Animating Water in Chinese Painting *

Transcription

1 Animating Water in Chinese Painting * YU Jin-hui, YIN Xiao-qin, PENG Qun-sheng (State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou , China) jhyu@cad.zju.edu.cn htt:// Abstract: In this aer we resent a method to animate water in Chinese ainting. Our aroach first detects ositions of water forms in the hand drawn Chinese ainting and synthesizes those forms using a arametric signal rocessing technique. Next, we render water forms using an image based rendering technique to roduce water forms with the loo of Chinese ainting. Finally, water forms are animated in hand drawn environments thus we bring water forms in Chinese ainting to life. Examles given in the aer demonstrate the caability of our method to cature the statistic roerties associated with the samle data and to roduce a variety of water forms for non-hotorealistic animation. Key words: water model; non-hotorealistic animation; comuter animation; Chinese ainting 1. INTRODUCTION Traditional animators have exerienced with various techniques for reroducing well nown ictures on the screen thus creating animations far more sohisticated than those of animated cartoons. In the west, Alexander Petro is nown for the rich, hand-ainted loo of his oil-on-glass animations such as The Cow and The Mermaid. Another examle is Joan Gratz, whose lighthearted film, Mona Lisa Descending the Staircase (1992) deftly morhs through dozens of wors of modern art including Picasso s nudes and Van Gouh s self-ortraits, always maintaining a ainterly quality thans to her innovative clayainting technique. In the Oriental, Chinese animators roduced a number of animations with the loo of Chinese ainting, which are famous in the traditional animation community. Comuter animation is only beginning to catch u to the variety of styles found in traditional and exerimental animation. Non-hotorealistic rendering (NPR) is a ste in the right direction. Most of existing NPR techniques aim at creating still ictures and a few of them can be used to generate non-hotorealistic animations such as imressionist ainting [1,2], en-and-in [3], the style of Dr. Seuss. [4,5] and Cartoon water [6]. Chinese ainting as a traditional art form in China attracted many researchers to attemt to numerically model this beautiful medium using comuter simulations [7,8,9]. Unfortunately, all of them focus on generating still ictures and little effort has been sent to animate objects with the style of Chinese ainting. In this aer we resent a method to animate water in Chinese ainting. It is nown that Chinese ainting is created by use of four main tools including the * PENG Qun-sheng was born in He received his PhD in the School of Comuting Studies from the University of East Anglia, U.K., in He is a Professor and his research interests include comuter grahics, comuter animation and virtual reality.

2 in brush, in stic, in stone and Xuan aer, and Chinese artists have long exlored the richness of in brush in a variety of styles. As a result, there are different visual interretations of water in Chinese ainting and Fig. 1 gives a few examles [10,11]. Fig.1 Examles of water interretations in Chinese ainting After careful observation of those examles we can find that, due to slight shaing of the hand during the drawing rocess, those forms deicting water in the first two ictures are never reeatable in shae but loo statistically similar on the whole, it is ossible for us therefore to regard them as the oututs from stochastic rocesses. According to the theory of signal rocessing, those forms can be synthesized sing arametric methods of signal rocessing, say, signal estimation techniques (As for how to deal with water forms in the third icture in Fig. 1 will be discussed in section 5). Parametric methods of signal rocessing are more aroriately called model-based methods [12], because each technique first assumes a re-secified model set (e.g., all-ole, all-zero, etc) and then estimates the aroriate model arameters. In fact, the model-based aroach consists of three essential ingredients: (1) data, (2) model, and (3) criterion. Once we select the model set, we fit the model (arameter estimatio to the data according to some criterion. The arametric aroach to signal rocessing is best summarized in Fig. 2. y(t) s(t, ) Parameter estimation Signal estimator Fig. 2 Parametric signal rocessing Here we see that once the model set is selected, the estimator is used to obtain the unnown arameters that secify the model. The signal estimate is then constructed using these arameters. There are different techniques for signal estimation and we adot the autoregressive (AR) model aroach, in art because it is simle in structure and comutationally efficient. The remainder of this aer is organized as follows. In section 2 we describe the estimation of AR model arameters using the data acquired from hand drawn water forms in Chinese ainting. Section 3 addresses the main issues in water form synthesis, dynamic control and rendering of water. In Section 4 we give the results by showing a number of examles. Section 5 contains a brief conclusion and discussion of areas for future wor. 2. ESTIMATION OF AR PARAMETERS The AR model is characterized by the difference equation for the inut-outut relationshi x( = a x( n ) + e( n = 1,2,... N = 1 2 where e( is white noise with zero mean and variance σ, the a are nown as the AR arameters. The basic arameter estimation roblem for the AR model is given as the minimum (error) variance solution to 2 E = E e( (2) e (1)

