JP3237790B2 - Method and apparatus for evaluating closed curve properties - Google Patents

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 handwritten input characters and symbols, and more particularly, to inputting a handwritten curve as fuzzy curve information including ambiguity information of the input. Comparing the curve sample model of the segment as a part of the input fuzzy curve information with the fuzzy expression reference model as a reference pattern to discriminate the pattern of the input curve whether the input curve sample model in the pattern recognition system is a closed curve TECHNICAL FIELD The present invention relates to a method and an apparatus for evaluating closed curve characteristics for evaluating whether or not a closed curve is evaluated.

[0002]

2. Description of the Related Art In recent years, attention has been paid to 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. Such a pen computer system
For example, it is configured to include a computer, a tablet with a display connected to the computer, and an input pen for input operation connected to the tablet. In this case, the tablet with a display serves both as a display device as an output device of the computer and an input device for input to the computer. In a system using such a handwritten input and an application program operating on such a system, since the handwritten pen input information of the operator is recognized in the computer, the meaning of the direct line graphic input data by the handwritten pen input is used. Must be recognized and determined in the computer. Since input data from a pen on a tablet is generally given as a sequence of points sampled at equal intervals in time, a spline interpolation process is performed to interpolate this as appropriate and theoretically treat it as a continuous curve. Is used.

As a spline interpolation process for obtaining an interpolation curve from a given point sequence, for example, a spline curve is passed through each point based on the coordinate information of each point given as a point sequence. In general, an interpolation curve is obtained by obtaining a control polygon of a spline curve by obtaining a coupling coefficient of a basis function to be represented. For example, in the case of a cubic spline curve, 3 is used to smoothly connect between each passing point to which the interpolation curve is given (for example, to satisfy a so-called “C ² continuous” condition).
Find a spline curve connected by the next Bezier curve.
Conventionally, in order to recognize and determine what kind of characters, symbols, and the like are represented by the spline-interpolated pattern information in this manner, matching between an input sample figure and a previously prepared reference figure is performed. The degree was checked, and the input sample graphic was recognized and determined as a character / symbol corresponding to the reference graphic that matched best.

In such a conventional system, it is assumed that a given point sequence is a determined point sequence in spline interpolation processing of a sample figure. In practice, the given input point sequence is vague In spite of the fact that points or strictly incorrect positions are often included, the information on each point given as a point sequence includes vague or incorrectly positioned points. Absent.
In addition, not only the sample figures but also the reference figures are processed as fixed information. As a result, information on the degree of matching is also obtained as fixed simple information. Therefore, in the above-described conventional system, the ambiguity is appropriately evaluated from an input point sequence that may include an ambiguous point or a point whose position is strictly incorrect, such as handwriting input in a pen computer or the like, and the operator It is very difficult to perform a recognition process in accordance with the intention of (1).

On the other hand, the present inventors have previously described Japanese Patent Application No. 157573/1992 appropriately evaluating and processing ambiguous elements from input information, and performing pattern recognition according to the operator's intention. A pattern recognition method and apparatus that can be performed has been proposed. 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 the sample figure, and obtains reference information. A predetermined number of representative point information expressed in fuzzy relations with respect to the figure are respectively obtained 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 section truth value of the entire graphic curve is obtained from the value to determine the degree of matching of the entire graphic curve.

As described above, in order to infer, discriminate and recognize a figure intended by a writer of handwritten input from curve information of an input sample figure represented by a fuzzy spline curve including ambiguity information, a system of an inference processing system is used. Since the processing capacity is limited and it is not possible to process huge or infinite information instantaneously, the input fuzzy spline curve is divided into segments of appropriate size by segmentation, and each segment is It is useful 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 compared with the reference figure in a state where the curve information is divided into segments by appropriate segmentation. In order to discriminate and recognize sample figures, a plurality of figure models for each unit figure almost corresponding to partial figures for each segment are prepared as reference figure models, and matching between these figure models and input curve sample models for each segment is performed. Will be determined. As described above, in order to discriminate and recognize an input sample graphic in a state where the input sample graphic is divided into segments, it is also important whether or not the input sample graphic is a closed curve, and therefore, the closed curve property of the input sample graphic is evaluated. . In this case, since the input curve sample model is fuzzy-represented curve information, if the closed curve property of the fuzzy-represented information is evaluated by effectively using the ambiguity information, the writer's intention It is thought that the discrimination and recognition of the curve can be performed more appropriately.

However, conventionally, processing of such a fuzzy-represented spline curve has not been common, and there has been no technique for evaluating whether or not a fuzzified input curve sample model is a closed curve. . The present invention has been made in view of such circumstances, and appropriately evaluates the closed curve property of a fuzzified input curve sample model by effectively using fuzzy information to discriminate and recognize input figures. It is an object of the present invention to provide a method and an apparatus for evaluating closed curve characteristics which can be provided.

[0009]

According to a method for evaluating closed curve characteristics according to the present invention, a handwritten curve is input as fuzzy curve information including input ambiguity information, and a curve of a segment as a part of the input fuzzy curve information is input. In order to evaluate whether or not the input curve sample model is a closed curve in pattern recognition for discriminating an input curve pattern by comparing the sample model with a fuzzy-represented reference model as a reference pattern, the fuzzy model of the input curve sample model is used. A start and end point extraction step for obtaining a start point and a fuzzy end point, and a fuzzy end point of the input curve sample model obtained in the start and end point extraction step,
Finding a possibility measure that is a fuzzy starting point of the input curve sample model obtained in the starting and ending point extracting step,
And a possibility evaluation step of evaluating the possibility that the input curve sample model is a closed curve.

An apparatus for evaluating closed curve characteristics according to the present invention inputs a handwritten curve as fuzzy curve information including input ambiguity information, and uses a curve sample model of a segment as a part of the input fuzzy curve information as a reference pattern. In a closed curve property evaluation device for evaluating whether an input curve sample model in a pattern recognition system that discriminates a pattern of an input curve by comparing with a fuzzy-represented reference model is a closed curve,
The start and end point extraction means for obtaining the fuzzy start point and the fuzzy end point of the input curve sample model, and the fuzzy end point of the input curve sample model obtained by the start and end point extraction means are obtained by the start and end point extraction means. The apparatus further comprises a possibility evaluation means for obtaining a possibility measure that is a fuzzy starting point of the input curve sample model and evaluating the possibility that the input curve sample model is a closed curve.

[0011]

According to the method and the apparatus for evaluating closed curve characteristics of 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 used as a reference pattern. In evaluating whether or not the input curve sample model in the pattern recognition for discriminating the input curve pattern by comparing with the fuzzy expression reference model as a closed curve, the fuzzy start point and the fuzzy end point of the input curve sample model are determined. The fuzzy end of the input curve sample model is determined to be a fuzzy start point of the input curve sample model, and the possibility of the input curve sample model being a closed curve is evaluated. The fuzziness of the curve sample model Properly evaluated by effectively utilizing the information, it can be subjected to discrimination and recognition of the input figure.

[0012]

【Example】

<< Fuzzy Spline Interpolation >> Prior to the description of the embodiment of the present invention, first, a point sequence data given as position information for each point is interpolated and approximated to obtain fuzzy spline curve information corresponding to these point sequences. Principle is explained. 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 graphic, and this is represented as a two-dimensional fuzzy point sequence (each of which is represented as a two-dimensional fuzzy set). Then, these fuzzy point sequences are interpolated under certain assumptions and expressed as a continuous and ambiguity curve, that is, a fuzzy spline curve. It is possible to save in an easy-to-use form.

