Automatic Generation of Artistic Chinese Calligraphy

Constraint-Based Reasoning

Songhua Xu, Zhejiang University

Francis C.M. Lau, University of Hong Kong

William K. Cheung, Hong Kong Baptist University

Yunhe Pan, Zhejiang University

hinese calligraphy is among the finest and most important of all Chinese art forms C and an inseparable part of Chinese history. Its delicate aesthetic effects are gen- erally considered to be unique among all calligraphic arts. Its subtle power is integral to traditional Chinese painting, where—as figure 1a shows—calligraphy is not just an

annotation but also a stylized visual component printing or display; Donald Knuth has done pioneer- affecting the viewer’s emotional response to a painting work in this area.1 We propose an intelligent sys- A novel intelligent ing. This emotional effect also explains why, as fig- tem that can automatically create novel, aesthetically ure 1b shows, calligraphy is often preferred to printed appealing Chinese calligraphy from a few training system uses a type in Asian banners, signage, newspaper mast- examples of existing calligraphic styles. To demon- heads, and other promotional contexts. The 2008 strate the proposed methodology’s feasibility, we have constraint-based Beijing Olympics Games logo (http://en.beijing- implemented a prototype system that automatically 2008.org) is a recent example. generates new Chinese calligraphic art from a small analogous-reasoning Chinese calligraphers predominantly use a soft training set—typically, fewer than 10 samples for each hair brush. Generating artistically appealing callig- character. To the best of our knowledge, no other pub- process to raphy with the brush can be highly challenging. The lished work uses our approach. One remotely related brush-stroke shapes as well as the topology over mul- project uses analogous reasoning to simulate the cre- automatically generate tiple strokes are often very complex. The Chinese ativity in jazz performance and to model other artis- language’s large character set—more than 3,000 tic activities from the simulation.2 original Chinese commonly used characters—presents a problem all its own. Being able to master some of the characters Overall approach and calligraphy that meets doesn’t mean that you can also write the other char- system architecture acters as satisfactorily. Similarly, mastery of one or Let P denote a model with a parameterization E visually aesthetic more styles doesn’t necessarily indicate mastery in that is flexible enough to represent a class of highly other styles, let alone creativity in generating new deformable shapes—different Chinese character requirements. styles. This is where computers can help. styles, in our case. Normally, constructing a flexible In the digital world, calligraphic art is most often model requires significant effort. At the same time, applied to creating typographic or artistic fonts for arbitrary instantiations from such models can easily

32 1541-1672/05/$20.00 © 2005 IEEE IEEE INTELLIGENT SYSTEMS Published by the IEEE Computer Society generate unacceptable results. Thus, a model- based approach to generating novel and yet aesthetically appealing calligraphy is by no means straightforward. Our approach uses a constraint-based analogous-reasoning process (ARP), which we apply to a given set of training examples. Analogous reasoning basically fuses knowledge from multiple sources to support a restricted form of reasoning.3 In our case, the knowledge sources are training examples, which are in the form of images. In our experiments using the prototype system, the training examples come from printed “copybooks” that present multiple calligraphic styles. Because Chinese characters derived from pictographs, which evolved over time into symbols, many basic features recur in different Chinese characters. To take advantage of this redundancy, we devised a hierarchical representation for Chinese characters as the basis for our process. The proposed ARP consists of three major phases:

• Shape decomposition. Decomposing (or recovering) the calligraphic shapes of a (a) (b) given training example is equivalent to the Figure 1. Artistic Chinese calligraphy in Asian societies: (a) Chinese painting with problem of extracting structural features calligraphy; (b) top—ceiling of a Kong Zi (Confucius) temple; bottom—masthead of for constructing a reference model P. The the China Daily newspaper. reference model is an instance of the model P that best represents the input example. The underlying mechanism in models; then, we combine the aligned Figure 2 shows the overall architecture of the our approach is character stroke segmen- models by interpolating or extrapolating proposed intelligent calligraphy generation tation and extraction. the parameterizations {E}. The newly system. • Calligraphy model creation from exam- derived shape family is essentially a “re- ples. Given n reference models {Pi}, parameterization” via the blending para- Character representation where i is the index of the reference model meters, , which control the contribution Our proposed system decomposes Chi- constructed from a set of training exam- of each training example. nese calligraphy into the six levels shown in ples, we can define a family of novel • Artistic calligraphy generation. Given figure 3a: constructive ellipse, primitive shapes P() by blending the reference P() and a set of aesthetics-related geo- stroke, compound stroke, radical, single models: first, we identify the correspond- metrical constraints, we identify some character, and complete artwork. We adopted ing structural features among the reference that satisfies the given constraints. parametric representations at all levels. Taken

Structural stroke database Input images of Shape recovery Hierarchical sample calligraphy through vision representation of from copybook techniques source calligraphy Calligraphy model Calligraphy generation through constraints analogous reasoning

Images of Hierarchical Appreciation through Hierarchical automatically representation of Rendering constraint representation of new generated artistic generated artistic satisfaction calligraphy candidates calligraphy calligraphy

Figure 2. System architecture for intelligent calligraphy generation.

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5th Calligraphy artwork

P4, 1 Single- 4th Single characters character level

P P P 3rd Radicals 3, 1 3, 2 3, 3 Radical level

P P P P P P P P P 2nd Compound strokes 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 2, 8 2, 9 Compound- stroke level

P P P P P P P P P P P 1st Primitive strokes 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 1, 7 1, 8 1, 9 1, 10 1, 11 Primitive- stroke level

0th Constructive ellipses (a) (b)

Figure 3. Chinese calligraphy representation: (a) six-level representation hierarchy; (b) four levels in the representation for the Chinese character “zhe.”

together, these representations form the para- and the other two rows store the lengths of through quantitative means—analogous meter space E for modeling Chinese callig- its major and minor axes. reasoning together with aesthetic constraint raphy artwork. Traversing the hierarchy from the bottom satisfaction. up, the system first “lines up” the construc- Hierarchical representation enables effi- Prototype implementation tive ellipses to form primitive strokes (level cient local learning of constructive elements In the prototype system, we’ve imple- 1). Then, using shape grammar rules, it com- and reduces the huge global-knowledge mented five typical, frequently occurring bines primitive strokes to form compound representation space to only local shape- primitive strokes: points, horizontals, verti- strokes (level 2), which are subsequently variation characterizations. It also supports cals, left slants, and right slants. Figure 4 combined to form radicals (level 3). By efficient retrieval (and thus reuse) of past shows these strokes as well as 24 typical, fre- grouping radicals according to their spatial calligraphy artwork reasoning results. quently occurring compound strokes and 36 proximity, the system forms single charac- The hierarchical parametric approach radicals. Figure 3b shows the hierarchical rep- ters (level 4). It blends learned examples of can represent all calligraphy styles— resentation of the Chinese character “zhe,” as the same character in different styles into a including cursive styles that are heavily in “Zhejiang,” a scenic coastal province and flexible character model. deformed and distorted—in a uniform six- the home of Zhejiang University. Finally, the top-level constructive element level hierarchy, and it can process the char- Level 0 of the hierarchical representation is calligraphy artwork (level 5), which might acters using the same reasoning pipeline. views an artwork as a collection of con- combine more than one character. This increases our system’s capability to structive ellipses (see figure 3a). The system learn and generate cursive calligraphy, will render the artwork’s “image” as the Advantages of the hierarchical which is an important aspect of calligraphic image space regions that the constructive parametric approach aesthetics. ellipses cover. This representation is inspired Because our approach generates new cal- by the Blum model,4 which defines a zonary ligraphic styles by reasoning from a set of Shape decomposition area by an ellipse moving along a predefined existing styles, it belongs to the hard domain In the first of its three phases, our system curve. A 4 1 matrix parameterizes each of qualitative reasoning. Our parametric extracts hierarchical and parametric represen- constructive ellipse: two rows store the coor- representation offers a tool to attack the tations from the knowledge sources, which are dinates of the constructive ellipse’s center, challenging qualitative-reasoning problem static images of calligraphy artwork.

