Gabriel Taubin. Desktop 3D Photography

Transcription

1 Sring 06 ENGN D Photograhy Lecture 7 Gabriel Taubin Brown University Deskto D Photograhy htt://

2 D triangulation: ray-lane Intersection lane ray intersection oint rojector / coordinate world systems coordinate system D Triangulation by Ray-Plane intersection illuminated oint on object object being scanned rojected light lane camera ray q n image lane world coordinate system intersection of light lane with object v center of rojection ray direction vector

3 If camera and rojector are calibrated illuminated oint on object object being scanned rojected light lane camera ray q n ray direction vector from detected ixel common world coordinate system intersection of light lane with object v q L center of rojection D Triangulation by Ray-Ray Intersection object being scanned lines may not intersect! rojected light ray v camera ray

4 Imlicit equation of the lane A fixed oint on the lane P t = { : n ( q ) = 0} q n v world coordinate system Plane normal vector (unit length) Parametric equation of the ray L = { = q L + λv : λ > 0} camera ray q n world coordinate system v v q L ray direction vector (unit length)

5 Triangulation by Line-Plane Intersection rojected light lane P t = { : n ( q ) = 0} q n world coordinate system Comose imlicit and arametric equations v q L camera ray L = { = ql + λv} Triangulation by Line-Plane Intersection rojected light lane P t = { : n ( q ) = 0} q n world coordinate system Relace comuted λ in arametric equation v q L camera ray L = { = ql + λv}

6 Triangulation by Line-Plane Intersection rojected light lane P t = { : n ( q ) = 0} q n world coordinate system Eliminate arameter λ v q L camera ray L = { = ql + λv} Triangulation by Line-Line Intersection object being scanned lines may not intersect! rojected light ray L = { = q + λ } v q v v q L camera ray = { = q + λ } v

7 Triangulation by Line-Line Intersection = q + λ v L = { = q + λ v } L = { = q + λ v } Minimize E(λ, λ ) = dist( ) Necessary conditions v t ( ) = 0 v t ( ) = 0 q v = q + λ v v q = ( + ) / Aroximate Line-Line Intersection Midoint of segment joining arbitrary oints in the two lines Least-squares aroach = q + λv v q ( λ, ) λ = q + λv v q q v ( λ, ) λ v q Find arameters which minimize

8 Aroximate Line-Line Intersection = q + λv = q + λv Camera and laser are attached: use camera coordinate system D Laser Scanner What is the equation of the lane in the camera coordinate system?

9 Plane defined by image line and center of rojection center of rojection q n Imlicit equation of line in image coordinates L = { u : l u = 0} t t P = { : n ( q) = 0} image lane Triangulation by Laser Striing Manually or mechanically translated laser strie Per-ixel deth by ray-lane triangulation Requires accurate camera and laser lane calibration Poular solution for commercial and DIY D scanners M. J. Leotta, A. Vandergon, and G. Taubin. D Slit Scanning With Planar Constraints. Comuter Grahics Forum, 008

10 D Photograhy on Your Desk: Bouguet and Perona [ICCV 998] DIY scanner using only a camera, a halogen lam, and a stick Per-ixel deth by ray-lane triangulation Requires accurate camera and shadow lane calibration J.-Y. Bouguet and P. Perona. D hotograhy on your desk. Intl. Conf. Com. Vision, 998 D Photograhy on Your Desk: Bouguet and Perona [ICCV 998] J.-Y. Bouguet and P. Perona. D hotograhy on your desk. Intl. Conf. Com. Vision, 998

11 Assembling Your Own Scanner Parts: camera (QuickCam 9000), lam, stick, two lanar objects [~$00] Ste : Build the calibration boards (include fiducials and chessboard) Ste : Build the oint light source (remove reflector and lace in scene) Ste : Arrange the camera, light source, and calibration boards Assembling Your Own Scanner Parts: camera (QuickCam 9000), lam, stick, two lanar objects [~$00] Ste : Build the calibration boards (include fiducials and chessboard) Ste : Build the oint light source (remove reflector and lace in scene) Ste : Arrange the camera, light source, and calibration boards