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

As a method of adding the ambiguity information described above, for example, it is conceivable to use pen acceleration and writing pressure information at the time of handwriting input. In general, it may be set so that the ambiguity is increased in proportion to the acceleration. As described above, if the input line graphic and the ambiguity information in each part thereof are simultaneously held in the computer as fuzzy spline curve information, for example, the elliptical data carefully drawn carefully and the circle drawn roughly. The elliptical data is stored in a form that can be distinguished in the computer. In this way, the fuzzy spline curve information once stored in the computer can be used as a material for inferring and recognizing a line figure that an operator intends to input from sampling data of a line figure input by hand. Should be possible. The principle of the above-described fuzzy spline interpolation will be described more specifically.

In the fuzzy spline interpolation, first, a fuzzy vector having a conical membership function is considered 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 interpolates the fuzzy point sequence on the plane containing the ambiguity while containing the ambiguity information. <Conical fuzzy vector and its operation> Consider a fuzzy vector having a conical membership function, and define a sum operation of the fuzzy vectors and a multiplication of the fuzzy vector by a crisp scalar quantity.

First, the membership function of the conical fuzzy vector and its notation will be discussed. 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 Equation 1 using _a vector a representing the position of the vertex of the cone and a radius ra of the base circle of the cone.

[0017]

(Equation 1)

Note that at this time, the first
The membership function of the fuzzy vector is given by Equation 2 for any variable vector v on the plane (where
The operator “∨” in Equation 2 is the largest one that takes the larger one.
(Maximum value) calculation).

[0019]

(Equation 2)

The conical fuzzy vectors shown in Expressions 1 and 2 are a direct extension of a symmetric triangular fuzzy number which is a fuzzy model of a scalar quantity. Next, the sum operation of the conical fuzzy vectors and the operation of the conical fuzzy vector and the crisp scalar will be discussed. Consider a second fuzzy vector as shown in Equation 3.

[0021]

(Equation 3)

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

[0023]

(Equation 4)

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

[0025]

(Equation 5)

Therefore, a linear combination of fuzzy vectors as shown in equation (6) is represented by a similar type of fuzzy vector as shown in equation (7).

[0027]

(Equation 6)

[0028]

(Equation 7)

<Fuzzy spline curve> Node sequence u
_i-1, ..., if the n-th normalized B-spline function defined by u i _{+ n} and N _i ⁿ (u), on the parameter space _{interval: [u n-1, u} n + L- An arbitrary n-order spline curve s ⁿ (u) having [ ₁ ] as a domain is represented by Expression 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 linear combinations of the vertices of the control polygon. Therefore, a fuzzy spline curve is defined by extending a position vector representing a vertex of the control polygon of Expression 8 to a fuzzy position vector based on the above-described fuzzy vector. That is, by giving Equation 9 as vertices of a fuzzy control polygon, an n-order fuzzy spline curve is defined as an extension of Equation 8 as shown in Equation 10.

[0032]

(Equation 9)

[0033]

(Equation 10)

Equation 10 indicates 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-mentioned operation rules of the fuzzy vector sum operation and the multiplication by the crisp scalar quantity, this point can be expressed by Expression 11, and it can be seen that the point 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 on a graphic plane by a fuzzy position vector, the control polygon of the fuzzy spline curve passing through these is as follows. It is obtained by solving the linear system represented by Expression 13.

[0037]

(Equation 12)

[0038]

(Equation 13)

Where m = L + n−1 and s _i
Is the value of the parameter u corresponding to the fuzzy point sequence of Expression 12, Expressions 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 with respect to the x-axis and y-axis components of the cone vertex of the fuzzy vector and the radius of the base circle of the cone, and therefore, the fuzzy vector is solved by solving these three linear systems. A control polygon for the spline curve is determined.
A specific example of the above-described fuzzy spline interpolation will be described. 4 to 6 show an example in which a fuzzy point sequence given in a graphic space is interpolated by a cubic fuzzy spline curve. The circles in FIGS. 4 to 6 indicate the base circle of the conical fuzzy vector. (1) A sequence of fuzzy points of Formula 17 having a conical membership function is given as shown in FIG.

[0044]

[Equation 17]

At this time, a point actually sampled is given as a vertex of a cone, and an ambiguity is given as a radius of a base circle. Ambiguity is given based on information such as acceleration. (2) By extending the normal spline interpolation method,
A fuzzy control polygon represented by Expression 18 is obtained. This fuzzy control polygon is shown in FIG.

[0046]

(Equation 18)

(3) Interpolation / evaluation is performed on the fuzzy control polygon represented by the equation (18) by a method obtained by extending the usual de Boer's algorithm, and a fuzzy curve as shown in FIG. Generate.

<< Fuzzy Segmentation of Handwritten Curve >> By applying the above-described fuzzy spline curve interpolation, the writer can write anything from handwritten input data of a line figure which is considered to include ambiguity input from a tablet or the like. In order to infer whether or not it has been done, 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 by 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 tried to write, in the segmentation, the stroke of the input line figure is detected, and the break of the stroke is detected. In the handwriting input, the input speed becomes slow at a break of a stroke, and appears in a line figure as a corner or a stop point. Therefore, it is considered that the break of the stroke can be extracted by checking whether or not a certain point has stopped.If it is fuzzyly evaluated whether or not a certain point has stopped for a certain period of time,
Fuzzy segmentation based on stroke boundaries can be performed. Input point sequence p _i sampled at regular time intervals <fuzzy spline interpolation of sample points> is not necessarily the intent of the writer of the curve have accurate position information that accurately reflect. In general, the coarser the curve, the more vague the position information. From this viewpoint, it is considered that each sample point has a position ambiguity that is proportional to the handwritten acceleration at that point. This can be expressed by using the fuzzy vector of Equation 19 to indicate each sample point p _i .

[0050]

[Equation 19]

Here, r _pi is set in proportion to the acceleration at the sample point p _i . The fuzzy spline curve can be obtained by interpolating the sample point sequence represented by such a fuzzy vector by the method described above. <Evaluation of Stopping Property by Section Truth Value> By using Expression 11, the spline curve is evaluated at fixed time intervals shorter than the original sampling interval. As a result, Expression 20 which is a finer fuzzy point sequence is obtained.

[0052]

(Equation 20)

The degree of stopping at each fuzzy point in Equation 20 is evaluated by an interval truth value [N _i , P _i ] based on the necessity measure _Ni and the possibility measure P _i shown in Equations 21 and 22 (note that , The operator “∨” in Equation 21 represents a max (maximum value) operation that takes the larger one.
The operator “∧” in 2 represents a min (minimum value) operation that takes the smaller one, and “in” in Expression 21 is used.
“f” indicates an operation to take the lower limit, and the operator “sup” in Expression 22 indicates an operation to take the upper limit).

[0054]

(Equation 21)

[0055]

(Equation 22)

Here, the necessity measure N _i and the possibility measure P _i shown in Expressions 21 and 22 are defined as the necessity and possibility that the proposition shown in Expression 23 holds for the fuzzy point, respectively. If an appropriate integer is selected for k, the above proposition states that the position on the curve at time i is
It is the same as the position on the curve a minute before (k hours). "

[0057]

(Equation 23)

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

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

[0060]

(Equation 24)

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

<< Fuzzy Recognition Algorithm of Handwritten Curve >> The fuzzy recognition algorithm of the handwritten curve in the handwritten curve fuzzy recognition system to which the embodiment of the present invention is applied will be described in detail. This system generates a curve with the desired geometric meaning of the writer in a computer by handwriting a curve with a stylus pen on an input device such as a pen computer that integrates a tablet and a display. It realizes a typical graphic input human interface. More specifically, these are "lines", "circles",
"Arc", "ellipse", "elliptical arc", "closed free curve",
This realizes a human interface that allows seven types of curve classes, "open free-form curves", to be handwritten separately and input to a computer. If this is used for CAD, etc. It is possible to realize a more direct and natural graphic input interface without relying on a manual operation.

