IPSJ SIG Technical Report Vol.2013-CG-153 No.19 Vol.2013-CVIM-189 No /11/29 1,a) 0 1 SIFT SURF 1. Scale-Invariant Feature Transform (SIFT)[16]
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1 1,a) 0 1 SIFT SURF 1. Scale-Invariant Feature Transform (SIFT)[16] [14], [17] [6] 1 *1 SIFT 1 Shibuya CROSS TOWER 28th Floor Shibuya Shibuya-ku Tokyo, Japan a) manbai@d-itlab.co.jp *1 Binary Features, Binary Descriptors, Binary Codes 1.1 SIFT[16] SURF[6] ( 1 ) SIFT 128 unsigned char 1 128byte 1,000 1, byte 125Kbyte ( 2 ) 2 x 1, x 2 R D (1)(2) d E d θ d E (x 1, x 2 ) = (x 1 x 2 ) (x 1 x 2 ) (1) ( ) x d θ (x 1, x 2 ) = arccos 1 x 2 (2) x 1 x 2 D D D 1 1 SIFT D 1
2 B y y { 1, +1} B (3) y {0, +1} B (4) y (3) (4) Binary Hashing (3) (3)(4) y B 0 1 *2 2 XOR 1 1 CPU 1.3 *2 (3) ( 1 ) ( 2 ) 64bits SIFT [25] BRIEF[9] BRISK[15] ORB[20] ORB OpenCV Willow Garage OpenCV ORB FREAK[3] D-BRIEF[26] BinBoost[25] positive 2
3 2 3 BRIEF negative positive negative 2.1 BRIEF: Binary Robust Independent Elementary Features Calonder [9] BRIEF 2 2 u i, v i R 2 B i = 1,, B I(u i ), I(v i ) I(u i ) I(v i ) 1, 0 B bits u i, v i 3 2 BRIEF SIFT SURF 2 BRISK ORB 2.2 BRISK: Binary Robust Invariant Scalable Keypoints Leutenegger [15] BRISK 2 BRIEF FAST[19] 3 BRISK (a) BRIEF 2 BRISK 60 3
4 (a) (b) L (c) S 4 BRISK 4(a) 60 u i R 2 (i = 1,, 60) BRISK δ min L δ max S 4(b)(c) L, S L S L (u i, u j ) L (5) g(u i, u j ) = (u j u i ) I(u j, σ j ) I(u i, σ i ) u j u i 2 (5) I(u i, σ i ), I(u j, σ j ) σ i, σ j g(u i, u j ) u j, u i 4(b) α L g g = (g x, g y ) = 1 L (u i,u j) L g(u i, u j ) (6) α = atan2(g y, g x ) (7) α u i, u j u α i, uα j (8) 1 I(u α j y ij =, σ j) > I(u α i, σ i), (u i, u j ) S (8) 0 (otherwise) S S 512 δ max ORB: Oriented FAST and Rotated BRIEF BRISK ORB BRIEF 2 FAST BRISK 2 ORB α 0,1 (intensity centroid, C) O C α O m pq C m pq = x,y C = x p y q I(x, y) (9) ( m10, m ) 01 m 00 m 00 α (10) θ = atan2(m 01, m 10 ) (11) 2 α ORB y i % y i, y j 4
5 5 ORB 6 FREAK ORB [27], [29] y i, y j y i y i 100% 0 y i y i 0 1 y i ORB 205,590 Greedy 256 ( 1 ) ( 2 ) ( 3 ) ( 4 ) ORB FREAK: Fast Retina Keypoint Alahi [3] FREAK ORB BRISK FREAK 6 FREAK Alahi FREAK ORB BRISK 43 ORB Greedy 512 Alahi 512 FREAK 512 Greedy coarse-to-fine FREAK % 128 FREAK 5
6 BRISK 2.5 D-BRIEF: Discriminative BRIEF BRIEF, BRISK, ORB, FREAK 2 x *3 x i y i (12) *4 y i = sgn(w i x + τ i ) (12) τ i = 0 w i BRIEF, BRISK, ORB, FREAK w i τ i Trzcinski [26] D-BRIEF w i τ i w i w i x D-BRIEF w i w i x w i = Ds i (13) D s i s i w i D-BRIEF (14) *3 N N x N 2 *4 3 Binary Hashing min (s i,τ i) i 1,,B sgn((ds i ) x + τ i )sgn((ds i ) x + τ i ) (x,x ) N sgn((ds i ) x + τ i )sgn((ds i ) x + τ i ) (x,x ) P + λ s i 1 subject to (Ds i ) (Ds j ) = δ ij (14) (x, x ) P (x, x ) N λ s i w i δ ij i = j 1 0 (Ds i ) (Ds j ) = δ ij ORB (14) x, x y, y (14) min y y y y + λ s i 1 (15) (s i,τ i) (x,x ) N (x,x ) P N P s i, τ i D-BRIEF y, y { 1, +1} B d H (y, y ) y y (16) y y = B 2d H (y, y ) (16) y, y y y (14) P N w i, τ i D-BRIEF (14) (14) s i, τ i sgn L1 s i w i (17) (x,x {w 0 i } = arg min ) P (w i (x x )) 2 {w i} (x,x ) N (w i (x x )) 2 i (17) w i Linear Discriminant 6
