HOG HOG LBP LBP 4) LBP LBP Wang LBP HOG LBP 5) LBP LBP 1 r n 1 n, 1

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1 1 1 1 Shwartz Histgrams of Oriented Gradients HOG PLS PLS KPLS INRIA PLS KPLS KPLS PLS Pedestrian Detection Using Kernel Partial Least Squares Analysis Takashi Abe, 1 Takayuki Okatani 1 and Kouichiro Deguchi 1 Shwartz et al. have recently proposed a method for pedestrian detection that uses a very high-dimensional, discriminative feature obtained by combining HOG descriptors with additional color and texture features. To deal with the high dimensional feature by classical machine learning algorithms, they employed Partial Least Squares (PLS) Analysis, an efficient dimensionality reduction technique, and reported promising results. In this paper, focusing on dimensionality reduction, we examine the possibility of applying Kernel Partial Least Squares (KPLS) Analysis, a variant of PLS that uses the kernel method widely used in other classification/recognition methods such as SVM. We experimentally compare PLS and KPLS in terms of detection accuracy using the INRIA pedestrian dataset. The results show that KPLS outperforms PLS. 1 Tohoku University 1. Dalal Triggs Histograms of Oriented Gradients HOG 1) HOG Zhu HOG HOG 2) Shwartz HOG Color Frequency 2 HOG 3) PLS PLS PLS KPLS SVM KPLS PLS 2. HOG HOG Local Binary Pattern LBP Color Frequency 2.1 HOG HOG 1 c 21 Information Processing Society of Japan

2 HOG HOG LBP LBP 4) LBP LBP Wang LBP HOG LBP 5) LBP LBP 1 r n 1 n, 1 LBP u LBP LBP L L > u LBP non-uniform LBP L, 1,..., u, non-uniform u + 2 LBP n = 8, r = 1, u = LBP Color Frequency Color Frequency 3) (x, y) Color Frequency C(x, y) C(x, y) argmax m c(x, y) c=r,g,b transition * 1111 LBP m c (x, y) (x, y) RGB Color Frequency C 3 HOG 44 LBP PLS PLS PLS 3.1 PLS 1 N x = [x 1, x 2,..., x N ] y n {(x i, y i )} i = 1,..., n n N X = [x 1, x 2,..., x n] n y = [y 1, y 2,..., y n ] {x i } {y i } n i=1 x i/n =, n i 1 y i/n = 2 c 21 Information Processing Society of Japan

3 PLS y x x i y i w w w = argmax[cov(xr, y)] 2. (1) r =1 cov[ ] n a, b [a, b] = a b/n w N PCA PLS w 1 t Xw t X tp 2 p X X X tp y y tc 2 c y y tc p = X t/ t 2 c = y t/ t 2 u y w X y p p W [w 1,..., w p] X y 6) PLS1 NIPALS Nonlinear Iterative Partial Least Squares t 1 k = 1,..., p t p u t k, p k, u k for k = 1 to p do w k = X y, w k w k / w k t k = Xw k, t k t k / t k u k = y, u k u k / u k X X t k t k X y y t k t k y end for X y X = TP + F, y = Uq + g. T [t 1,..., t p ] U [u 1,..., u p ] p n p P [p 1,..., p p ] q N p p F g n N n 3.2 PLS W = [w 1,..., w p ] N p x p (2a) (2b) z = W x (3) W W = X U (4) 7) k X X k, y y k w k = X k u k X k = X k 1 t k 1 t k 1X k 1 w k = X k 1(I t k 1 t k 1)u k l < k l t l u k = t k t l = δ kl u k = y k 1 m=1 t mt my t l t l u k = w k = X k 1u k k 1, k 2,... w k = X 1u k X 1 X W = XU 3.3 Kernel PLS KPLS x S F ϕ ϕ : x R N ϕ(x) F {x 1,..., x n} ϕ F F PLS ϕ i ϕ(x i) (i = 1,..., n) n S Φ [ϕ 1,..., ϕ n] F {ϕ 1,..., ϕ n } NIPALS w k = X y w k t k = Xw k X XX 3 c 21 Information Processing Society of Japan

4 for k = 1 to p do t k = ΦΦ y, t i t k / t k u k = y, u k u k / u k ΦΦ (Φ t k t k Φ)(Φ t k t k Φ) y y t k t k y end for ϕ(x) K(x i, x j) ϕ(x i) ϕ(x j) = ϕ i ϕ j K(x i, x j) (i, j) n n K K = ΦΦ for k = 1 to p do t k = Ky, t k t k / t k u k = y, u k u k / u k K (I t k t k )K(I t k t k ) y y t k t k y end for I n n 3.4 KPLS PLS (p) (3) W (4) ϕ PLS W = Φ U (5) x t ϕ t ϕ(x t ) z = U Φϕ t (6) K(x i, x j ) ϕ i ϕ t k t [K(x 1, x t),..., K(x n, x t)] z t = U k t (7) 8) z t = (U KT) 1 U k t (8) p 4. PLS KPLS INRIA INRIA HOG, LBP Color Frequency 222 SVM KPLS K(x, x ) = exp( β x x 2 ) (9) PLS, KPLS 4.1 PLS KPLS F alsep os F alsep os+t rueneg Error Trade off F alseneg DET Detection F alseneg+t ruep os PLS p 2, 24, 28 2 p = 24 KPLS q β 3 q = 15, β =.3 4 c 21 Information Processing Society of Japan

