CN101393643B - Computer stroke deforming system and method - Google Patents

Abstract

The invention provides a computer stroke deformation method and equipment. This method provides a sample space including multiple stroke sample vectors; sorts multiple sample vectors to minimize the sum of squares of the differences between the sorted sample vectors and their mean vectors; for the sorted sample vectors, finds all of the covariance matrix eigenvectors, and select the eigenvectors that best reflect the characteristics of the sample; use the selected eigenvectors to form a feature matrix, and establish a statistical model: <math><![CDATA[<mrow><mi>X</mi><mo>&ap;</mo><mover><mi>X</mi><mo>&OverBar;</mo></mover><mo>+</mo><mi>&Phi;b</mi></mrow>]]></math>

,in

is the average vector of the sorted sample vectors, Φ is the feature matrix, b is the parameter vector, and X is the stroke vector obtained after deformation. The present invention can obtain the deformed stroke vector by changing the components of the parameter vector. Since the present invention uses some main features of strokes as the basis for deformation during the modeling process, the overall effect and efficiency of font deformation can be improved. At the same time, by properly selecting the value of the parameter vector, it can reflect the personal aesthetic point of view.

Description

Computer stroke deformation system and method

technical field

The invention relates to an image transformation system and method for realizing calligraphy creation through computer simulation, in particular to a computer stroke deformation system and method.

Background technique

Looking back on the half a century since the birth of artificial intelligence, people have made encouraging achievements time and time again in the practice of understanding cognition and simulating thinking, such as proving the four-color theorem and defeating the chess champion, which shows that computer systems can be used in some Aspects can surpass those of specially trained people. However, for some of the most common cognitive functions that have evolved over a long period of time, such as artistic creation, visual recognition, and even picture recognition and intuition when playing Go, today's thinking simulations do not yet have the ability of infants. The fundamental reason, as Mr. Qian Xuesen pointed out, lies in the "bottleneck" of imagery thinking. Right-brain imagery has always been of paramount importance for such difficult tasks, for translating intuitive insights into logical, verbal sequences.

Computer simulation of imagery thinking can have two entry points: one is to start from the basic conclusions of cognitive neuroscience, which is fundamental and fundamental, but the current basis is still very limited; the other is to start directly from the process of imagery thinking. Calligraphy creation is a typical image thinking process.

The Letter Spirit project of Indiana University models and simulates the perception and creation of English alphabet fonts, attempts to model the central content of human advanced perception and creation, and designs different styles of a letter and the same style of different letters. This is described in "An Emergent Model of the Perception and Creation of Alphabetic Style" published by Hofstadter Douglas et al. in CRCC Technical Report, No.68, Bloomington: Indiana University. This article is hereby incorporated by reference. This modeling method uses one or several letters as a "seed" to form the beginning of a certain style, and then through the interaction of four agents (Agent), a different character set with a consistent style and complete design is formed. The four agents are imagine (Imaginer), draft (Drafter), check (Examiner) and adjust (Adjudicator), which are an iterative process. Since "creation" is limited to grid fonts (gridfont), the result is only a combination of different choices, so it is suitable for the creation of "art fonts", wherein the basic dotted line does not need to be changed. In fact, the above method is a kind of creation "with a mentor", and the final result has not been seen.

Grebert I. et al. published the article "An Example form Gridfont" in "Connectionist Generalization for Production" published by Neural Networks in May 1992, proposing to use a three-layer neural network to learn five grid fonts designed by humans, and then learn Fourteen letters in a raster font designed by someone else. Next, the network was asked to construct the remaining twelve letters. Although the method sometimes outputs unintelligible letters, it makes sense. However, this approach has no conceptual basis, no internal conceptual structure and boundaries, no temporal relationships and no interaction and feedback. Also, letter generation is parallel, and letter generation has no effect on the rest. The content of said article is hereby incorporated by reference.

Calligraphy creation is a process in which the human brain moves the pen through the hand. The pen is a tool for creation and expression. The result of image thinking activities needs a brush to reflect. Therefore, it was proposed to use parametric models to simulate the physical process of calligraphy stroke generation. For example, Wang Helena T.F. published "A Model-based Synthesis of Chinese Calligraphy" on pages 99-113 of "Computers & Graphics" No. 24, 2000. This article uses a virtual pen to capture the three-dimensional geometric parameters and brush characteristics of the pen. and the change of ink along the stroke track; Xu Songhua et al. also proposed a "virtual brush model for electronic calligraphy and painting creation" published on pages 1359-1374 of "Chinese Science (E)" in 2004 No. 34 (12) period 1359-1374. A virtual brush model based on physical modeling technology and a simulation framework for interactive electronic calligraphy and painting creation oriented to calligraphy and painting creation. Although the above two methods do not belong to image thinking, the computer simulation of calligraphy creation ultimately needs this kind of technical support. The contents of the above two articles are incorporated herein by reference.