7 Embedding (LDE)[8] sgn τ i LDE w i τ i (14) τ i *5 w 0 i w0 i Ds i s i w i s i {s 0 i } = arg mins i w 0 i Ds i λ s i 1 (18) 2.6 BinBoost Trzcinski [25] BinBoost K 1 x y i y i (x) = sgn(w i h i (x)) (19) { 1, +1} i h i R K K w i R K h i x D-BRIEF BinBoost AdaBoost N {(x n, x n, l n )} N n=1 x n x n l n = +1, l n = 1 (20) w i h i N L = min {w i,h i} B i=1 exp( γl n n=1 B i=1 c i (x n, x n; w i, h i )) (20) γ c i c i (x n, x n; w i, h i ) = y i (x)y i (x ) (21) = sgn(w i h i (x))sgn(w i h i (x )) l n = +1 l n = 1 (16) *5 τ i LDAHash[24] AdaBoost i = 1 h i w i (20) (22) N max l n W i (n)c i (x n, x n; w i, h i ) (22) w i,h i n=1 W i (n) i 1 W i (n) = exp( γl n c i (x n, x n; w i, h i )) (23) i =1 1,, i 1 AdaBoost c i sgn (22) sgn (24) max w i ( w i,h i N l n W i (n)h i (x)h i (x ) )w i (24) n=1 h i W i (n) BinBoost [23] K K B K B b i (24) h i (24) M = max w i w i Mw i (25) N l n W i (n)h i (x)h i (x ) (26) n=1 (19) w i w i 2 = 1 (25) M 7
8 7 sgn(p i x 1) sgn(p i x 2) sgn(p i x 1) = sgn(p i x 2) Random projections 3. Binary Hashing web (27) y = sgn(px + t) (27) x D y B t P B D P t Random projections[5], [10] (CARD[4], LDAHash[24]) CARD LDAHash 3.1 Random Projections Random projections [5], [10] Binary Hashing P x D B 2 (D = 2) x 1, x 2 θ (27) t = 0 P 2 Random projections P 2 θ x 1 x 2 θ x 1 x 2 x 1 x 2 θ (28) Pr[sgn(p i x 1 ) sgn(p i x 2 )] = θ π (28) (28) p i x 1 x 2 B B Random projections SIFT SURF (mean centering) Random projections Random projections Random Projections 3.2 CARD: Compact And Real-time Descriptors Ambai[4] CARD SIFT 2 (1) (2)Binary Hashing P CARD BRISK ORB Binary Hashing SIFT CARD K L CARD 4 4 8
9 8 CARD L M θ(x, y) M L M L θ(x, y) (29) l = Q L (Q 1 M (θ(x, y) α)) (29) (a) α = 0 (b) α = 3 9 l l = 0,, L 1 Q N ( ) 0 N 1 Q 1 N ( ) θ(x, y) α Q L (Q 1 M ( )) (29) θ(x, y) α M 10 M M (30) Binary Hashing y = sgn(px) (30) 10 8 K = 17, L = SIFT α SIFT 2 CARD α = 0, 1,, M 1 CARD α M M 9 M = 40 α = 0, 3 (x, y) x t Binary Hashing P B D (30) B D B (D 1) 2 P ( 1 ) ( ) P ( 2 ) P S 1, 0, 1 W (1) (2) (30) S P P 90% 9
