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1 NAIST-IS-MT
2 ( )
3 Λ SSD(Sum of Squared Differences) SSD Λ, NAIST-IS- MT , i
4 ii
5 Image Inpainting Based on Energy Minimization for Pattern Similarity Considering Intensity Change and Spatial Locality Λ Norihiko Kawai Abstract Image inpainting techniques have been widely used to remove undesired visual objects in images such as damaged portions of photographs and people who have accidentally entered into pictures. Conventionally, the missing or undesired parts of an image are completed by optimizing an objective function which is defined based on the sum of SSD (sum of squared differences). However, the naive SSDbased objective function is not robust against intensitychange in an image. Thus, unnatural intensity change often appears in the missing parts. In addition, when an image has continuously changing texture patterns, the completed texture in a resultant image sometimes blurs due to inappropriate pattern matching. In this paper, in order to improve the image quality of the completed texture, the conventional objective function is newly extended by considering intensity changes and spatial locality to prevent unnatural intensity changes and blurs in a resultant image. By minimizing the extended energy function, the missing regions can be completed without unnatural intensity changes and blurs. In experiments, the effectiveness of the proposed method is successfully demonstrated by applying our method to various images and comparing the results with those obtained by the conventional method. Λ Master's Thesis, Department of Information Systems, Graduate School of Information Science, Nara Institute of Science andtechnology, NAIST-IS-MT , February 1, iii
6 Keywords: image inpainting, image completion, energy minimization iv
7 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : SSD : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : v
8 1 Bertalmio [3] : : : : : : : : : : : : 5 2 [19] : : : : : : : : : : : : : : 6 3 Criminisi [27] : : : : : : : : : : : 8 4 Wexler [33] : : : : : : : : : : : : : 10 5 : : : : : : : : : : : : : : : : : : : : : : : : 13 6 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 18 9 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ( A 56) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ( B 09) : : : : ( C 41) : : : : : : ( D 78) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : A : : : : B : : : : C : : : : D : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Criminisi [27] : : : Wexler [33] : : : : : : : : : : : : : 44 vi
9 27 1( 83) : : : ( 90) : : : ( 04) : : : : 48 1 : : : : : : : : : : : : : : : : : : 24 2 [33] : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 40 4 : : : : : : : : : : : : : : : : : : : : 40 5 A D : : : : : : : : : : : : : : : : : : : : : : : : : : 40 vii
10 1. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] ffl [17, 18, 19, 20, 21] ffl [22, 23, 24, 25, 26, 27, 28, 29, 30] ffl [31, 32, 33] 1
