A Method for Generating Pointillism Based on Seurat's Color Theory

Junichi Sugita†,†† and Tokiichiro Takahashi†† (member)

Abstract We propose a method for generating pointillistic style images from input image considering the features of Seurat's pointillism. Georges-Pierre Seurat is a pioneer and prime exponent of neo-impressionist. He established a technique called pointillism based on scientific color theory. There are three important features of Seurat's pointillism: optical mixture, complementary color contrast and halo effect. The most important feature is the optical mixture. To implement the optical mixture faithfully, we present a pointillistic halftoning method for color halftoning on random dots by utilizing a spatial data structure of boundary sampling algorithm. In addition, we implement complementary color contrast and halo effect according to actual Seurat's painting steps.

Keywords: Non-photorealistic rendering, error diffusion, pointillism, boundary sampling, optical mixture, Georges Seurat.

1. Introduction

Georges-Pierre Seurat (1859-1891) is a pioneer, and prime exponent of "neo-impressionism". He established a painting technique called "pointillism" in which small and distinct dots of pure colors are applied in order to form a picture, instead of long strokes. One of the most important features of pointillism in neo-impressionism is based on the color theory such as optical mixture, complementary color contrast, and halo effect. Seurat applied the color theory to color arrangements particularly.

Fig.1 (a) is the most famous work of Seurat, entitled Fig.1 Seurat's work, "Sunday afternoon on the island of La "Sunday afternoon on the island of La Grande Jatte". Grande Jatte". According to the analysis on Seurat's work1)2), important characteristics of Seurat's pointillism are appeared in this work, and summarized as follows. (1) Pointillist painting: As shown in Fig.1 (a), pointillism is formed by small and distinct dots of pure colors instead of long strokes. (2) Use of primitive colors: 11 primitive color pigments from tubes are used without mixing them on his palette (Fig.2) for avoiding the reduction of saturation. Fig.2 Seurat's pallet. (3) Control of luminance by white pigment: Only white pigment is mixed to each color on his pallet Received March 11, 2013; Revised June 25, 2013; Accepted July 31, 2013 † Faculty of Healthcare, Tokyo Healthcare University in order to control the luminance as shown in Fig.2. (3-11-3 Setagaya, Setagaya-ku, Tokyo 154-8568, Japan) (4) Optical mixture is a visual effect of color fusion. †† School of Science and Technology for Future Life, Tokyo Denki Fig.1 (b) is an example of optical mixture. Juxtaposed University (5 Senju Asahi-cho, Adachi-ku, Tokyo 120-8551, Japan) vivid color dots cause similar spectra of colors