10 128bit 3.3 LDAHash Strecha [24] LDAHash 2 (x, x ) P 2 (x, x ) N P N P t LDAHash (31) L = αe{d H (y, y ) P} E{d H (y, y ) N } (31) d H y y E{ P}, E{ N } P, N P, N (31) (31) (32)(33) L = E{y y N } αe{y y P} (32) L = αe{ y y 2 P} E{ y y 2 N } (33) y { 1, +1} B (31) (32) d H y y (16) (31) (33) y y 2 = y 2 2y y + y 2 (34) (16) (34) (35) y y 2 = 4d H (y, y ) 2B + y 2 + y 2 (35) y { 1, +1} B y 2 = y 2 = B (31) (33) P, t (33) y, y sgn (33) sgn L = αe{ Px Px 2 P} E{ Px Px 2 N } (36) (36) t (33) (36) P P (32) t P Strecha (36) Linear Discriminant Analysis (LDA) Difference of Covariances (DIF) P, N Σ P, Σ N Σ P = E{(x x )(x x ) P} (37) Σ N = E{(x x )(x x ) N } (38) LDA Σ R = Σ P Σ 1 N DIF Σ D = ασ P Σ N Linear Discriminant Analysis (LDA) Σ P, Σ N (36) L = αtr(pσ P P ) tr(pσ N P ) (39) x Σ 1/2 N (39) (39) L tr(pσ 1/2 N Σ PΣ /2 N P ) (40) = tr(pσ P Σ 1 N P ) = tr(pσ R P ) (41) Σ R = Σ P Σ 1 N Σ P Σ N tr(pσ R P ) Σ R B S 1/2 R Ũ RΣ 1/2 N (42) S R B B B ŨR D B Difference of Covariances (DIF) (39) Σ D = ασ P Σ N L = tr(pσ D P ) (43) 10
11 LDA P Σ D B B B S D D B ŨD P (44) P = 1/2 S D Ũ D (44) LDA DIF P N α α Σ N Σ N = I t P (32) t t t i t i p i min t i E {sgn((p i x + t i ) (p i x + t i )) N } αe{sgn((p i x + t i ) (p i x + t i )) P} (45) P i 1 t i 4. 2, 3 1 LDAHash, D-BRIEF, Bin- Boost LDAHash Binary Hashing D-BRIEF BinBoost 1 1 msec #include "intrin.h" int _mm_popcnt_u32 ( unsigned int a); int _mm_popcnt_u64 ( unsigned int64 a); 11 SSE4.2 (46) y = sgn(pf(x) + t) (46) x R N 2 N N P R B D t R B f( ) x f : R N 2 R D (47) P, t, f( ) 2 BRIEF, BRISK, ORB, FREAK, D-BRIEF x Binary Hashing f(x) = x BinBoost f(x) D P Random projections, CARD, LDAHash f(x) SIFT SURF Binary Hashing f(x) BinBoost f(x) P Boosting XOR Intel Core i7 SSE4.2 C/C++ intrin.h include 32/64 ( 11) *6 64 mm popcnt u64() 64 *6 GCC (-msse4.2) 11
12 1 BRIEF (ECCV 2010) BRISK (ICCV 2011) ORB (ICCV 2011) FREAK (CVPR 2012) D-BRIEF (ECCV 2012) BinBoost (CVPR 2013) Random projections CARD (ICCV 2011) LDAHash (PAMI 2012) 2 P t f(x) BRIEF (ECCV2010) t = 0 f(x) = x BRISK (ICCV2011) t = 0 f(x) = x ORB (ICCV2011) t = 0 f(x) = x FREAK (CVPR2012) t = 0 f(x) = x D-BRIEF (ECCV2012) f(x) = x BinBoost (CVPR2013) t = 0 Random projections t = 0 (SIFT, SURF ) CARD (ICCV2011) { 1, 0, +1} t = 0 mean centering LUT mean centering LDAHash (PAMI2012) LDA DIF (SIFT, SURF ) inline unsigned int popcnt32(unsigned int x) { x = (x & 0x ) + ((x >> 1) & 0x ); x = (x & 0x ) + ((x >> 2) & 0x ); x = (x & 0x0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f); x = (x & 0x00ff00ff) + ((x >> 8) & 0x00ff00ff); x = (x & 0x0000ffff) + ((x >> 16) & 0x0000ffff); return x; } #define CSA(h,l,a,b,c) \ {unsigned u = a ^ b; unsigned v = c; \ h = (a & b) (u & v); l = u ^ v;} 13 (carry-save adder, CSA) 12 [18], [28] (a) 3 (b) 7 14 (carry-save adder, CSA) [18] 3 a, b, c 2 h, l C/C++ 13 a, b, c 12
