Physical Model to Achieve Virtual Mezzotint

Vol. 3 IPSJ Digital Courier May 2007 Regular Paper Physical Model to Achieve Virtual Mezzotint

Daisuke Tasaki,†1,†2 Megumi Katou,†3 Shinji Mizuno†4 and Minoru Okada†2

The authors propose a method of producing virtual mezzotint using a physics-based rendering approach. Mezzotint is a traditional copperplate printing technique. An important characteristic is its gradations from black to white. This is acquired in three phases during the plate-making process, i.e., by roughening, scraping, and burnishing. Numerous dots and burrs are created with a rocker in the roughening phase over the entire surface of the copper plate to obtain black areas in the print. The burrs are removed in the second phase with a scraper to yield halftones. The plate surface is ﬁnally polished with a burnisher in the last phase to produce the white areas. A method of simulating these phases and physical phenomena is discussed in this paper to make mezzotint enjoyable even for beginners and children. Zigzag-stroke patterns and paraboloidal-dot models are applied to the rocker to simulate the roughening phase. Reducing and smoothing models are applied to the scraper and burnisher to simulate the scraping and burnishing phases. The feasibility of the proposed method is demonstrated by observing and comparing actual and virtual plate surfaces with determined patterns and actual pieces of handcrafted work.

black to white. The plate’s surface needs to 1. Introduction go through three phases to acquire the effect of Mezzotint 6),8) was developed as a traditional mezzotint, i.e., roughening, scraping, and bur- technique of copperplate printing 10),15) in the nishing. A comb-like steel tool called a rocker mid-17th century. It has the potential to ac- is used in the roughening phase to create many quire various gray tones, as shown in Fig. 1.It dots on the plate. Each dot has burrs that are was utilized industrially to republish portraits raised above the surface of the plate. As these and duplicate oil paintings in the 19th century. dots and burrs hold ink, the resulting print It has achieved recognition for its artistic quali- has a black effect, as shown in Fig. 1 (rough- ties since the early 20th century, and has hence ened portions). The burrs are removed in the become known as a fine-art technique. second phase, using another steel tool called There are various kinds of copperplate print- a scraper to control the remaining ink around ing techniques apart from mezzotint, and these them. The scraped portions produce a halftone generally consist of four processes: (a) mak- effect in the print, as shown in Fig. 1 (scraped ing the plate, (b) applying ink to it, (c) wip- portions). If the artist wants lighter tones, as ing it, and (d) pressing it, as shown in Fig. 2. shown in Fig. 1 (burnished portions), the plate Tasaki, et al. has already proposed a method is polished using another steel tool called a bur- of non-photorealistic rendering (NPR) 21) in the nisher. Although these three phases result in computer graphics (CG) field to simulate dry- a variety of gray tones, they are very oner- point, which is another copperplate printing ous and laborious processes even for mezzotint technique. Mezzotint is categorized as a kind specialists. For example, it takes about 30–40 of the plate making methods in a more limited sense. While a drypoint print consists of many black lines achieved by incising the plate with a hard sharp point, an important characteristic of mezzotint is its smooth gradations from

†1 Research Fellow of the Japan Society for the Pro- motion of Science †2 Graduate School of Information, Production and Systems, Waseda University Fig. 1 A part of actual mezzotint print by K. †3 Faculty of Fine Arts, Kyushu Sangyo University Hasegawa 6) (left: magniﬁed 1/6 times, upper †4 Information and Media Center, Toyohashi Univer- right: exact size, lower right: diagram of con- sity of Technology stituents).