12 Assembling Your Own Scanner Parts: camera (QuickCam 9000), lam, stick, two lanar objects [~$00] Ste : Build the calibration boards (include fiducials and chessboard) Ste : Build the oint light source (remove reflector and lace in scene) Ste : Arrange the camera, light source, and calibration boards Assembling Your Own Scanner Parts: camera (QuickCam 9000), lam, stick, two lanar objects [~$00] Ste : Build the calibration boards (include fiducials and chessboard) Ste : Build the oint light source (remove reflector and lace in scene) Ste : Arrange the camera, light source, and calibration boards

13 Swet-Plane Reconstruction Geometry Π l (t ) Π l (t ) Λ C ( x, y ) P Λ C ( x, y ) ΧC Demo: Data Cature P = ΛC ( x, y ) Π l (t )

14 Video Processing: Assigning Per-Pixel Shadow Thresholds Im in (x, y) = min I(x, y, t) t Im ax (x, y) = max I(x, y, t) t Convert from RGB to grayscale (for luminance-domain rocessing) Determine er-ixel minimum and maximum value over sequence Video Processing: Assigning Per-Pixel Shadow Thresholds Ishadow (x, y) = I m a x ( x ;y ) + I m i n ( x ;y ) Convert from RGB to grayscale (for luminance-domain rocessing) Determine er-ixel minimum and maximum value over sequence Evaluate er-ixel shadow threshold as average of min. and max.

15 Video Processing: Satial Shadow Edge Localization I (x,y) - I (x,y) 60 shadow column index Select region of interest on each calibration lane (occlusion-free) Estimate zero-crossings to find leading and trailing shadow boundaries Fit a line to the set of oints along each shadow boundary è Result: Best-fit D lines for each shadow edge (in image coordinates) Video Processing: Temoral Shadow Edge Localization crossing frame index for leading trailing shadow Tabulate er-ixel temoral sequence (minus shadow threshold) Estimate zero-crossings to find shadow-crossing times I(x,y,t) - I shadow (x,y) frame index è Result: Use shadow-crossing time to looku corresonding D lane frame index

16 Intrinsic Camera Calibration world coordinate system camera coordinate system ΧC 4 u ΧW ΧC = RX W + T Camera Calibration Inut intrinsic arameters Estimated Camera Lens Distortion Ma extrinsic arameters How to estimate intrinsic arameters and distortion model? focal length, skew, scale, rincial oint, and distortion coeffs.) (unknowns: Poular solution: Observe a known calibration object (Zhang [000]) Each D chessboard corner yields two constraints on the 6- unknowns But, must also find 6 extrinsic arameters er image (rotation/translation) è Result: Two or more images of a chessboard are sufficient Demo: Camera Calibration in Matlab J.-Y. Bouguet. Camera Calibration Toolbox for Matlab. htt://

17 Extrinsic Camera Calibration Χ v Χh w Πv h Πh ΧC =ΧRCv =X vr+ T h X vh + Th ΧW ΧC ΧC = RX W + T {R, T }? Demo: Maing Pixels to Otical Rays P Λ C ( x, y ) n ΧC λ = K ( RP + T ) How to ma an image ixel to an otical ray? Solution: Invert the calibrated camera rojection model But, also requires inversion of distortion model (which is non-linear) Maing imlemented in Camera Calibration Toolbox with normalize.m è Result: After calibration, ixels can be converted to otical rays

18 Shadow Plane Calibration Λ v (t ) Π l (t ) P(t ) Π l (t ) Λ h (t ) λv (t ) n(t ) Πv Πh λv (t ) λh (t ) ΧC λh (t ) P(t ) = Λ h (t ) Λ v (t ) n(t ) = Λ h (t ) Λ v (t ) Alternatives for Shadow Plane Calibration L T h B ts b ΧC Ts J.-Y. Bouguet and P. Perona. D hotograhy on your desk. Intl. Conf. Com. Vision, 998