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# Lecture-19 - 1 Lecture-19 Structure from Motion...

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Unformatted text preview: 1 Lecture-19 Structure from Motion Program-3 (Due Tuesday April 24, 4PM) • Implement Lucas-Kanade optical flow method using pyramids. – You will need to implement the following pieces: • Simple Lucas-Kanade without pyramids • Gaussian pyramids • Interpolation of optical flow in order to propagate optical flow from higher level of pyramid to lower level of pyramid – You will be given two images, your program should compute • Optical flow without pyramids and displays the flow vectors on the screen. You will have to sample (e.g. show flow vector at every fourth pixel) and scale the flow vectors to show on the screen. Otherwise there will be too many vectors, you won’t be able to see them. • Optical flow with pyramids and displays the flow vectors on the screen. 2 Problem • Given optical flow or point correspondences, compute 3-D motion (translation and rotation) and depth. Main Points • What projection? • How many points? • How many frames? • Single Vs multiple motions. • Mostly non-linear problem . 3 Displacement Model Point Correspondences 3-D Rigid Motion (displacement ) Z Y X T Z Y X Z T Z Y X Y T Z Y X X + +-- = ′ +- + = ′ + +- = ′ g b 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 4 Orthographic Projection (displacement model) Z Y X T Z Y X Z T Z Y X Y T Z Y X X + +-- = ′ +- + = ′ + +- = ′ g b g a b a Y X T Z y x y T Z y x x +- + = ′ + +- = ′ g a b a Perspective Projection (displacement) Z T y x Z T y x y Z T y x Z T y x x Z Y Z X + + +- + + + = ′ + + +- + +- = ′ 1 1 g b g a g b b a Z Y X T Z Y X Z T Z Y X Y T Z Y X X + +-- = ′ +- + = ′ + +- = ′ g b g a b a 5 Instantaneous Velocity Model Optical Flow 3-D Rigid Motion...
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Lecture-19 - 1 Lecture-19 Structure from Motion...

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