CS231A Section 4 Camera MdlM odels (Problem Set...
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CS231A Section 4 C Mdl Camera Models (Problem Set 2) (Problem Set 2) 10/21/2011 10/21/2011 Hao Su Section 4 - Hao Su 1 10/21/2011
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Transcript of CS231A Section 4 Camera MdlM odels (Problem Set...
CS231A Section 4C M d lCamera Models(Problem Set 2)(Problem Set 2)
10/21/201110/21/2011
Hao Su
Section 4 -Hao Su 1 10/21/2011
AnnouncementAnnouncement
• Extra office hour for PS2:10/27, 8 ‐ 10pm, Gates 104/ , p ,
Section 4 -Hao Su 10/21/20112
TopicsTopics
C di• Homogeneous Coordinates– Why is it helpful?
• Transformations– Rotations– Affine– Homography– Solving for an affine transform matrix
• Camera matrixCa e a at• Fundamental and Essential Matrix
Section 4 -Hao Su 3 10/21/2011
Homogeneous CoordinatesHomogeneous Coordinates
h ?• Why?
• Without homogeneousg
Non‐linear i
3D World 2D Image
• With homogeneous
operation3 o d age
With homogeneousConvert to
homogeneousLinear
projectionConvert from homogenous
3D World 2D Imagehomogeneous projection homogenous
3D4D
Section 4 -Hao Su 4 10/21/2011
Homogeneous CoordinatesHomogeneous Coordinates
Section 4 -Hao Su 5 10/21/2011
Homogeneous Coordinates of LinesHomogeneous Coordinates of Lines
• The homogeneous coordinate of a line is• The dot product of the homogeneous
di t f li d i t it icoordinates of a line and a point on it is zero
• Cross product of two lines gives the homogeneous coordinate of their point of intersectionp
• Points at infinity (ideal points):• Line at infinity (ideal line): set of ideal points,
Section 4 -Hao Su 6 10/21/2011
Rotation MatricesRotation Matrices
Section 4 -Hao Su 7 10/21/2011
Homography/Projective/PerspectiveHomography/Projective/Perspective
Section 4 -Hao Su 8 10/21/2011
A Quick QuestionA Quick Question…
Section 4 -Hao Su 9 10/21/2011
Homography/Projective/PerspectiveHomography/Projective/Perspective
Section 4 -Hao Su 10 10/21/2011
Affine TransformAffine Transform
Section 4 -Hao Su 11 10/21/2011
Solving For an Affine Transform MatrixSolving For an Affine Transform Matrix
unknowns
Section 4 -Hao Su 12 10/21/2011
Solving For an Affine Transform MatrixSolving For an Affine Transform Matrix
unknowns
Section 4 -Hao Su 13 10/21/2011
Camera MatrixCamera Matrix
Section 4 -Hao Su 14 10/21/2011
Some NotationSome Notation…
Section 4 -Hao Su 15 10/21/2011
Epipolar GeometryEpipolar Geometry
Section 4 -Hao Su 16 10/21/2011
Essential and Fundamental MatrixEssential and Fundamental Matrix
Section 4 -Hao Su 17 10/21/2011
A Simple “Trick”A Simple Trick
Section 4 -Hao Su 18 10/21/2011