13 3 CSA 1 CSA 2 pop(a) + pop(b) + pop(c) = 2 pop(h) + pop(l) (48) pop( ) a, b, c 3 a, b, c CSA 1 h, l l h 2 CSA a, b, c CSA 3 14(a) CSA CSA CSA 14(b) 7 4 CSA 3 CSA CSA [18] CPU CPU CSA 6. Binary Hashing 2007 SIGIR Workshop Hinton RBM Semantic Hashing[21] Weiss 2008 NIPS Spectral Hashing[29] Binary Hashing 2011 CVPR Iterative Quantization[12] Binary Hashing [13] VLAD Fisher Vector [11] [22] Binary Hashing Mikolajczyk [17] Affine Covariant Regions Datasets[1] Homography Brown [7] Multi-view Stereo Correspondence Dataset[2] Difference of Gaussian (DOG) Harris [1] : Affine Covariant Regions Datasets, (online), available from vgg/data/dataaff.html (accessed ). [2] : Multi-view Stereo Correspondence Dataset, (online), available from mbrown/ patchdata/patchdata.html (accessed ). [3] Alahi, A., Ortiz, R. and Vandergheynst, P.: FREAK: Fast Retina Keypoint, CVPR, pp (2012). [4] Ambai, M. and Yoshida, Y.: CARD: Compact And Realtime Descriptors, ICCV, pp (2011). [5] Andoni, A. and Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions, Communications of the ACM (2008). [6] Bay, H., Ess, A., Tuytelaars, T. and Van Gool, L.: Speeded-Up Robust Features (SURF), Computer Vision and Image Understanding, Vol. 110, pp (2008). [7] Brown, M., Hua, G. and Winder, S.: Discriminant Learning of Local Image Descriptors, PAMI, Vol. 33, pp (2011). [8] Brown, M., Hua, G. and Winder, S.: Discriminative 13
14 3 BRIEF (ECCV2010) C++(OpenCV2.0 ) BRISK (ICCV2011) C++(OpenCV2.2 ), MATLAB OpenCV ORB (ICCV2011) OpenCV FREAK (CVPR2012) C++(OpenCV ) OpenCV MATLAB MATLAB R2013a Computer Vision System Toolbox 5.2 D-BRIEF (ECCV2012) C++(OpenCV2.0 ), MATLAB BinBoost (CVPR2013) C++ CARD (ICCV2011) MATLAB (Denso IT Laboratory, Inc.) ios : CARDesc, AppStore (Apple Inc.) LDAHash (PAMI2012) C++(OpenCV ) Learning of Local Image Descriptors, PAMI, Vol. 33, No. 1, pp (2011). [9] Calonder, M., Lepetit, V., Strecha, C. and Fua, P.: BRIEF: Binary Robust Independent Elementary Features, ECCV, pp (2010). [10] Goemans, M. X. and Williamson, D. P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, Journal of the ACM, Vol. 42, pp (1995). [11] Gong, Y., Kumar, S., Rowley, H. A. and Lazebnik, S.: Learning Binary Codes for High-Dimensional Data Using Bilinear Projections, CVPR, pp (2013). [12] Gong, Y. and Lazebnik, S.: Iterative quantization: A procrustean approach to learning binary codes, CVPR, pp (2011). [13] Heo, J.-P., Lee, Y., He, J., Chang, S.-F. and Yoon, S.-E.: Spherical hashing, CVPR, pp (2012). [14] Ke, Y. and Sukthankar, R.: PCA-SIFT: A More Distinctive Representation for Local Image Descriptors, CVPR, pp (2004). [15] Leutenegger, S., Chli, M. and Siegwart, R.: BRISK: Binary Robust invariant scalable keypoints, ICCV, pp (2011). [16] Lowe, D. G.: Distinctive Image Features from Scale- Invariant Keypoints, IJCV, Vol. 60, pp (2004). [17] Mikolajczyk, K. and Schmid, C.: A Performance Evaluation of Local Descriptors, PAMI, Vol. 27, pp (2005). [18] Oram, A. and Wilson, G.: Beautiful Code: Leading