Xu Songhua et al. published the article "Automatic Generation of Artistic Chinese Calligraphy" on pages 32-39 of the 20th (3) issue of "IEEE Intelligent Systems" in May/June 2005, introducing a calligraphy creation method based on comprehensive reasoning. Although this method uses the information of various image sources (calligraphy characters), due to the random selection of weights, it is difficult to reflect the aesthetic constraints, the efficiency of font deformation is also low, and the lines and subtleties cannot be involved. Therefore, from the perspective of image thinking or aesthetics, this method needs further improvement. The content of the aforementioned article is incorporated herein by reference.

True calligraphy creation is closely related to personal aesthetics, and is an indescribable psychological process. For a piece of work, small changes can sometimes make a big difference in beauty or ugliness. Therefore, there is a need for a method and system that can not only reflect personal aesthetic views, but also provide font deformation efficiency.

Contents of the invention

The purpose of the present invention is to provide a method and system that can not only reflect personal aesthetic point of view, but also improve font deformation efficiency.

According to one aspect of the present invention, a computer stroke deformation method is provided. The method comprises the steps of:

providing a plurality of stroke contour samples to form a sample space, wherein the plurality of contour samples are respectively represented by corresponding sample vectors;

sorting the plurality of sample vectors such that the sum of squares of differences between the plurality of sorted sample vectors and their mean vector is minimized;

For the sorted sample vectors, find all eigenvectors of its covariance matrix;

From the obtained eigenvectors, select a plurality of eigenvectors that can best reflect the characteristics of the samples;

Form a feature matrix with the multiple selected feature vectors, and set up a statistical model as follows:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&ap;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Phi;b</span>}$

是所述经排序的样本向量的平均向量，Φ是所述特征矩阵，b是参数向量，X是变形后获得的笔划向量；以及in,

is the average vector of the sorted sample vectors, Φ is the feature matrix, b is a parameter vector, and X is a stroke vector obtained after deformation; and

The components of the parameter vector are varied to obtain a deformed stroke vector.

In the method of the present invention, the step of sorting the plurality of sample vectors may include the following steps:

(a) translating the center of gravity of each sample vector in the plurality of sample vectors to the origin to obtain a plurality of translated sample vectors;

(b) normalizing the plurality of translated sample vectors with reference to one of the plurality of translated sample vectors to obtain a plurality of normalized sample vectors;

(c) performing an alignment operation on the plurality of normalized sample vectors with respect to the reference to obtain a plurality of aligned sample vectors;

(d) calculating an average vector for the plurality of aligned sample vectors, and performing an alignment operation on the average vector with respect to the reference to obtain an aligned average vector;

(e) judging whether the deviation between the aligned mean vector and the reference is greater than a set value;

(f) if the judgment result is greater than the set value, then use the aligned average vector as a new benchmark, normalize the plurality of aligned sample vectors, and repeat steps (c)-( d);

(g) If the judgment result is not greater than the set value, then obtain the plurality of sorted sample vectors.

In the method of the present invention, the deviation of the aligned mean vector from the reference may be the distance between the aligned mean vector and the reference.

In the method of the present invention, the step of selecting a plurality of eigenvectors that can best reflect the characteristics of the samples from the obtained eigenvectors may include the following steps:

find the eigenvalues corresponding to all the eigenvectors;

sorting the eigenvalues from large to small;

Multiple eigenvalues are selected from large to small, so that

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}$

Among them, _λi represents the eigenvalue, t represents the number of selected eigenvalues, V _T represents the sum of all eigenvalues _λi , and f _v is a set value, which is used to reflect the statistical model to be established The proportion value of the sample variation covered,

Wherein, the selected eigenvalues correspond to the selected eigenvectors respectively.

In the method of the present invention, the number of the selected feature vectors can be 3, and the parameter vector can have three components, wherein the first component basically characterizes the "fat" or "fat" of the stroke obtained through deformation. "Thin", the second component basically characterizes the "long" or "short" of the deformed stroke, and the third component basically characterizes the "square" or "circle" of the deformed stroke.

Method of the present invention can also comprise the following steps:

Sampling feature points on contours of multiple strokes to form contour samples of the multiple strokes;

Based on the deformed stroke vector, the deformed stroke is displayed.

In the method of the present invention, the feature points may include turning points on the contour, and Bezier curve control points located between the turning points.