3 where the estimation error is defined by and xˆ ( is the minimum-variance estimate obtained from (1) as e( = x( xˆ( (3) xˆ ( n ) = aˆ = 1 x ( n ) Note that xˆ ( is actually the one-ste redicted estimate based on the ast data samles, hence the oular name linear redictor. The estimator can easily be derived by minimizing the rediction error; e( obtained from (1) as e( = a = 0 x( n ) (4) with a = 0 1 (5) Minimizing (2) with resect to the AR arameters and substituting for e( in the resulting equations, we obtain = 0 aγ xx ( m ) = 0, m=1,2,, and a = 0 1 (6) where γ (m) is the autocorrelation sequence of x(. These are called normal equations. The minimum mean-square xx rediction error is simly min γ (0) a ( ) (7) xx + γ xx = 1 If we augment (7) to the normal equations given by (6), we obtain the set of augmented normal equations, which may be exressed as where 2 σ e Algorithm 2 σ e m = 0 a γ ( m ) = (8) xx 0 > = 0 m 0 = mine for the AR random rocess. The equations can be solved efficiently by use of the Levinson-Durbin [13]. One of the most imortant asects in the use of the AR model is the selection of the order, and much wor has been done by various researchers on this roblem. Exeriment results given in the literature indicate that for small data length, the order of the AR model should be selected to be in the range N/3 to N/2 for good results, where N is the number of the samle data. In our case, the data sequence is usually acquired from the ainting thus its length is not very long, we therefore adot N/3 as the model order. 3. WATER FORM ANIMATION Water form animation involves the water from synthesis, dynamic control and rendering which are the toics of the following subsections. 3.1 Water form synthesis The first ste of water form synthesis is dada acquisition. Given a hand-drawn water in Chinese ainting, we first detect some water forms using the snae algorithm [14] and then ut them into arrays, say, Form(_j (n 0, j 0), where n is oint index in an array and j is array index, resectively. Once the data sequences are acquired, the relevant AR mode arameters can be estimated using the rocedure described in section 2 and water forms can be synthesized using equation (1) with the corresonding AR model arameters estimated. The synthesized water forms SynForm(_j are actually sequences defined on 2D Cartesian coordinate system,

4 where the horizontal axis is n. Those sequences can be used directly to draw water forms on the water surface where water is not moving. While for the moving water, water forms are usually drawn in the shae formed by the artially immersed objects such as roc, boat etc and the water surface, as shown in Fig. 3. In this case, we need to devise seletons using a few control oints defining the shae required, and water forms (synthesized sequences) are drawn on these seletons. Note that in order to mae the resultant water forms loo more natural, we draw the synthesized sequences in the direction of the flowing water, as show in Fig. 4. Fig. 3 Waves near objects Fig. 4 Synthesized wave over a curve 3.2 Dynamic control Dynamic control of water forms aims at creating the illusion of the movement of the water. In the current hand-drawn examles, the movement of water forms is not very violent, thus, their dynamic behavior resemble very much to that of shimmering used in cartoon animation [15], which is a series of cels with varied interretations of required style (as shown in Fig. 5), the cels are then mixed one to another, at random, at the required seed. Fig. 5 Shimmering Note that, in shimmering, the interretations of water waves are comletely indeendent from one frame to the next that the frame coherence is maintained in the distribution of the massive interretations rather than their individual shaes and dynamic movements. Insired by the technique used in shimmering in cartoon, we adot the fowling rocedure to control water forms dynamically: Initialization: 1. Secifying the mean value and variance for the length of water forms; 2. Secifying the density of the water forms; 3. Secifying horizontal distribution; 4. Secifying vertical distribution. For frame t: 1. Generating a osition WtFormP according to the horizontal and vertical distribution; 2. Generating a seleton at length at WtFormP to control the length of the water form; 3. Synthesizing corresonding water form using the AR model. 4. Reeat those three stes until the density of the water form distribution is met. End (of each frame) 3.3 Rendering

5 In order to generate water forms with the style close to Chinese ainting, we use an image-based rendering technique which integrates our early wor, a hysically based brush model [16], with a different mechanism to generate the footrint of the brush with the loo of in brush. Our early brush model maes use of articles within a circle or rectangle to form a footrint, a brush stroe is simulated by emloying a seleton to model the trajectory of the footrint together with a few seleton attributes to control the size and color of the footrint, as shown in Fig. 6. The color of each article in the footrint may vary stochastically to generate a colored brush stroe. Fig. 6 Brush model Clearly, the texture of the footrint contributes very much to the final aearance of the brush stroe, hence, the distribution of ixel color inside the footrint is the ey to determine the loo of the stroe. To generate an in stroe more realistically, we roose two image-based aroaches to create the footrint. In the first aroach, we color the articles inside the footrint using the color iced u randomly from the samle image of the hand drawn brush stroe, this aroach is articularly suitable to generate a stroe with a mean color distribution. In order to coe with the variation of color along the trajectory of the stroe, we adot an alternate aroach described as follows. First, we use the snae algorithm to detect some hand-drawn water forms and tae the data describing those forms as the reference seletons. Next, based on the seletons, we subdivide hand-draw water forms into small segments from which a quadric olygon can be defined to cover the width of the water forms using a simle model. Texture inside each olygon is then maed onto the desired water forms synthesized by the AR model. The maing oeration is reeated in succession for each olygon until the water form is covered fully. 4. RESULTS This section resents a number of examles of water animation with the loo of Chinese ainting. Fig. 7 Comuter generated forms Fig.8 Comuter generated form s Fig.7 is a frame of water surface animation emulating the first icture in Fig.1 by use of the samle data acquired from its hand drawn counterart. In Fig. 8 we show a frame of animation with a loo close to the second icture in Fig. 1. In comarison to water shaes in Fig. 7 where several waves are drawn continuously, water shaes in Fig. 7 are drawn in a discrete manner regarding individual waves (That is, the artist uses two brush stroes to draw

