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1 2007
2 Graph Cuts Graph Cuts Graph Cuts Graph Cuts t-link Interactive Graph Cuts 4.7% Mean Shift Segmentation
3 i
4 5 SIFT Bag of Keypoints Bag of Keypoints A Mean Shift 51 A.1 (Kernel Density Estimation) A.2 (Density Gradient Estimation) B Scale-Invariant Feature Transform 55 B B.1.1 LoG B.1.2 Difference-of-Gaussian B.1.3 σ B.1.4 k B.1.5 DoG B B ii
5 B B B B B.5 SIFT C 69 iii
6
7 s-t cut Lazy Snapping ( [1] ) Grabcut ( [2] ) n-link t-link λ Bag of Keypoints Affine Invariant keypoint SIFT (a)affine Invariant keypoint (b) (c) 8 ( [3] ) GMM Mean-Shift SIFT v
8 A.1 (A.13) A.2 Mean Shift ( [4] ) B.1 LoG B.2 DoG B.3 σ B.4 s =2 DoG B B.6 DoG B B B B B B.12 SIFT vi
9 [%] [%] [s] [%] [%] ( [5] ) [%] (α =0.1) vii
10
11 1 Snake [6] Level Sets[7], Graph Cuts [1, 2, 8, 9, 10, 11] Snake Level Sets Graph Cuts Graph Cuts Boykov Inreractive Graph Cuts [9, 10] Interactive Graph Cuts minimum cut/maximum flow algorithm Interactive Graph Cuts Lazy Snapping[1] Grab Cut[2] Graph Cuts n-link Graph Cuts t-link 1
12 Mean Shift SIFT 2
13 2 2.1 Boykov minimum cut/maximum flow algorithms [8] minimun cut minimum cut max flow algorithm minimum cut/maximum flow algorithms image restoration [12, 13, 14, 15], stereo and motion [16, 17, 18, 19], image segmentation [9, 20, 21], multi-camera reconstruction [22] P p L p depth 2.1 E(L) E(L) = D p (L p )+ p P V (p,q) (L p,l q ) (2.1) (p,q) N 3
14 2.1: N D p (L p ) V (p,q) (L p,l q ) E Potts Interaction Energy Model Liner Interaction Energy Model 2 Potts Interaction Energy Model Potts Interaction Energy Model E(I) = I p Ip + p P K (p,q) T (I p I q ) (2.2) (p,q) N I = {I p p P } I = {Ip p P } K(p, q) T (I p,i q ) I p I q I p I q 1, 0 K(p, q) p q T (I p,i q ) 0 Potts Energy 2 max flow NP hard 4
15 Liner Interaction Energy Model Liner Interaction Energy Model. E(I) = I p Ip + p P A (p,q) I p I q (2.3) (p,q) N Potts Model A (p,q) K (p,q) A (p,q) p q Potts Energy 2.2 E min-cut/max-flow algorithm Graph Cuts Algorithm min-cut/max-flow algorithm min-cut/max-flow algorithm 2.2: G =(E,V ) V (node) E (edge) (source)s V (sink)t V n-link s t t-link n-link 5
16 t-link n-link t-link (2.1) V p,q D p 2.3(a) 2.3: s S t T = V S 2 s-t S T s-t s-t s-t 2.4: s-t cut Ford-Fulkerson Method[23] Push- Relabel Method[24] Ford-Fulkerson Method 6
17 0 s t Push-Relabel Method s Potts Interaction Energy Model E(L) = λ R(L)+B(L) (2.4) R(L) = p P R p (L p ) (2.5) B(L) = δ(l p,l q ) = {p,q}inn { B {p,q} δ(l p,lq) (2.6) 1 if L p L q 0 otherwise (2.7) R(L) B(L) λ R(L) E(L) : edge weight(cost) for {p, q} B { p, q} {p, q} N λ R p ( bkg ) p P, p /O B {p, S} K p O 0 p B λ R p ( obj ) p P, p /O B {p, T } 0 p O K p B R p ( obj ) = ln Pr(I p O) (2.8) R p ( bkg ) = ln Pr(I p B) (2.9) 7
18 B {p,q} exp ( (I ) p I q ) 2 1 (2.10) 2σ 2 dist(p, q) K = 1 + max B {p,q} (2.11) p P q:{p,q} N O, B, I p p O, B O, B seed Pr(I p O), Pr(I p B) seed t-link dist(p, q) p, q mincut/max-flow algorithm Li Lazy Snapping [1] Lazy Snapping 2.5 Rother GrabCut [2] GrabCut 2.5: Lazy Snapping ( [1] ) GMM Graph Cuts 2.6 8
![図 2.6: Grabcut によるセグメンテーション例 (文献 [2] より) 2.2.3 従来法の問題点 従来法である Interactive Graph Cuts[9], [20] では seed が与えられていない t-link の エッジコストには seed の色分布から得られる尤度を利用して計算するか 0 とする 尤 度の計算を行う場合 n-link に比べ t-link](/docs-images/91/106181000/images/19-0.jpg "が大きくなると 色分布による影響が強くなり 突発的な誤検出が多くなる場合がある そのため このような誤検出を抑制するためには λ によって n-link の影響を強くする必要がある n-link の影響が強いと 画像中のエッジ 情報に対しての依存性が強くなる そのため 図 2.")