According to another aspect of the present invention, a computerized stroke deformation device is provided. The equipment includes:

means for providing a plurality of stroke contour samples to form a sample space, wherein the plurality of contour samples are respectively represented by corresponding sample vectors;

means for sorting the plurality of sample vectors to minimize the sum of squares of the differences between the plurality of sorted sample vectors and their mean vector;

For said sorted sample vector, find all eigenvectors of its covariance matrix;

A device for selecting a plurality of eigenvectors that best reflect the characteristics of the sample from the obtained eigenvectors;

A device for forming a feature matrix from the plurality of selected feature vectors and establishing a statistical model as follows:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&ap;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Phi;b</span>}$

是所述经排序的样本向量的平均向量，Φ是所述特征矩阵，b是参数向量，X是变形后获得的笔划向量；以及in,

is the average vector of the sorted sample vectors, Φ is the feature matrix, b is a parameter vector, and X is a stroke vector obtained after deformation; and

means for altering components of said parameter vectors to obtain deformed stroke vectors.

In the apparatus of the present invention, the means for sorting the plurality of sample vectors may include:

means for translating the center of gravity of each sample vector in the plurality of sample vectors to the origin to obtain a plurality of translated sample vectors;

means for normalizing the plurality of translated sample vectors with reference to one of the plurality of translated sample vectors to obtain a plurality of normalized sample vectors;

means for performing an alignment operation on said plurality of normalized sample vectors relative to said reference to obtain a plurality of aligned sample vectors;

means for finding an average vector of the plurality of aligned sample vectors, and performing an alignment operation on the average vector relative to the reference to obtain an aligned average vector;

means for judging whether the deviation of the aligned mean vector from the reference is greater than a set value;

A means for normalizing the plurality of aligned sample vectors using the aligned mean vector as a new reference if the judgment result is greater than the set value;

means for obtaining the plurality of sorted sample vectors if the judgment result is not greater than the set value.

In the apparatus of the present invention, the deviation of the aligned mean vector from the reference may be the distance between the aligned mean vector and the reference.

In the device of the present invention, the means for selecting a plurality of eigenvectors that can best reflect the characteristics of the sample from the obtained eigenvectors may include:

means for finding eigenvalues corresponding to said all eigenvectors;

A device for sorting the feature values from large to small;

It is used to select multiple eigenvalues from large to small, so that the device that satisfies the following formula:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}$

Among them, _λi represents the eigenvalue, t represents the number of selected eigenvalues, V _T represents the sum of all eigenvalues _λi , and f _v is a set value, which is used to reflect the statistical model to be established The proportion value of the sample variation covered,

Wherein, the selected eigenvalues correspond to the selected eigenvectors respectively.

In the device of the present invention, the number of the selected feature vectors can be 3, and the parameter vector can have three components, wherein the first component basically represents the "fat" or "fat" of the stroke obtained through deformation. "Thin", the second component basically characterizes the "long" or "short" of the deformed stroke, and the third component basically characterizes the "square" or "circle" of the deformed stroke.

The device of the present invention may also include:

means for sampling feature points of contours of a plurality of strokes to form contour samples of said plurality of strokes;

means for displaying a deformed stroke based on said deformed stroke vector.

In the device of the present invention, the feature points may include turning points on the contour, and Bezier curve control points located between the turning points.

Since the present invention uses some main features of strokes as the basis for deformation during the modeling process, the overall effect and efficiency of font deformation can be improved to a certain extent. At the same time, the personal aesthetic point of view is reflected by taking appropriate values of the parameters representing the main features.

Description of drawings

Fig. 1 illustrates a kind of calligraphy copying and creation process based on computer simulation;

Fig. 2 illustrates the feature points obtained by automatic sampling of "horizontal stroke";

Fig. 3 is a sample sorting flowchart according to an embodiment of the present invention;

FIG. 4 is a flow chart of establishing a model by principal component analysis according to an embodiment of the present invention.

Figure 5(a) shows the contours of three "horizontal strokes" characters in the first sample space according to an embodiment of the present invention;

Figure 5(b) shows the contours of three "horizontal strokes" characters in the second sample space according to an embodiment of the present invention;

Figure 6(a) illustrates a change process of "horizontal stroke" in the first sample space;

Fig. 6(b) illustrates a change process of "horizontal stroke" in the second sample space;

Fig. 6 (c) illustrates another variation process of "horizontal stroke" in the second sample space;

Figure 7(a) illustrates a change process of "horizontal stroke" in the third sample space;

Fig. 7(b) illustrates another variation process of "horizontal stroke" in the third sample space;

Fig. 8 shows the contours of four "horizontal strokes" in the fourth sample space according to an embodiment of the present invention;

Fig. 9 (a)-(e) has illustrated a kind of change process of " cross stroke " character in the 4th sample space; And

Fig. 10(a)-(f) illustrate two kinds of change processes of the character "horizontal dash" in the fourth sample space.

Detailed ways

The evolution of Chinese characters not only conforms to the general law of character development, but also always has artistic connotation and aesthetic characteristics.