6 each water wave). Thus, we cannot synthesize them directly using the AR model. Our aroach to this roblem is detecting ositions of several water wave tis and utting them into arrays as the samle data, the sequences synthesized by the AR model are now used for controlling ositions of water wave tis rather than for drawing water forms directly. For each ti, we first define two vectors starting from the ti and ointing downward to the left and right sides resectively with small erturbation added to their angles. Using the starting and ending oints of each vector we can generate a slightly bend seleton by adding a control oint below the vector, the seleton is then used to draw in stroe using our brush rendering technique The first icture in Fig. 9 and 10 show two hand drawn environments and we animate water forms corresonding to that in Fig. 7 and 8 by lacing them locally near the objects above the water surface such as rocs, grass, boat etc, resectively. The animated effects loo correct when we lay bac water series generated by our model Fig. 9 Animated water forms in hand drawn environment Fig. 10 Animated water forms in hand drawn environment 5.CONCLUSIONS AND FUTURE WORK In this aer we resented the results of research dealing with non-hotorealistic water animation based on arametric signal rocessing aroach. The advantage of this aroach is that the AR model is able to cature the statistic roerties associated with the samle data, thus we can roduce a variety of water forms for non-hotorealistic animation as long as rovided with aroriate samles and shae visualization mechanisms in the system. Potential alications of our wor are generation of bacgrounds with the style of Chinese ainting in animation, education and entertainment. In the current imlementation, we animate only arts of hand ainted ictures such as water forms. It would be fascinating if we animate not only water, but also other arts in a tyical Chinese landscae ainting such as rocs, trees etc in 3D. To achieve this goal, additional wor need to be done for drawing other objects in 3D and this is a toic for future wor. As for shaes deicting cas in a more violent water movement as shown in the third icture in Fig. 1, the AR model synthesis is not adequate for a faithful recreation of those forms, because some curves in the forms have multile

7 values for a given oint on the horizontal axis, while the samle data and synthesized sequence in the AR model must be single value functions defined on 2D Cartesian coordinates where the horizontal axis is n. Nevertheless, we are still able to synthesize the single value curve deicting the u contour of the cas and the other arts below it can be dealt with using fractal models. This is also a future research wor. REFERENCES [1] Meier, B.J. Painterly rendering for animation. Proceedings of the ACM Comuter Grahics,1996, 477~484. [2] Litwinowiz, R. Processing Images and video for an imressionist effect. Proceedings of the ACM Comuter Grahics, 1997, 407~414. [3] Deussen, O. Strothotte, T. Comuter-generated en-and-in illustrations of trees. Proceedings of the ACM Comuter Grahics, 2000, 1~6. [4] Kalan, M., Gooch, B., Chen, E. Interactive artistic rendering. Proceedings of Non-Photorealistic Rendering and Animation, 2000, 67~74. [5] Kowalsi, M. A., Marosian, L., Northru, J.D., Bourdev, L., Barzel, R., Holden, L.S., Hughes, J. F. Art-based rendering of fur, grass, and trees. Proceedings of the ACM Comuter Grahics, 1999, [6] Yu, J., Xu, X., Wan, H. Peng, Q. A cartoon water model for stereo animation. Journal of Software, 2001, 12(7): 960~966. [7] Strassmann S. Hairy brushes. Proceedings of the ACM Comuter Grahics, 1986, [8] Guo, Q. and Kunii, T.L. Modeling the diffuse aintings of sumei. Modeling in Comuter Grahics, Sringer-Verlag, 1991 [9] Lee, J. Simulating oriental blac-in ainting. IEEE Comuter Grahics and Alications, 1999, 19(3), [ 10] Pu, S.C. Collections of techniques for landscae ainting. Peole s Art Press, (in Chinese) [11] Wu, Y. M. Fundamental techniques of Chinese ainting. Chaohua Press, Beijing, (in Chinese) [12] Candy, J. Signal rocessing: The model-based aroach. New Yor: McGraw-Hill, [13] Ljung, L., System Identification: Theory for the User, Prentice-Hall, 1987, [14] Yuen P.C., Wong, Y.Y, Tong. Contour detection using enhanced snaes algorithm. Electronics Letters, 1996, 32(3), [15] White, T. The animator's boo. Watson-Gutill, New Yor, [16] Yu, J., Zhang J. and Cong, Y. A Physically-based brush-en model. Journal of Comuter-Aided Design & Comuter Grahics, 1996, 8(4): (in Chinese) [10].., [11] [16].., 1996, 8(4): 2541~245

8 CAD&CG TP391