Lecture-5 - Pyramids Pyrramids Lecture-5 Pyramid Very useful for representing images Pyramid is built by using multiple copies of image Each level

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1 Pyrramids Lecture-5 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. Pyramid Gaussian Pyramids ) 2 , 2 ( ) , ( ) , ( 2 2 2 2 1 n j m i g n m w j i g mn l l ! ! " ## $ "$ " $ g REDUCE g ll " $ [] 1
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2 Convolution 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 ( ) 1 ( ˆ ) 2 4 ( ) 2 ( ˆ ) 2 ( 1 1 1 1 1 ! ! ! ! ! $ $ ! $ $ " $ $ $ $ $ l l l l l l g w g w g 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 0 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 pq n l n l $ $ " ## $ "$ " $
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3 Expand (1D) ) 2 ( ) ( ˆ ) ( 2 2 1 , , p i g p w i g p n l n l $ " # $ " $ g l , n (4) " ˆ w ( $ 2) g l , n $ 1 ( 4 $ 2 2 ) ! ˆ w ( $ 1) g l , n $ 1 ( 4 $ 1 2 ) ! ˆ w (0) g l , n $ 1 ( 4 2 ) ! ˆ w (1) g l , n $ 1 ( 4 ! 1 2 ) ! ˆ w (2) g l , n $ 1 ( 4 ! 2 2 ) g l , n (4) " ˆ w ( $ 2) g l , n $ 1 ! ˆ w (0) g l , n $ 1 (2) ! ˆ w (2) g l , n $ 1 (3) Expand (1D) ) 2 ( ) ( ˆ ) ( 2 2 1 , , p i g p w i g p n l n l $ " # $ " $ ) 2 2 3 ( ) 2 ( ˆ ) 1 1 3 ( ) 1 ( ˆ ) 2 3 ( ) 0 ( ˆ ) 2 1 3 ( ) 1 ( ˆ ) 2 2 3 ( ) 2 ( ˆ ) 3 ( 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 ) 2 ( ) 1 ( ˆ ) 1 ( ) 1 ( ˆ ) 3 ( 1 , 1 , , $ $ ! $ " n l n l n l g w g w g Expand Convolution Mask )] 2 ( ), 1 ( ), 0 ( ), 1 ( ), 2 ( [ w w w w w $ $
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4 Convolution Mask ! Separable ) ( ˆ ) ( ˆ ) , ( n w m w n m w " ) ( ˆ ) ( ˆ i w i w $ " ] , , , , [ c b a b c •Symmetric Convolution Mask !
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This note was uploaded on 10/04/2011 for the course CAP 6411 taught by Professor Shah during the Spring '09 term at University of Central Florida.

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Lecture-5 - Pyramids Pyrramids Lecture-5 Pyramid Very useful for representing images Pyramid is built by using multiple copies of image Each level

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