As a matter of course, there is a “shift” between the position information of the curve input and observed by handwriting and that of the ideal curve originally intended by the writer. Therefore, the position information of the input / observed curve sample cannot be handled deterministically. In this system, the input curve sample is represented by a fuzzy spline curve, so that the ambiguity of the observed position information itself is retained as information, and the inference of the ideal curve intended by the writer while considering the ambiguity of the handwritten curve is performed. Is given.

Here, the ambiguity information of the input curve sample is set and inferred / recognized based on the degree of politeness in which the curve is written. Realize a human interface that can write the intended curve class separately. As a result, according to the present system, the more carefully written, the more likely it is to be recognized as a complicated curve class having a higher degree of freedom, and the more coarsely written, it will be recognized as a simpler curve class. Therefore, when writing a simple class of curves, the writer expresses the shape symbolically by writing the curve appropriately coarsely, and conversely, when the intention is to write a more complicated shape intentionally, the actual writer is drawn. It can be expressed by carefully writing that the shape being drawn is intentional.

For example, by drawing a circle appropriately, a curve can be input so that even if the shape is slightly distorted, it can be recognized as a perfect circle, or a free curve slightly deviated from a perfect circle by writing carefully Can be intentionally input. Furthermore, in this method, inference is realized based on information that originally contains ambiguity.
That is, the “inferred curve class” and the “recognized curve shape” are themselves obtained as fuzzy expressions including ambiguity reflecting 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 human and a higher-level inference system without any excess or shortage. For this reason, it is possible to realize a natural and efficient next candidate selection operation by a human, and to realize a higher-order inference system that makes a judgment in combination with other information.

<Algorithm Flow> In the present algorithm, a handwritten curve input from, for example, a tablet is represented by a fuzzy spline curve by the above-described fuzzy spline interpolation. It is assumed that the segmentation is performed. At this time, the method uses the basic curve segments as “line segment”, “circle”, “arc”, “ellipse”, “elliptical arc”,
A means for fuzzy inference as to which of the seven curve classes “closed free curve” and “open free curve” is provided, and a basic curve sequence determined interactively is output as CAD data. Realize that. The conceptual configuration 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), the sample data point sequence is fuzzified based on acceleration and the like, and the obtained fuzzy sample data is further processed. 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 whole fuzzy spline curve is divided into portions corresponding to basic curves such as line segments, circles, and ellipses, depending on stroke breaks. This division is performed by a fuzzy segmentation method that takes into account the ambiguity of the input curve, and finally determines the division point interactively (fuzzy segmentation M3). When the above pre-processing is completed, the curve class of each divided basic curve segment is inferred fuzzy (process M4 for each fuzzy curve segment). This is performed as follows.

First, the possibility that the basic curve segment is a “line segment”, “circular arc (including a circle)”, or “elliptical arc (including an ellipse)” is fuzzyly obtained (curve class possibility evaluation M9). . This is achieved by hypothesis testing. That is, a curve reference model is constructed for each curve class based on several representative points of the basic curve segment represented as a part of the fuzzy spline curve (line segment reference model construction 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 construction M5). At this time, the basic curve segment is evaluated by fuzzy evaluating how much the curve sample model may actually match the curve reference model assumed for each curve class over the entire basic curve segment. Is obtained fuzzy.

On the other hand, the possibility that the basic curve segment is a closed curve is determined fuzzy 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 is performed using these possibilities as input, and the writer recognizes the intended curve class 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 the fuzzy inference result, one curve class is determined by interactive processing with the writer. This interactive processing is efficiently executed according to the ambiguity of the curve written to perform based on the fuzzy inference result.

When the curve class is determined, a recognition curve is obtained as a corresponding curve reference model.
However, since the curve reference model itself is in a fuzzy expression, a representative portion thereof is extracted as a normal curve according to the application (representative curve extraction M12). When the above processing is completed for all basic curve segments and representative curves of each segment are obtained, connection processing of these representative curves is performed according to the application (connection of representative curves M1).
3). This is a process for preventing each recognized curve segment from being necessarily connected even if the entire curve is drawn with one stroke. Finally, the expression form of each of the recognized representative curves 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 can be 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> A model representing the shape of the target basic curve segment of the input curve sample is configured as a curve sample model. Further, a fuzzy matching point set (hereinafter abbreviated as “FMPS”) is extracted from the curve sample model. The FMPS represents the overall shape of the curve with, for example, about 10 fuzzy points, and is used for verifying the degree of coincidence with a reference model described later.

According to the fuzzy segmentation method described above, the fuzzy start point [q] _s and the fuzzy end point [q] _{e of} one basic curve segment are two points on the fuzzy spline curve representing the entire original input curve. They are obtained as fuzzy points [q] _i and [q] _{i + k} , respectively. (Note that the fuzzy points are indicated by adding a tilde “〜” above the characters in mathematical expressions, drawings, and the like, but may be written with a tilde above the characters in the text of the specification. Since it is impossible, fuzzy points are indicated by enclosing them with "[" and "]" instead of adding a tilde for convenience of explanation.) Therefore, the curve sample model of the target basic curve segment is represented by this fuzzy point. starting [q] parameter gives the fuzzy end point [q] _{i + k} from the parameter values u _i giving _i value u _{i + k} until the parameter value sections [u _i,
u _{i + k} ] has already been given as a fuzzy spline curve.

Next, this curve sample model is evaluated at n _fmps fuzzy points, which is a number determined so as to be equally spaced along the curve, and the obtained n _fmps fuzzy points are evaluated. The set, that is, Equation 25 is defined as the FMPS of the curve sample model.

[0074]

(Equation 25)

9 (a) and 9 (b) to 11 (a) and
(b) shows an example of a curve sample model and an example of FMPS, respectively (in these explanatory diagrams, n _fmps = 5 for simplicity).
However, in practice, n _fmps is desirably set to about 10 or more so as to represent the characteristics of the entire basic curve segment.) However, it is difficult to strictly determine the points at which the fuzzy spline curve is divided at equal distance intervals. Therefore, the points that are approximately equidistantly divided 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 corresponding parameter values are determined, and the FMPS is determined by re-evaluating the fuzzy points on the fuzzy spline curve at these parameter values.

<Reference Model for Each Curve Class and Its FMPS> For the curve sample models of the respective basic curve segments extracted by the fuzzy segmentation method described above, they are referred to as “line segments” and “arcs (including circles)”. A hypothesis is made as to what kind of shape the curve can be if it is assumed that the curve is a certain class of "" and "elliptical arc (including an ellipse)". Here, this is called a reference model for each curve class. This reference model is constructed as a fuzzy rational Bezier curve using several representative fuzzy points of the curve sample model as clues. The fuzzy rational Bezier curve is a fuzzy extension of an ordinary rational Bezier curve that is a curve capable of expressing “line segments”, “circular arcs”, and “elliptical arcs”. The model is a fuzzy curve.

Next, similarly to the above-described curve sample model, the overall shape of the reference model configured as a fuzzy rational Bezier curve is represented by an FMPS as shown in Expression 26 represented by a set of about 10 fuzzy points. Is configured.

[0078]

(Equation 26)

The FMPS of this reference model is used for verifying the degree of matching with the curve sample model, which will be described later. <Construction method of line segment reference model> Assuming that the curve sample model of the target basic curve segment is a line segment, the reference model selects two fuzzy representative points from the curve sample model and satisfies these. It is configured as a fuzzy line segment. Next, the FMPS of the line segment reference model is extracted from the fuzzy line segment.

