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Unformatted text preview: 3D Motion Estimation 3D model construction 3D model construction Video Manipulation Visual Motion Allows us to compute useful properties of the 3D world, with very little knowledge. Example: Time to collision Time to Collision f f L L v v L L D D o l(t) l(t) An object of height An object of height L L moves with constant moves with constant velocity velocity v: v: At time At time t=0 t=0 the object is at: the object is at: D(0) = D D(0) = D o At time At time t t it is at it is at D(t) = D D(t) = D o vt vt It will crash with the camera at time: It will crash with the camera at time: D( D( ) = D ) = D o v v = 0 = 0 = D = D o /v /v t=0 t=0 t t D(t) D(t) Time to Collision f f L L v v L L D D o l(t) l(t) t=0 t=0 t t D(t) D(t) The image of the object has size l(t): The image of the object has size l(t): Taking derivative wrt time: Taking derivative wrt time: Time to Collision f f L L v v L L D D o l(t) l(t) t=0 t=0 t t D(t) D(t) And their ratio is: And their ratio is: Time to Collision f f L L v v L L D D o l(t) l(t) t=0 t=0 t t D(t) D(t) And And time to collision time to collision : : Can be directly Can be directly measured from measured from image image Can be found, without knowing Can be found, without knowing L L or or D D o or or v v !! !! Structure from Motion = r t z u 1 tr Z [ ] ( 29 ( 29 ( 29 r r z u = 1 rot F t, r Z rot tr u u u + = u Passive Navigation and Structure from Motion ( 29 ( 29 . velocity rotational and , velocity ional h translat motion wit rigid a with moves system The , T z y x T z y x t t t , , = = t ( 29 ( 29 f y x Z Y X T , , points image onto project , , points Scene = = r R ( 29 image in the observed is point scene a of , , velocity 3D the and z y x V V V = R ( 29 . . , velocity as v u = r Image Flow due to Rigid Motion The velocity of a point with respect to the XYZ coordinate system is X X W Z Z X V Y Y BZ U X + = + = + =  = R t R y v x u Z Y y Z X x f = = = = = ; then , 1 Let + + = = = + + = = = x y Z W y x Z V Z Z Y Z Y Z Y v x y Z W x y Z U Z Z X Z X Z X u 2 2 ( 29 ( 29 rot tr 2 rot tr 2 1 1 v Z v x xy y Z yW V v u Z u y x xy Z xW U u + = + + + = + = + + + + = ( 29 ( 29 ( 29 ( 29 r r z r t z z R r z R R z R r + = = = 1...
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This note was uploaded on 01/12/2012 for the course CMSC 733 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
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