244 Vol. 3 Physical Model to Achieve Virtual Mezzotint 245

is a method of plate making for copperplate printing have been reported by Leister 9), Ohno, et al. 11), and Pnueli, et al. 14) These studies have been based on the fact that engraved lines can be approximated only with lines, and they have focused their strategies on how to gener- (a) Plate making (b) Applying ink ate line patterns geometrically by imitating the look of engraving. Ostromoukhov 12) described another method of synthesizing a print from an engraving based on a plate model. Although the model could imitate engraved lines, it did not simulate the actual process. Tasaki, et al. reported a model-based method of virtual engraving 20) based on the idea of a method of (c) Wiping (d) Pressing virtual drypoint, which will be discussed in Sec- Fig. 2 Copperplate-printing processes. tion 3. The impression given by mezzotint prints is similar to the effect of halftoning or dithering. days to roughen a 50 × 65 cm plate. Therefore, Ostromoukhov, et al. 13) described a method of the purpose of this research was to make mez- dithering by using various space-filling curves zotint more safely and easily available with CG and Delauney triangulation, and they claimed techniques to a much broader range of novices that their results looked like a mezzotint print and children who were not specialists. It was in terms of appearance. These previous meth- therefore important to simulate the roughen- ods of copperplate printing used an appearance- ing, scraping, and burnishing procedures and based rendering (ABR) approach. Tasaki, et the physical phenomena of mezzotint to render al. proposed a pipeline for modeling and ren- images that looked like mezzotint prints. dering virtual drypoint, which is also a method An approach using a physical model corre- of plate making for copperplate printing, with sponding to the actual mezzotint process is pro- a physics-based rendering (PBR) approach 21). posed in this paper. Zigzag-stroke patterns It is expected to attain a similar appearance to and paraboloidal-dot models are introduced in an actual drypoint print with physical fidelity the roughening phase to simulate the manipu- to the original because the PBR method sim- lation of the rocker and its interaction with the ulates the production procedure and the phys- plate. A reducing model is applied to simulate ical phenomena that occur during the actual the scraping phase and a smoothing model is drypoint process. The inputs to incise the vir- applied to simulate that for burnishing. The tual plate with their method are stroke data be- feasibility of the proposed method is demon- cause a drypoint print can be represented with strated by observing and comparing actual and lines. In contrast, the target of this research virtual plate surfaces with determined patterns was mezzotint, which can be represented with and pieces of handcrafted work. The actual areas. Therefore, the inputs for scraping and pieces were made by one of the authors, who burnishing the virtual plate are region images. is also a copperplate-printing specialist. Tasaki, et al. also proposed methods of virtual mezzotint 22),23). They introduced a model 2. Related Works of random dots for the roughening phase, an NPR has been extensively studied 5),17),18) in evenly reducing model for the scraping phase, CG research fields, and it has been applied to and an evenly smoothing model for the burnish- various applications such as CG movies. NPR ing phase. Their observation and analysis were techniques have attracted many viewers and insufficient because they used a book-scanned CG researchers and most of these have focused mezzotint print as a reference in their exper- on line-art illustrations 3),24), oil paintings 7), iments. We improved on the studies done by and watercolors 2). A few research groups have Tasaki, et al. 22),23) by using detailed compar- concentrated on copperplate printing as an- isons and experiments with actual handcrafted other way of synthesizing artistic NPR images. mezzotint prints produced by a copperplate- Some studies on simulating engraving, which printing specialist to obtain the virtual mez- 246 IPSJ Digital Courier May 2007 zotint results. Sourin 16) proposed a functionally based rep- resentation to express the shape of the plate. Its shape with the method we propose is expressed with a height field. It is a convenient and straightforward way of simulating the shape of the plate and the behavior of the ink in all the production processes. Bosch, et al. proposed a method of rendering scratches 1) on the surface of metals by computing the Bidirectional Reflection Distribution Function based on mea- surements of actual scratches. As their model Fig. 3 Overview of copperplate printing. would also be useful for our system to render the shape of the plate’s surface more accurately, we intend to use it in future work. 3. Physical Models of Mezzotint The pipeline for virtual copperplate printing proposed by Tasaki, et al. 21)∼23) is illustrated in Fig. 3. It is based on intermediate expressions that uniformly deal with various kinds of devices as input. The pipeline can synthesize a virtual copperplate print from an intermediate (a) Rocker once it can be created from the inputs. The plate-making process for mezzotint consists of three phases: roughening, scraping, and burnishing. This section describes improved models for the three phases. Wiping and pressing models are also described. Note that the shape of the copperplate surface is expressed with a height field: P = {p(X) | X =(i, j) ∈N2}. (1) 3.1 Physical Model for Roughening Arockerintheshapeofacombwithmany small teeth, as shown in Fig. 4 (a), is placed on (b) Scraper (upper) and burnisher (lower) the copper plate, and it is rocked zigzag or back- Fig. 4 Tools for plate-making process used in and-forth. It produces many microscopic dots mezzotint techniques on metric scale. over the entire surface of the plate. A zigzag- stroke pattern, which consists of many strokes, as shown in Fig. 5, was introduced to simulate rocking. This was based on the same concept as the mark-making primitive proposed by Sousa, 17) Q Q et al. . Each stroke is defined by i and i−1 in this paper. The i-th Q is expressed as: V W Q X v w , i = + i |V | + i |W | (2) Fig. 5 Zigzag-stroke pattern for rocking. v =0, (3) µ ,σ2 0 N( v v) stands for the normal distribution of v v µ ,σ2 , µ i = i−1 +N v v (4) the stride for each stroke with average v and 2 i 2 standard deviation (SD) σ .N(µ ,σ )also wi =(−1) N µ ,σ , (5) v w w w w stands for the normal distribution of the width X where represents the beginning point for the of each stroke. Actual rocking is repeated lon- V zigzag pattern, is its direction and length, gitudinally, latitudinally, and diagonally in two W V and specifies the direction orthogonal to . directions, until the plate surface is evenly filled Vol. 3 Physical Model to Achieve Virtual Mezzotint 247

