skybox - github pages · skybox. photo acquisition. 204 photos. homography. errors in estimation of...
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![Page 1: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the](https://reader035.vdocuments.net/reader035/viewer/2022063012/5fc82b795215a755a44bcdf3/html5/thumbnails/1.jpg)
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Skybox
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Photo Acquisition
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204 Photos
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Homography
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Errors in estimation of homographies
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Homography-Rotation Relationship
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Idea
• Find the rotation of the camera for each photo
• Minimize the difference between measured homographies and rotation-induced homographies
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Definition of distance between homographies
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Solving with Ampl
• Input: coordinates of 9 transformed points for each pair of photos
• Fixed parameter: Alpha (identical for all photos)
• Variables: Rotation matrix of each photo (9 values), intermediate vars
• Objective function: Sum of homography distances
• Constraints: • Orthonormality
• First rotation = identity
• Intermediate constraints
• Solver: Baron, Couenne
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Solving with Ceres Solver
• Input: coordinates of 9 transformed points for each pair of photos
• Fixed parameter: None
• Variables: • Rotation of each photo in angle axis representation (3 values)
• Alpha of each photo
• Objective function: Sum of homography distances
• Constraints: None
• Solver: Dense Schur solver
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Display
• Z-buffer
• Interpolation
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Demo!