34 www.computer.org/intelligent IEEE INTELLIGENT SYSTEMS Extracting levels 0–1 elements To extract primitive strokes and thus the corresponding constructive ellipses from a training example, we first compute the input image’s skeleton—that is, a close approxi- mation to the brush’s actual trajectory when the calligrapher created the artwork. Various approaches exist for skeletoniz- ing binary character images. We employed the algorithm proposed by Rong He and (a) (b) (c) Hong Yan,5 which composes the extracted Figure 4. (a) Five primitive strokes, (b) 24 compound strokes, and (c) 36 radicals. skeleton from segmented primitive strokes. Figure 5 gives a step-by-step illustration. Such a stroke decomposition is by no means optimal, and our system can benefit from any highest overall confidence for the corre- ferent calligraphic styles. Our approach has improved decomposition algorithm. sponding stroke composition. roots in Herbert A. Simon’s notion of artistic To further enhance the robustness of the design generation and synthesis, discussed in stroke identification step, the system uses Extracting level 4 elements 1975,3 and in Mark Keane’s later application several structural variants of the five prim- To extract the level 4 constructive ele- of analogical mechanisms to problem solv- itive strokes in figure 4. Once it identifies ments, we must determine which radicals can ing.9 In general, we can view ARP as a the primitive stroke skeletons, the system be grouped to form a character. This is equiv- process that synthesizes new knowledge— uses Bresenham’s ellipse rasterization algo- alent to the well-known “character segmen- shapes, in our case—by fusing or blending rithm6 to compute all the constructive tation” problem in pattern recognition. In our with existing, independent knowledge ellipses. system, we use standard projection analysis8 sources—that is, the training examples. To to segment the individual characters in a cal- support the fusion, the process must establish Extracting levels 2–3 elements ligraphy artwork. feature correspondence between the knowl- We identify compound strokes and radi- edge sources. cals by analyzing the spatial relation between Calligraphy model creation In principle, we can apply ARP at differ- the primitive and compound strokes, respec- from examples ent hierarchical levels, resulting in different tively. The analysis uses carefully designed To generate new calligraphic art, we apply artistic effects. Assume that we apply it to shape grammar production rules. The syn- analogous reasoning to a training set of dif- Pk,m, the mth constructive element at the kth tactic description of any constructive element is represented using the production system’s syntax and generated using rule deduction. As an example, the shape production rule for the compound stroke in the upper left- most corner of figure 4b, denoted as CS1,is as follows:

IF horizontal(a) AND vertical(b) AND ontop(a,b) AND onleft(a,b) AND (a) (b) (c) touch(a,b) THEN CS1 := {a,b} where horizontal(a), vertical(b), ontop(a,b), onleft(a,b), and touch(a,b) are the predicates indicating the relationships of horizontal primitive stroke, vertical primitive stroke, a on top of b, a on left side of b, and {a,b} touching each other, respectively. (d) (e) (f) We use fuzzy set theory to increase the extraction process’s reliability.7 This approach Figure 5. Extracting levels 0–1 elements of a character from its image: (a) the input lets us associate a confidence value with each image, (b) the raw skeleton computed using a thinning algorithm, (c) the plausible shape production rule via the deduction short branches detected and color marked, (d) the short branches identified and process. The system derives an overall confi- removed, (e) the skeleton segmented into different strokes in the character and color dence value for the shape grammar produc- coded, and (f) the reconstructed character using the extracted levels 0–1 elements. tion from the confidence values of all its state- Note that the reconstructed image (f) and the original image (a) have slight ments. Then it applies the rule that yields the differences at the ends of some strokes, as shown in the red rectangles.

