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 by an iteration process with intensity gradients. Although the conventional method can generate ripple patterns in horizontal and vertical orientations, it is not possible to generate ripple patterns with arbitrary slope.

In this paper, we develop a method that can arbitrarily change the orientation 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 patterns of the proposed method is more linear or wavy than ripple patterns of the conventional method. In addition, by changing the value of the parameter, the proposed method can also change the interval between ripple patterns as the conventional method. To verify the effectiveness of the proposed method, experiments are conducted using Lenna image and other photographic images. As a result of the experiments, it is clarified that the proposed method can 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 first process, 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 the proposed method is shown in Figure 1. The detailed procedure in Figure 1 is shown as follows.

Figure 1

Flow chart of the proposed method.

The input pixel values for spatial coordinates (i, j) of a photographic image are defined as f_i,j. Then, the pixel values of the image at the t-th iteration number are defined as fi,j(t) , where fi,j(1)=fi,j . The pixel values fi,j(t) have value of M gradation from 0 to M − 1.

In the first process, the image with the pixel values fi,j(t) is smoothed using circular-sector-type smoothing filter that calculates an average of pixel values in circular sector as shown in Figure 2. The circular sector with a range of θ₁ radian and radius D rotates θ₂ radian, and the pixel values that the center of the pixel is included in circular sector at the target pixel (i, j) are gi,j,k(t)(k=1,2,⋯,Ki,j(t)) . The pixel values si,j(t) of the smoothed image are calculated as Equation (1).

Figure 2

Conceptual diagram of circular-sector-type smoothing filter.

In the second process, the pixel values fi,j(t+1) using inverse filtering are calculated as Equation (2).

In case fi,j(t+1) is < 0, then fi,j(t+1) must be set to 0. In case fi,j(t+1) is > M − 1, then fi,j(t+1) must be set to M − 1. An AOR image is obtained after the first and second processes of T times iteration.

3. EXPERIMENTS

We mainly conducted two experiments. First, the experiment with changing the values of the parameters in the proposed method is conducted 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 3

Lenna image.

Figure 4

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

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, θ₁, and θ₂ are set to 5, π/2, and π/4, respectively. The results of the experiment are shown in Figure 5. As the value of the iteration number T is larger, ripple patterns become clear and converge.

Figure 5

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

Arbitrarily-oriented ripple images by changing the radius D are visually confirmed using Lenna image. The radius D is set to 3, 5, 7, and 9. Other parameters T, θ₁, and θ₂ are set to 100, π/2, and π/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.

Figure 6

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

Arbitrarily-oriented ripple images by changing the angle θ₁ are visually confirmed using Lenna image. The angle θ₁ is set to π/6, π/3, π/2, and (2/3)π. Other parameters T, D, and θ₂ are set to 100, 5, and π/4, respectively. The results of the experiment are shown in Figure 7. As the value of the angle θ₁ is larger, ripple patterns become more linear. On the other hand, as the value of the angle θ₁ is larger, ripple patterns become wavier.

Figure 7

AOR images in the case of the angle (a) θ₁ = π/6, (b) θ₁ = π/3, (c) θ₁ = π/2, and (d) θ₁ = (2/3)π.

Arbitrarily-oriented ripple images by changing the angle θ₂ are visually confirmed using Lenna image. The angle θ₂ is set to 0, π/4, π/2, and (3/4)π. Other parameters T, D, and θ₁ are set to 100, 5, and π/2, respectively. The results of the experiment are shown in Figure 8. Depending on the value of the angle θ₂, the orientation of ripple patterns is changing.

Figure 8

AOR images in the case of the angle (a) θ₁ = 0, (b) θ₁ = π/4, (c) θ₁ = π/2, and (d) θ₁ = (3/4)π.

3.2. Experiment using Various Photographic Images

The proposed method is applied to eight photographic images shown in Figure 4. The parameters T, D, θ₁, and θ₂ are set to 100, 5, π/2, and π/4, respectively. The results of the experiment are shown in 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 to generate a ripple pattern by adding noise to the white area.

Figure 9

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

4. CONCLUSION

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 in AOR images by changing the values of the parameters were investigated. As a result of the experiments, by changing the value of the angle θ₂ in the proposed method, ripple patterns could be generated in any orientation. And, by changing the value of the angel θ₁, ripple patterns could be generated more linear or wavy.

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

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

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 Design in 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.