317 ITE Trans. on MTA Vol. 1, No. 4 (2013)

Blanc4), Chevreul5) and Rood6). As already mentioned above, the characteristics of Seurat's pointillism are summarized as follows: pointillist painting, use of primitive colors, control of luminance by white pigment, optical mixture, complementary color contrast, halo effect, and ebauche. There have been proposed several methods to generate pointillistic images from given input images. However, there Fig.3 Chevreul and RYB Color Wheel. are fewer methods to simulate the whole characteristics of Seurat's pointillistic painting styles. because the additive color mixtures on a retina 2.1 Pointillistic Image Generation blend these dots into one color. Hertzmann7) proposed a method that generated (5) Complementary color contrast is devised by various painterly images including pointillism Seurat. This visual effect generates very brilliant incidentally by using curved brush strokes of multiple color contrast by placing two or more complementary sizes. colors side by side. It is used to express shading. Hays and Essa8) applied the same kinds of rendering Seurat selected complementary colors based on techniques as Hertzmann to apply animation. Chevreul's color wheel (Fig.3 (a)) or RYB color These two algorithms only perturb the color of the wheel (Fig.3 (b)). Fig.1 (c) is an example of strokes randomly. Neither of these methods accurate complementary color contrast, where we can see pointillistic ways nor achieve the strict optical mixture blue dots on a man in orange T-shirt. effects. (6) Halo effect3) was introduced to emphasize the 2.2 Optical Mixture Only contrast of the motif and background. Fig.1 (d) is Luong, et al.9) and Jin, et al.10) proposed methods for an example of halo effect, where the contrast of generating pointillism style images taking into account background of black dress is enhanced. of optical mixture effect only. In their algorithms, (7) Ebauche2) is a kind of under-paint, and is drawn juxtaposed colors have the same luminance determined before painting pointillist strokes on a canvas. by an additive mixing model to enhance human visual Ebauche makes sure no dots overlapped, and is perception. visible between pointillist strokes. Hausner11) also achieves the optical mixture effect by Note that the important characteristics (4), (5), and (6) error diffusion approach efficiently, which relies on are derived from a scientific color theory. randomly placed dots. His algorithm builds a graph of In this paper, we propose a non-photorealistic pixels with links between neighbors on the image, and rendering (NPR) method that generates pointillistic diffuse an error to neighbors by using the graph. style images from input images taking into account of 7 However, they do not deal with other characteristics of important characteristics of Seurat's pointillism. In our the color theory of Seurat's pointillism. method, a given input image can be turned into a painterly 2.3 Pointillistic Image Generation Based on a style image with the presumably Seurat's pointillism. To Seurat's Color Theory implement the optical mixture effectively, the authors There are a few studies to reproduce almost all the propose a pointillistic halftoning method. The styles of the Seurat's painting. Yang, et al.12) proposed a pointillistic halftoning method is available for color method for simulating the Seurat's pointillistic painting halftoning on random dots. Our method can express styles. Seo, et al.13) also proposed another generation tonality of the input image by fewer colors efficiently method. These two methods simulated three important compared with conventional methods. phenomena based on the color theory such as optical Experimental results verify that our method can mixture, complementary color contrast and halo effect. effectively generate pointillistic images with features of In order to implement optical mixture effect, both of Seurat's painting styles. their methods are used perturbs colors make near colors of input image color be chosen within a narrow region. 2. Related Work As a result, their methods required 72 hue values, Seurat learned the color theory through the books of although Seurat used only 11 hue values. This is

318 Paper » A Method for Generating Pointillism Based on Seurat's Color Theory

because their algorithms are too naïve to implement the Table 1 Comparison with previous works. optical mixture by using fewer colors. None of them adopt error diffusion techniques to reduce color differences. Seo et al. took into account of shading expression by complementary colors. However, Yang et al. applied a simplistic manner on the whole canvas, without shading expression. Both of Yang, et al. and Seo, et al. synthesized halo effects by applying different simple weighted filters, which yield very bright or very dark and contrasty images. Proposal method improves these problems mentioned above. Our improvements compared to previous methods are summarized at Table 1.

3. Pointillistic Image Generation Method frequently in dark region for shading. In this section, we describe the pointillistic image Fourth, ebauche is generated by using several image generation method from input image based on the color processing filters (Fig.4 (e)). theory and steps. Overview of our method shows Fig.4. Finally, we synthesize three images in order First, we generate a halo filtered image (Fig.4 (b)) from mentioned above, which are ebauche, pure color input image (Fig.4 (a)). To calculate pure/complementary pointillist painting and complementary color painting colors of rendered dots, the halo filtered image is used. images for generating pointillistic image (Fig.4 (f)). Second, we render pure color pointillist dots (Fig.4 (c)). 3.1 Halo Effect These dots are rendered randomly but uniformly on a To generate halo, we use modified unsharp mask canvas. (modified UM), which introduces 2 types of weight

Third, we have to render complementary color dots function. Modified UM Ui at pixel i is expressed as (Fig.4 (d)). Complementary color dots are placed more follows:

Fig.4 Overview of proposal method.

319 ITE Trans. on MTA Vol. 1, No. 4 (2013)

=+ × ×() − 3.2 Pointillist Painting UIwii distlumi w IG i ()1 We adopt a halftorning approach to implement the

Where, Ii is the luminance at pixel i and Gi is a low optical mixture well by fewer colors. Error diffusion frequency component, which is obtained using Gaussian method15) is a commonly used halftoning algorithm. filter with a kernel size s. Ii –Gi is a high frequency Error diffusion relies on ordered grid of pixels. However, component. in pointillism, the dots are placed uniformly but