19 図 2.6: Grabcut によるセグメンテーション例 (文献 [2] より) 従来法の問題点 従来法である Interactive Graph Cuts[9], [20] では seed が与えられていない t-link の エッジコストには seed の色分布から得られる尤度を利用して計算するか 0 とする 尤 度の計算を行う場合 n-link に比べ t-link が大きくなると 色分布による影響が強くなり 突発的な誤検出が多くなる場合がある そのため このような誤検出を抑制するためには λ によって n-link の影響を強くする必要がある n-link の影響が強いと 画像中のエッジ 情報に対しての依存性が強くなる そのため 図 2.7 に示すように Interactive Graph Cuts では画像に複雑なエッジが存在する場合 局所的なエッジを乗り越えてセグメンテーショ ンすることが困難となる 図 2.7: 複雑なエッジを含む画像でのグラフカットによるセグメンテーション 9
20
21 3 Graph Cuts : seed σ l σ σ Graph Cuts Graph Cuts GMM(Gaussian Mixture Model) GMM t-link Graph Cuts σ<1 σ =0 σ = α σ Graph 11
22 Cut 0 <α<1 Step1. seed Step2. σ Step3. Step4. Graph Cuts Step5. Step6. σ<1 σ =0 σ = α σ(0 <α<1) Step : 12
23 3.2 I G(σ) L(σ) L(σ) =G(σ) I (3.1) σ σ I 1 σ 1 2 L 1 (σ) I I 2 I 2 σ =1 L 2 (σ) L 1 (σ) L 2 (σ) L 1 (2σ) =.. L 2 (σ) (3.2) σ 1 2 σ σ : 13
24 3.3 σ Graph Cuts Graph Cuts t-link (2.8), (2.9) 1 Graph Cuts t-link R p ( obj ) = ln Pr(O I p) (3.3) R p( bkg ) = ln Pr(B I p ) (3.4) Pr(O I p ) Pr(B I p ) (3.5), (3.6) Pr(O I p ) = Pr(O)Pr(I p O) Pr(I p ) Pr(B I p ) = Pr(B)Pr(I p B) Pr(I p ) (3.5) (3.6) Pr(I p ) Pr(O) Pr(B) Pr(I p O), Pr(I p B) Pr(O), Pr(B) t-link : Pr(I p O), Pr(I p B) GMM (Gaussian Mixture Model) [25] RGB 3 14
25 Pr(I p ) = p(i p µ, Σ) = K α i p i (I p µ i, Σ i ) (3.7) i=1 1 (2π) 3/2 Σ ( 1/2 ) 1 exp 2 (I p µ) T Σ 1 (I p µ) (3.8) GMM EM [26] GMM GMM (3.7) I p Pr(I p O) Pr(I p B) Graph Cuts Pr(O), Pr(B) d d obj d bkg { Pr(O) = d obj if d obj d bkg 1 d bkg if d obj <d bkg (3.9) Pr(B) = 1 Pr(O) (3.10) 3.4 GMM Pr(I p O), Pr(I p B) Pr(O), Pr(B) (3.3) Pr(O I p ) (3.4) Pr(B I p ) Pr(O I p ) (3.3) {p, T } t-link Pr(B I p ) (3.4) {p, S} t-link 3.2 Graph Cuts 15
26 (b) Interactive Graph Cuts[9] 3.5(c) n-link σ =0 n-link 3.5(c) n-link t-link Pr(O), Pr(B) Pr(I p O), Pr(I p B) 1 3.5(d) 3.5(e) Pr(O), Pr(B) Pr(I p O), Pr(I p B) t-link GrabCut 1 50 seed Interactive Graph Cuts [9] GrabCut[2] O = {O 1,O 2,...,O p,...,o P }, B = {B 1,B 2,...,B p,...,b P } L = {L 1,L 2,...,L p,...,l P } over segmentation under segmentation over seg. = under seg. = p P δ(l p B p ) P p P δ(l p O p ) P (3.11) (3.12) Graph Cuts λ Interactive Graph Cuts λ =0.005 seed t-link Grabcut λ = i3l/segmentation/grabcut.htm 16