Fuzzy representative point Since a straight line is determined by two points, basically, any two fuzzy points are selected from the curve sample model, and these are selected as fuzzy representative points for constructing a line segment reference model. do it. However, so that the fuzzy representative points represent the overall outline of the curve sample model,
It is desirable to choose such that they are not very close. 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, for example, for a curve sample model as shown in FIG.
As shown in FIG. 12, fuzzy representative points [a] ₀ and [a] ₁
Is described.

It can be easily understood that a line segment reference model can be constructed by the same method even in a generalized case where any two points on the curve sample model are selected as fuzzy representative points. Incidentally, 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 Reference Model The line reference model is configured 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 a Bezier curve as in the reference model of an arc and an elliptic arc described later). This is equivalent to the above, but the line segment is easy, so we will not treat it as a Bezier curve here).

For example, for a fuzzy representative point selected as shown in FIG. 12, a line segment reference model as shown in FIG. 13 is formed. 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 of the length along the curve to _e is the ratio of the distance from [a] ₀ to [a] ₁ and the distance from [a] ₁ to [q] _e ^Line on the line segment reference model. Determine to match. The internal fuzzy point and the external fuzzy point are obtained as follows. The vector v is calculated as R using the vector length R _v and the angle θ _v of the vector from the x-axis.
If expressed as _v exp (jθ _v ) (j is an imaginary unit), the α-level sets of arbitrary conical fuzzy vectors [a] and [b] such as Equations (1) and (3) are represented by numbers 27 and 28.

[0083]

[Equation 27]

[0084]

[Equation 28]

Here, on the basis of the extension principle, the α-level sets of [a] + [b], which are the operation results of [a] and [b], are the operation results of the respective α-level sets. , 29. Therefore, from this result, the sum of the fuzzy vectors is as shown in Expression 30.

[0086]

(Equation 29)

[0087]

[Equation 30]

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

[0089]

(Equation 31)

[0090]

(Equation 32)

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

[0092]

[Equation 33]

[0093]

(Equation 34)

Therefore, when Equations 32 and 34 are put together, 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] which internally or externally divides them into α: β can be defined as Equation 36. Here, a case where both α and β are positive is an internal dividing point, and a case where either α or β is negative is an external dividing point. Α + β is always a positive number.

[0097]

[Equation 36]

If the results of Expressions 30 and 35 are used for Expression 36, the internal dividing point and the external dividing point are finally obtained by Expression 37.

[0099]

(37)

FIG. 14 and FIG. 15, for example, show such a case. 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, care must be taken. In this case, [a] is given by Equation 38
And not Equation 39.

[0101]

(38)

[0102]

[Equation 39]

FMPS n _fmps fuzzy points are obtained on the line segment reference model so as to be divided at equal distance intervals, and are set as the _{FMPS of} the line segment reference model. Such FMPS can be easily obtained by the operation of obtaining the internal fuzzy points and the external fuzzy points of [a] ₀ and [a] ₁ . For example, an FMPS of Formula 40 as shown in FIG. 16 is obtained from a line segment reference model as shown in FIG.

[0104]

(Equation 40)

<Construction Method of Circular Arc Reference Model> Next, assuming that the curve sample model of the target basic curve segment is an arc (including a circle), the reference model is composed of three fuzzy representatives from the curve sample model. Points are selected and constructed as fuzzy arcs that satisfy them. Next, the FMPS of the arc reference model is extracted from the fuzzy arc. Representation of a quadratic rational Bezier curve of an arc A circular arc is a kind 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 that passes through and reaches b ₂ is a Bezier polygon b ₀
It can be represented as a parameter value section [0, 1] of a quadratic rational Bezier curve given by Equation 41 by b ₁ b ₂ and a certain weight w.

[0106]

[Equation 41]

The arc of the part extending from b ₂ to b ₀ through the opposite side of f is a quadratic rational given by the weight −w with the sign inverted from the Bezier polygon b ₂ b ₁ b _0. It can be represented as a part of the parameter value section [0, 1] of the type Bezier curve. Here, _Bi ² (t) is a second-order 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, an equidistant line is formed, and the relationship shown in Formula 43 is established between the weight w and the lengths l and h shown in the drawing.

[0110]

[Equation 43]

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

[0112]

[Equation 44]

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

[0114]

[Equation 45]

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

[0116]

[Equation 46]

Therefore, from Equations 44 to 46, the weight w
Is obtained by Expression 47.

[0118]

[Equation 47]

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

Here, in order for the fuzzy representative points to be representative of the overall outline of the curve sample model, it is desirable to select them so that they are not very close. Below is one of the fuzzy representative points
[A] ₀ , starting point of curve sample model [q]
_In the case where an arbitrary fuzzy point on the curve sample model is set as _s as the second fuzzy representative point [a] ₁ , for example, for the curve sample model as shown in FIG. The case where the fuzzy representative points [a] ₀ and [a] ₁ and [f] are obtained as described above will be described.

In a generalized case where arbitrary two points on the curve sample model are selected as fuzzy representative points [a] ₀ and [a] ₁ , it is possible to construct an arc reference model by the same method. Here, it is omitted. By the way, in the experiment, as ₀ [a] [q] _s,
To obtain good results by the linear distance from [q] _s within the second half of the curve sample model selects the farthest fuzzy point [a] as _one. Arc Reference Model The arc reference model is constructed as a fuzzy arc satisfying three fuzzy representative points. Here, the fuzzy arc is the vertex b of the Bezier polygon in Equations 41 and 42.
_i (i = 1, 2, 3) is converted to a fuzzy point [b] _i (i = 1,
Expressions 48 and 49 are defined by extending to 2, 3).

[0122]

[Equation 48]

[0123]

[Equation 49]

At this time, the fuzzy Bezier polygon [b] _{i is set} so that this fuzzy arc satisfies the given three representative fuzzy representative points [a] ₀ , [a] ₁ and [f].
(I = 1, 2, 3) and a weight w are determined, 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
And [a] ₁ are referred to as [b] ₀ and [b] ₂ respectively. Next, the fuzzy midpoint [m] of [a] ₀ and [a] ₁ is obtained by Expression 50.

[0125]

[Equation 50]

Here, [a] the distance between vertices of the membership functions of ₀ and [m] is set as 1 and the distance between vertices of the membership functions of [f] and [m] is set as h. The weight w is obtained by 43. Finally, [f] is [b] ₁ and the [m] 1: such that the fuzzy point which internally divides the w, determined by [b] ₁ the number 51.

[0127]

(Equation 51)

By constructing an arc reference model in this way, an arc reference model satisfying a fuzzy representative point as shown in FIG. 19 is obtained as shown in FIG. 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 curved sample model and [a] ₁ to [q] _e
The ratio of the length along the curve to is the length along the curve from [b] ₀ to [b] ₂ and the length along the curve from [b] ₂ to [q] _e ^Circle on the arc reference model. Determined to match the length ratio. On the FMPS arc reference model, n _fmps fuzzy points are obtained so as to divide the fuzzy points along the curve at equal distance intervals,
FMPS of the arc reference model, that is, Equation 52. For example, an FMPS as shown in FIG. 21 is obtained from the arc reference model shown in FIG.

[0129]

(Equation 52)

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

<Construction Method of Elliptic Arc Reference Model> When it is assumed that the curve sample model of the focused basic curve segment is an elliptic arc (including an ellipse), the reference model is composed of three fuzzy representative points and 1 One auxiliary point is selected and constructed as a fuzzy elliptic arc satisfying these. Next, the FMPS of the elliptic arc reference model is extracted from the fuzzy elliptic arc. Representation of a quadratic rational Bezier curve of an elliptic arc An elliptic arc is a type of conic curve, and can be represented by a quadratic rational Bezier curve. FIG. 22 shows an example of an elliptic arc represented by a quadratic rational Bezier curve. The elliptic arc from b ₀ to f ₂ through b _{0 in the} figure is a quadratic rational type given by Equation 53 by a 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)

The elliptic arc from b ₂ to b ₀ through the opposite side of f is a quadratic rational given by the weight −w with the sign inverted from that of the Bezier polygon b ₂ b ₁ b _0. It can be represented as a part of the parameter value section [0, 1] of the type Bezier curve. Here, _Bi ² (t) is a second-order Bernstein polynomial.

