reference model (step S4). ). In this step S4, the FMPS is obtained by, for example, an operation of obtaining the internally and externally fuzzy points of the first fuzzy representative point and the second fuzzy point.

In this way, as a reference model in the case where the input curve sample model is assumed to be a straight line segment, a fuzzy line which is appropriately fuzzy corresponding to the fuzzy input curve sample model is used. It is possible to generate a fuzzy line segment model composed of minutes, and generate, for example, FMPS from this fuzzy line segment model, and use this for evaluation of a curve class for curve inference using the ambiguity information. The formation of the fuzzy line segment model according to the present invention is not limited to the system shown in the above description of the principle, and any system that processes a fuzzified input curve sample model can be fuzzy. It can be applied when generating a fuzzy line segment model corresponding to the input curve sample model.

[0241]

As described above, according to the present invention, a handwritten curve is input as fuzzy curve information including input ambiguity information, and a curve sample model of a segment as a part of the input fuzzy curve information is obtained. Generating a fuzzy line segment model as a reference model assuming that the input curve sample model in pattern recognition that discriminates the pattern of the input curve by comparing with the reference model represented by fuzzy representation as a reference pattern is a straight line segment In doing so, two appropriate fuzzy points on the fuzzy spline curve representing the input curve sample model are selected as the first and second fuzzy representative points, and a fuzzy line satisfying these first and second fuzzy representative points is selected. The minute is the internal division between these first and second fuzzy keypoints. A fuzzy line segment model consisting of appropriately fuzzified straight line segment information corresponding to a fuzzified input curve sample model by constructing a set of fuzzy points and external fuzzy points It is possible to provide a fuzzy line segment model generation method and device capable of generating the.

[Brief description of drawings]

FIG. 1 is a block diagram showing a schematic configuration of a fuzzy line segment model generation device according to an embodiment of the present invention.

FIG. 2 is a flow chart for schematically explaining a fuzzy line segment model generation process in the fuzzy line segment model generation device of FIG.

FIG. 3 is a schematic diagram for explaining a conical membership function of a fuzzy position vector for explaining the principle of fuzzy spline interpolation in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 4 is a schematic diagram for explaining a given fuzzy point sequence for explaining the principle of fuzzy spline interpolation in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 5 is a schematic diagram for explaining a fuzzy control polygon obtained to interpolate a given fuzzy point sequence in order to explain a principle of fuzzy spline interpolation in fuzzy recognition of a handwritten curve to which the present invention is applied. It is a figure.

6 is a schematic diagram for explaining a fuzzy spline curve obtained from the fuzzy control polygon of FIG. 5 in order to explain a principle of fuzzy spline interpolation in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 7 illustrates the principle of segmentation in fuzzy recognition of a handwritten curve to which the present invention is applied.
It is a schematic diagram for explaining labeling, grouping, and representative point extraction from a section truth value of a fuzzy point sequence.

FIG. 8 is a block diagram showing a schematic configuration according to an algorithm of a system for explaining the principle of fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 9 is a schematic diagram showing an example of a curve sample model and an FMPS (fuzzy matching point set) of the curve sample model for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 10 is a schematic diagram showing another example of a curve sample model and an FMPS (fuzzy matching point set) of the curve sample model for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 11 is a schematic diagram showing another example of a curve sample model and an FMPS (fuzzy matching point set) of the curve sample model for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 12 is a schematic diagram showing an example of a curve sample model for explaining a generation principle of a line segment reference model according to the present invention in fuzzy recognition of a handwritten curve.

13 is a schematic diagram showing an example of a fuzzy line segment reference model corresponding to the curve sample model of FIG. 12 for explaining the generation principle of the line segment reference model according to the present invention in fuzzy recognition of a handwritten curve. Is.

FIG. 14 is a schematic diagram showing internal division fuzzy points between fuzzy points for explaining a generation principle of a line segment reference model according to the present invention in fuzzy recognition of a handwritten curve.

FIG. 15 is a schematic view showing outer-segment fuzzy points between fuzzy points for explaining a generation principle of a line-segment reference model according to the present invention in fuzzy recognition of a handwritten curve.

