MULTIRESOLUTION REPRESENTATION OF DATASETS WITH ...

2 downloads 36 Views 457KB Size Report
Benjamin Gregorski and Kenneth I. Joy. Center for Image Processing and Integrated Computing {CIPIC}. Department of Computer Science. University of ...
  

   

  !"#  $ &%  (' ( ) *)#(  +(  ,.-0/214365879/;:=-0?A@6OQPR@TS UWVYXTZ[VY\G]Y^4\`_badcfegVhi\j^lkmVYnmnmopXqerc4X2sd_mXtZ[Vue>\jc>Z[VvswUW^4a`x2yzZuopXqe|{fU6_vhG_4U2} ~ „ XTVxgop…Dc>Vb\b\YZua€nmopZuVb†‡XtZQ^v]€^v]€UEUEcqˆ ^>o ]Ya`^4x2\YXTyzoƒZ[cŠVY‰ \‚~ tc4kfoƒ…lVYopX2n kmV ‹J:w30-zŒW3A79F“9F;r:=O ŽW3679LQ?A36-zK>5&7 3A36/G/GFIFIPA”–@RLG•—/n n œœˆˆ c4c4a‡a‡^4^4n`nv‰Wž c>VbZu¡£op^>Xt¢wcqV¥ˆ ¤>› opcgk¥^§Ÿv^>¦0\jc>¨4Z9©f^4ªt\Y© † ”–36L¬3A79/G-T36• UWVYXTZ[VY\G]Y^4\`œixqx2ˆ ouVvs§tkfouVbXtZuo ­¬k§UW^4a`x2yzZuopXqe|{fU6œ®Ut} › c>¡—\vVYX2kmV › op…DVb\Yad^>\vV¯‚c4Zuoƒ^4X2c>ˆ › cgŸv^4\vc>Z9^4\Y† °r±—²l³l´Dµ2¶q³ ·¹¾mÉÎÄq¸‡½t¼ ºT»mÄ>¸lÆ)¼¥¸lÅt½z¿4¾ ¾b¿Ð¿§¼¥½2¸f¸f¾mÀ¼ž¾mÁ§ÃÑ¿D¸f¾‚¾mÃ2ÇlÄ0ÄqÅ|½z¾bÆp¿4Ä>ÉÊ» ½’ÇlÁrÄ>½2¿4¼v¾m¾¥¸f»m»mÈ2ÉÊ¿4ÇY¾m̬ÉÊÉνt½zː¾m¸fÁ‡»¥ÆƒÈ2¿>ÌÍÇl¾m¸lÉͼl»m¸lÒr¼¥ÄqÓ=ÌÎÈT¿4¾m¾mÉʸfÄ>»m½wÉÊ¿>»mÌQ¸lÉκt½0»m¾m¸l¸Y¼¥»¥¸fÆu¿>½0Çf¾b¸l¿D¼Ï ¸l¸f»¥Á‡»mÄ4Ô6»—¸ŠÅ2ƃÄ4ÅT»G¸Š¼¥Å ÉÊÁ§Éʽdºt¾mÌÎÃ2É Õ2¸QNJÁ§¿4¾m¸lÉÎÄ>¼¥Ã2½.