The history of calligraphy tells us that the general process of calligraphy evolution is: on the basis of existing fonts, according to the requirements of simplicity, standardization and aesthetic principles, add, delete, and merge strokes, change line types, adjust structures, strengthen echoes, and reflect individuality , which is the so-called "provincial reform and contract change". This is an image thinking process centered on transformation, addition and deletion.

In real life, to become a person with a certain level of calligraphy, it is not enough to just copy a kind of inscription. After copying several types of inscriptions, the characters written without copying the inscriptions will always be somewhat different from those copied, but still retain the characteristics of the inscriptions copied. For example, after learning several kinds of official scripts of the Han Dynasty, if one writes official scripts independently, the official scripts written independently will not be exactly the same as any of the inscriptions that one faced, but they all have different degrees of similarities. If there are many inscriptions copied and different styles of calligraphy are involved, then a personal style will gradually be formed.

Forming a personal style is actually a creative process, which can be summarized as "copy/memory-fusion-deformation/creation". Figure 1 shows a calligraphy copying and creation process based on computer simulation, which relies on image thinking when copying, memorizing and creating. The practice, imitation and silent reading of calligraphy works are the most important part of calligraphy learning. On the basis of this link, learners will naturally filter out the uneven "noise" on the outline of the inscription strokes to achieve smoothness and further fitting of the outline of the strokes. This is the basic function of thinking and a necessary preprocessing before creation . Next is the memory of calligraphy works, which is actually not a complete reproduction process, but the corresponding reproduction. Stroke fusion, glyph change and overall creation are gradual and in-depth processes, and some parts of the result can be used as objects for copying. Of course, when copying calligraphy works, the content of the original memory will also play a role.

When using a computer to simulate such a calligraphy creation process, the simulation process can be summarized as "basic text imagination" + "thinking development", in which the former is realized through storage, which is the specialty of computers, while the latter is the key content of computer simulation . Ideally, it would be better to use some kind of structural hierarchy as a template, but cognitive neuroscience has not yet concluded in this regard.

For the convenience of description, the following discussion will take lines as elements.

Chinese calligraphy pays attention to strokes, and the core is "horizontal strokes". On the basis of simulating the creation of "horizontal strokes", it is relatively easy to simulate the creation of other strokes, so that single characters and even chapters can be created.

First of all, the present invention uses the "fat" and "thin" of the font, the "long" and "short" of the stroke, the "square" and "circle" of the line end as characteristic parameters, and tries to use it to initially describe the basic appearance of the character. type features. Of course, other appearance features can also be used as parameters.

Then, build a model with parameters, and use the parameter b to control the shape of the stroke:

X＝M(b) (1)

where b is a parameter vector that can be used to adjust the dominant shape of samples in a sample space. In one embodiment, the samples are strokes, and the samples in a sample space can be all or part of the strokes taken from a specific inscription, or all or a part of the strokes taken from multiple inscriptions of a font , and can also be all or some strokes from multiple fonts. In some other embodiments, the sample can be strokes such as vertical strokes, dots, folded hooks, etc., or even a Chinese character. The dimension of vector b reflects the number of main features. M represents a statistical model, which is used to reflect the relationship between the change of b and the change trend of X. If this relationship can be determined, then when different components of b are adjusted, different X will be obtained, thus "creating" the output desired glyph.

Preferably, the established model M can associate the main characteristics of the sample with the characteristic parameters of the font through the parameter vector b. In one embodiment, it is expected that in the established statistical model M, the influence of the first component of the parameter vector b can reflect the change of the font "fat" and "thin", and the influence of the second component of the parameter vector b can reflect the stroke The change of "long" and "short", the influence of the third component of the parameter vector b can reflect the change of "square" and "circle" at the end of the line. At this time, the dimension of vector b is 3, "fat" or "thin", long" or "short", "square" and "circle" can constitute the three components of vector b. The following description is used to establish this The process of inventing statistical models.

1. Point set positioning

In order to build a model of the overall outline, it is first necessary to find some feature points from the outline of the text to outline its shape through human-computer interaction. These points reflect the structure and changes of the text. Such points are generally turning points on the boundary where the curvature changes greatly, and they are usually at the place where two strokes intersect, or where the stroke suddenly changes. However, only using these points is not enough to describe the shape information of text. In order to accurately describe the outline of the text, it is also necessary to automatically use the Béziér curve method to automatically take some points along the outline between the positioned marking points, so as to better outline the shape of the text.

Figure 2 shows the feature points obtained by automatic sampling of "horizontal stroke", where the square points represent the points with larger curvature on the contour line and the points added along the contour, and the circle points represent the control points of the Béziér curve. If there are too few feature points, the stroke features cannot be displayed; on the contrary, if there are too many feature points, it will not only increase the amount of calculation, but also introduce obvious noise.