16 is an FMPS of the line segment reference model shown in FIG. 13 for explaining the generation principle of the line segment reference model according to the present invention in fuzzy recognition of a handwritten curve.
It is a schematic diagram which shows an example.

FIG. 17 is a schematic diagram for explaining an example of a quadratic rational Bezier curve expression of a circular arc according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 18 is a schematic diagram for explaining an example of circle weights according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 19 is a schematic diagram showing an example of a curve sample model for explaining a generation principle of an arc reference model according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 20 relates to an algorithm for fuzzy recognition of a handwritten curve to which the present invention is applied and is a fuzzy arc reference model corresponding to the curve sample model of FIG. 19 for explaining the generation principle of the arc reference model. It is a schematic diagram which shows an example.

FIG. 21 is a schematic diagram showing an example of the FMPS of the circular arc reference model shown in FIG. 20 for explaining the generation principle of the circular arc reference model according to the description of the algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied. is there.

FIG. 22 is a schematic diagram for explaining an example of a quadratic rational Bezier curve representation of an elliptic arc according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 23 is a schematic diagram for explaining an example of a relationship between an auxiliary point of an ellipse and a weight according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 24 is a schematic diagram for explaining a relationship between an auxiliary point of an ellipse and a weight according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 25 is a schematic diagram for explaining another example of the relationship between the auxiliary points of the ellipse and the weight according to the description of the algorithm in the fuzzy recognition of the handwritten curve to which the present invention is applied.

FIG. 26 is a schematic diagram showing an example of a curve sample model for explaining a generation principle of an elliptic arc reference model according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 27 is a schematic diagram showing an example of selection of representative points in a curve sample model for explaining the generation principle of an elliptic arc reference model according to the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 28 is a schematic view showing another example of selection of representative points in a curve sample model for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, for explaining a generation principle of an elliptic arc reference model. is there.

29 is a fuzzy elliptic arc reference model corresponding to the curve sample model of FIG. 26, for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, for explaining a generation principle of an elliptic arc reference model. It is a schematic diagram which shows an example.

FIG. 30 relates to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and shows an example of selection of auxiliary points for weight determination in a curve sample model for explaining a generation principle of an elliptic arc reference model. It is a schematic diagram.

FIG. 31 is a schematic diagram showing an example of the FMPS of the elliptic arc reference model shown in FIG. 29, for explaining the generation principle of the elliptic arc reference model according to the description of the algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied. is there.

FIG. 32 is a schematic diagram for explaining a possibility verification of matching of FMPS between a curve sample model and a curve reference model according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 33 is a schematic diagram for explaining a possibility verification of matching of FMPS of a curve sample model and a line segment reference model according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 34 is a schematic diagram for explaining a possibility verification of matching of FMPS between a curve sample model and an arc reference model according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 35 is a schematic diagram for explaining a possibility verification of matching of FMPS between a curve sample model and an elliptic arc reference model according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 36 is a schematic diagram for explaining the evaluation of the closed curve property of the curve sample model according to the description of the algorithm in the fuzzy recognition of the handwritten curve to which the present invention is applied.

FIG. 37 is a schematic diagram for explaining an inclusion relation of curve classes according to the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 38 is a diagram for explaining an inference rule of a curve class according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 39 is a schematic diagram showing an example of a curve sample model and an inferred fuzzy curve class according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 40 is a schematic diagram showing an example of a recognized representative curve group for explaining connection processing of representative curves according to an algorithm in fuzzy recognition of handwritten curves to which the present invention is applied.

FIG. 41 is a schematic diagram showing an example of connection by parallel movement of a recognized representative curve group for explaining a process of connecting representative curves according to an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied. is there.

FIG. 42 relates to an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and relates to rotation of a recognized representative curve group for explaining a connection process of representative curves,
It is a schematic diagram which shows an example of the matching process of the end point by expansion / contraction.

FIG. 43 relates to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and illustrates an example of a representative curve group before connection processing and a representative curve group after connection processing for explaining connection processing of representative curves. It is a schematic diagram which shows.

FIG. 44 relates to an algorithm for fuzzy recognition of a handwritten curve to which the present invention is applied, and illustrates a representative curve group before connection processing and another representative curve group after connection processing for explaining connection processing of representative curves. It is a schematic diagram which shows an example.