27 3.5: n-link t-link % 2% 2% % t-link 17
28 3.1: [%] Interactive GrabCut[2] Graph Cuts[9] over seg under seg total (26 ) (24 ) 3.2: [%] Interactive GrabCut[2] Graph Cuts[9] over seg under seg total over seg under seg total (err) (3.11) over segmentation (3.12) under segmentation λ (2.1) t-link n-link λ Interactive Graph Cuts Interactive Graph Cuts [9] λ λ =0.005 n-link Interactive Graph Cuts λ t-link Interactive Graph Cuts 18
29 図 3.6: セグメンテーション例と誤検出率 は誤検出領域が多いが 提案手法では安定して物体領域を抽出できていることがわかる これは 従来法では t-link に色情報のみが使われているため 物体領域の色に似ている色 の背景領域が誤検出される 提案手法では繰り返し処理における 1 つ前の Graph Cuts の 結果から 大まかな物体領域と背景領域の形を捉えた t-link が得られるため λ を大きく した場合でも突発的な誤検出を抑制することができる このことから 提案手法は λ を変 化させても 安定したセグメンテーション結果を得ることができる 処理時間について 従来法と提案手法の処理時間の計測を行う 処理時間計測には画像サイズを 150x113, 300x225, 600x450 の 3 種類を用いる 使用した PC は Intel(R) Xeon 2.66GHz 8 メモ リ 4.0GB である 表 3.3 に各手法での処理時間と繰り返し回数を示す 表 3.3 より 提案 手法は繰り返し処理が入るため 処理時間が大幅に増加する 解決策として 繰り返し回 数の軽減や Lazy Snapping [1] のようにスーパーピクセルからグラフを作成することによ るグラフカットの高速化が考えられる 19
![Cuts[9] GrabCut[2] 150x113 0.](/docs-images/91/106181000/images/30-1.jpg "38 2.91 (4 ) 9.")
30 3.7: λ 3.3: [s] Interactive Graph Cuts[9] GrabCut[2] 150x (4 ) 9.81 (8 ) 300x (3 ) (10 ) 600x (12 ) (12 ) % 4.79% λ 20
31 4 4.1 Interactive Graph Cuts [9] n-link t-link Graph Cuts Mean Shift Segmentation [4] x i = {x s i, x t i, x r i } z i L i {y j } j=1,2,... ( n i=1 x x x ig i 2) h y j+1 = ( n i=1 g x x i 2) (4.1) h g(x) = ( C x s 2) ( h 2 sh t h p k x t 2) ( k x r 2) k (4.2) r h s h t h r 21
32 4.1: h s,h t,h r C k(x) Mean Shift Segmentation 1. ean Shift z i = y i,c 2. z i {C p } p=1,...,m 3. L i = {p z i C p } 4. M pixel Mean Shift Segmentation h s
![[%] over](/docs-images/91/106181000/images/33-3.jpg "segmentation 1.")
