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# Lecture-5 - Pyramids Pyrramids Lecture-5 Pyramid Very...

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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 m n l l ! ! " ## \$ " \$ " \$ g REDUCE g l l " \$ [ ] 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 p q n l n l \$ \$ " # # \$ " \$ " \$
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 (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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