5 PLS KPLS.1.1 miss rate miss rate.1.1 False positives per window 2 PLS p DET.1.1 False positives per window 4 KPLS PLS DET 3 miss rate False positives per window q=11, beta=.6 q=11, beta=.3 q=15, beta=.6 q=15, beta=.3 q=19, beta=.6 q=19, beta=.3 KPLS q β DET 4.2 KPLS vs PLS 4 KPLS PLS KPLS PLS.1% PLS 4.3% 3.% 5(a) 5(b) KPLS PLS 2 KPLS PLS 4.3 KPLS PLS KPLS PLS CPU Corei7-92, 24GB DDR PLS 18.6 PLS 5 c 21 Information Processing Society of Japan

6 情報処理学会研究報告単なる行列積を計算するだけであるが KPLS はカーネル関数の計算を何度も行う必要があるため所要時間に大きな違いがある.2 Negative samples Positive samples 5 5. 結論次元数が大きい特徴量の次元削減の手段として KPLS を用いた実験の結果他のカー second dimension.5 ネル法を用いた手法と同様に KPLS は PLS に比べて歩行者認識に対して優位な性能を持つことがわかった -.5 今後カーネル SVM と PLS 線形 SVM と KPLS のように分類器の種類と次元削減 - の方法の組み合わせが性能にどのような影響を与えるかを検討したい -5 計算時間の問題については前節で述べたように現状では実際のアプリケーションに用いることができる速度は達成できていないがアルゴリズムの見直しや GPU 上での実装など first dimension 5.2 により識別性能と計算量のバランスをはかれると考えている.25 参 (a) KPLS Negative samples Positive samples 15 second dimension first dimension (b) PLS 図5 文献 1) Dalal, N. and Triggs, B.: Histograms of Oriented Gradients for Human Detection, Computer Vision and Pattern Recognition, 25. CVPR 25. IEEE Computer Society Conference on, Vol.1, pp (25). 2) Zhu, Q., Yeh, M.-C., Cheng, K.-T. and Avidan, S.: Fast Human Detection Using a Cascade of Histograms of Oriented Gradients, CVPR 6: Proceedings of the 26 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Washington, DC, USA, IEEE Computer Society, pp (26). 3) Schwartz, W., Kembhavi, A., Harwood, D. and Davis, L.: Human Detection Using Partial Least Squares Analysis, Accepted to be presented in the International Conference on Computer Vision (29). 4) Ojala, T., Pietikainen, M. and Harwood, D.: A Comparative Study of Texture Measures with Classiﬁcation Basedon Feature Distributions, PR, Vol.29, No.1, pp (1996). 5) Xiaoyu Wang, Tony X. Han, S. Y.: An HOG-LBP Human Detector with Partial Occlusion Handling, Accepted to be presented in the International Conference on Computer Vision (29). 6) Rosipal, R. and Kra mer, N.: Overview and Recent Advances in Partial Least Squares, Subspace, Latent Structure and Feature Selection Techniques (et al., C.S., ed.), Springer-Verlag, pp (26). 7) Ra nnar, S., Lindgren, F., Geladi, P. and Wold, S.: A PLS kernel algorithm for data sets with many variables and fewer objects. Part 1: Theory and algorithm, 考 KPLS PLS による次元削減後のテストデータの第一第二次元 6 c 21 Information Processing Society of Japan

7 Chemometrics and Intelligent Laboratory Systems, Vol.8, pp (1994). 8) Rosipal, R. and Trejo, L.J.: Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space, Journal of Machine Learning Research, Vol.2, pp (21). 7 c 21 Information Processing Society of Japan

IPSJ SIG Technical Report Vol.2010-CVIM-170 No /1/ Visual Recognition of Wire Harnesses for Automated Wiring Masaki Yoneda, 1 Ta

IPSJ SIG Technical Report Vol.2010-CVIM-170 No /1/ Visual Recognition of Wire Harnesses for Automated Wiring Masaki Yoneda, 1 Ta 1 1 1 1 2 1. Visual Recognition of Wire Harnesses for Automated Wiring Masaki Yoneda, 1 Takayuki Okatani 1 and Koichiro Deguchi 1 This paper presents a method for recognizing the pose of a wire harness