Fast RANSAC with Preview Model Parameters Evaluation

Transcription

1 /2005/16(08) Journal of Software Vol.16, No.8 +, ( ATR, ) Fast RANSAC with Preview Model Parameters Evaluation CHEN Fu-Xing +, WANG Run-Sheng (National Key Laboratory of ATR, National University of Defense Technology, Changsha , China) + Corresponding author: Phn: , cft911@163.com, Received ; Accepted Chen FX, Wang RS. Fast RANSAC with preview model parameters evaluation. Journal of Software, 2005,16(8): DOI: /jos Abstract: RANSAC algorithm is one of the most widely used robust estimator in the field of computer vision, but, it s efficiency is low. The paper gives a preview model parameters evaluation RANSAC algorithm (PERANSAC): a preview model parameters evaluation selection is added to the RANSAC algorithm. With guaranteeing the same confidence of the solution as RANSAC, a very large number of erroneous model parameters obtained from the contaminated samples are discarded in the preview evaluation selection. PERANSAC algorithm is evaluated on both synthetic data and real-world images, a significant increase in speed is shown, and the solutions are the same as RANSAC s. Key words: RANSAC; PERANSAC; robust; fundamental matrix; LmedS estimation; outliers; inliers : RANSAC(random sample consensus) Robust, RANSAC. RANSAC (preview model parameters evaluation RANSAC, PERANSAC). RANSAC,,,, RANSAC., RANSAC, RANSAC. : RANSAC;PERANSAC; ; ;LmedS ;outliers;inliers : TP391 : A, Robust, outliers, outliers,inliers,,outliers., Robust, outliers [1]. M [2,3],.M : (1976 ),,,,, ; (1941 ),,,,,,.

2 1432 Journal of Software 2005,16(8),,,. M,,. Least-Median-Squares(LMedS) [2,3],,LMedS outliers. LMedS,, 50%,. Fishler Bolles [4] RANSAC, 50%, Robust,., [1 3,5] [6]. [7].,, Robust, MINPRAN [8],MLESAC [9]. RANSAC, M outliers,., RANSAC. PERANSAC(preview model parameters evaluation RANSAC) :,,,,., M, RANSAC. M,,,,,,. 1 RANSAC 1.1 RANSAC RANSAC,,M inliers. (1), M. m M 1 (1 (1 ε ) ) = P (1), ε (outliers ), m, P. (1), M ε, m, P. 1 P =0.95, M ε, m. Table 1 The number M of samples required to ensure P =0.95 for given ε and m 1 P =0.95, M ε,m Dimensionality Contamination levels 5% 10% 20% 25% 30% 40% 50% , ε,m, RANSAC. t s ; t c ; t, N ( ) Nt. RANSAC T = M ( ts + tc ) + MNt (2) M t s + t ) M, MNt M. ( c (2),RANSAC :(1) M ;(2).,, M.,,. 1.2 RANSAC (1) (1), P ε M; (2),, inliers ; (3) inliers ;

3 : 1433 (4) inliers. 2 PERANSAC 2.1,,,. inliers,,. outliers,,. M, ( inliers). (1), (1 ε) m,,,, P f,, (1 ε) m P f, (1) m 1 (1 (1 ε ) P ) M = P (3) (3), M, P,,., RANSAC,.,P f =1, (1), RANSAC., (3), P f <1, M RANSAC, outliers,,.,, RANSAC,,. 2.2 n, n f inliers P f, n f.,, P f, n, n f inliers, inliers n f,, outliers,., P f n f i n i i 1 ( ) C n (1 ) = Pf i= 0 f 1 ε ε (4) C n i., P f, n f, i n n f P f. inliers [8,9], (5), 1.96, inliers, outliers [8,9]. n 2m, σ : inliers, d t = 1.96σ z = (5) outlier, otherwise 5 σ = med i d i (6) n m d i,med i d i, n, m., (5) inliers, n f, n f,