¸l¿>¼—ÌÎË>Ä4Ä>Æ6»mÇlÉÍÄ>¾mÃ2Á§Á§º2¼—Èt¾bÔ6¿D¸l¾mÇlÉÎÄq¿>È2½Ñ¼¥¿4¸QÌTÅ2¾mÃ2¿4¸f¾b֞¿¯¼¥»m¸f¸f¾mºt¼¬»m¸l¿4¼¥»m¸l¸)½zÄ4¾GÆpÅT¾m¸lÉμ¥½€ÇlÄq¿½z¼¥¾mÄqÉÎÈT½0»mÈ2ÇlÉ;m¸ ÉθlÄ>¼ Æ ÉÎÉν‚½z¾m¾m¸fÃ2»¥¸GÆu¿4¼¥ÇlNJ¸l¿4¼GÌ׿D¸f»—ÚTº2Ä>»®ÌÎÉ ÇlØgÉ͸l¾mÇYÌÍÖz¾mÄ>Û>»EÀiÕ2¸)¸l¿4ÌÊŞ»m¸ ÄD¿>ØgÔ2¸fÌλ®¸iÁ§¾mĸl¼¥ºt»mÄD¸lØ0ÌθlÉÊÁ§Åt¸i¸l½z¼¥¸f¾mºÑ¼lÒE¿4»bÙQ¿DÖ¾m¸i»m¸lÕѺT¸f»mÌ׳¸l¼¥»m¸l¸l½zºT¾m»mÉν2¸l¼¥Ë`¸lÁr½z¾b¿4¿4¾m¾m¸YÉÎÄq»mÉ×½t¿4¼ Ì ÆpÌÎÉÄ>Ül»`Éν2¸ŠË¿4ÇY¼¥Ã¸lºÑÁr¿D»b¿4¿4¾m¾m¸f¸Q»mÉÊÕ2¿>¸lÌAÌÊÄDŞØg»m¸f¸l»)ºt¿d»m¸l¼¥¼¥Éθf½2½0Ë>¾bÌοD¸‚¾mÉÎÇlÄq¸l½2ÌÎu¼EÒ ÇŠÓ|¿>½dÈtÌÍ¿>¾mÇfÉλmÇl¸fÈt¼¥»bÄq¿DÌξmÈt¸l¾mÌÍÉÎÖdÄq½¿>º2»mºT¸l»mºtĊ»mÚt¸lÉμ¥Ár¸f½0¿D¾b¾m¿D¸Q¾mÉÎÅtÄq¿4½2¾b¼)¿4¼¥ÈT¸f¾m¾mÉÍ¼Ï ¾m¿DÃ2»mÄq¿4È2¾‚½2ÇlÅ.Ä>½z¾m¾bÃ2¿>¸¯ÉνÝÅtÉÎÅt¼¥ÇlÉμ¥Ä>Çl½0Äq¾m½zÉν0¾mÉÎÈ2½0Ä>È2È2É;m¼¬Éθl»m¼ž¸lËqÀ`ÉÎÄqÉͽt¾mÃ2¼lÄ>ÒiÈtÞ¾žÈtºt»iÌÊ¿>¿>ÇlÌÎËqÉν2Ä4Ë|»mÉξm¿ÐÃtÁßÌÊ¿D»mÈ2Ëq¼¥¸€¸f¼ º6¸Y¿‚»mÇlÁ€¸lÈt½z¾bÌξm¿>ÉÍË>»m¸l¸.¼¥Ä>Ä>ÌÎÆQÈtÇl¾m¸lÉÎÄqÌÎ ½ ¼ ¾m¸f¸f»¥¾¥»m»bÄ4¿4»GÃ2Ô6¸ŠÄqÅ0Èt»b½Ñ¿>Ì0ÅtÁ§¼®Æƒ¸lÄ>¼¥»—àÆp¸Š¼¥È2¿4¾mºtÈTº6»mÄ>¸ »¥ºt¾mÉλm½2¸fË`¼¥¸fÆu»m¿4Øq¼v¿D¾G¾mÇlÉÎÄqÄg½®¿D»màq¼¥¸f¸lÚT½2º2ÉνtÌÎÉ Ë‚ÇlÉ;—¿>½2»m¸lÅ ºt»m»m¸f¸fÕ2¼¥½2¸l½z¸l¾bÁ§¿4¸f¾mÉν0Äq¾®½‡ÇŠÄ>¿4Æ6ºÑÅT¿>ÔtÉμ¥ÉÎÇlÌÊÉÍÄq¾m½zÉθl¾m¼lÉÍÏ à À`½0È2É;mÉ;mÃ2ÉÎÉθl½w¼ ¿‡À`ÉÍÇl¾m¸lÃ2ÌÎuÉνÒ Çl¸lÌÎ ¼làÑ¿4½ÑÅr¼¥¸lºÑ¿D»b¿4¾m¸žÕѸfÌ×ŧ»m¸lºT»m¸l¼¥¸l½z¾b¿4¾mÉÎÄq½t¼)ƃÄ>»`¸l¿>ÇbÃ|Ár¿4¾m¸Y»mÉ׿4Ì áâTãRädå ´4æW²qçJÓ=Ó|¸l¿D¼¥¾mÃt¸f»m¸lÉʼl¿>ÛAÌdÓ|èj½zÈt¾mÌ;m¸fÉλ¥»mÆu¸f¿4¼¥ÇlÄq¸lÌμlÈtÛ ¾mÉÎé‚Äq½Ý¿D¾bìt¿N»b¿4ê0Á§ÉÎÁ§¸fÀ º2ÌÎÄ4ÉÍÕÑ»mí0NJ¼l¿DÛ2¾mÉÊìtÄ>È2½®½2ÛdÇYÓ|¾mÉÊÄ>Èt½=Ì;mî¯Éλm¸fº2¼¥ºtÄq»mÌÎĊÈtÚT¾mÉÎÉÎÄqÁr½–¿4¾mëEÉÎÄq¸f½ ¾¥»b¿4Ã2¸ŠÅ0»b¿>Ì ï



