RANSAC RANSAC Amerini [8] RANSAC LO-RANSAC(Locally Optimized RANSAC)[9] LO-RANSAC 2.2 SIFT SIFT SIFT 128 SIFT SIFT SIFT SIFT p i p j d ij SIF

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1 RANSAC SIFT LO-RANSAC Improving the method detecting partially duplicated regions using RANSAC Kenji Kawashima 1 Tetsuya Matsumoto 1 Hiroaki Kudo 1 Yoshinori Takeuchi 2 Noboru Ohnishi 1 Abstract: This paper proposes a method to detect partial duplications in images with scaling, rotation, and reflection. The proposed method matches SIFT features each other and build the clusters based on a positional relationship between matched points. For each cluster, we estimate an affine transformation matrix between duplicated regions using LO-RANSAC. We detect duplicated region from difference between input image and image transformed by estimated matrix, and calculate confidence value from the statistic of difference in the detected region. Finally, the region whose confidence value is the highest is colored and outputted. The proposed method gives better performance than the conventional method. 1. [1] 1 Graduated School of Information Science Nagoya Unicersity 2 School of Informatics Daido University [2] SIFT(Scale-Invariant Feature Transform) [3] RANSAC(Random Sample Consensus)[4] [5] SIFT [6] Zheng [7] SIFT c 2014 Information Processing Society of Japan 1

2 RANSAC RANSAC Amerini [8] RANSAC LO-RANSAC(Locally Optimized RANSAC)[9] LO-RANSAC 2.2 SIFT SIFT SIFT 128 SIFT SIFT SIFT SIFT p i p j d ij SIFT v pi v pj v pi l v pi l d ij d ij (v pi, v pj ) = 128 l=1 (v pi l v pj l ) 2 (1) p i d ij d ij1 d ij2 < T h p (2) 1 SIFT SIFT 2 LO-RANSAC d ji1, d ji2 d ij 2 T h p SIFT c 2014 Information Processing Society of Japan 2

3 ( 1 ) P (a, a ) ( 2 ) a 2 b c a b a c R 1 R height width R = max(width, height) 4 (3) ( 3 ) b b c c 1 (a b) (a c) angle = cos a b a c angle = cos 1 (a b ) (a c ) a b a c length = a b a c length = a b a c (4) (5) (6) (7) ( 4 ) (8) (a, a ) (b, b ) (c, c ) 1 angle angle < T h angle T h length < length 1 length < (8) T h length ( 5 ) P (a, a ) (b, b ) (c, c ) (a, a ) ( 6 ) a 2 (b, b ) (c, c ) 2 R 5 ( 7 ) (a, a ) (b, b ) (c, c ) (5) (7) (8) (a, a ) P 5 ( 8 ) P 1 ( 9 ) P RANSAC(Random Sample Consensus) RANSAC LO-RANSAC(Locally Optimized RANSAC) LO-RANSAC LO-RANSAC p = (x, y, 1) T p = (x, y, 1) T x x y = H y (9) 1 H 3 3 [ ] a 11 a 12 t x A t H = = a 21 a 22 t y (10) A t H H H (p i, p i ) E E = p i H p i (11) E T h E (p i, p i ) H I H c 2014 Information Processing Society of Japan 3

4 I H I I H E g (12) diff H E g = I(x, y) I H (x, y) x, y I I H (12) I H 1 I H 1 I diff H 1 E g T h g 1 0 det(h) T h g (13) a g det(h) if det(h) 1.0 T h g = a g / det(h) otherwise a g (13) R I I H D I I H 1 D D D D D D D T h o (14) D D D D 2.5 RANSAC H [6] H H D D n c (x, y) diff H diff H (x, y) c c = n + 5 avg + 1 sdv (15) avg sdv c 0 [6] c D D H c k I k ( 1 ) I k H ( 2 ) H θ I k ( 3 ) I k H I k n c H ( 4 ) θ 1 θ c 2014 Information Processing Society of Japan 4

