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1CSE152, Spr 04 Intro Computer VisionStereo Vision IIIntroduction to Computer VisionCSE 152Lecture 13CSE152, Spr 04 Intro Computer VisionAnnouncements• Assignment 3: Due today.– Extended to 5:00PM, sharp. Turn in hardcopy to my office 3101 AP&M• No Discussion section this week.• Guest lecturer, Dr. Jeff Ho, next week.• Today– Midterm summary– Shape from X– Stereo Vision ICSE152, Spr 04 Intro Computer VisionMidterm• High: 87• Low: 31• Mean: 57• Median: 55Problem regrades: Must be requested today in class and in writing.CSE152, Spr 04 Intro Computer VisionShape-from-X(i.e., Reconstruction)• Methods for estimating 3-D shape from image data. X can be one (or more) of many cues.– Stereo (two or more views, known viewpoints)– Motion (moving camera or object)– Shading– Changing lighting (Photometric Stereo)– Texture variation– Focus/blur– Prior knowledge/context– structured light/lasersCSE152, Spr 04 Intro Computer VisionExample: Helmholtz StereoDepth + Normals + BRDFCSE152, Spr 04 Intro Computer VisionStereo2CSE152, Spr 04 Intro Computer VisionBinocular Stereopsis: MarsGiven two images of a scene where relative locations of cameras are known, estimate depth of all common scene points.Two images of MarsCSE152, Spr 04 Intro Computer VisionAn Application: Mobile Robot NavigationThe Stanford Cart,H. Moravec, 1979.The INRIA Mobile Robot, 1990.Courtesy O. Faugeras and H. Moravec.CSE152, Spr 04 Intro Computer VisionCommercial Stereo HeadsTrinocular stereoTrinocular stereoBinocular stereoBinocular stereoCSE152, Spr 04 Intro Computer VisionStereo can work wellCSE152, Spr 04 Intro Computer VisionNeed for correspondenceTruco Fig. 7.5CSE152, Spr 04 Intro Computer VisionTriangulationNalwa Fig. 7.23CSE152, Spr 04 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 04 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 04 Intro Computer VisionReconstruction: General 3-D case• Linear Method: find P such that• Non-Linear Method: find Q minimizingCSE152, Spr 04 Intro Computer VisionTwo Approaches• A) From each image, process “monocular” image to obtain cues.B) Establish correspondence between cues.• Directly compare image regions between the two images.CSE152, Spr 04 Intro Computer VisionHuman Stereopsis: Binocular FusionHow are the correspondences established?Julesz (1971): Is the mechanism for binocular fusiona monocular process or a binocular one??• There is anecdotal evidence for the latter (camouflage).• Random dot stereograms provide an objective answerBP!CSE152, Spr 04 Intro Computer VisionRandom Dot Stereograms4CSE152, Spr 04 Intro Computer VisionRandom Dot StereogramsCSE152, Spr 04 Intro Computer VisionA Cooperative Model (Marr and Poggio, 1976)CSE152, Spr 04 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 04 Intro Computer VisionEpipolar Geometry• Epipolar Plane• Epipoles• Epipolar Lines• BaselineCSE152, Spr 04 Intro Computer VisionFamily of epipolar Planes(standard approach)CSE152, Spr 04 Intro Computer VisionJEFF, HERE’s WHERE I ENDED• Jeff, I covered up to this point.• I suggest that you – review the pictorial part of the epipolar geometry, • discuss the essentnial matrix, showing how it can be computed from R&T, and that this can come from calibration.• Discuss rectification in qualitative way, showing that result is epipolar lines become parallel lines.• Then discuss matching, mostly SSD & SAD metric. • The mention issue with half occluded regions.• Perhaps mention some challenges, dynamic programming, etc.5CSE152, Spr 04 Intro Computer VisionFamily of epipolar Planes(standard approach)CSE152, Spr 04 Intro Computer VisionEpipolar Constraint: Calibrated CaseEssential Matrix(Longuet-Higgins, 1981)CSE152, Spr 04 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 04 Intro Computer VisionCalibrationDetermine intrinsic parameters and extrinsic relation of two camerasCSE152, Spr 04 Intro Computer VisionThe Eight-Point Algorithm (Longuet-Higgins, 1981)|F |=1.Minimize:under the constraint2Set F33to 1CSE152, Spr 04 Intro Computer VisionEpipolar geometry example6CSE152, Spr 04 Intro Computer VisionExample: converging camerascourtesy of Andrew ZissermanCSE152, Spr 04 Intro Computer VisionExample: motion parallel with image plane(simple for stereo → rectification)courtesy of Andrew ZissermanCSE152, Spr 04 Intro Computer VisionExample: forward motionee’courtesy of Andrew ZissermanCSE152, Spr 04 Intro Computer VisionRectificationGiven a pair of images, transform both images so that epipolar lines are scan lines.CSE152, Spr 04 Intro Computer VisionRectificationAll epipolar lines are parallel in the rectified image plane.CSE152, Spr 04 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 rectangular7CSE152, Spr 04 Intro Computer VisionRectificationGiven a pair of images, transform both images so that epipolar lines are scan lines.Input ImagesCSE152, Spr 04 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 04 Intro Computer VisionFeatures on same epipolar lineTruco Fig. 7.5CSE152, Spr 04 Intro Computer VisionMobi: Stereo-based navigationCSE152, Spr 04 Intro Computer VisionEpipolar correspondenceThis version is feature-based: detect edges in 1-D signal, and use dynanic progrmaming toe find correspondences that minimize an error function.CSE152, Spr 04


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UCSD CSE 152 - Stereo Vision II

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