Fig. 6 Dot shape by rocker tooth. Fig. 8 Reducing model for scraping.

Equation (7) is approximately applied under a 2-D cross-sectional area, and rb is determined from this equation. rb ar2 − b dr =0, (7) 0 b √ r 3 r . b = a = 3 i (8) Fig. 7 Measurement of actual rocker. 3.2 Physical Model for Scraping A scraper that looks like a blade, shown with a vast amount of dots. at the top of Fig. 4 (b), is utilized to cut the The rocker during each stroke makes a num- burrs away during the actual scraping phase. ber of dots according to Nt, which is engraved A lighter gray tone appears in the resulting on the side of the actual rocker and indicates print when the plate is scraped more because the number of teeth per inch (#65, #85, and the burrs hold less ink. Scraping in the vir- #100 are commonly used). Nt is also utilized tual phase is expressed by reducing the plate for the virtual rocker to calculate how many heights, as illustrated in Fig. 8.Thisopera- dots will be incised by a stroke. When the tion is completed on the basis of the region rocker produces a dot, the plate material rises image, which specifies the area and the level around it, and this is called a burr. These tobescrapedwithanintegervalue. The dots and burrs hold the ink during the apply- highest plate value, pmax,inregionR = ing ink, wiping, and pressing processes. The X =(i, j) ∈N2 is calculated as: shape of a dot incised by a virtual-rocker tooth pmax =maxp(X). (9) is illustrated in Fig. 6. Thisisbasedonthe X∈R paraboloidal model for drypoint 21),andisex- Scraping the plate is expressed by reducing the pressed as: plate’s height, p(X), from pmax close to 0, as: h ar2 − b ≤ r ≤ r , p X {p X ,αp f X } , = (0 i) (6) ( )=min ( ) max s( ) (10) D b where α is the reduction rate. There are irreg- a = ,b= DF + f, r = , R2 i a ularities during the actual scraping because of D R fluctuations in hand movements. The function, where indicates the depth and indicates f X the radius of an incised dot. Their values were s( ), is a fractal component that expresses these irregularities. Although there are many measured against a digital photo of an actual f X rocker (N = 85), as shown in Fig. 7. f rep- kinds of fractal algorithms, function s( )is t generated by a method of two-dimensional mid- resents fluctuations in manual force, and fol- 4) σ ,σ2 point displacement with SD fs; this is one lows a normal distribution, N(0 r ). Although F represents the rocker pressure, this has not of the most straightforward fractal methods. yet been considered and is fixed at the present These calculations with Eqs. (9) and (10) are stage. Burrs formed around dots are also ex- iterated several times as specified by the region pressed with the drypoint model. The domain image. 3.3 Physical Model for Burnishing of a burr, (ri

