lect826h

lect826h - Comments Algorithm-1 works only for small...

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1 Comments • Algorithm-1 works only for small motion. • If object moves faster, the brightness changes rapidly, 2x2 or 3x3 masks fail to estimate spatiotemporal derivatives. • Pyramids can be used to compute large optical flow vectors. Pyramids • Very useful for representing images. • Pyramid is built by using multiple copies of image. • Each level in the pyramid is 1/4 of the size of previous level. • The lowest level is of the highest resolution. • The highest level is of the lowest resolution.
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2 Pyramid Gaussian Pyramids ) 2 , 2 ( ) , ( ) , ( 2 2 2 2 1 n j m i g n m w j i g m n l l + + = ∑∑ - = - = - g REDUCE g l l = - [ ] 1
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3 Convolution Gaussian Pyramids ] [ 1 , , - = n l n l g EXPAND g ) 2 , 2 ( ) , ( ) , ( 2 2 2 2 1 , , q j p i g q p w j i g p q n l n l - - = ∑ ∑ - = - = -
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4 Reduce (1D) ) 2 ( ) ( ˆ ) ( 2 2 1 m i g m w i g m l l + = - = - ) 2 4 ( ) 2 ( ˆ ) 1 4 ( ) 1 ( ˆ ) 4 ( ) 0 ( ˆ ) 1 4 ( ˆ ) 1 ( ˆ ) 2 4 ( ) 2 ( ˆ ) 2 ( 1 1 1 1 1 + + + + + - - + - - = - - - - - l l l l l l g w g w g w w g w g w g ) 6 ( ) 2 ( ˆ ) 5 ( ) 1 ( ˆ ) 4 ( ) 0 ( ˆ ) 3 ( ˆ ) 1 ( ˆ ) 2 ( ) 2 ( ˆ ) 2 ( 1 1 1 1 1 - - - - - + + + - + - = l l l l l l g w g w g w w g w g w g Reduce
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5 Expand (1D) ) 2 ( ) ( ˆ ) ( 2 2 1 , , p i g p w i g p n l n l - = - = - ) 2 2 4 ( ) 2 ( ˆ ) 1 1 4 ( ) 1 ( ˆ ) 2 4 ( ) 0 ( ˆ ) 2 1 4 ( ) 1 ( ˆ ) 2 2 4 ( ) 2 ( ˆ ) 4 ( 1 , 1 , 1 , 1 , 1 , , + + + + + - - + - - = - - - - - n l n l n l n l n l n l g w g w g w g w g w g ) 3 ( ) 2 ( ˆ ) 2 ( ) 0 ( ˆ ) 1 ( ) 2 ( ˆ ) 4 ( 1 , 1 , 1 , , - - - + + - = n l n l n l n l g w g w g w g Expand
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6 Convolution Mask )] 2 ( ), 1 ( ), 0 ( ), 1 ( ), 2 ( [ w w w w w - - Convolution Mask • Separable ) ( ˆ ) ( ˆ ) , ( n w m w n m w = ) ( ˆ ) ( ˆ i w i w - = ] , , , , [ c b a b c •Symmetric
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7 Convolution Mask
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lect826h - Comments Algorithm-1 works only for small...

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