The wdist is the weight factor for applying only randomly. The authors propose the pointillistic surrounding edges defined as follows: halftoning method, which is an algorithm were available ⎛ ⎞ for color halftoning on random dots by the using spatial Di wA=×−⎜12⎟ () dist ⎝ s ⎠ data structure of boundary sampling algorithm16). < < Where, A is a constant for tuning effect, Di (0 = Di = s) 3.2.1 Boundary Sampling Algorithm is a distance map obtained by distance transform from This section describes the method to determine the edges detected by Canny's method14), s is the kernel size disk locations by boundary sampling algorithm. of Gaussian filter Gi. Boundary sampling is a variation of Poisson disk In bright or dark area of input image, the UM lead to sampling algorithm17) that runs in linear time and marked loss of detailed information. For this reason, we space. Boundary sampling algorithm samples a halo introduced another weight factor wlum as follows: filtered image, and places disks sequentially to

⎛ 2 ⎞ appropriate locations on the canvas randomly but 1 ⎜ ()L − μ ⎟ wB=×exp − i (3 ) uniformly. The procedure is as follows. lum ⎜ 2 ⎟ 2πσ 2 ⎜ 2σ ⎟ ⎝ ⎠ Step1: A disk, radius r, is sampled at random.

Where, Li is a luminance at pixel i. Here, constant B = Step2: Push the disk sampled at Step1 into the σ 100, expectation µ = 127 and variance = 40. This is a candidate list {Sk}. ∈ Gaussian distribution (peak is the intermediate value of Step3: Pop the disk Si {Sk} out of candidate list {Sk} luminance). In this weight function, the modified UM randomly. will not be applied to extremely bright or dark region. Step4: The disk Sj is sampled on the circumference of

Fig.5 shows examples of halos generated by our the circle at the center of the disk Si from Step3 method. Fig.5 (a) is input image, (b) is edges detected with radius 2r. A collection of circular arcs from (a), and (c) is the distance map generated from (b). centered at Si, which enable sampling Sj called

(d) is the result without weight function wlum, which is available boundary. An example of available same as Seo's result of halo generation13). (e) is our boundary shows Fig.6 (a). As shown in Fig.6 result of halo generation by using Equation 1. As shown (a), solid line portion is available boundary. in (d), we can observe lack of details, for example, the Step5: Step4 is recurred until available boundary is women's hand is extremely darker. As shown in (e), we undetectable. Then push the disk sampled on can observe improvement of them. available boundary into the candidate list {Sk}.

Fig.5 Generation of Halos. Fig.6 A spatial data structure of boundary sampling.

320 Paper » A Method for Generating Pointillism Based on Seurat's Color Theory

Step6: Step3~5 is recurred until the candidate list Next, diffuse the error to the points {Sm} on available

{Sk} is empty. boundary (See Fig.6 (b)) as following formula: 3.2.2 Error Diffusion ′ e Pointillist dots are rendered by colors of each sampled HHD=+×H nnLm point which determined by boundary sampling mentioned ′ e Sa=+ Sa S ()5 previous section. However, Seurat had been used 11 nnm e primitive color pigments. Thus we require quantization ′ =+L LLnn of halo filtered image colors. We adopt error diffusion m method to express tonality of input image. In this Where, m is the number of disks on available section, we will show a method to diffuse error to boundary at Si, and DL is inverse function of probability sampled disks. density function of Laplace distribution and defined as We diffuse error to disks sampled by boundary following formula: sampling algorithm. In HSL color space, we quantize ⎧ ⎪φμln205UifU+< ( . ) each channel, hue, saturation, lightness. Then the D = ⎨ ()6 L ⎪−−()φμln21( U) + otherwise difference between input image value and quantized ⎩ value is error. We diffuse the error to the collection of Where, the parameter µ is the mean or expectation ϕ disks {Sm} on the available boundary at the center of the (location of the peak), 2 is the variance and U is arbitrary disk Si, which is sampled by the boundary uniform random numbers in the range [0, 1]. In this sampling algorithm. The m is the number of disks on paper, µ = 0, ϕ = 6. Seo13) reported his analysis that available boundary of Si. Laplace distribution is the best fit for Seurat's color Π/ < First, the color, which is each channel of hue, saturation, arrangement. We diffuse the amplified error eH, – 2 = < Π lightness in HSL color space, at disk Si is quantized. eH = /2, based on Laplace distribution.