       ! "#$%'&(*),+ "#-.+/+ "01%&0! "2$%+3!4 576'58$ 5.49! "#$ 6:&0!4 6'5.4;'$% +'? (!f3%+EUaD5b%4958+E5.4 I'58\

      !#"$   &%' )(*+  ,.-,/  )102 ,

3

m»Ãt4 ¸f¸Šoͺte>ÅT»myz»b¸l\v¿4¼¥V$Ì®¸l½zÁ§57¾b6 ¸f¿D¼¥¾mîÉÊÄ>Ò'é½28u¼l¸lÉÎÒQ½z½2¾më ¼¥¸fÉ;j»¥Ã2ÖÝÆu¸¿4ÇlÕÑÌʸY¸ ¸fÆpÌ×¾¯¸fÅ»¥º2»mÈtÉÎÄ>Çf¼¥»:¾mÉÎÈT½29@Ċ?YÌÎÀ`É Ò Çl¼ É;€¾mÃ2Éνz¸¾mÕѸf»¥¸lƃÌÊ¿>Å|Çl¸r¿4ÌÎÄq»m¸l½2ºtˇ»m¸fÀ`¼¥Éθl¾m½zÃоb¿4¾m¾mÃ2Éθ‚Äq½t¿4¼.º2ºT¿>»m½2ÄDÅÚTÉμ¥Ár¸lºÑ¿4¾m¿DÉλb½t¿4Ëd¾m¸r¾m¸fÕѾ¥¸l»bÌÊ¿DÅ Ï "#$ 6rD&2)6'$%'&%58+9( 58+bGH(%"#&25j%4958+E5.4 I,"#$ 6r+  49?W'-S5!EE49"2a E58+Z+ %-K(i'+$ '49;'& I'58-SE'49+.O_-S4958'+E58+.O_'$ + ( 5N&#!4 6'5N58+ (dE/GB"2 (%"#$o1-S5.4  '"0$i5.494 '4E&25.49'$%-S5%+ "0$ 6 M+9 a+E '$> "#'&#&2)F+ o'&#&25.4/$>%1aD5.41'?HE49"#'$ 6:+.I @ Ct58+ (~!%4 8R "#;! "2$~'$%< + "#&0"2V-.! "2$'&26''4K"2 (%;+Z-.'$iaD5%58+Z'$%< 4 5858+ (%"0$ 6/E58-9(%$%"0s> 58+8@

cN 4i!%4 8R "#;! "#$ '?Y;!E5.4K"#'&H"0$*E5.4 ?e'-S58+d?W'&0&#+o"#$>E` (%5M-.!E5.6''4 ) '? 4 5858+ (%"0$ 6rE58-9($%"#s 58+.@Š+Z< 58+9-S49"2aD58r58+ (]O ("#+N$%!  49'&fV%58&0< 4 5.%4 58+E58$> ! "2$`GB"#&#&UaD5;-S$* "0$> +r'-S4 + +3-S58&#&laD%$% '?f'49"26"#$%'&DE5.4 ?e'-S58+Z'$%E5.57 (%!1495.%4 58+E58$> ! "2$%+1'? V%58&#E58V58&# "#$>"2L)'@ Z)w495.%4 58+E58$> "#$ 6; (%5Y+  4 ?e'-S5r'?%"#L)5SR '-S &2)'O' 4f+ "#&0"2V-.! "2$'&26''4K"2 (% 58+U$ '_$%5.58½2Å|¿4º2ºt»mĊÚTÉÎÁr¿4¾m¸ŠÅÐÉν0¾m¸Y»¥Æu¿>Çf¸l¼lÒ 





I'58-SE'4 ! @ g ? D"#$* +YEvG!49E5.4 ?W'-S58+fGH"2 (%"#$3N!4  "#-|\ %&#!4E5.E49'( 58< 49,@ g $d6'58$ 5.49'&D/-S!49+E5r-S58&0&"0$o ( 558+9(iGH"#&#&-S$> '"#$w/&#!4 6'5 $>%1aD5.4Y'?B"0$*E5.4 ?e'-S5d&#)>6'$%+8OU'$% '"#$ M+9;'&#&b$%1aD5.41'?"#$*E5.49?W'-S57D&2)6'$%+.@FA ( 57+ "26$ 58 '"#$7'$*)o"0$*E5.4 ?e'-S58+.O $ ;+ "26$ 58' (M-. 4 I'5 '$%N (%!r ( 5;+ "#6$ 58E5.4 ?e'-S58+L)"#-.'&0&2)h'&#+ t(%8I'5o \ "2 "258+j"#$7 ( 5YV%58&#E5.49+E58-S +8@MA (%5o5.4 4 '43?W'41 ( 5d6"2I'58$ V%58&#E:"2 +o-K(%"#&#E5.4 ?e'-S58+b?W4 ‹ 4!%4 8R "#;!E58< "#$*E5.49?W'-S58+.@lЉ-S58&#&  (%!58+$%'-S$* '"#$i;!E5.49"#'&"#$*E5.49?W'-S5 "#+l-S$+ "#< 5.4 58< Eo(%8I'53'$t"#$>E5.4 ?e'-S5r5.4 4 '4 ' ? .5.4  @