der heavy pressure during the pressing process was approximated with a random walk model with the former methods. The spreading ink affects the resulting print due to linear interpo- lation between the paper and the ink according to the latter’s thickness. Two improved models were applied to the pressing process. The first was an ink-spread model that produced many unexpected white dots in the resulting Fig. 9 Smoothing model for burnishing. print. A simple Gaussian filtering model with a mask size of Ng was utilized to separate prob- Fig. 4 (b), is utilized to polish the plate’s sur- lems from artifacts. face during the actual burnishing phase. The The second model was for paper deformation. concept of virtual burnishing is comparable to Tasaki, et al. 19) stated that a characteristic of virtual scraping. The virtual burnisher refills copperplate prints was deformation in the pa- the dents with burrs instead of cutting them per sheets according to the plate’s shape dur- away. This operation is expressed by smoothing the pressing process under heavy pressure, ing the plate’s height, as illustrated in Fig. 9, and this affected their appearance. They in- and is treated based on the region image as well vestigated the properties of the paper after the as the virtual scraping mentioned in Section 3.2. pressing process in detail. They then concluded The average plate height in region R is calcu- that these properties could be achieved by ex- lated as: pressing the deformation with a combination of macroscopic and microscopic shapes. The p 1 p X , ¯ = N ( ) (11) macroscopic shape of the paper represents de- X∈R formation that is caused by the plate’s shape where N is the number of plate cells in R.Bur- as: nishing the plate’s surface is expressed by re- S(X)=− (p(X)+Pth) . (13) ducing the plate’s height from p(X)closeto¯p where Pth stands for the thickness of the cop- as: per plate. The microscopic shape, T (X), rep- p (X)=(1− βfb(X))p(X)+βfb(X)¯p, resents slight bumps on the paper’s texture as: (12) T (X)=Tσ(X)Tmax (1 − D(X)) , (14) where β is the smoothing rate. The function, where Tσ(X) is a bump map expressing irregularities on the paper’s surface, and this is gener- fb(X), is a fractal component to express irregularities in burnishing, in the same way as the ated with a fractal method of two-dimensional 4) T scraping operation mentioned above, and it is mid-point displacement . max represents the generated by a method of two-dimensional mid- amplitude of the bumps. D(X) denotes the ra- 4) tio of deformation: point displacement with SD σfb.Thesecal- culations with Eqs. (11) and (12) are iterated S(X)+Pth − Slow D(X)= , (15) several times as specified by the region image. Shigh − Slow 3.4 Physical Model for Wiping Pro- where Shigh and Slow are values that restrict cess the effect of microscopic deformation near the 21) The wiping process proposed by Tasaki, plate’s surface. Finally, the shape of the de- et al. is briefly introduced in this section where formed paper, S(X), is expressed as: the user wipes a virtual cloth interactively to S (X)=S(X)+T (X). (16) determine the amount of the ink remaining on the surface of the virtual copperplate. The sys- This gives the virtual print a slight shading ef- tem pre-calculates the lowest height curve for fect, which can be observed in an actual mez- the wiping cloth based on a simple spring model zotint print. before interactive operation occurs. This calcu- 4. Experiments and Discussion lation is iterated until the values are converged. 3.5 Physical Model for Pressing Pro- The physical models of mezzotint proposed cess in Section 3 were implemented on a computer. The ink-spreading phenomenon occurring un- Table 1 lists the values of the parameters used Vol. 3 Physical Model to Achieve Virtual Mezzotint 249