4 1434 Journal of Software 2005,16(8),. 2.3 PERANSAC T ( outliers) P error, t, PERANSAC T = M + M )( P P Nt + (1 P ) P t + P (1 P ) Nt + (1 P )(1 P ) t ) + ( M + M )( t + t ) (7) ( f mean error mean s c m, M (1) ; M (3) (1) M ; P = ( 1 ε ) inliers. (7) (2), RANSAC,PERANSAC T = ( M + M )(1 P P P (1 P )) t M ( t + t Nt) (8) s c +, P P P (1 P ). t = Nt t 1. nt, t = ( N n) t, (8) T = ( M + M )(1 P P P (1 P ))( N n) t M ( t + t Nt) (9) mean s c + (9), T,, P mean, t s, t c, t, N, n, T P f,p error.p error,,, Perror P f. (4), P f ε. ε, ε,ε P f P error,.,., P f, P error., P f,, P error, ) (4),, n, n f ε; 2) (3), P f, P ε M ; 3), ; 4) n,, 3),., 1).,, ; 5), inliers ; 6) inliers ; 7) inliers. 3 RANSAC ;,, [9], 100., 2. : P = 99% ; n = 15 ; P f >80%; =. RANSAC PERANSAC. 1,,.,PERANSAC

5 : 1435 RANSAC,. 2 ; 3 PERANSAC RANSAC, 30%~50%., RANSAC,. Fig.1 The average epipolar distance 1 Fig.2 Time at different contamination levels 2 Fig.3 Percentage of speed increase : ( 4 ) 250; P = 99% ; n = 15 ; P f >80%. Fig.4 The images of left and right views of scene one RANSAC PERANSAC.,PERANSAC RANSAC,.,.,,,., ;,,,, RANSAC. Fig.5 The average epipolar distance 5 Fig.6 Time at different contamination levels 6 Fig.7 Percentage of speed increase 7

6 1436 Journal of Software 2005,16(8) 6 7 RANSAC PERANSAC PERANSAC RANSAC.,PERANSAC RANSAC 70%.,, inliers.,,,.,,, ( 8 ) 268, Fig.8 Images of left and right views of scene two 8 2 9~ 11 PERANSAC RANSAC. Fig.9 The average epipolar distance 9 Fig.10 Time at different contamination levels 10 Fig.11 Percentage of speed increase 11 4 RANSAC, RANSAC (PERANSAC), RANSAC,,,,, RANSAC. PERANSAC, PERANSAC.., RANSAC, RANSAC. inliers,.,,..,,. References: [1] Brandt S. Maximum likelihood robust regression with known and unknown residual models. In: Proc. of the ECCV [2] Murray PTD. The development and comparison of robust methods for estimating the fundamental matrix. Int l Journal of Computer Vision,

7 : 1437 [3] Zhang ZY. Determining the epipolar geometry and its uncertainty: A review. Int l Journal of Computer Vision, 1998,27(2): [4] Fischler MA, Bolles RC. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. CACM, 1981,24(6): [5] Chen ZZ, Wu CK. A linear algorithm with high accuracy for estimating fundamental matrix. Journal of Software, 2002,13(4): (in Chinese with English abstract). [6] Rousseeuw PJ. Robust Regression and Outlier Detection. New York: John Wiley & Sons, [7] Torr PHS, Murray DW. Outlier detection and motion segmentation. SPIE 93, [8] Stewart CV. MINPRAN: A new robust operator for computer vision. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1995,17(10): [9] Torr PHS, Zisserman A. MLESAC: A new robust estimator with application to estimating image geometry. Computer Vision and Image Understand, 2000,78: : [5],..,2002,13(4): /840.pdf,,,,..,,,. 1.,,,,. 2.,,,,,,.,. 3.,, ( ),,. 4.,, ( ),. 5., (,, ),.,. 6.,,.,,,,. 7.,,,,. 8.,,..,.,.