33 4.2: 4.3: 4.3 seed 10 ( ) Mean Shift ( ) : [%] over segmentation under segmentation total % Mean Shift Segmentation 23
34 4.4: % Mean Shift Segmentation 24
35 5 SIFT SIFT(Scale Invariant Feature Transform) 5.1 Bag of Keypoints Bag of Keypoints [3] Bag of Keypoints Bag of Keypoints Bag of Word Bag of Word Bag of Keypoints (keypoint, visual work, visual term) Bag of Keypoints 5.1 Bag of Keypoints Bag of Keypoints 25
36 5.1: Bag of Keypoints Bag of Keypoints SIFT SIFT SIFT 26
37 SIFT SIFT SIFT 2 Interest point detector SIFT Quelhas [27] SIFT [28] DoG Csurka [3] Affine Invariant keypoint [29] SIFT : Affine Invariant keypoint SIFT (a)affine Invariant keypoint (b) (c) 8 ( [3] ) Regular grid SIFT Fei-Fei [5] SIFT 13 DoG 5.1: [%] ( [5] ) Descriptor Grid Random DoG 11x11 pixel N/A 128-dim SIFT Bag of Keypoints 27
38 SVM Naive Bayes plsa LDA plsa LDA Bag-of-Word Naive Bayes Naive Bayes w = {w 1,w 2,...,w n }, c Naive Bayes c c = arg max p(c w) p(c)p(w c) =p(c) c n p(w n c) (5.1) plsa plsa (Probabilistic Latent Semantic Analysis) [30] 2 d D = {d 1,...,d N }, w W = {w 1,...,w M }, z Z = {z 1,...,z K } p(d, w) =p(d) p(w z)p(z d) (5.2) z Z p(d, w) = z Z p(z)p(d z)p(z w) (5.3) LDA plsa Sivic [31] plsa Translation and Scale invariant plsa (TSI-pLSA) 28
39 5.3: 5.2 SIFT [32, 33] (u, v) I x i = {u i,v i,i i } T Φ = {α j, φ j =(µ j, Σ j )} c j=1 x (5.4) EM(DAEM:Deterministic Annealing EM) [34] Φ ML Φ ML = arg max Φ c (α j p j (x µ j, Σ j )) β j=1 1 p(x µ j, Σ j ) = (2π)3 Σ j { exp 1 } 2 (x µ j) T Σ 1 j (x µ j ) (5.4) p j (x µ j, Σ j ) µ j Σ j φ j = {µ j, Σ j } β DAEM β EM α j α j > 0 c j=1 α j = Φ ML 3 2 (u, v) 29
40 5.4: GMM Φ ML x φ i C i = arg max p i (x φ i ) (5.5) i 5.4(c) Mean-Shift [4] 5.5 x i = {u i,v i,i i } T 3 30
![5.5: Mean-Shift 5.2.2 SIFT descriptor [28] SIFT Descriptor SIFT descriptor L(x, y) θ(x, y) m(x, y) m(x, y) = f x (x, y) 2 + f y (x, y) 2 (5.6) ( ) θ(x, y) = tan 1 fy (x, y) (5.](/docs-images/91/106181000/images/41-0.jpg "7) f x (x, y) f x (x, y) = L(x +1,y) L(x 1,y) (5.8) f y (x, y) = L(x, y +1) L(x, y 1) (5.9) m θ w(x, y) = G(x, y, σ) m(x, y) (5.10) h θ = w(x, y) δ[θ, θ(x, y)] (5.")
41 5.5: Mean-Shift SIFT descriptor [28] SIFT Descriptor SIFT descriptor L(x, y) θ(x, y) m(x, y) m(x, y) = f x (x, y) 2 + f y (x, y) 2 (5.6) ( ) θ(x, y) = tan 1 fy (x, y) (5.7) f x (x, y) f x (x, y) = L(x +1,y) L(x 1,y) (5.8) f y (x, y) = L(x, y +1) L(x, y 1) (5.9) m θ w(x, y) = G(x, y, σ) m(x, y) (5.10) h θ = w(x, y) δ[θ, θ(x, y)] (5.11) x y G(x, y, σ) θ
42 5.6: 5.7: SIFT 4x4 8 4x SIFT SIFT SIFT LBG SIFT
43 5.8: 5.3 k-nn :
