lect923h - Estimation Using Flexible Wireframe Model Main...

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1 Estimation Using Flexible Wireframe Model Main Points • Model photometric effects • Simultaneously compute 3D motion and adapt the wireframe model.
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2 Generalized Optical Flow Constraint dt dN L f v f u f t y x . r = + + dt dN L dt t y x df . ) , , ( r = L t N t y x f ). ( ) , , ( r = Lambertian Model Albedo Surface Normal (-p,-q,1) Lambertian Model S=L, light source ) , , ).( , , ( . ) , ( z y x z y x l l l n n n L n y x f = = ) , , )).( 1 , , ( 1 1 ( . ) , ( 2 2 z y x l l l q p q p L n y x f - - + + = =
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3 Sphere ( 29 ) , , ( 1 ) , , ( 2 2 2 z y x R n n n z y y z q z x x z p y x R z z y x = - = = - = = - - = Orthographic Projection (u,v) is optical flow 3 2 1 2 1 3 1 3 2 2 1 3 1 3 2 V X Y Z V Z X Y V Y Z X V Z x y v V y Z x u + - = + - = + - = + × = + - = = + - = = V X X
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4 Optical flow equation dt dN L f V Z x f V y Z f t y x . ) ( ) ( 2 1 3 1 3 2 r = + + - + + - + + - - - + + - - = + + - + + - 1 ) 1 , , ( 1 ) 1 , , ( . ) ( ) ( 2 2 2 2 2 1 3 1 3 2 q p q p q p q p L f V Z x f V y Z f T T t y x r Equation 24.8, page 473. Homework 3.1 Show this. Error Function = i ithpatch y x i e E e ) , ( 2 2 / 1 2 2 2 / 1 2 1 1 2 2 2 1 1 2 2 3 2 1 2 1 1 3 1 1 2 3 ) 1 ( ) 1 , , ( ) 1 ) 1 ( ) 1 (( ) 1 , 1 ( ).( , , ( ) ) ( ( ) ) ( ( ) , ( + + - - - + - + - + + + - - + - + + - - - + + + + + - + + + + - = i i i i i i i i i i i i t i i y i i x i q p q p q q p p q q p p L L L f V c y q x p x f V c y q x p y f y x e r j ij j ij j i ij i ij i c x q x p c x q x p + + = + + ) ( 2 ) ( 1 ) ( 2 ) ( 1 Homework 3.3 Show this.
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5 Equation of a Planar Patch ) , , ( ) , , ( ) , , ( ) , , ( ) ( ) ( ) ( ) ( ) ( 3 ) ( 3 ) ( 3 ) ( 3 ) ( 2 ) ( 2 ) ( 2 ) ( 2 ) ( 1 ) ( 1 ) ( 1 ) ( 1 i i i i i i i i i i i i i i i i Z Y X P Z Y X P Z Y X P Z Y X P = = = = 0 ) .( ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( = × i i i i i i P P P P P P P 1 P 2 P 3 Equation of a Planar Patch ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 1 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2 ) ( 1 ) ( 3 ) ( 1 ) ( 2
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This note was uploaded on 06/12/2011 for the course CAP 6411 taught by Professor Shah during the Spring '09 term at University of Central Florida.

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lect923h - Estimation Using Flexible Wireframe Model Main...

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