Table 1 Values of parameters used in models. Parameters Values Radius of incised dot, R 64.9 µm† Depth of incised dot, D 37.1 µm† ‡ SD for depth of incised dots, σr 2.0 µm † Number of teeth on rocker, Nt 80 †‡ Width of zigzag stroke, µw 17.5 µm ‡ SD for zigzag stroke width, σw 1.0 µm †‡ Stride of zigzag stroke, µv 0.3 µm ‡ SD for zigzag stroke stride, σv 0.1 µm Reduction rate for scraping, α 0.9‡ ‡ SD for scraping fluctuations, σfs 0.01 Smoothing rate for burnishing, β 0.9‡ ‡ SD for burnisher fluctuations, σfb 0.01 Plate thickness, Pth 800 µm Amplitude of paper bumps, Tmax 30 µm Higher limit for deforming ratio, Shigh −127 µm Lower limit for deforming ratio, Slow 128 µm Fig. 10 Comparison of actual and virtual mezzotint Mask size for Gaussian filter, Ng 170 µm patterns (actual: lower left triangle, virtual: † upper right triangle in small square regions, The dagger indicates that the value has been deter- magnified 0.5 times). mined by actual measurement, and the others have been determined by experiments. The double dagger ‡ indicates that the value depends on the artist. study). 4.1 Experiment with Predetermined in the experiments. The dagger † indicates that Phantom Pattern the value has been determined by actual mea- An experiment with a predetermined phan- surement, and the others have been determined tom pattern was first conducted to paramet- by trial and error. The double dagger ‡ indi- rically indicate how effective the scraping and cates that the value depends on the artist be- burnishing operations were. Note that Is spec- cause this has been determined based on his ifies the index for scraping and Ib specifies or her work. Therefore, these values are sta- that for burnishing. These symbols in this sec- ble while simulating touches by the same artist. tion correspond to the ones in Fig. 10. Fig- The plate has a resolution of 2,540 dpi to repre- ure 12 (a) is an actual mezzotint print consist- sent the shape of the incised dots in detail. For ing of 5 × 5 (= 25) patterns, whose differences example, an 8.5 × 6.6 cm image is composed of are caused by the varying amounts of scrap- 8,500 × 6,600 pixels. Various 3-D images rep- ing and burnishing. Although artists can ob- resenting plate surfaces rendered with OpenGL tain more than 25 gray tones in their work in are also presented in this section to indicate the practice, it is too difficult to produce these pat- flexibility of the proposed method. terns with various tones. The usual combina- A copperplate-printing specialist, who is one tion of scraping and burnishing done by cop- of the authors, created two actual mezzotint perplate specialists is on the path (Is,Ib)= plates and took prints from them in the first (0, 0) → (1, 0) → (2, 0) → (3, 0) → (4, 0) → stage of the experiments. The first consisted (4, 1) → (4, 2) → (4, 3) → (4, 4). Because it is of systematically determined phantom patterns difficult to only control the tones by burnish- to confirm the capabilities of the proposed ing, it can produce prints that are unexpect- method. The roughening phase is generally edly light in tone. Almost artists therefore pro- repeated until the plate surface is uniformly duce most tones only by scraping. However, roughened, and the gray tones are controlled it is important to use all combinations because by scraping and burnishing. We therefore con- the proposed method is based on a PBR ap- centrated on the effect of scraping and burnish- proach. We synthesized 17 × 17 (= 289) pat- ing in the experiments. The second was an ac- terns for the experiment to interpolate and ex- tual handcrafted piece of work to demonstrate trapolate the domain of actual patterns. Fig- that the method could be applied to practical ure 12 (b) is a virtual mezzotint selected from use. The intermediate expressions for scraping 25 patterns obtained from all the results. Its and burnishing operations in the experiments average light tone matches that of the actual were displayed with a color bar for better visu- one, and the patterns have been tessellated to alization, as shown in Fig. 11 (17 tones in this fit together. The region image for scraping is 250 IPSJ Digital Courier May 2007

(a) Actual (b) Virtual (c) Region image (d) Region image mezzotint mezzotint for scraping for burnishing Fig. 11 Color bar to indicate Fig. 12 Experimental results with predetermined phantom pattern scraping and burnishing levels. (original size: 10×10 cm, magniﬁed 0.2 times).

(a) Is =0,Ib =0 (b) Is =4,Ib =0 (c) Is =0,Ib =4 (d) Is =4,Ib =4 Fig. 13 Surface of actual plate observed through loupe (magniﬁed ×3.5, upper right: ×1.0).

(a) Is =0,Ib =0 (b) Is =4,Ib =0 (c) Is =0,Ib =4 (d) Is =4,Ib =4 Fig. 14 Surface of virtual plate (magniﬁed ×3.5, upper right: ×1.0).

(a) Is =0,Ib =0 (b) Is =4,Ib =0 (c) Is =0,Ib =4 (d) Is =4,Ib =4 Fig. 15 Actual printed pattern (magniﬁed ×3.5, upper right: ×1.0).

(a) Is =0,Ib =0 (b) Is =4,Ib =0 (c) Is =0,Ib =4 (d) Is =4,Ib =4 Fig. 16 Virtual pattern (magniﬁed ×3.5, upper right: ×1.0). Vol. 3 Physical Model to Achieve Virtual Mezzotint 251

(a) Part of actual handcrafted mezzotint (b) Part of virtual hancrafted mezzotint (Original size: 8.5×6.6 cm, ROI size: 7.5×6.6 cm, (Original size: 8.5×6.6 cm, ROI size: 7.5×6.6 cm, exact size created by one of the authors) exact size)

(c) Region image for (d) Region image for (e) Surface of actual plate (f) Surface of virtual plate scraping burnishing with slight inking with slight inking Fig. 17 Comparison of actual and virtual mezzotints using hancrafted work.