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std level of the hierarchical representation, and from that of Pk,m, as follows: style. When the number of knowledge 1 that n different versions of Pk,m exist, Pk,m,…, sources is greater than two, ARP mimics n i i std P k,m, derived from n training examples—the Fk,m Pk,m Pk,m combined thinking activity, which will make independent ARP knowledge sources. The use of several knowledge reference cases r ARP result is denoted as Pk,m. We can then After computing all the deviations of the during the reasoning process. 1 n state the general mathematical principle: reasoning sources Fk,m, , F k,m, we can then derive the overall deviation Fr as follows: Artistic calligraphy generation n k,m PPri= ∑ω i With the mechanisms of calligraphic km,,km Fr = ∅(F 1 , , Fn , ) shape decomposition and model creation i=1 k,m k,m k,m from examples in place, we can easily gen- where i(i = 1, …, n) is defined as the anal- where ∅ is defined as the analogous reason- erate candidates for original calligraphy art- i ogous reasoning intensity for Pk,m with the ing mechanism simulation operator, which work by randomly perturbing the reasoning n i constraint that i=1 = 1. our prototype system implements as an inter- intensities. The analogous reasoning steps i i Obviously, a Pk,m with a higher value polation or extrapolation process, and is apply equally as well to a single parameter would contribute more to the overall reason- the aesthetic viewpoint sequence dictating of a constructive ellipse as they do to all the ing result. the weights and contribution order for dif- parameters of a character. This provides a We can interpret the proposed ARP as ferent sources. The ordered set of intensities highly flexible system for varying shapes to either an interpolation or an extrapolation is ARP’s viewpoint sequence. So not only dif- generate many possible candidates. process. We’re assuming a one-to-one corre- ferent reasoning intensities affect the final A filtering step ensures that only candi- spondence among different versions of Pk,m. output, but also different orders of the train- dates meeting aesthetic requirements are In reality, a constructive element, such as a ing examples. output. std constructive ellipse or a primitive stroke, Finally, by adding back the P k,m shape derived from a training example can corre- (that is, the standard constructive element Extracting aesthetic constraints r spond to one element in another training associated with ARP’s reasoning result Pk,m), from training examples example in more than one way. The process we obtain Aesthetic constraints are criteria that quan- therefore requires a feature correspondence tify the aesthetic quality of a candidate or its r r std step before it can blend together features Pk,m = Fk,m ⊕ P k,m parts. There are two categories: extracted from the different examples. In our intelligent calligraphy generation system, the where the operator ⊕ is a reverse function of • constraints for the visual appearance of a user can either adjust all the analogous rea- the operator . constructive element, and soning intensities manually through a graph- Note that the system can apply ARP not • constraints for the spatial relationship ical interface or generate them randomly. The only to the constructive elements from all the between neighboring constructive ele- intensities are fed to a subsequent phase that reasoning sources but also to some topolog- ments. automatically filters out those that violate ical constructors in the form of geometric aesthetic constraints. transformation matrices for the correspond- Fortunately, the proposed ARP can auto- ing constructive elements. The topological matically guarantee satisfaction of the first Fusing knowledge sources in ARP constructors further increase the reasoning constraint—at least under most circum- To establish the feature correspondence power. Simple ARP simulation operators for stances—because the constructive elements between training examples, we first derive a the topological constructors include arith- are parametric. Therefore, we need focus discrete planar curve for each constructive metic mean, geometric mean, and harmonic only on deriving and applying constraints of i element Pk,m using the centers of all the con- mean. the second type to guarantee the generation structive ellipses associated with it. The of visually pleasing calligraphy. curve forms the element’s skeleton, and we A computational-psychology An important consideration for a quantifi- use Pengfei Zhu and Paul Chirlian’s algo- perspective able constraint on aesthetics is the degree of rithm10 for detecting the critical points on the If all the knowledge sources’ intensities overlap between two constructive elements. planar curves as the key points for setting up fall within (0, 1), ARP is simulated using an Our system uses three types of overlapping the correspondence. Details of this process interpolation process; otherwise, it’s simu- between a pair of elements, a and b: the x- are available online at http://pantheon. lated using an extrapolation process. From a dimensional overlapping ϑx(a, b), the y- yale.edu/~sx25/ca. psychological point of view, the negative val- dimensional overlapping ϑy(a, b), and the In our application, we first assume the ues for the reasoning intensities reflect the area overlapping ϑs(a, b). All three measures shape of a constructive element in the font brain’s inverse reasoning activities, which are based on the constructive element’s style “Kai” (the GB2312 character set used treat certain input source knowledge as neg- bounding boxes. After computing the over- in the recent version of Microsoft Word) to be ative examples. lapping measures for all element pairs of the the standard reference, which we denote as By contrast, positive values correspond to training examples, the system records their std P k,m. Because the shape decomposition exaggeration of brain activities, in which the upper and lower bounds. The upper bound phase has already extracted the Pk,m’s shape, larger an input example’s reasoning inten- keeps two neighboring elements in a new cal- i we can easily compute the deviation Fk,m by sity, the more heavily the generated result ligraphy artwork from being squeezed too i which the shape of the ith source Pk,m differs will follow the input source knowledge’s closely together while the lower bound keeps

