Object Recognition Based on Photometric Alignment Using Random Sample Consensus

Transcription

1 Vol. 44 No. SIG 9(CVIM 7) July attached shadow photometrc algnment RANSAC RANdom SAmple Consensus Yale Face Database B RANSAC Object Recognton Based on Photometrc Algnment Usng Random Sample Consensus Takahro Okabe and Yoch Sato Photometrc algnment s a technque that represents both dffuse reflecton components and attached shadows under an arbtrary pont lght source wth three bass mages. In ths paper, we propose a method based on photometrc algnment for object recognton under varyng llumnaton. In order to synthesze a test mage relably n the face of outlers such as specular reflecton components and shadows, our method utlzes RANSAC (RANdom SAmple Consensus) whch has been used successfully for estmatng the bass mages. To demonstrate the effectveness of the proposed method, we conducted experments by usng the Yale Face Database B and confrmed that RANSAC s effectve not only for estmaton of the bass mages but also for object recognton under varyng llumnaton. 1. attached shadow cast shadow 4 22),23) Lambert generatve methods Insttute of Industral Scence, The Unversty of Tokyo Lambert 3 attached shadow 0 attached shadow attached shadow 3 22),23) 2 3 attached shadow cast shadow 124

2 Vol. 44 No. SIG 9(CVIM 7) RANSAC photometrc stereo 26) SVDMD Sngular Value Decomposton wth Mssng Data 24) 8) SVDMD 7) 14) RANSAC 6) 11) 16) 11),16) RANSAC attached shadow Yale Face Database B 7) RANSAC RANSAC feature-based methods appearance-based methods 2 5) 3),15),18),21),25) Lambert Lambert 3 22),23) 3 attached shadow cast shadow 7),8) attached shadow Lambert convex cone llumnaton cone 3 4) attached shadow 7),8) attached shadow attached shadow 1 2) 3) 7) 8) 10) 12) lnear subspace method

3 126 July ) 7),8) 4 9 1),20) 9 10),12) 10),12) 1 segmented lnear subspace method 2) 3 attached shadow attached shadow attached shadow 3. attached shadow 3.1 Lambert x (D) x (D) = ρ n T s b T s, ( =1, 2,,n) (1) ρ n s x (D) b T n n 3 B x (D) = Bs (2) (2) n L = {x x = Bs, s R 3 } (3) llumnaton subspace 4) 3 3 e (j) (j =1, 2, 3) x (D) = c 1 e (1) + c 2 e (2) + c 3 e (3). (4) c j (j =1, 2, 3) 3 attached shadow 3.2 attached shadow attached shadow

4 Vol. 44 No. SIG 9(CVIM 7) RANSAC 127 Attached shadow (1) b T s < 0 attached shadow attached shadow x (D+AS) 0 x (D+AS) = max (Bs, 0). (5) max(z, 0) z 0 3 attached shadow ( 3 ) x (D+AS) = max c j e (j), 0. (6) j=1 attached shadow attached shadow 22),23) attached shadow cast shadow ),8),11),14),16),26) 4.1 attached shadow cast shadow 4 (4) 3 (6) attached shadow attached shadow Lambert 3 RANSAC attached shadow 4.2 RANSAC (1) 3 ĉ j (j =1, 2, 3) (2) (1) attached shadow ( 3 ) ˆx = max ĉ j e (j), 0, ( =1, 2,,n). e (j) j=1 (7) j

5 128 July 2003 { 1 ( x (test) ˆx <t : nler) ξ = 0 ( x (test) ˆx t : outler) (8) x (test) t Lambert 19) (3) nler n support = ξ (9) =1 (4) (1) (3) (1) (3) support (5) nler t attached shadow { 1 (ξ =1,t< ˆx < 1 t) w = (10) 0 (others) ( n C = w =1 x (test) 3 j=1 ĉ j e (j) ) 2 (11) ĉ j (j =1, 2, 3) (6) (2) (7) (5) (6) (5) (6) ξ, ( =1, 2,,n) (8) support support support 8bt RANSAC RANSAC 11) 2 3 attached shadow cast shadow attached shadow cast shadow 3 nler nler attached shadow nler (4) attached shadow support support (5) 5. Yale Face Database B 7) 13) ,850 2 θ 5 650

6 Vol. 44 No. SIG 9(CVIM 7) RANSAC 129 (a) (b) (c) Fg Cropped mages of ten ndvduals. (d) (e) Subset1 12 Subset2 25 Subset3 50 Subset4 77 Subset5 77 Fg. 4 4 A test mage and syntheszed mages. 2 Fg. 2 Example mages n each subset: varablty due to llumnaton. 3 Fg. 3 Bass mages attached shadow cast shadow SVDMD 8) 3 (8) t σ t IS 3 PA1 3 RANSAC PA2 4 RANSAC 4 PA2 (a) (b) (d) t (c) (e) cast shadow 3 1 t 4σ IS attached shadow PA1 PA σ 5.5σ 4 1% 5 2%

7 130 July (%) Table 1 Recognton error rates (%). Method Subset2 Subset3 Subset4 Subset5 IS PA PA IC: attached 7) PL 12) PL 10) Segm. LS 2) attached shadow RANSAC cast shadow 5 2 cast shadow ) ),12) 2) 3 6. attached shadow 3 RANSAC attached shadow RANSAC cast shadow cast shadow 7),8) cast shadow 17) cast shadow Yale Face Database B 7) C ) Basr, R. and Jacobs, D.: Lambertan reflectance and lnear subspaces, Proc. IEEE ICCV 2001, pp (2001). 2) Batur, A.U. and Hayes III, M.H.: Lnear subspaces for llumnaton robust face recognton, Proc. IEEE CVPR 2001, 2, pp (2001). 3) Belhumeur, P.N., Hespanha, J.P. and Kregman, D.J.: Egenfaces vs. fsherfaces: recognton usng class specfc lnear projecton, IEEE Trans. PAMI, Vol.19, No.7, pp (1997). 4) Belhumeur, P.N. and Kregman, D.J.: What s the set of mages of an object under all possble lghtng condtons?, Int l. J. Computer Vson, Vol.28, No.3, pp (1998). 5) Brunell, R. and Poggo, T.: Face recognton: features versus templates, IEEE Trans. PAMI, Vol.15, No.10, pp (1993). 6) Fschler, M.A. and Bolles, R.C.: Random sample consensus: a paradgm for model fttng wth applcatons to mage analyss and automated cartography, Comm. ACM, Vol.24, No.6, pp (1981). 7) Georghades, A.S., Belhumeur, P.N. and Kregman, D.J.: From few to many: llumnaton cone models for face recognton under varable lghtng and pose, IEEE Trans. PAMI, Vol.23, No.6, pp (2001). 8) Georghades, A.S., Kregman, D.J. and Belhumeur, P.N.: Illumnaton cones for recognton under varable lghtng: faces, Proc. IEEE CVPR 98, pp (1998). 9) Hallnan, P.W.: A low-dmensonal representaton of human faces for arbtrary lghtng condtons, Proc. IEEE CVPR 94, pp

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