[0134]

(Equation 54)

At this time, assuming that the middle point of the line segment b ₀ b ₂ is m, the intersection f between the line segment b ₁ m and the elliptical arc is farthest from the line segment b ₀ b ₂ among the points on the elliptical arc. Gives the point Also,
As shown in FIG. 23, another auxiliary point p is arbitrarily set on the elliptic arc.
Is given, and t is a foot of a line segment drawn down to the straight line fm so as to be parallel to the line segment b ₀ b ₂ from the point p.
A relationship represented by the following 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, a method of calculating the weight of the ellipse by the auxiliary points will be described. It is assumed that the auxiliary point p is set on an elliptical arc as shown in FIG. Then, the weight w becomes Equation 56, and Equation 57 is obtained by squaring Equation 56.

[0138]

[Equation 56]

[0139]

[Equation 57]

On the other hand, as shown in FIG. 24, since equation 58 is obtained, equation 59 is obtained.

[0141]

[Equation 58]

[0142]

[Equation 59]

In addition, since equation 60 is obtained, equation 61 is obtained. Further, since Equation 62 is obtained, Equation 63 is obtained.

[0144]

[Equation 60]

[0145]

[Equation 61]

[0146]

(Equation 62)

[0147]

[Equation 63]

Here, if equation 61 is substituted for equation 63 and rearranged, equation 64 is obtained, and if equation 59 is further rearranged and arranged, equation 65 is obtained.

[0149]

[Equation 64]

[0150]

[Equation 65]

Here, the values of both sides of Equation 65 are set to P and Equation 6
If we take 6 and 67, we get 68 and 69,
Equation 70 is obtained.

[0152]

[Equation 66]

[0153]

[Equation 67]

[0154]

[Equation 68]

[0155]

[Equation 69]

[0156]

[Equation 70]

If attention is further paid to equation 59, equation 71 is obtained.

[0158]

[Equation 71]

Now, Equation 68, Equation 69 and Equation 71
By substituting the result of (5) into Equation 57 and rearranging it, Equation 72 is obtained.

[0160]

[Equation 72]

Since A and B are obtained by replacing Expression 66 and Expression 67 with each other and substituting these into Expression 72, Expression 73 is obtained.

[0162]

[Equation 73]

Here, in the case of an ellipse, since −1 <w <1, w ≠ −1. Therefore, Equation 74 is obtained.

[0164]

[Equation 74]

If Equation 74 is solved for w, the weight is Equation 75
Is required.

[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. In this case, however, note that β becomes negative. I do. Fuzzy representative point According to the above property, two points b ₀ and b on the elliptic arc
_2, given the line segment b ₀ b ₂ from Gokuto become point f, by giving a weight made appropriately, ellipse passing through these three points is obtained as a secondary rational Bezier curve.
Therefore, three fuzzy points having the same relationship as above may be selected from the curve sample model, and these may be used as fuzzy representative points for constructing an elliptic arc reference model. In other words, 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, [a] ₀ and [a] ₁ A fuzzy point [f] that is farthest from a straight line connecting the vertices of the membership function is obtained, and this is set as a third fuzzy representative point.

Here, in order for the fuzzy representative points to be representative of the overall outline of the curve sample model, it is desirable that they are not very close. 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 an arbitrary fuzzy point on the curve sample model is set as the second fuzzy representative point [a] ₁ ,
For example, a case in which 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. 11 (a) will be described.

In a generalized case where arbitrary two points on the curved sample model are selected as fuzzy representative points [a] ₀ and [a] ₁ , an elliptic arc reference model can be constructed by the same method. Here, it is omitted. By the way, in the experiment, as ₀ [a] [q] _s,
To obtain good results by the linear distance from [q] _s within the second half of the curve sample model selects the farthest fuzzy point [a] as _one. FIGS. 27 and 28 show examples of the case where the fuzzy representative point is selected as described above. Elliptic Arc Reference Model The elliptical arc reference model is constructed as a fuzzy elliptic arc satisfying three fuzzy representative points. Here, the fuzzy elliptic arc is obtained by connecting the vertices b _i (i = 1, 2, 3) of the Bezier polygon in Equations 53 and 54 to a fuzzy point [b] _i (i =
Equations (76) and (77) by expanding to 1, 2, 3)
Is defined as

[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 representative fuzzy representative points [a] ₀ , [a] ₁ and [f].
(I = 1, 2, 3) and weight w are determined, 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 respectively set to [b] ₀ and [b] _{2 as} they are. Next, the fuzzy midpoint [m] of [a] ₀ and [a] ₁ is obtained by Expression 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 a straight line connecting the vertices of the membership functions of [b] ₀ and [b] ₂ from the point p.
23 or 25 in FIG. 23 or FIG.
After obtaining the values corresponding to d, α, and β, the weight w is calculated by Expression 55. Finally, [f] becomes [b] ₁ and [m]
[B] ₁ so as to become a fuzzy point that internally divides
Is obtained as Equation 79.

[0175]

[Expression 79]

By configuring the elliptic arc reference model in this manner, an elliptic arc reference model satisfying the fuzzy representative point as shown in FIG. 26 is 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 on the elliptic arc reference model and the length along the curve from [b] ₂ to [q] _e ^Ellipse It is determined to match the length ratio.

Here, the auxiliary point p can basically be selected from a point on an arbitrary curve sample model that is somewhat distant from the three fuzzy representative points. In some cases, the deviation of the original curve sample model becomes partially large. Therefore, in the experiment, three auxiliary points p ₀ , p ₁ , and p ₂ are selected as shown in FIG. 30, and three types of convenient elliptic arc reference models are constructed for each of the auxiliary points. Good results have been obtained by adopting the elliptic arc reference model that has the highest possibility in the evaluation of the possibility of the curve class 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 of [a] ₀ and [f], line segments connecting the vertices of the membership functions of [f] and [a] ₁ , respectively, [ a) ₁ and [a] ₀
The farthest point from the line segment connecting the vertices is selected.

FMPS On the elliptic arc reference model, n _fmps fuzzy points are determined so as to divide the fuzzy points along the curve at equal distance intervals, and are set to _{FMPS of} the elliptic arc reference model, that is, Equation 80. For example, an FMPS as shown in FIG. 31 is obtained from the elliptic arc reference model of FIG.

[0179]

[Equation 80]

Here, it is difficult to divide the fuzzy rational Bezier curve exactly at regular intervals along the curve. Therefore, first, an approximate polygon of an elliptic arc is constructed by evaluating the elliptic arc reference model with an appropriate number of points so as to be equally spaced on the parameter t. Next, the relationship between the parameter and the distance along the curve on the elliptic arc is approximately determined as a line graph, and the parameter value corresponding to the point at which the distance on the curve is divided into equal intervals is approximately determined.
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, a curve sample model of the target basic curve segment is obtained, and the curve sample model is composed of “line segments”, “circular arcs”, and “elliptical arcs”. Curve models assuming that there are "line segment reference model", respectively
Obtained as "Arc Reference Model" and "Elliptical Reference Model". However, here, these reference models are hypothesis models configured to satisfy at most several fuzzy representative points of the curve sample model, and in fact, how much these hypotheses are over the entire basic curve segment , It is necessary to verify that it matches the original curve sample model.

