3D Modeling from Range Images
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1 1 3D Modeling from Range Images A Comprehensive System for 3D Modeling from Range Images Acquired from a 3D ToF Sensor Dipl.-Inf. March 22th, 2007
2 Sensor and Motivation 2 3D sensor PMD 1k-S time-of-flight (ToF) infrared signal (active illumination) 3D point cloud in real-time resolution: camera resolution (pixels) 1k-S 19k 16 x x 160 v v v scene acquisition via an arbitrary camera flight reconstruction of point cloud representing the whole scene
3 Overview 3 PREPROCESSING REGISTRATION COARSE REGISTRATION FINE REGISTRATION RESULTS AND EVALUATION
4 Preprocessing n frames 4 preprocessing n frames preprocessed + n 3D point clouds 2 consecutive frames coarse registration R 0, t0 fine registration Rk, tk R, t iterative process preprocessing median filter on distances amplitudes intensities thresholding on amplitudes edge point removal on median filtering distance-adaptive dis (mm) 1k-S < < > k < 3000 < 6000 > 6000 filtermask distances back-projection of distances thresholding threshold amp = 13 mean value of all amplitudes i of a frame rejection of all pixels i with: i amp
5 Preprocessing n frames 5 preprocessing n frames preprocessed + n 3D point clouds 2 consecutive frames coarse registration R 0, t0 Rk, tk fine registration R, t iterative process preprocessing median filter on distances amplitudes intensities thresholding on amplitudes edge point removal on distances edge point removal for each pixel i computing of distances to its neighbors in the 8-neighborhood rejection of pixels with less than 2 near neighbors back-projection of distances back-projection assumption of ideal perspective projection intrinsic parameters, assumed as known: focal length pixel size position of optical center position of the principal point
6 Registration 6 sequential processing of N frames F0, F1,..., FN of a sequence problem of registering whole sequence reduced to the problem of estiming optimal motion (Ri, ti) between 2 frames A (= Fi ) and B ( = Fi-1) coarse registration: computing an initial transformation between Fi and Fi-1 frame Fi fine registration: frame Fi-1 optimizing the initial estimate frame F2 Rg, i, tg, i Rg, i-1, tg, i-1ri, ti frame F1 frame F0 Rg, 2, tg, 2 y Rg, 1, tg, 1 R2, t2 R1, zt1 x common coordinate system
7 Coarse Registration n frames preprocessing 7 n frames preprocessed + n 3D point clouds 2 consecutive frames coarse registration R0, t0 Rk, tk R, t fine registration iterative process coarse registration find good features in frame A intensity image amplitude image distance image C track features Lucas & Kanade tracker RANSAC for rejection of outliers in point correspondences C' SVD R 0, t0 frame B feature extraction in frame A edge, corners structure tensor feature tracking in frame B optical flow local method of Lucas&Kanade point correspondences C ={ i, j a i A and b i B } rejection of bad correspondences via RANSAC computing of initial transformation (R0, t0) via SVD
8 Fine Registration n frames preprocessing 8 n frames preprocessed + n 3D point clouds 2 consecutive frames coarse registration R 0, t0 R, t fine registration Rk, tk iterative process Picky ICP frame B frame A Calculation of next neighbors R0, t 0 Rk, t k Ck Rejection of bad point pairs Ck,r extrapolation SVD R k, tk Breakconditions fulfilled? yes R, t no NN-Search: reverse calibration, region of interest rejection of bad point pairs pairs with a distance greater than dis = median { b j a i } i, j C several points have same NN-Point (overlapping point clouds) rejection of all pairs apart from the pair with the smallest Euclidean distance
9 Fine Registration n frames preprocessing 9 n frames preprocessed + n 3D point clouds 2 consecutive frames coarse registration R 0, t0 R, t fine registration Rk, tk iterative process Picky ICP frame B frame A Calculation of next neighbors R0, t 0 Rk, t k Ck Rejection of bad point pairs Ck,r SVD extrapolation computation of optimal transformation (Rk,tk ) by minimizing f min R k, t k = 1 C i, j C b j R k a i t k via SVD extrapolation recognize drift direction in transformations R k, tk Breakconditions fulfilled? yes R, t no additional break conditions (convergence) only small changes in computed transformation or in the adjust2 ment error e= 1 b j a i C i, j C number of maximal iteration steps exceed
10 Results 10 pr acquisition ss ce ro ep g in ct tru ns co re Pentium 4 with CPU 3.00GHz and 1.00GB RAM Intel Performance Primitives io n performance time per frame (s) 1k-S Ø k Ø 9.40
11 Evaluation 11 overall reconstruction error: 1k-S: =17 mm, 19k: =73 mm NN-search (on all points): (rev. calib.: acceleration factor ~6.5) 1k-S: =15mm, 19k: =61 mm preprocessing: (3 x 3 median filter) 1k-S: =17 mm, 19k: =95 mm coarse registration: (recon. time without c.r.: 39s vs. 9.4s with c.r.) 1k-S: =21 mm, 19k: =90mm given: P ={ p i } point set, R d, t d real motion, R e, t e motion estimated P d ={ p di =R d p i t d }, P e ={ p ei = R e p i t e } error: = P1 p ie p di i
12 12 Thank you for your attention!
13 Extrapolation 13 different representation of motion (R, t) R ℝ 3 3 transform to unit quaternion q R ℝ 4 combination to one complete registration vector q= qr 7 ℝ t consider difference vector sequence: qk= qk qk-1 compute the angle between the two last directions in 7D: T q k q k 1 k =arccos,if k 10 then start extrapolation q k q k 1 extrapolation is based on three 2D points: T T T 0, e k, q k, e k 1, q k q k 1, e k 2
14 Extraplation 14 linear update by a line fitting the first and the third point: e k q k q k 1 zero point: v l = e k e k 2 interpolation of the three points by a parabola: q k e k 2 e k q k q k 1 e k 1 e k extreme value: v q = 2 q k e k 2 e k q k q k 1 e k 1 e k updating factor v: v l 0 v q 0: v=max 0, v l, v q v l 0 v q 0: v=min v l, v q limitation: v=min v, ex_max q k updated motion: qk q k ' =q k v normalization is necessary q k
15 Direct Linear Motion Estimation cross-covariance matrix K = i, j C rotation matrix R=VU 15 T T b j b a i a =VDU T translation vector t = b R a
16 Feature extraction and tracking x k, y k N : E v x, v y = 16 I x k, y k,t I x k, y k,t I x k, y k,t v x v y =0 x y t x k, y k N [ ] 2 I x k, y k, t I x k, y k,t I x k, y k,t!, v = min. x y t
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