Input image Initialize variables Loop for period of oscillation Update height map Make shade image Change property of image Output image Change time L

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1 1,a) 1,b) 1/f β Generation Method of Animation from Pictures with Natural Flicker Abstract: Some methods to create animation automatically from one picture have been proposed. There is a method that gives a flicker to a picture to make animation. However, the flicker generated by the simple harmonic motion causes monotonous animation. In this study, we propose the method of creating complex and natural flicker by using 1/f β noise seen often in nature. We carried out the experiment that compares the proposed method to the conventional method by the subjective appraisal, and confirmed the adequacy of the proposed method. 1. [1] [2] [3] 1 Graduate School of Information Science and Technology, Hokkaido University a) k b) [4] [4] 1/f β c 212 Information Processing Society of Japan 1

2 Input image Initialize variables Loop for period of oscillation Update height map Make shade image Change property of image Output image Change time Loop end Input image Height map Shade image Output image (1) H ij (t) C A H ij (t) C + A A C 2 A = 127.5, C = A C ω T ω T ω = 2π/T α ij (1) t = H ij () H ij () = A sin α ij + C (2) α ij ( ) α ij = sin 1 Hij () C A (3) α ij α ij π/2 π/2 < α ij π H ij () H ij (t) 1 Fig. 1 Overview of preceding study [4] 1 (i, j) H ij H ij H ij [5] Lambert H ij H ij (t) = A sin(ωt + α ij ) + C (1) H ij (t) (i, j) t H ij () H ij (t) H ij (t) 255 A C 2.2 (1) A ω t /f β [6] 2 f 1/f β β β β = β = 1 1/f β = 2 1/f 2 1/f c 212 Information Processing Society of Japan 2

3 1/f [6] 3.2 1/f β 3.1 1/f (1) (1) A ω α α ω A ω /f = A X A (t) (4) A X A (t) X A (t) [, 1] X A (t) 1 1 X A (t) ω (4) (1) ω (4) X A (t) X A (t) = n N(t i)p (i) (5) i= X A (t) [, 1] (5) n N(t) t 1/f P (t) τ P (t) = exp ( t ) τ (6) (5) P (t) (FIR: Finite impulse response) n FIR (4) (5) (6) H(t) ω(t) = ω X f (t) (7) ω X f (t) X f (t) A ω A ω A ω (4) (7) (1) H ij (t) = A X A (t) sin(ω X f (t)t + α ij ) + C (8) 3.3 1/f β 3.1 1/f β 1/f 1/f β N(t) [, A] n Z n n Z n n/2 A n/12 A 2 Z n n/2 A N(t) /f 1/f [7] N(t) + un(t) z N(t) <.5 N(t + 1) = 2N(t) 1.5 < N(t) < 1 (9) N(t) > 1 u > 1 < z < /f 1/f 1/f N(t) c 212 Information Processing Society of Japan 3

4 (a) Poplar (b) Rowan (a) (b) (c) River (d) Waterfall 2 Fig. 2 Images used for making animation. [8] N(, 1) N w (t) N(t) t N(t) = N w (s) (1) s= Poplar Rowan River Waterfall 48 4 Poplar Rowan Poplar Rowan (c) 3 1/f Fig. 3 Frames in generated animation of image Poplar with 1/f noise and difference of them. 12fps ω 1.2π[rad/s] A Poplar Rowan River Waterfall Rowan River [9] Poplar Waterfall C# GUI 12fps PC CPU Intel R Core TM i7-26k 3.4GHz 8.GB RAM Poplar 1/f 3(a) 3(b) (a).5 3(c) (a) (b) A = (a) (b) 1/f (c) 1/f 2 (d) (a) (d) 5 ω 1/f c 212 Information Processing Society of Japan 4

5 5 1 (a) White noise 5 1 (b) 1/f noise Table 1 1 Score of subjective evaluations (c) Brownian noise (d) Constant A = Fig. 4 Amplitude in time domain (in case A = 127.5). 5 H(t) /f H(t) Fig. 5 Height H(t) using frequency with 1/f noise. Vote A C A N A C A N 3 s 1 s 3 s 1 s 3 s 1 s 3 s 1 s Fig. 6 6 A C : Animation with constant parameters A N : Animation with noise Presentation of animation. ω(t) [1] Poplar 1/f 1/f [8] 5 5 = /f 1/f River Waterfall c 212 Information Processing Society of Japan 5

6 2 Table 2 Result of subjective evaluation (for noise). Freq. Amp. Constant White noise 1/f by chaos 1/f by filter Brownian noise Constant White noise /f by chaos /f by filter Brownian noise Table 3 Result of subjective evaluation (for input image). Image Noise for amp. Noise for freq. Score Poplar 1/f 2 1/f Rowan 1/f by filter Constant 3.2 River 1/f by filter Constant 2.6 Waterfall 1/f by filter Constant 3.2 Poplar Rowan 5. A ω 1/f A [4] [2] 2 Vol. J84-D-II No. 9 pp (21). [3] Vol. No. 4 pp (21). [4] Vol. 32 No. 46 pp (28). [5] Blinn, J. F.: Simulation of wrinkled surfaces, ACM SIG- GRAPH 78 Proceedings, pp (1978). [6] Peitgen, H. O. and Saupe, D.: The Science of Fractal Images, Springer-Verlag New York (1988). 199 [7] 1/f p. 24 (22). [8] lyuka/technote/pinknoise/ ( ). [9] 22 1B2-1 (212). [1] Subjective video quality assessment methods for multimedia applications, ITU-T Recommendation P. 91 (1999). [1] Chuang, Y.-Y., Goldman, D. B., Zheng, K. C., Curless, B., Salesin, D. H. and Szeliski, R.: Animating Pictures with Stochastic Motion Textures, ACM Transactions on Graphics pp (25). c 212 Information Processing Society of Japan 6

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