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

[0183]

[Equation 81]

Here, the two terms on the left and right which are 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 portion of Expression 82 in Expression 81 indicates the possibility 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 is determined by the measure.

[0185]

(Equation 82)

Since Equation 81 is the possibility of taking the AND (logical product) of such a possibility at all the fuzzy matching points, P ^Class is “F of the sample model.
All MPSs are FMPSs of the reference model. " Since the membership function of [s] _i and [r] _i ^Class can be easily obtained from a section cut by a line connecting their vertices, for example, as shown in FIG.
^{Class is} also easily required. When such a P ^Class is obtained for each of “line segment”, “circular arc”, and “elliptical arc”, the possibilities P ^Line , P ^Circle , P
^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 how to verify the possibility of
FIG. 35 shows how the FMPS of the curve sample model shown in FIG. 34A is likely to be the FMPS of the circular reference model shown in FIG. 36. FIG. 35 shows the FMPS of the curve sample model shown in FIG. FM
The manner in which the possibility of becoming a PS is verified will be described.

<Possibility of Closed Curve> Next, evaluation of closed curve property according to the present invention, that is, evaluation of whether or not a curve sample model of a focused basic curve segment is a closed curve will be described. 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 probability that the curve is closed P ^Closed is calculated using a probability measure that is a type of fuzzy measure as shown in ^Equation 83. Is defined.

[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 taking the smaller one. Here, the operator min indicating the min operation taking the smaller one
The left and right terms connected by represent the conical membership functions of [q] _s and [q] _e , respectively. Equation 83 shows the possibility of the proposition "the end point [q] _e is the start point [q] _s ", and the value is shown in FIG.
As shown in FIG. 6, the membership functions of [q] _s and [q] _e can be easily obtained from a section cut by a line connecting their vertices.

<Fuzzy Inference of Curve Class> Possibility P ^{Line of} a line segment, arc (including circle) obtained as described above
From the possibility P ^Circle and the possibility P ^Ellipse of an elliptical arc (including an ellipse) and the possibility of a closed curve P ^Closed , the curve sample model of the target basic curve segment is “line segment”, “circle”, “circle arc” , "Ellipse", "elliptical arc", "closed free curve", and "open free curve" are determined by fuzzy inference as to which one of them is intended to be written. The degrees of freedom of the curve classes “line segment”, “circular arc”, “elliptical arc”, and “free curve” increase in this order, and have an inclusion relationship as shown in FIG. Therefore, it is general that the relationship of Equation 84 is established between the possibilities obtained separately for each curve class for 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)
ne, Circle, Ellipse)), it is necessary to infer a curve class. In other words, if the possibility of a simple curve class with a low degree of freedom is sufficiently high, even if it is somewhat lower than the possibility of a curve with a high degree of freedom, it is necessary to make inference that a simple curve class is selected. On the other hand, each curve class can be subdivided depending on whether or not the curve is a closed curve. For example, "elliptical arc"
And "ellipses" can be subdivided into separate curve classes. Here, the open curve includes the closed curve as a special case, so that the "ellipse" can be regarded as a special case of the "elliptic arc", and the open curve can be considered as a curve having a higher degree of freedom than the closed curve. .

By summing up the above facts, a curve class that would have been intended by the writer of the curve is obtained by fuzzy inference using the inference rules shown in FIG. For example, the first rule in FIG. 38 is “if there is a possibility of a line segment, it is a line segment”. The fourth rule is that “there is no possibility of a line segment, there is no possibility of an arc, and there is no possibility of an elliptic arc. Yes, it is elliptical if it may be closed. "The seventh rule is that there is no possibility of a line segment, no possibility of an arc, no possibility of an elliptical arc, and no possibility of being closed. If it is an open free curve, it is a rule. Note that, since this inference is performed as fuzzy inference, not one of the inference rules in FIG. 38 is applied, but all seven rules are evaluated in parallel. Further, as a result, the obtained curve class is obtained as a discrete fuzzy set whose domain is defined by Equation 85.

[0195]

[Equation 85]

More specifically, each grade value of the inference result [C] _I of the curve class based on the inference rule of FIG. 38 is obtained as shown in Formulas 86 to 92.

[0197]

[Equation 86]

[0198]

[Equation 87]

[0199]

[Equation 88]

[0200]

[Equation 89]

[0201]

[Equation 90]

[0202]

[Equation 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 therefrom. In this example, the grade of the “elliptical arc (EA)” (Equation 90) is the highest, but the grades of the other curve classes are also quite high, and the inferred curve class is quite ambiguous. . This is because the inference result by the present method can reflect the roughness of the writing method of the input curve sample model itself and the ambiguity of the shape. On the other hand, when the curve sample model is more carefully written or has a characteristic shape, a definite inference result with less ambiguity can be obtained.

The inferred fuzzy curve class [C] _I is presented to the writer so that the final curve class can be efficiently selected interactively and transmitted to a higher-level inference system having more judgment information. The curve class is determined to be one by passing as one input information. In the experimental system, an efficient human interface is realized by sequentially presenting the highest grade curve classes on the screen until the writer accepts them. When the curve class is uniquely determined, a reference model corresponding to the curve class is adopted as a recognition curve. However, if it is determined as a free curve, the curve sample model is used as it is 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 display on a screen or for use in a normal CAD system. Then, a normal (non-fuzzy) curve is calculated by extracting a part of the obtained fuzzy curve with a grade of 1 as a representative value (representative curve) of the recognition curve. In the case of a line segment When the recognition curve class is a line segment, a line segment reference model as shown in FIG. 13 is a recognition curve. Therefore,
Vertex of [q] _s ^Line membership function and [q] _e ^Line
A line segment connecting the vertices of the membership function is set as a 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 ordinary Bezier polygon b ₀ b ₁ b ₂ is formed by the vertices of the respective membership functions of the obtained fuzzy Bezier polygon [b] ₀ [b] ₁ [b] ₂ , Equation 41 and Number With 42, a circle which is a representative value of the recognition curve in the form of a rational Bezier curve is obtained. Here, the domain of the parameter t is set to [0, 1] regardless of the position of the end point [q] _e ^Circle so as to form a closed circle.

In the case of a circular arc When the recognition curve class is a circular arc, like FIG.
An arc reference model such as 0 becomes the recognition curve.
Therefore, the obtained fuzzy Bezier polygon [b]
₀ [b] Representative recognition curve in the form of a rational Bezier curve by ₁ [b] ₂ normal Bezier polygon b by the vertex of the respective membership functions ₀ b ₁ b ₂ number 41 and number 42 By configuring the The resulting arc is obtained. However, the domain of the parameter t in Equation 42 is limited to the range from 0 to the parameter value giving [q] _e ^Circle .

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 an ordinary Bezier polygon b ₀ b ₁ b ₂ is constructed by the vertices of the respective membership functions of Equations (5) and (5),
4 yields an ellipse that is a representative value of the recognition curve in the form of a rational Bezier curve. Here, regardless of the position of the end point [q] _e ^Ellipse , the domain of the parameter t is set to [0, 1] so as to form a closed ellipse.

Elliptic Arc When the recognition curve class is an elliptic arc, an elliptic arc reference model as shown in FIG. 29 becomes a recognition curve as in the case of an ellipse. Therefore, if the ordinary Bezier polygon b ₀ b ₁ b ₂ is constituted by the vertices of the respective membership functions of the obtained fuzzy Bezier polygon [b] ₀ [b] ₁ [b] ₂ , 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 from 0 to [q] _e
^Ellipse is limited to the range up to the parameter value.

In the case of a 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. This is used as a representative value of the recognition curve. In the case of an open free curve When the recognition curve class is an open free curve, an appropriate number of fuzzy points on the curve sample model are obtained, and an open B-spline curve passing through the vertices of these membership functions is obtained. This is a representative value of the recognition curve.