For an outline sample of a stroke, if the coordinates of the i-th feature point on the sample are {( _xi , y _i )}, then this stroke can be represented by the following column vector:

X=(x ₁ , . . . , x _n , y ₁ , . . . , y _n ) ^T (2)

Among them, T means transpose. X is a column of vectors. If there are s samples in the sample space, it means that there are s column vectors. These s column vectors form a matrix in the sample space.

2. Sample sorting

When building a model, it is desirable to eliminate components that have no or little relationship to shape. Generally, a large number of sample superimposition methods are required to arrange the data. In one embodiment, a generalized Procrustes Analysis (GPA) method is used. The main idea of the GPA method is: firstly translate the center of gravity of each sample vector to the origin, then normalize the amplitude of the translated sample vectors, and finally rotate the observation object repeatedly until the average shape is obtained to obtain the arranged vector.

Fig. 3 is a flowchart of sample sorting according to an embodiment of the present invention. In this embodiment, it is assumed that the sample space has s samples, and n feature points are sampled for each sample, and each feature point is located in a 2-dimensional space. Then, each sample vector in the sample space can be expressed as:

X=(x ₁ , ..., x _n , y ₁ , ..., y _n ) ^T (3)

As shown in Fig. 3, in step S2, the center of gravity G of each sample vector X is translated to the origin. For example, the center of gravity G of each sample vector can be calculated first:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Then, translate the center of gravity of each sample vector to the origin. The translated sample vector can be expressed as:

X=(x ₁ , . . . , x _n , y ₁ , . . . , y _n ) ^T ,

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In step S4, the magnitude of each translated sample vector is normalized, also called scaling. For example, the vector length |X| can be calculated first. The normalized sample vector can be expressed as:

X=(x ₁ ,...,x _n ,y ₁ ,...,y ₂ ) ^T

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In step S5, one of the normalized sample vectors is set as the reference vector X ₀ . In one embodiment, let X ₀ =X ₁ . In step S6, an alignment operation is performed on the normalized sample vectors based on X ₀ . For example, the aligned sample vectors can be obtained by the following calculation:

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{the\; s}=\sqrt{a^2+b^2},$ θ＝tan ^-1 (b/a)

$\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\\ \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\end{array}\right)$

$\left(\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}\end{array}\right)<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; sA</span>}\left(\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right)$

X _m = (x _m1 , . . . , x _mn , y _m1 , . . . , y _mn ) ^T , m=1, . . . , s (7)

In step S8, the average vector is calculated for the aligned sample vectors

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

进行对齐操作，获得经对齐的平均向量。In step S10, still taking _X0 as the benchmark, according to equation (7), the mean vector

Perform the alignment operation to obtain the aligned mean vector.

In step S12, the aligned average vector is compared with the reference vector X ₀ . compared to. If the deviation between the two vectors is greater than a set value, the process proceeds to step S14. In step S14, the current reference vector X ₀ is replaced by the aligned average vector, and the magnitude of the current aligned sample vector is normalized. Subsequently, the procedure returns to step S6, and a loop is performed.

If the deviation between the two vectors is not greater than the set value in step S12, then the process proceeds to step S16 to output the aligned sample vectors obtained in step S6 in this cycle, thereby obtaining the arranged sample set .

In a preferred embodiment, step S12 compares the distance L between the two vectors with a set value L ₀ , wherein the distance L can be calculated according to equation (9).

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Step S12 may also calculate other parameters to represent the deviation between the aligned mean vector and the reference vector X ₀ .

The GPA method arranges all the samples so that the sum of the squares of the differences between them and the average vector is the smallest, that is

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

3. Model building

If a sample space contains s samples, each sample contains n feature points, and each feature point is located in a 2-dimensional space, then when the value of n is large, the amount of calculation will be very large. Therefore, in order to facilitate calculation, it is necessary to reduce the number of samples s in the sample space to a range that is easy to calculate.

In one embodiment of the present invention, after calculating all eigenvectors φ _i and their corresponding eigenvalues λ _i of the covariance matrix S of all s samples, principal component analysis (Principal Components Analysis, PCA) is used to analyze The eigenvalues of the sample covariance matrix, from which t eigenvectors are selected to form a eigenmatrix Φ. Here, the selected t feature vectors must be able to reflect the main features of the sample.