Then, define the set of quantized hue values as {Hn}, 3.2.3 Effectgiveness of Pointillisitic Halftoning saturation as {San}, lightness as {Ln}, the hue values of To the verifying effect of the optical mixture, the input image at point Si as Hinput, saturation as Sainput, authors performed preliminary experiments for lightness as Linput. {Hn}, {San}, {Ln} employ values divided generating a halftoned image by our pointillistic each HSL value into each nH, nS, nL equal part. Where halftoning method. Fig.7 shows the results of the number of nS and nL is 24, nH is as a parameter. generating pointillistic halftoning method by altering Categorize the HSL values of input image as one of the the number of quantize hue values from 11 (Fig.7 (a)) to each {Hn}, {San}, {Ln}. After that, calculate Euclidean 72 (Fig.7 (e)). As shown in Fig.7, we can observe the distance d between each HSL value of input images and gradation of the color wheel by optical mixture. each set of quantized HSL values, and replace the HSL Especially, we could perceive the tonality of the color values of point Si with the minimum value of distance d. wheel with less number of primitive colors. Here, the error of each channel after replacement is 3.3 Complementary Color Contrast defined as following formula: Seurat uses complementary colors more frequently in dark areas for shading. In order to shade expression by eH=− H H input n using complementary color, we modify the pointillistic eSaSa=− ()4 S input n halftoning method for generating stippling18). Here, it is eL=− L L input n necessary to distinguish between stippling and pointillism.

Fig.7 Results of the pointillistic halftoning method by using different colors.

321 ITE Trans. on MTA Vol. 1, No. 4 (2013)

In stippling, the focus is mainly on the placement of points, where are used to produce shading. Complementary color dots are used for expression of shading. Stippling is used for deciding the location of dots rendered with complementary colors. We enable both optical mixture and complementary color contrast by error-diffusion-based approach with the spatial data structure of the boundary sampling algorithm. 3.3.1 Stippling for Complementary Color After replacing the color to monochrome, diffuse the error to a neighboring point by using spatial data structure of the boundary sampling algorithm. For adapting the stippling to the error diffusion algorithm, Fig.8 Determination of Complementary Color. we are placing black dots rather than black (luminance = 0) and white (luminance = 255) pixels. We could place stipple rendered with complementary color for every black point.

Diffuse the error to the set of points {Sm} on available boundary at arbitrarily disk Si. Here, m is a number of ∈ disks on available boundary at Si. Then, luminance fi

[0, 255] of input image at Si is updated as following formula: ⎪⎧255if() f > 127 = ⎨ i gi ()7 ⎩⎪0 otherwise Fig.9 Effectiveness of complementary colors. Here, the error after replacement as e = fi –gi. Diffuse the error e to the points {Sm} on available boundary: 20) e RYB color wheel (Fig.3 (b)), which is similar to Chevreul's IIw′ =+× ()8 nn sm color wheel (Fig.3 (a)). Calculate complementary color by Π Where I'n is the new luminance at point {Sm} after adding to the hue value in HSL color space, which diffusing error, In is the luminance of input image at convert from RYB color space. Finally, each channel of point {Sm} and the density of point is controlled by hue, saturation, lightness are quantized as is the case 19) spatially-related adjustment weight factor ws, which is with the previous section. gamma collection. Gamma collection is the effectively 3.3.3 Effectiveness of Complementary Color technique for tuning contrast. Here, weight factor ws is Let us demonstrate the shade expression by complementary defined as following formula: color dots. Fig.9 (a) shows the result of pointillist painting ⎧ without complementary color dots. Fig.9 (b) shows the result ⎛ ⎞ G− ⎪ 1 ⎪⎜ ⎟ if() e < 0 of pointillist painting with complementary color dots. As w = ⎨⎝⎜ r ⎠⎟ (()9 s ⎪ s shown in Fig.9 (b), we can observe many complementary ⎪rG+ otherwise ⎩ s color dots in the dark areas, but the brighter areas contain

Where, rs is the radius of the disks at point Si fewer complementary colors. calculated by Equation 10 described in Section 4.5. G– 3.4 Ebauche and G+ are able to control error: increasing positive error As mentioned in Section 1, under-paint or outline and decreasing negative error. called ebauche is created before pointillist stroke 3.3.2 Calculation of Complementary Color paintings. To simulate ebauche, covert input image to Dots are rendered by complementary color on the set of smoothed image with a faint color. First, colors of input 21) points {Sstip} of generated stippling in the previous section. image are reduced by popularity algorithm . Next, the Fig.8 shows a method for determining complementary image is smoothed by median filter. color in HSL color space. First, perturb the hue value of 3.5 Stroke Rendering input image at {Sstip} based on a Laplace distribution using Pointillistic image is composited by many textures Equation 6. Next, Complementary color is calculated using that imitate short brush stroke as shown in Fig.10. The

322 Paper » A Method for Generating Pointillism Based on Seurat's Color Theory

same as the order of the boundary sampling algorithm. First, pointillist strokes of pure colors are rendered on ebauche. Next, previously rendered image added with strokes of complementary colors.