<Connecting Process of Recognition Curve Representative Value (Representative Curve)> By performing all the above-described processes for each basic curve segment, the entirety of the first input curve is changed to several representative curves. Recognized as a set. However, here, although the original input curve is drawn in one stroke, the recognized representative curves are not always obtained as being connected to each other, and are obtained, for example, as shown in FIG. Therefore, when it is necessary to recognize them as being connected, connection processing by post-processing is required. Note that it is necessary to save the curve class of the recognized curve. The affine transformation of the curve that can be used for the connection process is limited to translation, rotation, and enlargement / reduction. Therefore, the following connection processing is performed.

First, as shown in FIG. 41, the second and subsequent representative curves are translated so that the start and end points of the representative curves of each curve segment coincide. At this point, the end point of the last representative curve (p ′ ^e _{4 in} FIG. 41) is accumulated due to the translation, and the deviation from the original point ( ^pe _{4 in} FIG. 40) may be large. . Therefore, the starting point of the first representative curve (FIG. 41) is selected so that the global shape is not changed as much as possible.
Then, a connection point (p ′ ^s _{3 in} FIG. 41) furthest from p ′ ^s ₁ ) is obtained, and a representative curve after this point is rotated and enlarged / reduced around this point, and the last representative curve of the last representative curve is obtained. The conversion is performed so that the end point matches the position of the original end point (FIG. 4).
2).

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

<Parameter of Recognition Curve Representative Value (Representative Curve)>
Data conversion> Among the representative curves obtained above, "circle", "circle"
Arc, ellipse, and elliptical arc are rational Bezier curves
This is expressed as a normal CAD system.
It is not a common expression. Therefore, this method
To provide the output results of the
It needs to be converted to a general parameter expression. For circles and arcs Center and radius for circles, center, radius, start point for arcs
And the end point. Where the starting point of the arc and
Since the end point has already been found, if you find the center and radius,
Good. The center o is b as shown in FIG.₀Through b₀b
₁Perpendicular to b_TwoThrough b_Twob ₁As the intersection of the perpendiculars
Can be Once the center o is determined, the radius is b₀And the distance between o and
Required.

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

[0219]

[Equation 93]

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

[0219]

[Equation 94]

[0220]

[Equation 95]

[0221] To determine the major axis and minor axis, we obtain the two solutions of the quadratic equation for t as a first number 96, smaller solution of t _a of larger solution of a t _b.

[0222]

[Equation 96]

Next, when the equation (97) is obtained, the major axis (length of the major axis) d _l and the minor axis (length of the minor axis) _ds are obtained by the equations (98) and (99).

[0224]

(97)

[0225]

[Equation 98]

[0226]

[Equation 99]

To determine the inclination θ of the long axis, first,
Is determined so 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. FIG. 47 shows the parameters of the ellipse as described above.

<Recognition Experiment Example> FIGS. 48 (a) and (b) to FIGS. 51 (a) and (b) show a curve sample model composed of one curve segment and some of the fuzzy curve classes inferred therefrom. Here is an example. FIG. 48 (a) and
(b) is an example in which a circular arc is symbolically input by roughly writing, FIGS. 49 (a) and (b) are examples in which an elliptical arc is input with a medium roughness, and FIG. 50 (a) (B) shows an example in which a free curve is input by careful writing, and FIGS. 51 (a) and (b) show inference results of a fuzzy curve class in an example in which writing and shape are delicate. From the examples of FIGS. 48 to 50, it can be seen that curve classes can be distinguished by the roughness and shape of writing. FIG.
It can be seen from the example that if the writing style and shape are delicate and it is difficult to judge, the information that the ambiguity is output is an ambiguous fuzzy curve class in which the grades of all the curve classes are high.

FIGS. 52 (a) and 52 (b) and FIG. 53 (a)
(B) shows an example of recognizing an input curve composed of a plurality of curve segments. (A) and (b) in each figure are the representative curves corresponding to the fuzzy spline-curved input curve and the highest graded fuzzy curve class inferred for each curve segment, respectively. Are connected as described above.

<< Embodiments of the Invention >> Embodiments of the present invention based on the above principle will be described below with reference to the drawings. FIG.
Shows a schematic configuration of a closed curve evaluation device according to an embodiment of the present invention applied to the above-described system.
The apparatus for evaluating closed curve characteristics of this embodiment is a closed figure possibility evaluation M10 in the processing of the pattern recognition system shown in FIG.
The fuzzy evaluation of the possibility that the basic curve segment of the input curve sample model subjected to fuzzy spline interpolation and segmentation is a closed curve is fuzzy evaluated and verified. That is, a curve sample model of a basic curve segment represented as a part of a fuzzy spline curve is constructed, and the basic curve segment is closed using the start and end points of the basic curve segment obtained as fuzzy points on the fuzzy spline curve. Is fuzzy.

The apparatus for evaluating closed curve characteristics shown in FIG. 1 includes a sample model generator 1, a start / end point extractor 2, a possibility measure calculator 3, and an evaluation processor 4. This apparatus typically includes a CPU (Central Processing Unit) and is configured to function as specified mainly by software. Of course, a part or all of this device may be configured by hardware corresponding to each functional element. The sample model generation unit 1 converts the input curve information input as fuzzy point sequence information including ambiguity information into a continuous fuzzy spline curve by fuzzy spline interpolation, and further segments the input curve information by fuzzy segmentation to obtain a basic curve of the input curve. Generate a fuzzy sample model of the segment (M2 in FIG. 8)
M5).

The start / end point extractor 2 has a start point extractor 21 and an end point extractor 22, and obtains a start / end point composed of fuzzy points for the fuzzy curve sample model of the basic curve segment obtained by the sample model generator 1. . That is, the starting point extracting unit 21 extracts the starting point of the basic curve segment from the fuzzy curve sample model of the basic curve segment obtained by the sample model generating unit 1 as a fuzzy point. Further, the end point extracting unit 22 extracts the end point of the basic curve segment from the fuzzy curve sample model of the basic curve segment obtained by the sample model generating unit 1 as a fuzzy point.

The possibility measure calculation unit 3 calculates the possibility measure that the end point of the fuzzy curve sample model of the basic curve segment obtained by the start point extraction unit 21 and the end point extraction unit 22 of the start / end point extraction unit 2 is the start point. Equation 83 mentioned earlier
, And it is assumed that the basic curve segment may be a closed curve. The evaluation processing unit 4 evaluates the possibility that the basic curve segment of the curve sample model is a closed curve based on the possibility measure of the closed curve obtained by the possibility measure calculation unit 3 and outputs the result.

Next, the operation of the closed-curve evaluation apparatus of the present embodiment having the structure shown in FIG. 1 will be described in detail. FIG. 2 shows a flowchart of the processing operation of the evaluation apparatus for closed curve characteristics of the present embodiment. In FIG. 2, when the system starts, first, input curve information based on handwritten curve information input as fuzzy point sequence information including ambiguity information by, for example, a tablet device is continuously sampled by the sample model generation unit 1 by fuzzy spline interpolation. A fuzzy sample model of the basic curve segment of the input curve segmented by fuzzy segmentation is obtained by the system (step S1).

Next, from the input curve sample model of the basic curve segment represented as the fuzzy spline curve taken in at step S1, the start and end points of the basic curve segment are extracted by the start and end point extraction unit 2. Is performed (step S2).

