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by: Sam Robel


Sam Robel
GPA 3.68

S. Todorovic

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S. Todorovic
Class Notes
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This 6 page Class Notes was uploaded by Sam Robel on Monday October 19, 2015. The Class Notes belongs to ECE 468 at Oregon State University taught by S. Todorovic in Fall. Since its upload, it has received 25 views. For similar materials see /class/224421/ece-468-oregon-state-university in Engineering Electrical & Compu at Oregon State University.

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Date Created: 10/19/15
ECE 468 Digital Image Processing Lecture 10 Prof Sinisa Todorovic sinisaeecsoregonstateedu Oregon S39a BUmvelsily 2D Subband Coding using 1D Orthonormal Filters 139 IN ll u IIIIIl approximation Columns along I Rows alongv m k 1 illnul vertical fully Columns detail hMI WWW Columns horizontal d ll IHIIJ doom diagonal C l o umnx detail ab cd FIGURE 79 A fourband split of the vase in Fig 71 using the subband coding system of Fig 77 The four subbands that result are the a approximation b horizontal detail c vertical detail and d diagonal detail subbands 3 2D Subband Coding using 1D Orthonormal Filters amn Columns alongn 1Vmn fmn d mn Daubechies Filters PW lhnm 1 Columns Dump 0 Tum o 57 4157 1 9391 1n90Keven 1 13001 13101 39oiiiwm 39ownlulii h n giKeven 1 n i01 Example 2D Subband Coding Prominent aliasing Multiresolution Subband Coding dVquot39l n Columns along n dHmn dD m 11 Columns along n dVmrx dHm n Example Multiresolution Subband Coding Multiresolution Expansions Example Haar Scaling Functions 17111101 A39 1111 1511quot 11 1 1 1 j J 1 1 11 i i 1 1 X 11 1 z 3 0 1 2 3 151111139w 2 lr c11139 12171 1 I J 1 11 b 1 c d c f 1 1 FIGURE 711 11 1 2 3quot 11 1 3 quot39 01110 H nar sc lmg functlons 11112 V1 1111111611 1 1 1 1 15 117 I 1 xx 1 Wm 1 11111 39 11 1 2 3 n 1 2 3 1 gt 1 1 gt 1 1 gt 7 J J J 7 051017033 1017133 0251017433 99011 901211 172k1 Example Haar Scaling Functions 111110 m 15111111 7 m 7 11 1 1 J j 1 1 1 1 l 7 i 1 V V 0 l 2 3 0 2 11111112uc12x 1511111 711312 71 1 1 1 1 a b 1 C 1 c 1 1 1 1 FIGURE 7 I 11 1 2 3quot U 2 Some H1131 scaling functions 1111611 111111 5 1 1 1 l Function NW in V1 1 1 151 111 U l 2 3 U l 2 3 1 1 m3 7 05101913 10171133 02510174133 900106 590121120 m Nested Function Spaces WCKCQ FIGURE 712 The nested lunction spzxccs spanned by a sculng l39unclion


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