Journal of Robotics, Networking and Artificial Life
Vol. 6(4); March (2020), pp. 213–216
DOI: https://doi.org/10.2991/jrnal.k.200222.001; ISSN 2405-9021; eISSN 2352-6386
https://www.atlantis-press.com/journals/jrnal

Research Article

Generation of Arbitrarily-Oriented Ripple Images using
Circular-Sector-Type Smoothing Filter and Inverse Filter
Toru Hiraoka*
Department of Information Systems, University of Nagasaki, 1-1-1 Manabino Nagayo, Nishisonogi, Nagasaki 815-2195, Japan

ARTICLE INFOABSTRACTArticle History

A Non-photorealistic rendering method for generating ripple images from photographic images has been proposed using
intensity gradient. Ripple patterns imitate a wave on the water surface and are composed of continuous lines with fluctuations.
Ripple images are expressed by superimposing ripple patterns on photographic images. However, the conventional method can
only generate vertical and horizontal ripple patterns. Therefore, in this paper, we develop a method that can generate ripple
patterns in any orientation. Ripple images generated by the proposed method are called Arbitrarily-Oriented Ripple (AOR)images. The proposed method is executed by an iterative process using circular-sector-type smoothing filter and inverse filter.
To verify the effectiveness of our method, we investigate the changes in AOR images by changing the values of the parameters.

Received 23 November 2019
Accepted 25 November 2019
Keywords
Non-photorealistic renderingripple patternarbitrarily orientation
circular-sector-typesmoothing filter
inverse filter© 2020 The Authors. Published by Atlantis Press SARL.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
Non-photorealistic Rendering (NPR) is a technology of computer graphics that can generate effective illustrations and artistic images. Many NPR methods have been proposed to simulate
effective illustrations and artistic images [1–5]. In the past NPR
methods, an NPR method for generating ripple images has been
proposed [6]. Ripple patterns imitate a wave on the water surface
and are composed of continuous lines with fluctuations. Ripple
images are expressed by superimposing ripple patterns on photographic images. The conventional method was conducted byan iteration process with intensity gradients. Although the conventional method can generate ripple patterns in horizontal andvertical orientations, it is not possible to generate ripple patterns
with arbitrary slope.
In this paper, we develop a method that can arbitrarily change theorientation of ripple patterns, then expand the range of expression of
the conventional method. Ripple images generated by the proposed
method is called Arbitrarily-Oriented Ripple (AOR) images. The
proposed method is executed by an iterative process using inverse
filter [7,8] and circular-sector-type smoothing filter. By adjusting
the value of the parameter in the proposed method, ripple patternsof the proposed method is more linear or wavy than ripple patternsof the conventional method. In addition, by changing the value ofthe parameter, the proposed method can also change the interval
between ripple patterns as the conventional method. To verify theeffectiveness of the proposed method, experiments are conductedusing Lenna image and other photographic images. As a resultof the experiments, it is clarified that the proposed method canEmail: hiraoka@sun.ac.jp*automatically generate AOR images. In addition, through experiments that change the values of parameters in the proposed method,
it is also revealed the changes in appearance of AOR images.
The rest of this paper is organized as follows. Section 2 describes
the proposed method for generating AOR images. Section 3 shows
experimental results, and reveals the effectiveness of the proposed
method. Finally, Section 4 concludes this paper.

2. PROPOSED METHOD
The proposed method is executed in two processes. In the firstprocess, images are smoothed using circular-sector-type smoothing filter. In the second process, the smoothed images are restored
using inverse filter. By repeating the two processes, AOR images
are generated. Accumulation of errors due to the iterative process
is a factor that can generate ripple patterns. A flow chart of theproposed method is shown in Figure 1. The detailed procedure inFigure 1 is shown as follows.
The input pixel values for spatial coordinates (i, j) of a photographic image are defined as fi,j. Then, the pixel values of the image(t )at the t-th iteration number are defined as fi , j , where fi(, 1j ) = fi , j .
(t )The pixel values fi , j have value of M gradation from 0 to M − 1.
(t )In the first process, the image with the pixel values fi , j is smoothedusing circular-sector-type smoothing filter that calculates an averageof pixel values in circular sector as shown in Figure 2. The circularsector with a range of q1 radian and radius D rotates q2 radian, andthe pixel values that the center of the pixel is included in circularsector at the target pixel (i, j) are g i(,tj), k (k = 1, 2,, K i(,tj) ) . The pixelvalues si(,tj) of the smoothed image are calculated as Equation (1).

T. Hiraoka / Journal of Robotics, Networking and Artificial Life 6(4) 213–216

214		   s = ∑(t )i, j

K i(,tj)g (t )

k =1 i , j , k(t )
i, jK

(1)

In the second process, the pixel values fi(, tj +1) using inverse filtering
are calculated as Equation (2).
fi(, tj +1) = fi(, tj ) − si(,tj) + fi , j (2)		 In case fi(, tj +1) is < 0, then fi(, tj +1) must be set to 0. In case fi(, tj +1) is >(t +1)

M − 1, then fi , j must be set to M − 1. An AOR image is obtained
after the first and second processes of T times iteration.

3. EXPERIMENTS

Figure 4 | Various photographic images. (a) Airplane, (b) Barbara, (c)boat, (d) cameraman, (e) girl, (f) lighthouse, (g) text, (h) woman.

We mainly conducted two experiments. First, the experiment withchanging the values of the parameters in the proposed method isconducted using Lenna image shown in Figure 3. Second, the experiment is conducted to verify that patterns can be generated using various photographic images shown in Figure 4. All photographic images
used in the experiments are 512 * 512 pixels and 256 gradation.