36 www.computer.org/intelligent IEEE INTELLIGENT SYSTEMS them from being too far apart. These overlapping measures then direct the process of generating the upper-level constructive elements from the lower-level ones. The overall effect is to constrain ARP from perturbing the spatial relationships of each constructive element’s subcomponents too much beyond what they are in the training examples. Thus, for example, if ARP generates a calligraphy candidate that con- tains subconstructive elements whose x- dimensional overlapping is smaller than the derived lower bound, the prototype system will reject the candidate. If needed, end users can relax the upper- and lower-bound constraints to allow for new styles that cannot be easily imagined. In our system, users can adjust the two bounds interactively according to their preferences. Thus, choosing the best values for the two bounds becomes a matter of personal aes- Figure 6. A single character in many styles; the first row is the training examples, and thetic taste. According to our experience with the other rows are automatically generated by our system. the prototype system’s behaviors, relaxing or ignoring the ARP constraints seems to create a more cursive and running-style writing. In addition, we analyzed the system’s sen- Xingkai, Xingchao, and Kuangchao. We sitivity in terms of its “creativity” by vary- invited six calligraphic fans with at least two Using past results for ing the number of training examples. In this years’ writing experience and four profes- efficient reasoning experiment, we used training examples in sional calligraphists to form a review com- You could choose a random process to sim- training examples of different calligraphy mittee. They cast votes on the system-gener- ulate ARP, but this might be computationally styles, including Kai, Li, Xingshu, Weibei, ated calligraphic art. If a result received more intensive. Reusing past results can make the reasoning process more efficient. In addition, the hierarchical representation lets users reuse whole or partial results. Our proposed system therefore offers a high degree of reusability of past reasoning results.

Experimental results Figure 6 shows the results our prototype system obtained using six training examples as the input knowledge sources and linear interpolation to simulate the ARP generation step. Figure 7 shows the results of using five (a) (b) (c) (d) training examples and a nonlinear interpolation process. In the latter case, you can easily see the consistency in style among characters within the same newly generated calligraphic piece. Space limitations restrict the results shown to a small set; more results are available at http://pantheon.yale.edu/~sx25/ca. The results show that our approach can yield novel calligraphy styles given some existing ones. To verify that the system was generating quality outputs, we asked practic- ing artists, art school professors, and calligra- (e) (f) (g) (h) (i) (j) (k) (l) phy enthusiasts to examine the outputs; most of them considered the generated calligraphy Figure 7. A calligraphic couplet, or epigram, in many styles: (a) the training examples; to be novel with regard to their writing style. (b)–(l) selected computer-generated results.