Fig.10 The texture of brush stroke. 4. Experimental Results

To verify that proposed method is able to generate strokes have the following properties: pointillistic image effectively from input image, the Position, Color: The way to determine the position and authors performed several experiments. the color of strokes is different in pure color and 4.1 Examples of Generated Pointillistic Images complementary color. In pure color, position and color are Fig.11 shows generated results by the proposed determined as mentioned in Section 3.2. In complementary method. Table 2 lists the parameters used in our method. color, they are also determined as mentioned in Section 3.3. Where the parameters of pointillistic halftonig describe P Size: In pointillism, short strokes are used. (0.003, 1.5, 1.2, 11). The notation P (0.003, 1.5, 1.2) means α β (1) Pure color: The size of strokes is basically r = 0.003, p = 1.5, p = 1.2, nH = 11. The parameters of determined by the radius of the disk of the boundary stippling for complementary color described as following:

sampling algorithm. In actual pointillism, each stroke the notation Pc (0.012, 10, 5, 1.2, 1.0, 0.003) means rs = α β has multiple sizes by hand. Thus radius r of disks 0.012, G– = 10, G+ =5, c = 1.2, c = 1.0, rc = 0.003. (c) is

is modified based on the luminance values of input generated from (a) as P (0.003, 1.7, 1.3, 11), Pc (0.008, 10, image as following formula: 10, 1.5, 1.2, 0.003). (d) is generated from (b) as P (0.003, 1.7, 1.4, 11), P (0.008, 5, 5, 1.5, 1.2, 0.0025). ()− ×− c rrmax min ()255 Ioriginal rr′ =+ ()10 4.2 Validation for Features of Seurat's min 255 Pointillism × α × β α β Where, rmax = r p, rmin = r p. p and p is Fig.12 shows how our algorithm simulates some of

parameters. Ioriginal is a luminance of input image at the features of Seurat's pointillism. (a) is generated as

sampled point. Radius r varies linearly with the P(0.002, 1.7, 1.5, 11), Pc(0.007, 10, 10, 1.6, 1.4, 0.002). < < original intensity Ioriginal in the range rmin = r' = rmax. (b), (c), (d) show detail of (a). We can observe the The width and height of the texture are specified by juxtaposition of different color dots from (b), more width =2r', height = 1.5 × width as shown in Fig.10. complementary colors at the shaded region from (c), and (2) Complementary color: Strokes painted with that halo are expressed from (d). complementary colors become less dense as 4.3 Comparison with Actual Seurat's work compared to the case of pure color pointillist Fig.13 demonstrates our claimed resemblance by strokes. Therefore, large size of the radius of the placing Seurat's paintings and our generated results boundary sampling algorithm as compared pure side by side for comparison. (a) and (b) compare halo

color strokes is used. As a parameter, the radius rc for rendering complementary color strokes in Table 2 Parameters used in our method. distinction from radius rs of boundary sampling for

complementary color stipping is defined. The rc is < < modified by Equation 10 in range rmin = rc = rmax. × α × β α β Where, rmax = rc c, rmin = rc c. c and c is parameters. Direction: Seurat paint strokes aligned with the contours of the motif. Thus the strokes should flow along the edges of input image. To achieve this, the direction of the texture is determined by applying an edge tangent flow (ETF)22). The ETF is extracted by computing the gradient magnitude and tangent orientation. Then the ETF is smoothed by them of the neighboring pixels. Order: The order of rendering textures of stroke is

323 ITE Trans. on MTA Vol. 1, No. 4 (2013)

Fig.11 Results of our pointillistic image generation method.

