CS223B-L9-StructureFromMotion

CS223B-L9-StructureFromMotion - Stanford CS223B Computer...

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Stanford CS223B Computer Vision, Winter 2008/09 Lecture 9 Structure From Motion Professor Sebastian Thrun CAs: Ethan Dreyfuss, Young Min Kim, Alex Teichman
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Summary SFM Problem Determine feature locations (=structure) Determine camera extrinsic (=motion) Two Principal Solutions Bundle adjustment (nonlinear least squares, local minima) SVD (through orthographic approximation, affine geometry) Correspondence (RANSAC) Expectation Maximization
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion camera features Recover : structure (feature locations), motion (camera extrinsics)
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Sebastian Thrun CS223B Computer Vision, Winter 2009 “Recovery” Problems 1 image 2+ images Camera Location known calibration stereo, tracking, background subtraction Location unknown Optical flow, SFM
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion (1) [Tomasi & Kanade 92]
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion (2) [Tomasi & Kanade 92]
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion (3) [Tomasi & Kanade 92]
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion (4a): Images Marc Pollefeys
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion (4b) Marc Pollefeys
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion (5) http://www.cs.unc.edu/Research/urbanscape
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Sebastian Thrun CS223B Computer Vision, Winter 2009 SFM = Holy Grail of 3D Reconstruction Take movie of object Reconstruct 3D model live.com
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion Problem 1: – Given n points p ij =( x ij , y ij ) in m images – Reconstruct structure: 3-D locations P j =( x j , y j , z j ) – Reconstruct camera positions (extrinsics) M i =(A i , b i ) Problem 2: – Establish correspondence: c ( p ij )
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Sebastian Thrun CS223B Computer Vision, Winter 2009 Structure From Motion camera features Recover : structure (feature locations), motion (camera extrinsics)
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Sebastian Thrun CS223B Computer Vision, Winter 2009 SFM: General Formulation ( 29 i z j z j y j x i i i i i i i i i y i x j z j y j x i i i i i i i i i i i i j y j x b P P P b b P P P f p p , , , , , , , , , , , cos sin 0 sin cos 0 0 0 1 cos 0 sin 0 1 0 sin 0 cos 1 0 0 cos sin 0 sin cos 0 0 0 1 cos 0 sin 0 1 0 sin 0 cos 0 cos sin 0 sin cos + - - + - - - = ψ ϕ φ f Z Z f X x = X O -x
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Sebastian Thrun CS223B Computer Vision, Winter 2009 SFM: Bundle Adjustment ( 29
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CS223B-L9-StructureFromMotion - Stanford CS223B Computer...

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