11 [33]
12 2. [34, 35, 36, 37] [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] [1] 3
13 Masnou [2] ffl (Partial Differential Equation) [3, 4, 5, 6, 7, 8] ffl (Total Variation) [9, 10] ffl [11] ffl [12] ffl [13, 14, 15] ffl [16]
![1 Bertalmio [3] [17] Hirani](/docs-images/91/105660777/images/14-0.jpg "[18] BPLP [19] BPLP kbplp")
14 1 Bertalmio [3] [17] Hirani [18] BPLP [19] BPLP kbplp [20] 5
![2 [19] 2](/docs-images/91/105660777/images/15-0.jpg "[19] [21]")
15 2 [19] 2 [19] [21] FID 6
16 2.1.3 ffl 3 1 Efros [22] Bertalmio [23] [3] [22] [24, 25, 26, 27, 28] [24] inverse matte[25] [26] [27] 7
![[27] [28]](/docs-images/91/105660777/images/17-1.jpg "[29, 0] 8")
17 3 Criminisi [27] [28] [29, 30] 8
18 ffl [31, 32, 33] Komodakis [31] Belief Propagation Priority-BP Allene [32] Wexler [33] SSD 4 9
19 4 Wexler [33] 10
20 2.2 [38] Wexler [33] 11
21 SSD 5 (a) (b) (c) 3.2 SSD SSD Wexler SSD [33] [33] [33] 6 Ω Ω 0 Ω 0 Φ Ω 0 Φ W Ω Ω 0 Ω 0 x Φ ^x org 12
22 (a) y ( ) (b) v (c) ªªªª ªªªª 5 13
23 Φ ªªª ªª x ˆ = ( xˆ, yˆ) W ªª x = ( x, y) W Ω Ω 6 SSD E org = X x2ω 0 w x SSD(x; ^x org ) (1) SSD(x; ^x org ) SSD(x; ^x org )= X p2wfi(x + p) I(^x org + p)g 2 (2) I(x) x ^x org Ω 0 x Φ E org ^x org ^x org = f org (x) = argmin SSD(x; x 0 ) (3) x 0 2Φ w x Ω 0 Ω w x =1 Ω w x = c d 14
24 d Ω c [33] E org I(x) x org 3.3 (1) E org X E = w x [SSD 0 (x; ^x)+w dis SD(x; ^x)] (4) x2ω 0 SSD 0 (x; ^x) SD(x; ^x) x ^x X SSD 0 (x; ^x) = fi(x + p) ff x^x I(^x + p)g 2 (5) p2w SD(x; ^x) = k W k 1+e f K(kx ^xk X 0)g K X 0 k W k ^x E Φ ^x = f(x) = argmin(ssd 0 (x; x 0 )+w dis SD(x; x 0 )) (7) x 0 2Φ ff x^x x ^x ff x^x (6) 15
25 Æ Ç È Ç È SD( x, xˆ) { x xˆ 7 (8) (1 D» ff x^x» 1+D D 0 <D< 1 ) ff x^x = 8 >< >: 1 D (fi x^x < 1 D ) fi x^x (1 D» fi x^x» 1+D ) (8) 1+D (fi x^x > 1+D ) fi x^x = qp q2w I(x + q)2 (9) qpq2w I(^x + q)2 7 (6) 16
26 3.4 Greedy Algorithm (4) E (7) (x; ^x) ff x^x E Ω (I) ( ) (II) ^x ( ) (I) (II) (I) (4) E I(x) I(x) E E(x) 8 x x W x + p (p 2 W ) x + p (7) f(x + p) x f(x + p) p x E E(x) x f(x + p) p x f(x) X E(x) = w x+p fi(x) ff x+pf (x+p)i(f(x + p) p)g 2 p2w + w dis k W k 1+e f K(kx ^xk X 0)g (10) 17
27 f ( x + p) p Φ x f f ( x + p) Š ªª Ω x +p 8 E E(x) E = X x2ω E(x)+C (11) C Ω Ω 0 E I(x k ) E I(x k k ) =0 k ) x2ω I(x k ) xi x j ) =0 (8x i; x j 2 Ω; 8x 0 2 Φ) (13) 18
28 k )=0 (x 6= x k ) I(x k k ) k ) =0 (14) x I(x) I(x) = P p2w w x+pff x+pf (x+p)i(f(x + p) p) P p2w w x+p (15) (15) (13) I(x) ff (II) (I) Φ SSD 0 SD (7) ^x Φ 9 Ω (I) (II) Φ 2 (7) (x; ^x) SSD 0 (x; ^x)+w dis SD(x; ^x) 19
29 (17) ªªª ªªª 9 20
30 S min Φ S min T (T : ) x 0 SSD 0 (x; x 0 )+w dis SD(x; x 0 ) <TS min (16) T x x SSD f( p T 1)=2g 2 S min x ψ X pt! 2 1 fi 0 (x + p) I(x + p)g 2 < S min (17) 2 p2w I 0 I 3.5 Greedy Algorithm
31 È 1/4 ªªªª 1/2 ªªªª Ç Ç È Ç Ç Ç Ç Ç ªªªª 10 22
32 10 23
33 ( ) 4 Wexler [33] 100 PC(CPU:Xeon 3.2GHz :8GB) 1 ( 11 ) 1% % [33] 1 W 9 9 w dis 120 K 0.4 X 0 20 ff D 0.1 T 4 24
34 図 実験で用いた入力画像 H
35 (2/3) 26
36 (3/3) 27