Fig.12 Characteristics of Seurat's pointillism mimicked by the proposed method.

effect, while (c) and (d) color juxtaposition, which is the parameters. Several examples are shown in Fig.14. similar in coloration. Through these comparisons, we (b), (c), (e) shows examples generated by altering the size believe that our method can express characteristics of and density of dots while keeping the other parameters. Seurat's pointillism faithful. Control of size and density of dots is important, because 4.4 Comparison with Various Parameters the size and density of dots have a relationship to the It is possible to generate various images by altering optical mixture closely. We tried some cases altering the

324 Paper » A Method for Generating Pointillism Based on Seurat's Color Theory

Fig.13 Comparison with actual Seurat's paintings.

Fig.14 Results with various parameters.

number of hue values nH = 11 in (d), nH = 24 in (e), nH = Most potentially influential parameter in regard to the 72 in (f). We could observe color reproducibility by the appearance of generated image is a radius r of sampled optical mixture even with less number of colors. disks. We might well be able to get an effective outcome as

325 ITE Trans. on MTA Vol. 1, No. 4 (2013)

pegging r at range [0.002, 0.003] approximately. Seurat m−1 n−1 1 ⎡ σ =−+∑∑ ⎢Ri(, j ) Ri (, j ) Gi (, j ) had been drawing complementary color strokes smaller 3mm ⎣ i=0 i=0 ()12 2 than pure color pointillist strokes. Thus rc should be set ⎤ −+Gij(, ) B (iij,)− Bij (,) α β ⎦⎥ smaller values than r. p = 1.7, p = 1.4, are considered reasonable and proper. In the same manner as rc, Here, m and n is width and height of an image. [R(i, j), α β α parameters c and c should be set smaller than p and G(i, j), B(i, j)] is RGB values at position (i, j) of input image. ~ ~ ~ β p respectively. The parameter rs at range [0.007, 0.008] [R(i, j), G(i, j), B(i, j)] is RGB values at position (i, j) of are considered proper. pointillistic image. 4.5 Comparison with Conventional Methods In our method, we calculate PSNR values with Fig.15 compares our generated result with altering hue values as 11, 24 and 72. As shown in Table conventional methods. (a) is input image, (b) is the 3, we can observe that the more the number of hue, the result of Yang's mehod16), (c) is Seo's one17) and (d) is better reproduction rate of the input image tonality is proposed method. (d) is generated as P (0.0025, 1.8, 1.4, achieved. However, we can also see that PSNR value of

11), Pc(0.008, 5, 5, 1.7, 1.3, 0.0025). By contrast with our our method with 11 hue values is better than PSNR method obtained using 11 hue values, conventional values of conventional methods with 72 values. This can method requires 72 hue vales for color reproduction. be considered as an effect of the error diffusion method. Table 3 shows PSNR values of pointillistic images Thus our method can express tonality of input images by generated by our method (Fig.15 (d)) and the conventional fewer colors efficiently. It is said that Seurat was using methods (Fig.15 (b) and (c)). PSNR values of Table 3 are 11 colors as the original colors, and regarding this point, calculated by following formula: we believe that our proposed method is superior to other 2552 conventional methods. PSNR = 10log (11 ) 10 σ As mentioned in Section 4.1, conventional method for Where, σ is represented by: generating halo has the possibilities of loss of detailed information. Our method improvemed this problem.

5. Conclusion

Table 3 Comparison of PSNR values between our method and The method of generating pointillistic image was previous methods. proposed in this paper corresponding to the features of Seurat's pointillism, which including optical mixture, complementary color contrast and halo effect. Especially, the pointillisitc halftoning method using the spatial data structure of the boundary sampling algorithm for

Fig.15 Comparison with conventional methods. The lower images show expand region of the red rectangle of (a).