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than seven votes, it was considered a new cal- knowledge. On the basis of these knowledge ligraphic work. With more training examples sources, the system could simulate the pro- of different styles, the chance of generating posed ARP but now with the additional cri- a creative and yet aesthetically acceptable terion to best match the user inputs. The uni- calligraphic art increased. Also, nonlinear formity of the hierarchical representation ARP generated more creative calligraphic art means that the resulting set of intensities than linear APR. Using from six to seven applies directly to the full character set of all training examples, the linear process gener- the existing fonts, generating a font cus- ated about 30 acceptable calligraphic works tomized to the user’s handwriting. and the nonlinear process generated more Figure 9 shows the results from a simple than 50. test. The top row shows handwritten input Figure 8 shows an interesting example. An characters from different users, and the rows artist generated the horse using paint-brush below show the characters generated by software.11 Our prototype system automati- mimicking the input style. The results are cally generated the calligraphy (the charac- impressive. Of course, if the user’s hand- ter “forever” in Chinese). writing is so peculiar that it lies outside the feasible space composed from all the existing Applications fonts, the system might fail. This system for computer-generated orig- An application along the same lines could inal Chinese calligraphy has several poten- make an individual’s handwriting style more tial applications. beautiful, which could improve readers’ For example, users could generate per- impressions of the writer. With our system, sonalized fonts with it. First, they would users can input their handwriting as one ARP import computer-installed fonts. Then our source and then specify an appealing existing system could compute a flexible model of style as another source. By manually setting each character by aligning all corresponding the reasoning intensities, users could choose Figure 8. “Forever running.” The calligra- characters of the different fonts. Next, the the extent to which they rectified their per- phy is styled to match a horse created system would ask for a small set of charac- sonal handwriting while still preserving a with paint-brush software. ters in the user’s handwriting as additional degree of its unique qualities.

(a) (b) (c) (d) (e) (f) (g) (h)

Figure 9. Personalized font generation from a single character. The first row shows a single character written by different users in their respective handwriting styles, and the second row shows automatically generated characters that mimic the captured handwriting style.