FIG. 45 relates to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and illustrates a representative curve group before connection processing and other representative curve groups after connection processing for explaining connection processing of representative curves. It is a schematic diagram which shows an example.

FIG. 46 is a schematic diagram for explaining a Bezier polygon of a circle and its center according to the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

[Fig. 47] Fig. 47 is a schematic diagram for explaining parameters of an ellipse according to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 48 is a schematic diagram for describing an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied and an example of a curve sample model and an inference result of a fuzzy curve class by the present algorithm.

FIG. 49 is a schematic diagram for explaining another example of the inference result of the fuzzy curve class according to the curve sample model and the present algorithm according to the description of the algorithm in the fuzzy recognition of the handwritten curve to which the present invention is applied.

FIG. 50 is a schematic diagram for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied and a curve sample model and another example of the inference result of the fuzzy curve class by the present algorithm.

FIG. 51 is a schematic diagram for explaining an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and is a schematic diagram for explaining still another example of the inference result of the fuzzy curve class by the curve sample model and the present algorithm.

FIG. 52 is a schematic diagram for describing an example of a fuzzy recognition of a handwritten curve to which the present invention is applied and an example of a curve sample model and a recognition curve by the present algorithm.

[Fig. 53] Fig. 53 is a schematic diagram for describing another example of a curve sample model and a recognition curve according to the present algorithm according to the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Sample model generation part, 2 ... Representative point selection part, 3 ... Line segment model generation part, 4 ... FMPS extraction part, 31 ... Internal division fuzzy point calculation part, 32 ... External division fuzzy point calculation part, 33 ... End point calculation Part, 34 ... Line segment forming part.

[Equation 101]

Claims (4)

[Claims] 1. A handwritten curve is input as fuzzy curve information including input ambiguity information, and a curve sample model of a segment as a part of the input fuzzy curve information is compared with a fuzzy expressed reference model as a reference pattern. The input curve sample pattern used to discriminate the input curve pattern is a fuzzy spline curve that represents the input curve sample model when generating a fuzzy line segment model as a reference model assuming that the sample model is a straight line segment. From the top, select two fuzzy points, first and second.
And a fuzzy line segment satisfying the first and second fuzzy representative points is internally divided between the first and second fuzzy representative points. And a step of constructing a fuzzy line segment model as a set of fuzzy points. 2. The line segment constructing step comprises: an end point of the fuzzy line segment model; a length along a curve from a first fuzzy representative point to a second fuzzy representative point of the curve sample model;
The ratio of the length along the curve from the second fuzzy representative point to the end point of the curve sample model is the distance from the first fuzzy representative point to the second fuzzy representative point on the fuzzy line segment model. And the step of determining the ratio of the distance from the second fuzzy representative point to the end point of the fuzzy line segment model to match. 3. A handwritten curve is input as fuzzy curve information including input ambiguity information, and a curve sample model of a segment as a part of the input fuzzy curve information is compared with a fuzzy expressed reference model as a reference pattern. A fuzzy line segment model generator for generating a fuzzy line segment model as a reference model when the input curve sample model in the pattern recognition system that discriminates the pattern of the input curve is assumed to be a straight line segment. And two appropriate fuzzy points on the fuzzy spline curve representing the input curve sample model.
Representative point selecting means for selecting the fuzzy representative points, and fuzzy line segments satisfying the first and second fuzzy representative points are internally divided fuzzy points between the first and second fuzzy representative points and A fuzzy line segment model generation device, comprising: a line segment constructing unit configured as a set of outer segment fuzzy points to form a fuzzy line segment model. 4. The line segment constructing means defines the end point of the fuzzy line segment model as the length along the curve from the first fuzzy representative point to the second fuzzy representative point of the curve sample model, and the second fuzzy. The ratio of the length from the representative point to the end point of the curve sample model along the curve is the distance from the first fuzzy representative point to the second fuzzy representative point on the fuzzy line segment model and the second distance. 4. Means for determining the ratio of the distance from the fuzzy representative point to the end point of the fuzzy line segment model to match the ratio.
The fuzzy line segment model generation device described in 1.