Abstract. Detection of Feature Points for Computer Vision. Harris. (feature point) (interest point) (corner) Moravec. Harris.

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1 Detection of Feature Points for Computer Vision Abstract Harris Harris Harris 1. (1 7) (8 10) (9) Moravec Yasushi KANAZAWA, Member (Department of Knowledge-based Information Engineering, Toyohashi University of Technology, Toyohashi-shi, Japan) and Kenichi KANATANI, Member (Department of Information Technology, Okayama University, Okayama-shi, Japan). Vol.87 No.1 pp Harris. (feature point) (interest point) (corner) p q ( 1) (residual sum of squares) J(p, q) = T p (i, j) T q (i, j) (1) (i,j) N ( 1) T p(i, j), T q(i, j) 0 1 (normalized correlation) 1043

2 1 Harris (Laplacian) f = f xx + f yy () x f(x, y) (gradient) f (Hessian) H ( ) ( ) fx fxx f xy f =, H = f y f xy f yy (3) () f (= trh) T p (i, j), T q (i, j) p, q N p q J (operator) 1 Harris 3. (x, y) f(x, y) x, y f(x, y) 3.1 x (invariant) x f x x f = f x + f y (4) det H = f xx f yy f xy (5) ( f, H f) = f xx f x + f xy f x f y + f yy f y (6) a, b (a, b) 3. (normal plane) (normal curvature) κ 1, κ (principal curvature) H = κ 1 + κ, K = κ 1 κ (7) (mean curvature) (Gaussian curvature) (total curvature) (11) K 0 (elliptic) (hyperbolic) (parabolic) ( ) 0 (minimal surface) H 0 H K (11) H = f xx + f yy + f xx fy f xy f y f x + f yy fx (1 + fx + fy ) = 1 ( ( f, H f) ) f 1 + f K = f xxf yy f xy 1 + f x + f y (8) = det H 1 + f (9) 1044 Vol.87, No.1, 004

3 (a) K > 0 (b) K < 0 (c) K = 0 K 3.3 (9) K f det H (1) Kitchen-Rosenfeld (13) Kitchen-Rosenfeld = f xxfy + f yy fx f xy f x f y fx + fy (10) (8) x f f y = 0 f yy (10) Dreschler Nagel (14) det H det H = 0 ( ) Kitchen-Rosenfeld (15) Zuniga-Haralick (16) Zuniga-Haralick = f xxf y + f yy f x f xy f x f y (f x + f y ) 3/ (11) f yy /f x ( 3) (9) f K f x, f x, f xx, f xy, f yy ( ) det H K (9) det H f K ( 3) (16) (17) Zuniga Haralick (16) Wang Brady (18) (11) Zuniga-Haralick 4. Harris 4.1 Harris (19) Harris = det Ĉ k(trĉ) (1) ( ) Gσ (f Ĉ = x) G σ (f x f y ) (13) G σ (f x f y ) G σ (fy ) k ( 4) G σ ( ) σ (1) G σ ( ) ( 4) Harris

4 4. C ( ) f C = x f x f y = f f (14) f x f y f y (direction tensor) f f 0 C 1 det C = 0 Ĉ Ĉ = G σ ( f f ) = α W α f α f α (15) f α α W α Ĉ f det Ĉ 0 0 det Ĉ (15) trĉ = G σ( f ) = α W α f α (1) ( 5) 4.3 G σ ( ) (1) k f G σ ( ) f(x, y) f(x + δx, y + δy) = f + f x δx + f y δy + 1 (f xxδx + f xy δxδy + f yy δy ) + (16) ( 5) trĉ det Ĉ f trĉ G σ ( ) G σ (δx) = G σ (δy) = 0 σ G σ (δx ) = G σ (δy ) = σ, G σ (δxδy) = 0 G σ (f) = f + σ f + O(σ4 ) (17) ( f () G σ (f x) = f x + σ f x/ +, G σ (f y ) = f y + σ f y / +, G σ (f x f y ) = f x f y + σ (f x f y )/ + (13) ( 6) ( Ĉ=C+σ H + 1 (( f)( f) +( f)( f) )) +O(σ 4 ) (18) Ĉ f 4.4 Harris f x, f y (13) G σ ( ) ( 7) (1) () 4.5 (13) Ĉ λ 1, λ Harris Ĉ xy Harris (1). Harris = λ 1 λ k(λ 1 + λ ) (19) Harris λ 1, λ λ 1 λ ( 6) (0) ( 7) (13) G σ( ) 1046 Vol.87, No.1, 004

5 (a) Moravec (b) KLT (c) SUSAN 3 1 Tomasi (3) Web ( 8) Kanade-Lucas- Tomasi (KLT) ( 9) min(λ 1, λ ) (4) Chabat (5) 1 (λ1 λ ) /(λ 1 + λ ) f ( 10) 5. Harris (6 8) (9, 30) Moravec (31) Moravec = 1 8 k,l=0,±1 f(x+k, y+l) f(x, y) (0) (3) (33) Moravec 8 SUSAN (Smallest Univalue Segment Assimilating Nucleus) (34) ( 11) ( 8) birch/klt/ ( 9) Ĉ (3) ( 10) ( 11) steve/susan/ SUZAN = c x,y (x, y ) = (x,y ) M x,y c x,y (x, y ) (1) { 1, f(x, y ) f(x, y) t 0, f(x, y ) f(x, y) > t () M x,y (x, y) t (1) (1) 50% 5% 75% MIC (Minimum Intensity Change) (35) ( MIC = min (f(x + t, y + s) f(x, y)) t +s =r +(f(x t, y s) f(x, y)) ) (3) r (x, y) SUSAN MIC f f (36) (37) 6. Harris 1047

[11],,, 1998. [1] P.R. Beaudet, Rotationally invariant image operators, Proc. 4th Int. Joint Conf. Patt. Recog, pp.579 583, Tokyo, Japan, 1978. [13] L. Kitchen and A.