44 5.10: N = {n 1,...,n 4 } T E = {e 1,...,e 6 } T T = {N 1,...,N 4, e 1,...,e 6 } T } T X cost(t, X) = 4 n t i nx i + i=1 6 j=1 e t j ex j (5.12) T X T X T X Cost(T, X) = min i {cost(t, X i )} (5.13) Cost l Cost g α Cost = α Cost l +(1 α) Cost g (5.14) (0 α 1) knn 34
45 (SH) (HG) (BK) (VH) : α % 5.3 α =0.1 (α =0) (a)(b) (e)(f) (c)(d) (g)(h)
46 5.2: [%] α SH HG Class BK VH : (α =0.1) out SH HG BK VH correct rate[%] SH HG in BK VH Caltech database bok1 [3] Bag of keypoints SIFT bok2 [35] proposed method GMM 1 Datasets/Caltech256/ 36
47 bok1 17.6% bok2 5.6% 45 bok1 bok GMM 5.16 GMM bok2 bok2 5.5 SIFT 3.2% Bag of keypoints 17.6% 37
48 5.12: 38
49 5.13: 5.14: 39
50 5.15: 5.16: 40
51 % λ 4 Mean Shift Segmentation 4.23% 5 3.2% Bag of keypoints 17.6% Mean Shift Segmentation 41
52
53 43
54
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59 [1],,.,, Vol 22, 2008( ) [1] S. Shimizu, T. Nagahashi, and H. Fujiyoshi. Robust and Accurate Detection of Object Orientation and ID without Color Segmentation, Proc. on ROBOCUP2005 SYMPOSIUM, [2] Tomoyuki Nagahashi, Hironobu Fujiyoshi, and Takeo Kanade. Object Type Classification Using Structure-based Feature Representation, MVA2007 IAPR Conference on Machine Vision Applications, pp , May, [3] Tomoyuki Nagahashi, Hironobu Fujiyoshi, and Takeo Kanade. Image Segmentation Using Iterated Graph Cuts Based on Multi-scale Smoothing, Asian Conference on Computer Vision 2007, Part II, LNCS 4844, pp , [1],,. ID, 21 SIG-Challenge, pp , May, [2],,., CVIM 154, pp ,
60 [3],,. SIFT, SC-07-8, pp39-44, Jan [4],,., 10 (MIRU2007), pp , Jul, [1],,.,, O-455, Sep, [1] MIRU2007 [2]
61 A Mean Shift A.1 (Kernel Density Estimation) n d {x i } i=1,...,n (Kernel Density Estimation Method) Parzen ˆf h,k (x) = 1 nh d n ( ) x xi K h i=1 (A.1) (A.1) K x ˆf h,k (x) h h K(x) (A.1) K(x) = c k,d k( x 2 ) (A.2) c k,d K(x) Normal Kernel k N (x) = exp ( 12 ) x x 0 (A.3) K N (x) = (2π) d/2 exp ( 12 ) x 2 (A.4) Epancechnikov Kernel k E (x) = K E (x) = { 1 x 0 x 1 0 x>1 { 1 2 c 1 d (d + 2)(1 x 2 ) x 1 0 otherwise (A.5) (A.6) 51
62 (A.1) ˆf h,k (x) = c k,d nh d ( n x x i 2) k (A.7) h i=1 A.2 (Density Gradient Estimation) ˆf(x) ˆf(x) f(x) 0 (A.7) ˆ f h,k (x) ˆ f h,k (x) ˆf h,k (x) = 2c k,d nh d+2 n i=1 (x x i )k ( x x i h k(x) k (x) 2) (A.8) g(x) = k (x) (A.9) G(x) = c g,d g ( x 2) (A.10) c g,d (A.9) (A.8) ( B ) ˆ f h,k (x) = 2c k,d nh d+2 = 2c k,d nh d+2 ( n x x i (x i x)g h i=1 ( [ n ( x x i )] n 2 i=1 x ig g h i=1 2 ) x x i h n i=1 g ( x x i h 2 ) x (A.11) 2 ) (A.7) G x ˆf h,g (x) ˆf h,g (x) = c g,d nh d Mean Shift Vector m h,g (x) m h,g (x) = ( n x x i 2) g (A.12) h i=1 n i=1 x ig ( x x i h n i=1 g ( x x i h 2 ) ) x (A.13) 2 52