38 www.computer.org/intelligent IEEE INTELLIGENT SYSTEMS The proposed system is essentially a specific version of a deformable model for modeling The Authors Chinese characters of different calligraphic styles. The model’s representation power Songhua Xu is a member of the CAD and CG State Key Lab of China at Zhejiang University and an honorary researcher in the Department of Com- makes the system suitable for deformable puter Science at the University of Hong Kong. He is also pursuing computer model-based handwriting recognition. In graphics research with the Computer Science Department at Yale University. addition, the unified ARP modeling approach His research interests include artificial intelligence, computer graphics, and is an excellent candidate for writer adapta- human-computer interaction. He received his bachelor of engineering summa tion in existing or emerging handwriting cum laude in computer science from Zhejiang University. He is a member of the AAAI and Eurographics. Contact him at the CAD and CG State Key Lab recognition systems. of China, Zhejiang Univ., Hangzhou, China, 310027; [email protected]. Carnegie Mellon University’s CAPTCHA project (www.captcha.net) presents another Francis C.M. Lau is head of the Department of Computer Science at the Uni- possible application of our approach. versity of Hong Kong. His research interests are in parallel and distributed computing, object-oriented programming, operating systems, Web and Inter- CAPTCHA stands for “Completely Automated net computing, computer graphics, and AI. He received his PhD in computer Public Turing Test to Tell Computers and science from University of Waterloo. He is a senior member of the IEEE. Humans Apart.” A CAPTCHA is any program Contact him at the Dept. of Computer Science, University of Hong Kong, that can generate and grade tests that com- Hong Kong; [email protected]. puters cannot pass, and one kind—popular for protecting Web sites from massive auto- William K. Cheung is an assistant professor in the Department of Computer mated registrations—uses words written in Science at Hong Kong Baptist University. His research interests include distorted letters that humans can read but model-based pattern recognition, machine learning, and artificial intelligence computers cannot. Our system could be used with applications to data mining, information extraction, recommender systems, and Web and Grid service management. He received his PhD in com- to develop a Chinese CAPTCHA agent that puter science from the Hong Kong University of Science and Technology. would generate similarly distorted Chinese Contact him at the Dept. of Computer Science, Hong Kong Baptist Univ., writing that humans but no machine-com- Hong Kong; [email protected]. putable algorithms could read. Yunhe Pan is a full professor in the Department of Computer Science and president of Zhejiang University, as well as an honorary professor of the Uni- versity of Hong Kong. His research interests include artificial intelligence, computer graphics, and multimedia computing. He received his MS in com- arametric hierarchical knowledge rep- puter science and engineering from Zhejiang University. Contact him at the Presentation enables computer-gener- President’s Office, Zhejiang Univ., Hangzhou, China, 310027; panyh@ zju.edu.cn. ated Chinese calligraphy artwork in a vari- ety of styles—fully automated in real time from a compact set of printed calligraphic inputs. The creative capability of the proposed intelligent system lies mainly in the References huge feasible space available for the simulated analogous reasoning process. Our pro- 1. D.E. Knuth, Tex and Metafont: New Direc- Arcs,” Comm. ACM, vol. 20, no. 2, 1977, pp. tions in Typesetting, Am. Mathematical Soc., 100–106. totype system has generated artwork that can 1979. stand among existing instances, whether real- 7. H.M. Lee, C.W. Huang, and C.C. Sheu, “A istic or completely inventive in appearance. 2. G. Ramalho and J.-G. Ganascia, “Simulating Fuzzy Rule-Based System for Handwritten We are considering several extensions to Creativity in Jazz Performance,” Proc.12th Chinese Characters Recognition Based on our proposed system. We could extend the Nat’l Conf. Artificial Intelligence (AAAI 94), Radical Extraction,” Fuzzy Sets and Systems, 1994, pp. 108–113. vol. 100, nos. 1–3, 1998, pp. 59–70. approach to other languages. We might also add a feedback component to fine-tune the 3. H.A. Simon, “Style in Design,” Spatial Syn- 8. B.A. Yanikoglu and P.A. Sandon, “Recogniz- aesthetic constraints through reinforcement thesis in Computer Aided Building Design, ing Offline Cursive Handwriting,” Proc. learning. Finally, we could capture and C.M. Eastman, ed., Applied Science, 1975. Computer Vision and Pattern Recognition, IEEE CS Press, 1994, pp. 397–403. translate the “psychological” states of other 4. H. Blum, “A Transformation for Extracting media and then link them to the corre- New Descriptors of Shape,” Models for the 9. M. Keane, “Analogical Mechanisms,” Artifi- sponding states in calligraphy—for exam- Perception of Speech and Visual Form,W. cial Intelligence Rev., vol. 2, no. 4, 1988, pp. ple, allowing music to direct the generation Wathen-Dunn, ed., MIT Press, 1967, pp. 229–250. of calligraphy. 362–380. 10. P. Zhu and P.M. Chirlian, “On Critical Point 5. R. He and H. Yan, “Stroke Extraction as Pre- Detection of Digital Shapes,” IEEE Trans. processing Step to Improve Thinning Results Pattern Analysis and Machine Intelligence, of Chinese Characters,” Pattern Recognition vol. 17, no. 8, 1995, pp. 737–748. Letters, vol. 21, no. 9, 2000, pp. 817–825. Acknowledgments 11. S. Xu et al., “Virtual Hairy Brush for Painterly We are grateful to the reviewers whose com- 6. J.E. Bresenham, “A Linear Algorithm for Rendering,” Graphical Models, vol. 66, no. ments have been most useful and encouraging. Incremental Digital Display of Circular 5, 2004, pp. 263–302.

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