(a) Photograph (b) Virtual mezzotint work (c) Region image for (d) Region image for scraping burnishing Fig. 18 Experimental results with photograph (size: 6.8×6.8 cm, magniﬁed 0.5 times).

(a) CG image (b) Virtual mezzotint work (c) Region image for (d) Region image for scraping burnishing Fig. 19 Experimental results with a CG image (size: 3.4×3.4 cm, exact size). 252 IPSJ Digital Courier May 2007 shown in Fig. 12 (c) and that for burnishing is trast than the actual one, comparing the ex- in Fig. 12 (d). Actual and virtual tones can si- perimental results with the phantom patterns multaneously be compared in Fig. 10 by tiling (Fig. 12 (a) and Fig. 12 (b)). A slight oil slick re- up the triangular regions for them. The states mained on the high-contrast portions after the of the actual plate’s surface can be observed actual wiping process, and created a half-tone through a loupe, as shown in Fig. 13.The effect in the print. The phenomenon caused by loupe has an aluminum plate with a square the oil slick has not yet been modeled in the pro- hole in its center and metric scales are arranged posed method, and this can be approximated by around the hole. Figure 14 compares the manually controlling the contrast. As the inter- states of the virtual plate’s surfaces with the face for the virtual-wiping process is poor, the actual ones. Figure 15 shows the state of an process is done by evenly bearing the virtual actual printed pattern and Fig. 16 shows that wiping cloth down on the plate. The interface of a virtual pattern. should therefore be improved to enable users to 4.2 Practical Experiment intuitively control the amount of wiping. Some The results of a practical experiment using highlighted lines can be observed in Fig. 13, es- an actual mezzotint are presented in Fig. 17. pecially in Fig. 13 (a). These were caused by Its original size in (a) is 8.5 × 6.6 cm, and it has the differences in force during rocking. Vari- been trimmed to demonstrate its actual size on ations in force during operation have not yet this paper. The regions to generate the im- been considered in the proposed method. ages for scraping and burnishing in Fig. 17 (c) The virtual print in Fig. 17 (b) appears sim- and Fig. 17 (d) have been manually and sub- ilar to the actual one in Fig. 17 (a), compared jectively segmented referring to the gray tones to the results of the practical experiment, al- of the actual print with image processing soft- though there is the same problem with con- ware (Adobe Photoshop), and the levels have trast. The region images are also not opti- been defined on the basis of the results of the mized. All the region images used in the ex- phantom experiment. A virtual mezzotint work periments were created manually and subjec- was obtained with the proposed method on this tively. One purpose of the proposed method basis, as shown in Fig. 17 (b). Figure 17 (e) was to establish a way of simulating the cre- shows the state of the actual plate surfaces and ation of a mezzotint with the region image, i.e., Fig. 17 (f) shows that of the virtual after the an intermediate expression. Thus, how to make pressing process. These states can clearly be region images fit user or artist sensibilities is a observed because a slight amount of ink remains topic for future study. Figure 18 and Fig. 19 on the plate even after cleanup. have other examples whose region images have 4.3 Discussion been generated by mainly utilizing the ‘Magic The difference in tones caused by scraping Wand Tool’ in Photoshop. The scraping regions and burnishing can be macroscopically seen in to be acquired are first determined according the experimental results presented in Fig. 10 to the required gray tones based on the re- and Fig. 12. Differences in touches can be sults mentioned above. The burnishing regions microscopically observed as differences in the are also determined to emphasize the main ob- maximum and minimum gray levels. The tops jects in the image. This gives some indication of the burrs have been flattened by scraping, of the possibility of automatically applying our and the area interacting with the wiping cloth method to various kinds of inputs. increases during the wiping process, as shown The experiments were done with a computer in Fig. 13 (b) and Fig. 14 (b). However, ink still running PowerPC G5 (2.5 GHz and dual CPU) remains in the incised dots. Therefore, the re- and 2.5 GBytes of memory with C language. It sulting print is high in contrast, as shown in took about 2.5 hours to synthesize the virtual Fig. 15 (b) and Fig. 16 (b). However, the plate’s mezzotint (Fig. 17 (b)), i.e., roughening took surface has been polished by burnishing to re- 88.0 [sec], scraping took 200.3 [sec], burnishing fill the burrs into the incised dots, as shown in took 173.4 [sec], wiping took 3,723.4 [sec] (about Fig. 13 (c) and Fig. 14 (c). There is no dispro- 1 hour), and pressing took 56.3 [sec]. However, portionate amount of ink in this case as there it took about 2 weeks to create the actual mez- is in scraping. Therefore, the resulting print zotint work (Fig. 17 (a)). The proposed method is low in contrast, as shown in Fig. 15 (c) and is therefore able to remarkably reduce the time Fig. 16 (c). The virtual print has more con- required. However, it still took a long time to Vol. 3 Physical Model to Achieve Virtual Mezzotint 253 calculate the shape of the wiping cloth, and this 3) Elber, G.: Interactive Line Art Rendering of is the main bottleneck impeding practical use in Freeform Surfaces, Computer Graphics Forum, the future. Vol.18, No.3, pp.C–1–12 (1999). 