6 3 1 (38) Harris ( 1) [1],,, 000. [] O. Faugeras and Q.-T. Luong, The Geometry of Multiple Images, MIT Press, Cambridge, Massachusetts, U.S., 001. [3] R. Hartley and A. Zisserman, Multiple View Geometry, Cambridge University Press, Cambridge, U.K., 000. [4],,, [5] :,,, ( ),, [6],,, [7], CG &,, 001. [8],, ( ),, [9], ( ),, 00. [10], ( ),, [11],,, [1] P.R. Beaudet, Rotationally invariant image operators, Proc. 4th Int. Joint Conf. Patt. Recog, pp , Tokyo, Japan, [13] L. Kitchen and A. Rosenfeld, Gray-level corner detection, Pattern Recognit. Lett., vol.1, no., pp.95 10, Dec [14] L. Dreschler and H.-H. Nagel, Volumetric model and 3D trajectory of a moving car derived from monocular TV frame sequences of street scenes, Comput. Graph. Image Process,, vol.0, no.3, pp.199 8, 198. [15] H.-H. Nagel, Displacement vectors derived from second-order intensity variations in image sequences, Comput. Vis. Graph. Image Process., vol.1, pp , [16] O.A. Zuniga and R.M. Haralick, Corner detection using the facet model, Proc. IEEE Conf. Comput. Vision Patt. Recog., pp.30 37, Washington, DC, June [17] J.A. Noble, Finding corners, Image Vis. Comput., vol.6, no., pp.11 18, May [18] H. Wang and M. Brady, Real-time corner detection algorithm for motion estimation, Image Vis. Comput., vol.13, no.9, pp , Nov [19] C. Harris and M. Stephens, A combined corner and edge detector, Proc. 4th Alvey Vision Conf., pp , Manchester, U.K., Aug [0] R. Deriche and G. Giraudon, A computational approach for corner and vertex detection, Int. J. Comput. Vis., vol.10, no., pp , April [1] K. Mikolajczyk and C. Schmid, Indexing based on scale invariant interest points, Proc. Int. Conf. Comput. Vision, vol.1, pp , Vancouver, Canada, July 001. [] K. Mikolajczyk and C. Schmid, An affine invariant interest point detector, Proc. Euro. Conf. Comput. Vision, vol.1, pp.18 14, Copenhagen, Denmark, May 00. [3] C. Tomasi and T. Kanade, Detection and tracking of point features, CMU Tech. Rep. CMU-CS-91-13, April birch/klt/ [4] J. Shi and C. Tomasi, Good features to track, Proc. IEEE Conf. Comput. Vision Patt. Recogn., pp , Seattle, WA, June [5] F. Chabat, G.Z. Yang, and D.M. Hansell, A corner orientation detector, Image Vis. Comput., vol.17, no.10, pp , Aug [6] K. Rangarajan, M. Shah, and D.V. Brackle, Optimal corner detector, Comput. Vis. Graph. Image Process., vol.48, no., pp.30 45, Aug [7] K. Rohr, Modeling and identification of characteristic intensity variations, Image Vis. Comput., vol.10, no., pp.66 76, March 199. [8] A. Singh and M. Shneier, Gray level corner detection: A generalization and a robust real time implementation, Comput. Vis. Graph. Image Process., vol.51, no.1, pp.54 69, July [9] S. Baker, S. K. Nayar, and H. Murase, Parametric feature detection, Int. J. Comput. Vis., vol.7, no.1, pp.7 50, March [30] P. Perona, Deformable kernels for early vision, IEEE Trans. Pattern Anal. Mach. Intell., vol.17, no.5, pp , May [31] H.P. Moravec, Towards automatic visual obstacle avoidance, Int. Joint Conf. Art. Intell., Cambridge, MA, USA, p.584, Aug [3] K. Paler, J. Föglein, J. Illingworth, and J. Kittler, Local ordered gray levels as an aid to corner detection, Pattern Recognit., vol.17, no.5, pp , [33] J. Cooper, S. Venkatesh, and L. Kitchen, Early jump-out corner detector, IEEE Trans. Pattern Anal. Mach. Intell., vol.15, no.8, pp.83 88, Aug [34] S. M. Smith and J. M. Brady, SUSAN A new approach to low level image processing, Int. J. Comput. Vis., vol.3, no.1, pp.45 78, May [35] M. Trajković and M. Hedley, Fast corner detection, Image Vis. Comput., vol.16, no., pp.75 87, Feb [36] D. Reisfeld, H. Wolfson, and Y. Yeshurun, Context-free attentional operators: the generalized symmetry transform, Int. J. Comput. Vis., vol.14, no., pp , March [37] R. Laganière, Morphological corner detection, Proc. Int. Conf. Comput. Vision, pp.80 85, Bombay, India, Jan [38] C. Schmid, C. Mohr, and C. Bauckhage, Evaluation of interest point detectors, Int. J. Comput. Vision, vol.37, no., pp , March ( ) IEEE ( 1) Vol.87, No.1, 004

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