63 (A.12), (A.13) (A.11) ˆ f h,k (x) = ˆf h,g (x) 2c k,d h 2 c g,d m h,g (x) (A.14) m h,g (x) = 1 2 h2 c ˆ f h,k (x) ˆf h,g (x) (A.15) c (A.15) G Mean Shift Vector m h,g (x) K Mean Shift Vector Mean Shift Vector Mean Shift Vector (A.13) Mean Shift Vector m h,g (x) A.1 A.1: (A.13) { y j }j=1,2,... y j+1 = n i=1 x ig ( y x j i h n i=1 g ( y j x i h 2 ) ) (A.16) 2 y j y j+1 Mean Shift Vector A.2 Mean Shift 53
64 A.2: Mean Shift ( [4] ) 54
65 B Scale-Invariant Feature Transform SIFT [28] SIFT ( ) (detection) { (description) 2 1. detection 2. { 3. description DoG B.1 1 DoG B.1.1 LoG Koenderink[36] Lindeberg[37] Lindeberg Scale-normalized Laplacian-of-Gaussian( LoG ) LoG σ (B.1) LoG ( B.1) 55
66 B.1: LoG ) LoG = f(σ) = x2 + y 2 2σ 2 exp ( x2 + y 2 2πσ 6 2σ 2 (B.1) σ x y LoG Lowe[38] Differenceof-Gaussian(DoG) DoG LoG G σ = σ 2 G (B.2) G 2 (LoG) (B.2) G σ G(x, y, kσ) G(x, y, σ) kσ σ (B.3) (B.2) (B.3) σ 2 G = G σ G(x, y, kσ) G(x, y, σ) kσ σ (B.4) (k 1)σ 2 2 G G(x, y, kσ) G(x, y, σ) (B.5) σ 2 2 G LoG (B.5) DoG LoG LoG DoG SIFT DoG 56
67 B.1.2 Difference-of-Gaussian G(x, y, σ) I(u, v) L(u, v, σ) (DoG ) L(u, v, σ) = G(x, y, σ) I(u, v) (B.6) ) 1 G(x, y, σ) = ( 2πσ exp x2 + y 2 (B.7) 2 2σ 2 DoG D(u, v, σ) DoG D(u, v, σ) = (G(x, y, kσ) G(x, y, σ)) I(u, v) = L(u, v, kσ) L(u, v, σ) (B.8) σ 0 k B.2 DoG σ SIFT σ B.2: DoG B.1.3 σ σ B.3 σ 0 L 1 (σ 0 ) σ 0 k kσ 0 57
68 L 1 (kσ 0 ) σ 1 1 2σ 0 L 1 (2σ 0 ) 1/2 1 k 1/2 L 2 (σ 0 ) 2σ 0 L 1 (2σ 0 ) L 1 (2σ 0 ) L 2 (σ 0 ) (B.9) σ B.3: σ 58
69 B.1.4 k σ k 1 s 1 σ 0 2σ 0 σ k k =2 1/s B.4 DoG s =2( 2) k =2 1/2 = 2 DoG 3 1 s s +2 DoG s +2 DoG s +3 1 s +3 [28] s=3 σ 0 = / B.4: s =2 DoG 59
70 B.1.5 DoG DoG DoG σ DoG B.5 DoG 3 DoG ( B.5 ) ( B.5 ) 26 ( B.5 ) σ DoG DoG DoG B.6 DoG ( ) B.6(a) 2 (b) DoG B.6(a) DoG σ 1 B.6(b) σ 2 σ 2 =2σ 1 2 DoG σ 2 SIFT σ B.5: B.2 B.1 DoG (low contrast) 60
71 B.6: DoG B H [ ] H = D xx D xy (B.10) D xy D yy DoG 2 1 α 2 β(α >β) Tr(H) Det(H) Tr(H) = D xx + D yy = α + β (B.11) Det(H) = D xx D yy (D xy ) 2 = αβ (B.12) γ 1 2 α = γβ Tr(H) 2 Det(H) = (α + β)2 αβ = (γβ + β)2 γβ 2 = (γ +1)2 γ (B.13) 61
![B.7: α β Tr(H) 2 Det(H) < (γ th +1) 2 γ th (B.14) (B.14) γ th [28] γ th =10 12.1 B.7(a) B.7(b) B.2.2 3 (x, y, σ) 2 x =(x, y, σ) T DoG D(x) D(x) =D + D T x + 1 2 D x 2 xt x x 2 (B.](/docs-images/91/106181000/images/72-0.jpg "15) (B.15) x 0 D x + 2 D x ˆx = 0 2 (B.16) 62")
72 B.7: α β Tr(H) 2 Det(H) < (γ th +1) 2 γ th (B.14) (B.14) γ th [28] γ th = B.7(a) B.7(b) B (x, y, σ) 2 x =(x, y, σ) T DoG D(x) D(x) =D + D T x D x 2 xt x x 2 (B.15) (B.15) x 0 D x + 2 D x ˆx = 0 2 (B.16) 62