37 4.1 12(a) 15(a) 4 4 ffl ( A 56) ffl ( B 09) ffl ( C 41) ffl ( D 78) (b) (c) 3.2 SSD [33] (d) A D A ( 12) 12 B( 13) C( 14) 28
38 D( 15) (13) 2 [33] A(56) B(09) C(41) D(78)
![(a) (b) (c) [33]](/docs-images/91/105660777/images/39-0.jpg "(d) 12 ( A 56)")
39 (a) (b) (c) [33] (d) 12 ( A 56) 30
![(a) (b) (c) [33]](/docs-images/91/105660777/images/40-0.jpg "(d) 13 ( B 09)")
40 (a) (b) (c) [33] (d) 13 ( B 09) 31
![(a) (b) (c) [33]](/docs-images/91/105660777/images/41-1.jpg "(d) 14 ( C 41)")
41 (a) (b) (c) [33] (d) 14 ( C 41) 32
42 (a) (b) (c) [33] (d) 15 ( D 78) 33
43 16 A 17 B 34
44 18 C 19 D 35
45 Wexler [33] Criminisi [27] 37 ( ) [27] [33] % t [33] 36
46 20 37
47 図 修復結果の採点ページ 3
48 t A D 5% t [33] A B D 4.1 A D 27(a) 28(a) [33] 1 w dis = (d) 28(d) 29(a) [33] [27] 29(d) (c) [27] (d) 2% 39
49 3 100 [27] 2.21 [33] [27] 7 [33] A D A B C D [27] [33]
50 Criminisi [27] Wexler [33] 41
51
52
53 (1/2) 44
54 (2/2) 45
![(a) (b) [33] (c)](/docs-images/91/105660777/images/55-0.jpg "(d) 27 1( 83) 46")
55 (a) (b) [33] (c) (d) 27 1( 83) 46
![(a) (b) [33] (c)](/docs-images/91/105660777/images/56-0.jpg "(d) 28 2( 90) 47")
56 (a) (b) [33] (c) (d) 28 2( 90) 47
![(a) (b) [33]](/docs-images/91/105660777/images/57-0.jpg "(c) (d) 29 (")
57 (a) (b) [33] (c) (d) 29 ( 04) 48
58 5. SSD 37 PSNR (Peak Signal to Noise Ratio) 49
59 50
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4. C i k = 2 k-means C 1 i, C 2 i 5. C i x i p [ f(θ i ; x) = (2π) p 2 Vi 1 2 exp (x µ ] i) t V 1 i (x µ i ) 2 BIC BIC = 2 log L( ˆθ i ; x i C i ) + q
![4. C i k = 2 k-means C 1 i, C 2 i 5. C i x i p [ f(θ i ; x) = (2π) p 2 Vi 1 2 exp (x µ ] i) t V 1 i (x µ i ) 2 BIC BIC = 2 log L( ˆθ i ; x i C i ) + q](/thumbs/92/110416683.jpg "4. C i k = 2 k-means C 1 i, C 2 i 5. C i x i p [ f(θ i ; x) = (2π) p 2 Vi 1 2 exp (x µ ] i) t V 1 i (x µ i ) 2 BIC BIC = 2 log L( ˆθ i ; x i C i ) + q")
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IPSJ SIG Technical Report 1,a) 1,b) 1,c) 1,d) 2,e) 2,f) 2,g) 1. [1] [2] 2 [3] Osaka Prefecture University 1 1, Gakuencho, Naka, Sakai,
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1,a) 1,b) 1,c) 1,d) 2,e) 2,f) 2,g) 1. [1] [2] 2 [3] 1 599 8531 1 1 Osaka Prefecture University 1 1, Gakuencho, Naka, Sakai, Osaka 599 8531, Japan 2 565 0871 Osaka University 1 1, Yamadaoka, Suita, Osaka
本文6(599) (Page 601)
(MIRU2008) 2008 7 525 8577 1 1 1 E-mail: matsuzaki@i.ci.ritsumei.ac.jp, shimada@ci.ritsumei.ac.jp Object Recognition by Observing Grasping Scene from Image Sequence Hironori KASAHARA, Jun MATSUZAKI, Nobutaka
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NAIST-IS-MT0851100 2010 2 4 ( ) CR CR CR 1980 90 CR Kerberos SSH CR CR CR CR CR CR,,, ID, NAIST-IS- MT0851100, 2010 2 4. i On the Key Management Policy of Challenge Response Authentication Schemes Toshiya
(a) 1 (b) 3. Gilbert Pernicka[2] Treibitz Schechner[3] Narasimhan [4] Kim [5] Nayar [6] [7][8][9] 2. X X X [10] [11] L L t L s L = L t + L s
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