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# Lecture-2 - Lecture-2 Displacement Model 1 Orthographic...

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1 Lecture-2 Displacement Model

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2 Orthographic Projection (X,Y,Z) Image Plane image y World point X x Y y = = Orthographic Projection (x,y)=image coordinates, (X,Y,Z)=world coordinates x X y Y = = ′ = + + + ′ = + + + x r x r y r Z T y r x r y r Z T X Y 11 12 13 21 22 23 ( ) ( ) 2 4 3 1 2 1 b y a x a y b y a x a x + + = + + = Affine Transformation ′ = + x Ax b = + = + X Y Z R X Y Z T r r r r r r r r r X Y Z T T T X Y Z 31 32 33 = = 2 1 4 3 2 1 , b b a a a a b A
3 Orthographic Projection (contd.) Y X T Z y x y T Z y x x + - + = + + - = g a b a + - - - = + = Z Y X T T T Z Y X T Z Y X R Z Y X 1 1 1 g b g a b a Perspective Projection (X,Y,Z) Lens Image Plane image Z y f Z fX x Z fY y Z f Y y - = - = = - World point

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4 Perspective Projection = + = + X Y Z R X Y Z T r r r r r r r r r X Y Z T T T X Y Z 11 12 13 21 22 23 31 32 33 ′ = + + + + + + ′ = + + + + + + x r x r y r T Z r x r y r T Z y r x r y r T Z r x r y r T Z X Z Y Z 11 12 13 31 32 33 21 22 23 31 32 33 ′ = x X Z ′ = y Y Z focal length = -1 scale ambiguity Z Y X T Z r Y r X r Z T Z r Y r X r Y T Z r Y r X r X + + + = + + + = + + + = Plane+Perspective(projective) aX bY cZ + + = 1 [ ] a b c X Y Z = 1
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Lecture-2 - Lecture-2 Displacement Model 1 Orthographic...

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