Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of...

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Transcript of Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of...

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
Page 2: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Skybox

Page 3: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Photo Acquisition

Page 4: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

204 Photos

Page 5: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Homography

Page 6: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Errors in estimation of homographies

Page 7: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Homography-Rotation Relationship

Page 8: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Idea

• Find the rotation of the camera for each photo

• Minimize the difference between measured homographies and rotation-induced homographies

Page 9: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Definition of distance between homographies

Page 10: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

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

Page 11: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

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

Page 12: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Display

• Z-buffer

• Interpolation

Page 13: Skybox - GitHub Pages · Skybox. Photo Acquisition. 204 Photos. Homography. Errors in estimation of homographies. Homography-Rotation Relationship. Idea •Find the rotation of the

Demo!


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