4) Fournier, A., Fussell, D. and Carpenter, L.: 5. Conclusion Computer Rendering of Stochastic Models, A physics-based method of virtual mezzotint Comm. ACM, Vol.25, No.6, pp.371–384 (1982). was proposed in this paper corresponding to 5) Gooch, B. and Gooch, A.: Non-Photorealistic the actual mezzotint process, which consists Rendering, A K Peters, Ltd. (2001). 6) Hasegawa, K.: The Modern Japanese Print of three phases: roughening, scraping, and Artists Series Kiyoshi Hasegawa, Reifu Shobo burnishing. A zigzag-stroke pattern and a (1994). paraboloidal-dot model were applied to roughen 7) Hertzmann, A.: Painterly Rendering with the plate’s surface with a virtual rocker. A re- Curved Brush Strokes of Multiple Sizes, Proc. ducing model was introduced that used a vir- SIGGRAPH ’98, pp.453–460 (1998). tual scraper. A smoothing model was intro- 8) Leaf, R.: Etching, Engraving and Other In- duced to burnish the plate’s surface with a vir- taglio Printmaking Techniques, Dover Publica- tual burnisher. These models accomplished the tions (1984). effect of gradation, which is an important char- 9) Leister, W.: Computer Generated Copper acteristic of mezzotint. The authors demon- Plates, Computer Graphics Forum, Vol.13, strated the effects of the proposed method by No.1, pp.69–77 (1994). observing and comparing actual and virtual 10) Luijten, G.: Rembrandt’s Etchings, Waanders plate surfaces with systematically determined Printers, Zwolle (2000). patterns and a practical piece of work that had 11) Ohno, Y. and Boh, A.: Interactive Portrait been created by a copperplate-printing special- Generating Technique for Intaglio Printing (in Japanese), IPS. Japan SIG Notes, No.92–CG– ist. The synthesis of a virtual mezzotint from 58, pp.89–96 (1992). an input image was used to demonstrate how 12) Ostromoukhov, V.: Digital Facial Engraving, scraping and burnishing regions could be used Proc. SIGGRAPH ’99, pp.417–424 (1999). as intermediate expressions. 13) Ostromoukhov, V. and Hersch, R.D.: Stochas- We intend to improve the model for wiping tic Clustered-dot Dithering, J. of Electronic and pressing processes in future work to take Imaging, Vol.8, No.4, pp.434–445 (1999). i the effect of oil slicks into consideration to ac- 14) Pnueli, Y. and Bruckstein, A.M.: Dig Durer¨ – quire better impressions. The coloring model a Digital Engraving System, The Visual Com- is simply approximated with a linear interpola- puter: Int’l J. of Computer Graphics, Vol.10, tion between paper and ink colors. It should be No.5, pp.277–292 (1994). improved with various kinds of non-linear meth- 15) Slooten, E.O., Holtrop, M. and Schatborn, P.: ods to acquire more accurate impressions. The The Rembrandt House, Waanders Publishers, wiping process should be improved so that it Zwolle (1991). calculates the shape of the wiping cloth more 16) Sourin, A.: Functionally Based Virtual Em- quickly in practical use. A more accurate bossing, The Visual Computer, Vol.17, No.4, pp.258–271 (2001). method of rendering is required for better vi- 17) Sousa, M.C. and Buchanan, J.W.: Computer- sualization. A pressure sensitive stylus to con- Generated Graphite Pencil Rendering of 3D struct a user-friendly interface needs to be uti- Polygonal Models, Computer Graphics Forum, lized to control the amount of scraping, bur- Vol.18, No.3, pp.195–207 (1999). nishing, and wiping. 18) Strothotte, T. and Schlechtweg, S.: Non- References Photorealistic Computer Graphics; Modeling, Rendering and Animation, Elsevier Sci. (2002). 1) Bosch, C., Pueyo, X., Mérillou, S. and 19) Tasaki, D., Katou, M., Mizuno, S. and Okada, Ghazanfarpour, D.: A Physically-Based Model M.: A Study on Wiping and Paper Deform- for Rendering Realistic Scratches, Computer ing for Virtual Copperplate Printing, Proc. Vi- Graphics Forum, Vol.23, No.3, pp.361–370 sual Computing Workshop 2005 in Yamaguchi, (2004). No.10, 6 pages (2005). 2) Curtis, C.J., Anderson, S.E., Seims, J.E., 20) Tasaki, D., Mizuno, S. and Okada, M.: A Fleischer, K.W. and Salesin, D.H.: Computer- Study for Virtual Copperplate Printing and Generated Watercolor, Proc. SIGGRAPH ’97, Its Applications to Drypoint and Engraving, pp.421–430 (1997). Information Technology Letters, Vol.3, No.LJ- 254 IPSJ Digital Courier May 2007