FIG. 4 is a flow chart of establishing a model by principal component analysis according to an embodiment of the present invention. As shown in Figure 4, in step S22, the average vector of s sample vectors arranged according to equation (11) is calculated

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Then, in step S24, the covariance matrix S is calculated:

$\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

In step S26, all eigenvectors φ _i of the covariance matrix S and their corresponding eigenvalues λ _i are obtained. In step S28, the feature vectors φ _i are sorted in the order of λ _i ≥ _{λ i+1} . In step S30, t eigenvalues λ _i are selected from large to small to satisfy the following formula (13):

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Wherein, V _T represents the sum of all eigenvalues λ _i , and f _v is a predetermined proportion value used to reflect the sample variation covered by the statistical model to be established, such as 96%.

In step S32, the eigenvectors φ _i corresponding to the selected t eigenvalues λ _i are combined into a feature matrix Φ:

Φ＝(φ ₁ |φ ₂ |...φ _t ) (14)

The t feature vectors selected in this way can reflect the main features of the sample.

Then, in step S34, the following statistical model is established:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Phi;b</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

是根据等式(11)计算得到的平均向量，Φ是由t个特征向量组成的矩阵，b是一个t维的列向量，对应的是“主成份”。in,

is the average vector calculated according to equation (11), Φ is a matrix composed of t eigenvectors, and b is a t-dimensional column vector, corresponding to the "principal component".

In one embodiment, t=3. At this time, b is a 3-dimensional column vector, b=[b ₁ , b ₂ , b ₃ ]. When assigning reasonable values to each component of the vector b, a new stroke similar to the original sample can be obtained by using the statistical model (23).

4. Simulation results of strokes

Figure 5(a) and Figure 5(b) respectively show the contours of three "horizontal strokes" obtained from two original samples of different monuments. Assuming that the outlines of the three "one" characters shown in Fig. 5(a) constitute the first sample space, and Fig. 5(b) shows that the outlines of the three "one" characters constitute the second sample space.

In one embodiment, corresponding statistical models are established for the first sample space and the second sample space through the aforementioned three steps of point set location, sample sorting, and model building. Then, the shape change of "horizontal stroke" is performed in the first and second sample spaces respectively. For example, the parameter b=(b ₁ , b ₂ , b ₃ ) ^T can be taken, wherein b ₁ represents the "fat" and "thin" features of the font, b ₂ represents the "long" and "short" features of the stroke, and b ₃ represents the "square" and "circle" features of the line end. Fig. 6(a) illustrates a change process of "horizontal stroke" in the first sample space. From top to bottom, the values of _b1 are 0.10, 0.05, 0, -0.05 and -0.10 (determined by human-computer interaction); _b2 and _b3 always take 0. In the change shown in Figure 6(a), the "horizontal stroke" basically changed from "fat" to "thin", but the length and square circle remained basically unchanged. Fig. 6(b) illustrates a change process of "horizontal stroke" in the second sample space. From top to bottom, the values of _b1 are 0.10, 0.05, 0, -0.05 and -0.10; _b2 and _b3 are always 0. In the change shown in Figure 6(b), the "horizontal stroke" basically changes from "fat" to "thin", but the length basically remains the same. Fig. 6(c) illustrates another variation process of "horizontal stroke" in the second sample space. From top to bottom, b ₁ and b ₃ always take 0; the values of b ₂ are 0.20, 0, -0.20 and 0.50 in turn. In the changes shown in Figure 6(c), the length of the "horizontal stroke" changes, but the "fat", "thin", "square" and "round" basically remain unchanged.

In another embodiment, the above-mentioned "horizontal strokes" in the first and second sample spaces are combined into a third sample space, and a statistical model is established through the aforementioned three steps of point set positioning, sample sorting, and model building. Fig. 7(a) illustrates a change process of "horizontal stroke" in the third sample space. From top to bottom, the values of _b1 are 0.15, 0.10, 0.05, 0, -0.05, -0.10 and -0.15; _b2 and _b3 are always 0. In the change shown in Fig. 7(a), the "horizontal stroke" basically changes from "fat" to "thin", but the length and square circle are basically unchanged. Fig. 7(b) illustrates another variation process of "horizontal stroke" in the third sample space. From top to bottom, b ₂ takes 0.05, 0 and -0.05 in turn; b ₁ and b3 are always 0. In the changes shown in Figure 7(b), the length of the "horizontal stroke" changes, but the "fat", "thin", "square" and "round" basically remain unchanged. Compared with the font changes in Figures 6(a)-6(c), the fonts in Figures 7(a)-7(b) have undergone richer changes, resulting in a difference from the first sample space and the second sample space. The shape of the space.