Based on the fuzzy start point and end point of the basic curve segment obtained in step S2, the possibility measure calculation unit 3 determines that the basic curve segment is a closed curve and determines the end point of the basic curve segment as the basic curve. The possibility measure that is the start point of the segment is calculated according to Equation 83 (Step S4). Based on the possibility measure that the end point of the basic curve segment obtained in step S4 is the start point, the evaluation processing unit 4 evaluates the possibility that the basic curve segment of the curve sample model is a closed curve (step S4).

In this manner, a curve sample model of a basic curve segment represented as a part of a fuzzy spline curve is formed, and the possibility that the basic curve segment is a closed curve, that is, a closed figure is fuzzy effectively evaluated. Can be evaluated and subjected to curve inference. It should be noted that the evaluation of the closed curve property according to the present invention is not limited to the system described in the above principle description, and any system that processes a fuzzified input curve sample model may be used for any system. It can be applied when evaluating the possibility that the curve sample model is a closed curve.

[0240]

As described above, according to the present invention, a handwritten curve is input as fuzzy curve information including ambiguity information of input, and a curve sample model of a segment as a part of the input fuzzy curve information is obtained. In order to evaluate whether or not an input curve sample model in a pattern recognition for discriminating an input curve pattern by comparing with a fuzzy expression reference model as a reference pattern is a fuzzy starting point and a fuzzy point of the input curve sample model. An end point is obtained, a fuzzy end point of the input curve sample model is determined as a possibility measure that is a fuzzy start point of the input curve sample model, and a fuzzy conversion is performed by evaluating the possibility that the input curve sample model is a closed curve. The closed curve property of the input curve sample model Properly evaluated by effectively utilizing the Ajii information, it is possible to provide a closed curve of the evaluation method and apparatus capable of subjecting the discrimination and recognition of the input figure.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a schematic configuration of a closed curve property evaluation apparatus according to one embodiment of the present invention.

FIG. 2 is a flowchart for schematically explaining a closed curve property evaluation process in the closed curve property evaluation apparatus of FIG. 1;

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 in order to explain 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 illustrating a fuzzy control polygon obtained to interpolate a given fuzzy point sequence in order to explain the principle of fuzzy spline interpolation in fuzzy recognition of a handwritten curve to which the present invention is applied. FIG.

6 is a schematic diagram for explaining a fuzzy spline curve obtained from the fuzzy control polygon of FIG. 5 for explaining the 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.
FIG. 7 is a schematic diagram for explaining labeling, grouping, and extraction of a representative point 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 a 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 describing an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

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

FIG. 11 is a schematic diagram illustrating another example of a curve sample model and an FMPS (fuzzy matching point set) of the curve sample model for describing 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 the principle of generating a line segment reference model in connection with the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 13 relates to an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and illustrates a fuzzified line segment corresponding to the curve sample model of FIG. 12 for explaining the principle of generating a line segment reference model. It is a schematic diagram which shows an example of a reference model.

FIG. 14 is a schematic diagram showing internally divided fuzzy points between fuzzy points for explaining the principle of generation of a line segment reference model in connection with the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 15 is a schematic diagram showing external fuzzy points between fuzzy points for explaining the principle of generating a line segment reference model in connection with the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 16 is a schematic diagram showing an example of the FMPS of the line segment reference model shown in FIG. 13 for explaining the principle of generating a line segment reference model in connection with the description of the algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied. FIG.

FIG. 17 is a schematic diagram for explaining an example of a quadratic rational Bezier curve representation of an arc in connection with the description 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 a weight of a circle in the description 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 the principle of generation of an arc reference model in connection with the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

20 is a diagram illustrating a fuzzy algorithm for fuzzy recognition of a handwritten curve to which the present invention is applied. FIG. 20 illustrates a fuzzified arc reference model corresponding to the curve sample model of FIG. It is a schematic diagram which shows an example of.

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

FIG. 22 is a schematic diagram for explaining an example of a quadratic rational Bezier curve expression of an elliptic arc in connection with the description of the 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 the relationship between auxiliary points and weights of an ellipse in describing 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 in the description 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 weights in the description of the algorithm in fuzzy recognition of a 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 the principle of generating an elliptic arc reference model in connection with the description 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 a representative point in a curve sample model for explaining the principle of generating an elliptic arc reference model, in connection with the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 28 is a schematic diagram showing another example of selection of a representative point in a curve sample model for explaining the principle of generating an 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. 29 is a view illustrating an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied, and illustrates a fuzzified elliptic arc reference model corresponding to the curve sample model of FIG. 26 for explaining the principle of generating an elliptic arc reference model. It is a schematic diagram which shows an example of.

FIG. 30 is a diagram illustrating an example of selection of an auxiliary point for determining a weight in a curve sample model for explaining a principle of generating 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. 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 principle of generation of an 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 the possibility of matching of the FMPS between the curve sample model and the curve reference model in connection with the description of the algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

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

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

FIG. 35 is a schematic diagram for explaining verification of possibility of matching of FMPS between a curve sample model and an elliptic arc reference model, in connection with the description 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 evaluation of closed curve property of the curve sample model according to the present invention in fuzzy recognition of a handwritten curve.

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

FIG. 38 is a diagram for describing an inference rule of a curve class in connection with description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 39 is a schematic diagram illustrating an example of a curve sample model and an inferred fuzzy curve class in connection with the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 40 is a schematic diagram illustrating an example of a recognized representative curve group for describing a connection process of a representative curve, in connection with description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

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

FIG. 42 relates to an explanation of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.
It is a schematic diagram which shows an example of the matching processing of the end point by enlargement / reduction.

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 subjected to connection processing for describing connection processing of representative curves. FIG.

FIG. 44 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 the connection processing and another example of the connected representative curve group for describing the connection processing of the representative curve. 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 a connection process and another example of a connection-processed representative curve group for describing a connection process of a representative curve. 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 in the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

FIG. 47 is a schematic diagram for explaining parameters of an ellipse in the description of an algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

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

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

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

FIG. 51 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 in connection with the description of the algorithm in fuzzy recognition of a handwritten curve to which the present invention is applied.

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

FIG. 53 is a schematic diagram for explaining another example of a curve sample model and a recognition curve according to the present algorithm in connection with 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 ... Start and end point extraction part, 3 ... Possibility measure calculation part, 4 ... Evaluation processing part, 21 ... Start point extraction part,
22 ... End point extraction unit.

[Equation 101]

────────────────────────────────────────────────── ─── Continuation of the front page (56) References Saga et al., "Proposal of Fuzzy Spline Interpolation and Its Application", 5th Sapporo International Computer Graphics Symposium, November 1991, pp.156-161 ( 58) Fields surveyed (Int. Cl. ⁷ , DB name) G06T ⁷ /00-7/60 G06K 9/46 G06K 9/62 JICST file (JOIS)

Claims (2)

(57) [Claims] 1. A handwritten curve is inputted 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 step of extracting a fuzzy start point and a fuzzy end point of the input curve sample model in evaluating whether or not the input curve sample model is a closed curve in the pattern recognition for discriminating a pattern of the input curve; The fuzzy end point of the input curve sample model determined in the extraction step is determined as a possibility measure that is the fuzzy start point of the input curve sample model determined in the start and end point extraction step, and the input curve sample model is a closed curve. Possibility evaluation to evaluate the possibility Closed curve of the method of evaluation, characterized in that a step. 2. 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 closed curve characteristic evaluation device for evaluating whether or not an input curve sample model is a closed curve in a pattern recognition system for discriminating a pattern of an input curve by determining a fuzzy start point and a fuzzy end point of the input curve sample model The fuzzy end point of the input curve sample model obtained by the start and end point extracting means and the fuzzy end point of the input curve sample model obtained by the start and end point extracting means is obtained as a possibility measure. The input curve sample model is a closed curve Closed curve of the evaluation device, characterized by comprising the evaluating means for evaluating the likelihood.