5 ( 5 ) c H k θ 2.6 T T RANSAC [10] ϵ m ϵ m T 1 (1 ϵ m ) T η 0 (1 η 0 ) T = log(1 η 0) log(1 ϵ m ) (16) ϵ η 0 ϵ m = [6] [pixels] [pixels] T h p = 0.49 T h E = 10 T h angle = 10 T h length = 0.7 a g = 3 T h o = 0.5 η 0 = 0.94 ϵ = 0.2 θ LO-RANSAC (%) = (17) 70% LO-RANSAC 5 5(b) 5(c) 5(d) 5(e) LO-RANSAC 0 4 c 2014 Information Processing Society of Japan 5

6 (a) IC:Inconsistency Coefficient 1 IC [pixels] (b) (c) 58% (d) (e) 87% 5 SIFT SIFT Amerini [8] [pixels] [pixels] IC 7 7(a) 7(b) c 2014 Information Processing Society of Japan 6

7 情報処理学会研究報告 も重要である 参考文献 [1] (a) クラスタリング結果 (b)lo-ransac に 同じ色の点が同じ 入力した対応点 [2] クラスターに属している [3] [4] [5] (c) 検出結果 再現率 55% 図 7 階層的クラスタリングの例 [6] [7] [8] (a)lo-ransac に (b) 検出結果 入力した対応点 再現率 76% 図 8 提案手法の例 [9] を加えた また LO-RANSAC による局所最適化処理を 追加した これにより 回転やスケーリングに対する頑健 性を維持しつつ 複写領域を結ぶ正しい対応と誤った対応 を分類し 検出結果の高精度化を試みた また 検出領域 [10] A. Popescu and H.Farid: Exposing digital forgeries by detecting duplicated image regions, Department of Computer Science, Dartmouth College, Tech. Rep. TR (2004). 野田恵司, バシャール カイルル, 竹内義則, 大西昇 ディジタル画像内での部分複写の検出, 映像情報メディ ア学会誌, 63, 11, pp (2009). D. Lowe, Distinctive image features from scaleinvariant keypoints, Proc. of International Journal of Computer Vision (IJCV), 60(2), pp , M. A. Fischler, R.C.Bolles, Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography, Communications of the ACM, vol. 24, no. 6, pp (1981). I. Amerini, L. Ballan, R. Caldelli, A. DelBimbo, and G. Serra, Geometric tmapering estimation by means of a SIFT-based forensic analysis, in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Dallas, USA, 富澤 圭, 松本 哲也, 工藤 博章, 竹内 義則, 大西 昇, 改ざん画像におけるアフィン変換を伴う部 分複写領域の検出, 電子情報通信学会技術研究報告, IE, 画像工学 111(442), , Jiming ZHENG, Wanrui HAO, Wei ZHU, Detection of Copy-move Forgery Based on Keypoints Positional Relationship, Journal of Information & Computational Science 9: 16, (2012). I. Amerini, L. Ballan, R. Caldelli, A. DelBimbo, and G. Serra, A SIFT-BASED Forensic Method for Copy-Move Attack Detection and Transformation Recovery, IEEE Transactions on Information Forensics and Security, Vol. 6, No. 3(2011). O. Chum, J. Matas, and J. Kittler, Locally Optimized RANSAC, Proc. DAGM, Springer-Verlag, Rahul Raguram, Jan-Michael Frahm, Marc Pollefeys, A Comparative Analysis of RANSAC Techniques Leading to Adaptive Real-Time Random Sample Consensus, ECCV 2008, Part II, LNCS 5303, pp (2008). の差分値の統計量を RANSAC の信頼値計算に加えること で 誤検出を減らすことを試みた 基にした従来手法との比較実験から 提案手法は回転や スケーリングへの頑健性を保持しつつ 検出精度を向上さ せた また 従来手法よりも誤検出は少なくなった クラスタリングの性能評価として 階層的クラスタリ ングを用いた手法との比較を行った その結果提案手法 は 比較手法よりも多くの画像に対して高精度な検出を行 なった 今後の課題として 特徴点の対応付けが取れないために 複写領域のアフィン変換推定が行えない場合への対応があ る 対応が取れない理由として 複写領域の輝度変化が緩 やかなために効果的な SIFT 特徴点が検出できないことが 考えられる そのため 特徴点を用いないブロックマッチ ング手法と組み合わせた手法が必要となる また 誤検出を減らすために 人工物などの周期的なパ ターンと部分複写を分離 判別できる手法を確立すること c 2014 Information Processing Society of Japan 7

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