FIG. 8 shows the contours of four "scratches", which constitute the fourth sample space. In this embodiment, a corresponding statistical model is established for the fourth sample space through the aforementioned three steps of point set location, sample sorting, and model building. Then, change the font of "horizontal stroke" in the fourth sample space. In Fig. 9, vector b contains 3 elements b ₁ , b ₂ and b ₃ , in (a), b=[-0.10, 0, 0], in (b), b=[-0.05, 0, 0] , in (c), b=[0,0,0], in (d), b=[0.05,0,0], in (e), b=[0.10,0,0]. In the changes shown in Figures 9a-9e, the "horizontal stroke" basically changes from "fat" to "thin", but the length and square circle are basically unchanged. In Fig. 10, images (a)-(c) correspond to the adjustment component b ₂ , and the rest of the components remain unchanged. The length of the "horizontal stroke" changes, but the "fat", "thin" and "square" and "circle" are basically constant. The images (d)-(f) correspond to the adjustment component b ₃ , and the other elements remain unchanged, among which the "square" and "circle" of the "horizontal stroke" are changed, but the "fat", "thin" and length are basically unchanged.

Although the three components b ₁ , b ₂ , b ₃ of the vector b can mainly affect the "fat" and "thin" features of the font, the "long" and "short" features of the strokes, and the "square" and " “circle” feature, but it can be seen from Figures 6, 7, 9 and 10 that the change of a component b _i in the parameter b does not only cause the change of a single feature, it will cause the change of the entire font to a certain extent.

5. Creation of text

On the basis of the above-mentioned stroke simulation, characters can be created.

Those skilled in the art can understand that each step described in the foregoing embodiments can be implemented by computer hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, various illustrative components, blocks, modules, circuits and steps have generally been described in terms of their functionality. Whether these functionalities are implemented as hardware or software depends on the specific application system design adopted by the overall system. Skilled artisans will recognize the interoperability of hardware and software in these cases, and how best to implement the described functions for each particular application. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.

Implementation or execution of the various steps described in conjunction with the embodiments described herein may be implemented using a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other Programmable logic devices, discrete gate or transistor logic, discrete hardware components, or any combination designed to perform the functions described herein. A general-purpose processor may be a microprocessor, however, in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented with a combination of computing devices, eg, a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in combination with a DSP core, or any other such configuration.

Although the preferred embodiments of the present invention have been described above, the present invention is not limited thereto. Those skilled in the art can make various changes and changes on the basis of the above description. Various changes and changes without departing from the spirit of the invention should fall within the protection scope of the present invention. The protection scope of the invention is defined by the appended claims.

Claims (12)

1. A computer stroke morphing method, the method comprising the steps of:

providing a plurality of outline samples of the stroke to form a sample space, wherein the plurality of outline samples are respectively represented by corresponding sample vectors;

sorting the plurality of sample vectors to minimize a sum of squares of differences of the plurality of sorted sample vectors and an average vector thereof;

for the ordered sample vectors, solving all eigenvectors of a covariance matrix of the ordered sample vectors;

selecting a plurality of feature vectors which can reflect the features of the sample most from the obtained feature vectors;

forming a feature matrix by using the plurality of selected feature vectors, and establishing a statistical model according to the following formula:

<math> <mrow> <mi>X</mi> <mo>&ap;</mo> <mover> <mi>X</mi> <mo>&OverBar;</mo> </mover> <mo>+</mo> <mi>&Phi;b</mi> </mrow> </math>

wherein,

is the average vector of the ordered sample vectors, phi is the feature matrix, b is a parameter vector, and X is a stroke vector obtained after deformation; and

changing components of the parameter vector to obtain a deformed stroke vector,

wherein the step of ordering the plurality of sample vectors comprises the steps of:

(a) translating a center of gravity of each of the plurality of sample vectors to an origin to obtain a plurality of translated sample vectors;

(b) normalizing the plurality of translated sample vectors with respect to one of the plurality of translated sample vectors to obtain a plurality of normalized sample vectors;

(c) performing an alignment operation on the plurality of normalized sample vectors relative to the reference to obtain a plurality of aligned sample vectors;

(d) for the plurality of aligned sample vectors, finding an average vector, and aligning the average vector with respect to the reference to obtain an aligned average vector;

(e) judging whether the deviation of the aligned average vector and the reference is larger than a set value;

(f) if the result of the judgment is larger than the set value, using the aligned average vector as a new reference, normalizing the plurality of aligned sample vectors, and returning to the step (c) for circulation;

(g) and if the judgment result is not larger than the set value, outputting the obtained plurality of aligned sample vectors as the plurality of ordered sample vectors.

2. The method of claim 1, wherein the deviation of the aligned average vector from the reference is a distance between the aligned average vector and the reference.