73 ˆx ( ) 2 D ˆx = D x2 x (B.17) 2 D x 2 2 D xy 2 D xσ 2 D xy 2 D y 2 2 D yσ 2 D xσ 2 D yσ 2 D σ 2 x y σ = D x D y D σ (B.18) (B.18) ˆx x y σ = 2 D x 2 2 D xy 2 D xσ 2 D xy 2 D y 2 2 D yσ 2 D xσ 2 D yσ 2 D σ 2 1 D x D y D σ (B.19) (B.19) ˆx =(x, y, σ) B.2.3 DoG (B.19) ˆx = 2 D 1 D x 2 x (B.20) (B.20) (B.15) D(ˆx) =D T D ˆx x (B.21) D DoG ˆx (B.21) DoG DoG [28] 0.03 DoG ( ) B.7(c) 63
74 B.3 2 L(u, v) m(u, v) θ(u, v) { m(u, v) = f u (u, v) 2 + f v (u, v) 2 (B.22) θ(u, v) = tan 1 f v(u, v) (B.23) f u (u, v) f u (u, v) =L(u +1,v) L(u 1,v) f v (u, v) =L(u, v +1) L(u, v 1) (B.24) m(x, y) θ(x, y) B.8 h h θ = w(x, y) δ [θ,θ(x, y)] (B.25) x y w(x, y) = G(x, y, σ) m(x, y) (B.26) h θ 36 w(x, y) (x, y) G(x, y, σ) m(x, y) δ Kronecker θ(x, y) θ % B.8 1 B B.4 SIFT descriptor 128 B.10 64
75 B.8: ( B.10 ) 4 16 B.11 8 (45 ) B = =
76 B.9: 2 B.10: B.5 SIFT SIFT SIFT JPEG 5 1 B.12 SIFT (128 ) B.12 B.12(b), (c), (d), (e) JPEG ( ) B.12(f) Mikolajczyk 66
77 B.11: SIFT [29] 67
78 B.12: SIFT 68
79 C [1],,.,, Vol 22, 2008( ) [1] S. Shimizu, T. Nagahashi, and H. Fujiyoshi. Robust and Accurate Detection of Object Orientation and ID without Color Segmentation, Proc. on ROBOCUP2005 SYMPOSIUM, [2] Tomoyuki Nagahashi, Hironobu Fujiyoshi, and Takeo Kanade. Object Type Classification Using Structure-based Feature Representation, MVA2007 IAPR Conference on Machine Vision Applications, pp , May, [3] Tomoyuki Nagahashi, Hironobu Fujiyoshi, and Takeo Kanade. Image Segmentation Using Iterated Graph Cuts Based on Multi-scale Smoothing, Asian Conference on Computer Vision 2007, Part II, LNCS 4844, pp , [1],,. ID, 21 SIG-Challenge, pp , May, [2],,., CVIM 154, pp , [3],,. SIFT, SC-07-8, pp39-44, Jan
80 [4],,., 10 (MIRU2007), pp , Jul, [1],,.,, O-455, Sep,
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(b) BoF codeword codeword BoF (c) BoF Fergus Weber [11] Weber [12] Weber Fergus BoF (b) Fergus [13] Fergus 2. Fergus 2. 1 Fergus [3]
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[II] Optimization Computation for 3-D Understanding of Images [II]: Ellipse Fitting 1. (1) 2. (2) (edge detection) (edge) (zero-crossing) Canny (Canny operator) (3) 1(a) [I] [II] [III] [IV ] E-mail sugaya@iim.ics.tut.ac.jp
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2,a) 2,b) 2,c) 2,d),e) WiFi WiFi WiFi 1. SNS GPS Twitter Facebook Twitter Ustream 1 Graduate School of Information Science and Technology, Osaka University, Japan 2 Cybermedia Center, Osaka University,
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1,a) 1,b) Obstacle Detection from Monocular On-Vehicle Camera in units of Delaunay Triangles Abstract: An algorithm to detect obstacles by using a monocular on-vehicle video camera is developed. Since
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