Programmers Explain How They Think, Oreilly & Associates Inc (2007). [19] Rosten, E. and Drummond, T.: Machine learning for high-speed corner detection, ECCV, pp (2006). [20] Rublee, E., Rabaud, V., Konolige, K. and Bradski, G.: ORB: An efficient alternative to SIFT or SURF, ICCV, pp (2011). [21] Salakhutdinov, R. R. and Hinton, G. E.: Semantic hashing, SIGIR workshop on Information Retrieval and applications of Graphical Models (2007). [22] Sato, I., Ambai, M. and Suzuki, K.: Sparse Isotropic Hashing, IPSJ Transactions on Computer Vision and Applications, Vol. 5, No. 0, pp (2013). [23] Shakhnarovich, G.: Learning Task-Specific Similarity, Ph.D thesis, Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science (2006). [24] Strecha, C., Bronstein, A., Bronstein, M. and Fua, P.: LDAHash: Improved Matching with Smaller Descriptors, PAMI, Vol. 34, No. 1, pp (2012). [25] Trzcinski, T., Christoudias, M., Lepetit, V. and Fua, P.: Boosting Binary Keypoint Descriptors, CVPR, pp (2013). [26] Trzcinski, T. and Lepetit, V.: Efficient Discriminative Projections for Compact Binary Descriptors, ECCV, pp (2012). [27] Wang, J., Kumar, S. and Chang, S.-F.: Sequential Projection Learning for Hashing with Compact Codes, ICML (2010). [28] Warren, H. S.: Hacker s Delight (2nd Edition), Addison-Wesley Professional (2012). [29] Weiss, Y., Torralba, A. and Fergus, R.: Spectral Hashing, NIPS, pp (2008). 14
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1,a) 2 4 WC C WC C Grading Student programs for visualizing progress in classroom Naito Hiroshi 1,a) Saito Takashi 2 Abstract: To grade student programs in Computer-Aided Assessment system, we propose
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Vol. 52 No. 1 257 268 (Jan. 2011) 1 2, 1 1 measurement. In this paper, a dynamic road map making system is proposed. The proposition system uses probe-cars which has an in-vehicle camera and a GPS receiver.
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情報処理学会研究報告 い認識率を示す事が出来なかったと報告している 視覚特徴量としては SIFT や SURF のような局所的な 領域から特徴量を抽出する方法がある [4] [5] これらの 特徴量とフローベクトルを使いダイナミックなシーンの分 類を行う手法が提案されている しかし これらの画像特
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paper.dvi
SIFT 23 (410M5B1) SIFT(Scale Invariant Feature Transform) SIFT SIFT SIFT SIMD SIFT SIMD MIMD Gaussian SIMD Abstract Currently, with the development of image-recognition technique, to recognize a large
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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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a) Change Detection Using Joint Intensity Histogram Yasuyo KITA a) 2 (0 255) (I 1 (x),i 2 (x)) I 2 = CI 1 (C>0) (I 1,I 2 ) (I 1,I 2 ) 2 1. [1] 2 [2] [3] [5] [6] [8] Intelligent Systems Research Institute,