3. The method of claim 1, wherein said step of selecting a plurality of feature vectors that best reflect sample features from said derived feature vectors comprises the steps of:

finding out the characteristic values corresponding to all the characteristic vectors;

sorting the characteristic values from big to small;

selecting a plurality of characteristic values from large to small so that

<math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>t</mi> </munderover> <msub> <mi>&lambda;</mi> <mi>i</mi> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>f</mi> <mi>v</mi> </msub> <msub> <mi>V</mi> <mi>T</mi> </msub> </mrow> </math>

Wherein λ is_iRepresenting a characteristic value, t representing the number of said characteristic values selected, V_TRepresenting all eigenvalues λ_iSum of (a) and f_vIs a set value used for reflecting the proportion value of the sample change covered by the statistical model to be built,

wherein the selected plurality of feature values respectively correspond to the selected feature vectors.

4. A method as recited in claim 3, wherein the number of feature vectors selected is 3 and the parameter vector has three components, wherein a first component substantially characterizes the "fat" or "thin" of the morphed resulting stroke, a second component substantially characterizes the "long" or "short" of the morphed resulting stroke, and a third component substantially characterizes the "square" or "circle" of the morphed resulting stroke.

5. The method of claim 1, further comprising the steps of:

sampling feature points of contours of a plurality of strokes to form contour samples of the plurality of strokes;

displaying the deformed stroke according to the deformed stroke vector.

6. The method of claim 5, wherein said feature points comprise turning points on said contour, and Bezier curve control points located between said turning points.

7. A computer stroke morphing device, the device comprising:

means for providing contour samples of a plurality of strokes to form a sample space, wherein the plurality of contour samples are each represented by a respective sample vector;

means for sorting the plurality of sample vectors to minimize a sum of squares of differences of the plurality of sorted sample vectors and an average vector thereof;

means for solving for all eigenvectors of their covariance matrix for the ordered sample vector;

means for selecting a plurality of feature vectors that best reflect the characteristics of the sample from the obtained feature vectors;

means for constructing a feature matrix from the plurality of selected feature vectors and for building a statistical model according to the following equation:

<math> <mrow> <mi>X</mi> <mo>&ap;</mo> <mover> <mi>X</mi> <mo>&OverBar;</mo> </mover> <mo>+</mo> <mi>&Phi;b</mi> </mrow> </math>

wherein,

is the average vector of the ordered sample vectors, phi is the feature matrix, b is a parameter vector, and X is a stroke vector obtained after deformation; and

means for altering components of the parameter vector to obtain a deformed stroke vector, wherein the means for ordering the plurality of sample vectors comprises:

means for translating a center of gravity of each sample vector of the plurality of sample vectors to an origin to obtain a plurality of translated sample vectors;

means for normalizing the plurality of translated sample vectors with respect to one of the plurality of translated sample vectors to obtain a plurality of normalized sample vectors;

means for performing an alignment operation on the plurality of normalized sample vectors relative to the reference to obtain a plurality of aligned sample vectors;

means for finding an average vector for the plurality of aligned sample vectors and aligning the average vector relative to the reference to obtain an aligned average vector;

means for determining whether the aligned average vector deviates from the reference by more than a set value;

means for normalizing the plurality of aligned sample vectors using the aligned average vector as a new reference if the determination result is greater than the set value;

means for outputting the obtained plurality of aligned sample vectors as the plurality of ordered sample vectors if the determination result is not greater than the set value.

8. The apparatus of claim 7, wherein the deviation of the aligned average vector from the reference is a distance between the aligned average vector and the reference.

9. The apparatus of claim 7, wherein said means for selecting a plurality of feature vectors from said derived feature vectors that best reflect sample features comprises:

means for finding feature values corresponding to all the feature vectors;

means for sorting the eigenvalues from large to small;

means for selecting a plurality of eigenvalues from large to small such that the following equation is satisfied:

<math> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>t</mi> </munderover> <msub> <mi>&lambda;</mi> <mi>i</mi> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>f</mi> <mi>v</mi> </msub> <msub> <mi>V</mi> <mi>T</mi> </msub> </mrow> </math>

wherein λ is_iRepresenting a characteristic value, t representing the number of said characteristic values selected, V_TRepresenting all eigenvalues λ_iSum of (a) and f_vIs a set value used for reflecting the proportion value of the sample change covered by the statistical model to be built,

wherein the selected plurality of feature values respectively correspond to the selected feature vectors.

10. The apparatus as recited in claim 9, wherein the number of the selected feature vectors is 3, and the parameter vector has three components, wherein a first component substantially characterizes "fat" or "thin" of the morphed obtained stroke, a second component substantially characterizes "long" or "short" of the morphed obtained stroke, and a third component substantially characterizes "square" or "circle" of the morphed obtained stroke.

11. The apparatus of claim 7, further comprising:

means for sampling feature points of a plurality of strokes' contours to form contour samples of the plurality of strokes;

means for displaying the deformed stroke from the deformed stroke vector.

12. The apparatus of claim 11, wherein said feature points comprise turning points on said contour, and Bezier curve control points located between said turning points.

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