# lect824h - Perspective Projection(X,Y,Z World point Image...

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1 Perspective Projection (X,Y,Z) Lens Image Plane image Z y f Z fX x Z fY y Z f Y y - = - = = - World point Orthographic Projection (X,Y,Z) Image Plane image y World point X x Y y = =

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2 Plane+Perspective(projective) aX bY cZ + + = 1 [ ] a b c X Y Z = 1 = + X Y Z R X Y Z T [ ] = + X Y Z R X Y Z Ta b c X Y Z equation of a plane 3d rigid motion = X Y Z A X Y Z [ ] A R T a b c = + Plane+perspective (contd.) 1 1 8 7 6 5 4 8 7 3 2 1 + + + + = + + + + = y a x a a y a x a y y a x a a y a x a x a 9 1 = scale ambiguity ′ = + + X AX b C X T 1 = - - - - y x a a a a a a a a y y y x y x x y x x y x 8 7 6 5 4 3 2 1 1 0 0 0 0 0 0 1
3 Displacement Models ′= + + + + ′= + + + + x a ax ay ax a xy y a ax ay a xy ay 1 2 3 4 2 5 6 7 8 4 5 2 Pseudo Perspective ′= + + + + + ′= + + + + x a ax ay ax ay a xy y a ax ay a x a ya xy 1 2 3 4 2 5 2 6 7 8 9 10 2 11 2 12

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lect824h - Perspective Projection(X,Y,Z World point Image...

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