CSE152, Spr 07 Intro Computer VisionStereo Vision IIIntroduction to Computer VisionCSE 152Lecture 14CSE152, Spr 07 Intro Computer VisionAnnouncements• Midterm was returned on Tuesday• Next HW assigned tomorrowCSE152, Spr 07 Intro Computer VisionStereo Vision Outline• Offline: Calibrate cameras & determine “epipolar geometry”• Online1. Acquire stereo images2. Rectify images to convenient epipolar geometry3. Establish correspondence 4. Estimate depthABCDCSE152, Spr 07 Intro Computer VisionBINOCULAR STEREO SYSTEMEstimating DepthZX(0,0) (d,0)Z=fXLXRDISPARITY(XL-XR)Z = (f/XL) XZ= (f/XR) (X-d)(f/XL) X = (f/XR) (X-d)X = (XLd) / (XL-XR)Z = d f(XL-XR)X = d XL(XL-XR)(Adapted from Hager)CSE152, Spr 07 Intro Computer VisionReconstruction: General 3-D case• Linear Method: find P such that• Non-Linear Method: find Q minimizingCSE152, Spr 07 Intro Computer VisionRandom Dot StereogramsCSE152, Spr 07 Intro Computer VisionEpipolar Constraint• Potential matches for p have to lie on the corresponding epipolar line l’.• Potential matches for p’ have to lie on the corresponding epipolar line l.CSE152, Spr 07 Intro Computer VisionEpipolar Geometry• Epipolar Plane• Epipoles• Epipolar Lines• BaselineCSE152, Spr 07 Intro Computer VisionFamily of epipolar PlanesFamily of planes π and lines l and l’Intersection in e and e’OO’CSE152, Spr 07 Intro Computer VisionEpipolar Constraint: Calibrated CaseEssential Matrix(Longuet-Higgins, 1981)⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−−=×000][xyxzyztttttttwhereCSE152, Spr 07 Intro Computer VisionProperties of the Essential Matrix• E p’ is the epipolar line associated with p’.• ETp is the epipolar line associated with p.• E e’=0 and ETe=0.• E is singular.• E has two equal non-zero singular values(Huang and Faugeras, 1989).TTCSE152, Spr 07 Intro Computer VisionCalibrationDetermine intrinsic parameters and extrinsic relation of two camerasCSE152, Spr 07 Intro Computer VisionThe Eight-Point Algorithm (Longuet-Higgins, 1981)|F |=1.Minimize:under the constraint2Set F33to 1CSE152, Spr 07 Intro Computer VisionEpipolar geometry exampleCSE152, Spr 07 Intro Computer VisionExample: converging camerascourtesy of Andrew ZissermanCSE152, Spr 07 Intro Computer VisionExample: forward motionee’courtesy of Andrew ZissermanCSE152, Spr 07 Intro Computer VisionRectificationGiven a pair of images, transform both images so that epipolar lines are scan lines.CSE152, Spr 07 Intro Computer VisionImage pair rectificationsimplify stereo matching by warping the imagesApply projective transformation so that epipolar linescorrespond to horizontal scanlineseemap epipole e to (1,0,0)try to minimize image distortionHe001=⎥⎥⎦⎤⎢⎢⎣⎡Note that rectified images usually not rectangularCSE152, Spr 07 Intro Computer VisionRectificationGiven a pair of images, transform both images so that epipolar lines are scan lines.Input ImagesCSE152, Spr 07 Intro Computer VisionRectificationGiven a pair of images, transform both images so that epipolar lines are scan lines.Rectified ImagesSee Section 7.3.7 for specific methodCSE152, Spr 07 Intro Computer VisionFeatures on same epipolar lineTruco Fig. 7.5CSE152, Spr 07 Intro Computer VisionMobi: Stereo-based navigationCSE152, Spr 07 Intro Computer VisionEpipolar correspondenceThis version is feature-based: detect edges in 1-D signal, and use dynanic progrmaming to find correspondences that minimize an error function.CSE152, Spr 07 Intro Computer VisionSymbolic MapCSE152, Spr 07 Intro Computer VisionA challenge: Multiple InterpretationsEach feature on left epipolar line match oneand only one feature on right epipolar line.CSE152, Spr 07 Intro Computer VisionMultiple InterpretationsEach feature on left epipolar line match oneand only one feature on right epipolar line.CSE152, Spr 07 Intro Computer VisionMultiple InterpretationsEach feature on left epipolar line match oneand only one feature on right epipolar line.CSE152, Spr 07 Intro Computer VisionMultiple InterpretationsEach feature on left epipolar line match oneand only one feature on right epipolar
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