Figure 1 | Flow chart of the proposed method.

Figure 5 | AOR images in the case of the iteration number (a) T = 10,(b) T = 20, (c) T = 50, and (d) T = 100.

3.1. Experiment with Changing Parameters
Arbitrarily-oriented ripple images by changing the iteration
number T are visually confirmed using Lenna image. The iteration number T is set to 10, 20, 50, and 100. Other parameters D, q1, and q2 are set to 5, p /2, and p /4, respectively. The
results of the experiment are shown in Figure 5. As the value ofthe iteration number T is larger, ripple patterns become clearand converge.

Figure 2 | Conceptual diagram of circular-sector-type smoothing filter.

Figure 3 | Lenna image.

Arbitrarily-oriented ripple images by changing the radius D arevisually confirmed using Lenna image. The radius D is set to 3, 5, 7,and 9. Other parameters T, q1, and q2 are set to 100, p /2, and p /4,respectively. The results of the experiment are shown in Figure 6.
As the value of the radius D is larger, the intervals between ripple
patterns become wider.
Arbitrarily-oriented ripple images by changing the angle q1 arevisually confirmed using Lenna image. The angle q1 is set to p /6,p /3, p /2, and (2/3)p. Other parameters T, D, and q2 are set to 100,5, and p /4, respectively. The results of the experiment are shownin Figure 7. As the value of the angle q1 is larger, ripple patterns
become more linear. On the other hand, as the value of the angle q1is larger, ripple patterns become wavier.

T. Hiraoka / Journal of Robotics, Networking and Artificial Life 6(4) 213–216

215

Arbitrarily-oriented ripple images by changing the angle q2 arevisually confirmed using Lenna image. The angle q2 is set to 0, p /4,p /2, and (3/4)p. Other parameters T, D, and q1 are set to 100, 5, andp /2, respectively. The results of the experiment are shown in Figure 8.
Depending on the value of the angle q2, the orientation of ripple
patterns is changing.

3.2. Experiment using Various
Photographic Images

Figure 6 | AOR images in the case of the radius (a) D = 3, (b) D = 5,(c) D = 7, and (d) D = 9.

The proposed method is applied to eight photographic images
shown in Figure 4. The parameters T, D, q1, and q2 are set to 100, 5,
p /2, and p /4, respectively. The results of the experiment are shownin Figure 9. In all cases, ripple patterns can be automatically generated on the whole image. However, no ripple patterns are generated
in the white areas shown in Figure 9f and 9g. It is conceivable togenerate a ripple pattern by adding noise to the white area.

Figure 7 | AOR images in the case of the angle (a) q1 = p /6, (b) q1 = p /3,(c) q1 = p /2, and (d) q1 = (2/3)p.

Figure 8 | AOR images in the case of the angle (a) q1 = 0, (b) q1 = p /4,(c) q1 = p /2, and (d) q1 = (3/4)p.

Figure 9 | AOR images. (a) Airplane, (b) Barbara, (c) boat,(d) cameraman, (e) girl, (f) lighthouse, (g) text, (h) woman.

T. Hiraoka / Journal of Robotics, Networking and Artificial Life 6(4) 213–216

216

4. CONCLUSIONREFERENCES

We proposed an NPR method for generating AOR images from photographic images. The proposed method was executed by an iterative
process using inverse filter and circular-sector-type smoothing filter.
To verify the effectiveness of the proposed method, the changes inAOR images by changing the values of the parameters were investigated. As a result of the experiments, by changing the value of theangle q2 in the proposed method, ripple patterns could be generated
in any orientation. And, by changing the value of the angel q1, ripple
patterns could be generated more linear or wavy.

[1]
[2]
[3]
[4]

And, by changing the value of the radius D, the proposed method
could also change the interval between ripple patterns.

[5]

A subject for future study is to expand the proposed method for
application to color photographic images and videos.

[6]
[7]

CONFLICTS OF INTEREST
The author declares they have no conflicts of interest.

ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI Grant Number
JP19K12664.

AUTHOR INTRODUCTION
Dr. Toru Hiraoka
He graduated Doctor course at Designin Kyushu Institute of Design. He is a
Professor in the Faculty of Information
Systems in University of Nagasaki. His current research interests are non-photorealistic
rendering and disaster prevention.

[8]

P. Haeberli, Paint by numbers: abstract image representations,
ACM SIGGRAPH Comput. Graph. 24 (1990), 207–214.
D.D. Seligmann, S. Feiner, Automated generation of intent-based3D illustrations, ACM SIGGRAPH Comput. Graph. 25 (1991),123–132.
W. Qian, D. Xu, K. Yue, Z. Guan, Y. Pu, Y. Shi, Gourd pyrography
art simulating based on non-photorealistic rendering, Multimed.
Tools Appl. 76 (2017), 14559–14579.
D. Martín, G. Arroyo, A. Rodríguez, T. Isenberg, A survey of digital stippling, Comput. Graph. 67 (2017), 24–44.
W. Qian, D. Xu, J. Cao, Z. Guan, Y. Pu, Aesthetic art simulationfor embroidery style, Multimed. Tools Appl. 78 (2019), 995–1016.
T. Hiraoka, Generation of ripple images using intensity gradient,ICIC Expr. Lett. 13 (2019), 1097–1101.
J.M. Ortega, W.C. Rheinboldt, Iterative solutions of nonlinear
equations in several variables, Society for Industrial Applied
Mathematics, Philadelphia, PA, 2000.
Z. Yu, K. Urahama, Iterative method for inverse nonlinear image
processing, IEICE Trans. Fundam. Electron. Commun. Comput.
Sci. E97–A (2014), 719–721.