326 Paper » A Method for Generating Pointillism Based on Seurat's Color Theory

applying error diffusion to uniform but random sampled 12) C.K. Yang and H.L. Yang: "Realization of Seurat's Pointillism via Non-photorealistic Rendering", The Visual Computer, 24, 5 (May points was proposed. Proposed method enabled the 2008) optical mixture faithful with fewer hue values. The 13) S.H. Seo and K.H. Yoon: "Color Juxtaposition for Pointillism authors demonstrated the effect of the proposed method Based on an Artistic Color Model and a Statistical Analysis", The Visual Computer, 26, 6-8, pp.421-431 (June 2010) by generating several experimental results. The authors 14) J. Canny: "A computational Approach to Edge Detection", IEEE believe that it is possible to get closer to Seurat's style. Trans. Pattern Analysis and Machine Intelligence, 8, 6, pp.679-698 (Nov. 1986) In future work, the authors would like to reveal the 15) R.W. Floyd and L. Steinberg: "An Adaptive Algorithm for Spatial relationship of distance between viewer and generated Grey Scale", Society for Information Display, 17, 2, pp.75-77 (1976) 16) D. Dunbar and G. Humphreys: "A Spatial Data Structure for Fast image to size of dots for best optical mixture. In any Poisson-disk Sample Generation", ACM Trans. Graph., 25, 3, case, starting with a 2D image imposes limitations, pp.503-508 (July 2006) which is a lack of depth information and a lot of noise. 17) R.L. Cook: "Stochastic Sampling in Computer Graphics", ACM Trans. Graph., 5, 1, pp.51-72 (Jan. 1986) The authors would like to consider generating the 18) A. Secord: "Weighted Voronoi Stippling", 2002 Non-Photorealistic pointillistic image from 3D scene. Animation and Rendering, pp.37-43 (Jane (2002) 19) H. Li and D. Mould: "Structure-preserving Stippling by Priority- References based Error Diffusion", 2011 Graphics Interface, pp.127-134 (May 2011) 1) H. Dutching: "Georges Seurat: 1859-1891: The Master of 20) N. Gossett and B. Chen: "Paint inspired color mixing and Pointillism (Taschen Basic Art Series)", TASCHEN Japan (2000) compositing for visualization" 2004 IEEE Symp. on Information 2) POLA Museum of Art: "Sparks of Color: Pointillism and Fauve Visualization, pp.113-118 (Oct. 2004) Paintings from the Collection", POLA museum of Art, POLA 21) P. Heckbert: "Color Image Quantization for Frame Buffer Foundation, Japan (2004) Display", Computer Graphics, 16, 3, pp.297-307 (July 1982) 3) T. Luft, C. Colditz and O. Deussen: "Image Enhancement by 22) H. Kang, S. Lee and C. Chui: "Flow-based Image Abstraction". Unsharp Masking the Depth Buffer", ACM Trans. Graph., 25, 3, IEEE Trans. Visualization and Computer Graphics, 15, 1, pp.62- pp.1206-1213 (July 2006) 76 (Jan. 2009) 4) C. Blanc: "The Grammar of Painting and Engraving", The received his B.E. and M.E. Riverside Press, Cambridge (1874) Junichi Sugita degrees from Tokyo Denki Uiversity, Japan, in 2006 5) M.E. Chevreul: "The Principles of Harmony and Contrast of and 2008, respectively. He had been working at Toppan Colors", SCHIFFER Publishing, Atglen (1987) Printging Co., Ltd. from 2008 to 2012. Since 2012, he 6) O.N. Rood: "Modern Chromatics, with Applications to Art and has been an assistant in Faculty of Healthcare, Tokyo Industry", Appleton, New York (1879) Healthcare University. He received IIEEJ Nishita 7) A. Hertzmann: "Painterly Rendering with Curved Brush Strokes of award in 2008. His research interests include computer Multiple Sizes", 1998 ACM SIGGRAPH, pp.453-460 (July 1998) graphics, especially non-photorealistic rendering. 8) J. Hays and I. Essa: "Image and Video Based Painterly Animation" 2004 Non-Photorealistic Animation and Rendering, pp.113-120 Tokiichiro Takahashi received his B. E. (June 2004) degrees from Niigata Uiversity in 1977, and Ph. D. 9) T.Q. Luong, A. Seth, A. Klein and J. Lawrence: "Isoluminant Color from the University of Tokyo in 2005, respectively. He Picking for Non-photorealistic Rendering", 2005 Graphics had been working at Nippon Telegraph and Telephone Interface, pp.233-240 (May 2005) Corporation since 1977. Since 2003, he has been a professor at Tokyo Denki University. His research 10) L. Jing, K. Inoue and K. Urahama: "An NPR Technique for interests include computer graphics, image processing, Pointillistic and Mosaic Images with Impressionist Color and visual computing. Arrangement", 2005 Int'l Symp. Visual Computing, pp.1-8 (Dec. 2005) 11) A. Hausner: "Pointillistic Halftoning", 2005 Computer Graphics and Imaging, pp.134-139 (Aug. 2005)

327