003, pp.209–212 (2004). Shinji Mizuno received his 21) Tasaki, D., Mizuno, S. and Okada, M.: Virtual B.S., M.S., and Ph.D. degrees Drypoint by a Model-driven Strategy, Com- in Information Engineering from puter Graphics Forum, Vol.23, No.3, pp.431– Nagoya University in 1993, 1995, 440 (2004). and 1998, respectively. He is 22) Tasaki, D., Mizuno, S. and Okada, M.: Model- currently an Assistant Professor driven Virtual Mezzotint Techniques, Short in the Information and Media Presentations of Eurographics 2005, pp.29–32 Center of the Toyohashi University of Tech- (2005). nology. His research interests include com- 23) Tasaki, D., Mizuno, S. and Okada, M.: Virtual puter graphics, image processing, and informa- Mezzotint using a Model-driven Strategy, Proc. SIGGRAPH ’05 Posters, 1 page (2005). tion technology in agriculture. 24) Veryovka, O. and Buchanan, J.: Comprehen- sive Halftoning of 3D Scenes, Computer Graph- Minoru Okada received his ics Forum, Vol.18, No.3, pp.C–13–22 (1999). B.S.E.E. and Ph.D. degrees in 1984 and 1992 from Nagoya In- (Received July 28, 2006) stitute of Technology, Japan and (Accepted February 1, 2007) Nagoya University, Japan, re- (Released May 9, 2007) spectively. From 1988 to 1990 he was a Research Fellow of the Daisuke Tasaki went on to Japan Society for the Promotion of Science. the Master Course of Graduate Since 1988, he had been with Nagoya Uni- School of Information, Produc- versity, and since 1999, he was with Chubu tion, and Systems of Waseda University, Japan. Since 2003, he is a Pro- University, Japan with comple- fessor in the Graduate School of Information, tion of the Junior grade at Production and Systems, Waseda University, Chubu University, Japan. He Japan. During 1995–1996, he was a Visiting has been a Doctoral Candidate in the Grad- Associate Professor in the Department of Elec- uate School of Information, Production, and trical and Computer Engineering in the Uni- Systems of Waseda University, and also a Re- versity of Michigan, on leave from Nagoya Uni- search Fellow of the Japan Society for the Pro- versity. His research interests are in the areas motion of Science since 2005. His research in- of pattern recognition and media understand- terests include computer graphics and pattern ing, computer graphics, and intelligent media recognition, especially non-photorealistic ren- computing. He co-authored books, “Progress dering with physical models. He is a member of in Handwriting Recognition” and “Automatic the IPS Japan, IEICE Japan, and ACM SIG- Bankcheck Processing”, World Scientiﬁc Publ. GRAPH. Co. He is a member of ACM SIGGRAPH, IEEE CS (Senior), Eurographics, IEICE Japan, Megumi Katou received her IPS Japan and IIEE Japan. B.F.A. in 1998 and her M.F.A. in 2000 both from Kyushu Sangyo University. She has been on the Faculty of Fine Arts of Kyushu Sangyo University since 2000. Her research interests include ﬁne arts, especially copperplate printing and its possibilities for expressiveness. She is a member of the Japan Print Association and the Kyoto Print Exhibition Executives.