,j

€  ,Nƒ  ‚ y 5(%vI'5ZE58+ E58)5.4K+E$%"#-"#'-SlaD5. GZ5.58$i%4 J¥E58-S "#&25j'$%E5.4 ?e'-S5iaD5. GZ5.58$™58% ):+E'-S5 '$%1-S'49$%5.4Y"#+r (%5o"#$>E5.4 ?W'-S5oa5S\ LG5.58$7 ( 5H4 J¥¦58-S "0&25'$ Eo'$h5.4 4 '4B'?  ,@ /\!@  !  GB( 58$ -S$%+ "#< 5.4958@™A ( 58+E5d5.4 4 '458'+9 4 5858$> +"#$% +.@Š‹D&2)6'$F"#+rE5.49"#$ 6  ( 5ta&2,- ” e %D5.4E\L.?Q;-S'49$%5.4 !K@ A (%5t&#"#$ 58!4o"0$*E5.4 D&#! "#$~'? (%5C< 58$%+ "#L) IJ'&#%58+Z"#$i ( 54 5.6"2$iGB( 5.4 5 ( 5%4 J¥E58-S "#&25"#+Z"0'-S "#$ 61 ( 5a&2,- ”o+ ;>' (%+  l ( 5 < 58$%+9"2L)1V%58&# +j;!E5.49"0'&"0$*E5.4E\ ?W'-S58+.@cN 4'&26''49"# (%u-S$%+EE49%-S +'$F!%4 8R "#;! "#$h (!r-.'$[a5/%+E58–!§–!§C8G!49< 58»r¾¥»mÉÊ¿>½tËqÈtÌ׿D¾m¸ŠÅ™¼¥ÈT»¥Æu¿4Çl¸qÛ = È2Ë>È2¸l¼ =,Äq; º2º6¸>Ò —»mÄqË4»m¸l¼¥¼¥ÉÎØg¸¯Ó|¸l¼¥Ã2¸f¼lÛ mÛ QÃt¸ŠÄqÅT½t»bË ¿4ÌÑ6ìtÃ2»bÄq¿4ȀÁ§¿>¸f½2À Å.Ä4Ù »m퇿>ÄÆpÄ>z!» È2¿>½ Éμ¥iÈÑ¿4ÃtÌʸlÉÎÜl½§Éνt¿>Ë ½2Å.¯¸lî¯Ë>»mÈ2ÉθÌÊ¿4)»Ò Q Ä>ÌÊ¿4ÈtÈtÁ§ÆpÁr¸ ¿>邽®¿DÒg¾bÓ|¿TÛgÈ2è Ì;mÉÍ»m¸l,¼¥Ä>ÌÊÈTÉξm¼¥ÉÎÈ2Äq¿>½rÌÎÉ ëE܊¿4¸f¾m¾¥ÉλbÄq¿D½ Ï 0Û.= > =  Ò Ó—|»¥ÉλmÇbÄ>ÃÑ»ž¿4¸lÓ|Ì ¸fž¾¥»m¿DÉλmÇlÌʼl¿>Û6½ÑêTÅ‡è ¿> ½2 Å —î ¿4È2ÌtêAÒ ¸fiÇYí0ÄqÔ6½T¸fƃ¸f»¥»m¾Š¸fÒ>½2ê0ÇlÈt¸ »¥Æu—¿4Çl»mÄz¸`Çlê0¸lÉʸŠÁ§ÅTÉʺt½tÌÎËqÉ Õ2¼lÇŠÛ ¿4 ¾m; ÉÎÄ>D½Ï  = 0¼¥ÒÉʽtË È2¿qÅ0»mÉÊÇ  éÈ2¿D¾mÇbÃ2ÃÑÌο>¸lÉθl½t½¹¸Š¿>êAÈÒ6Ùi¿4½ÑÄq½tÅ ½2¸lÙiÌθf¬»m¿>½2½2Å ÅJžéž¿4¿>Ár½2Éο>¸l½2Ì ½R Ò ÒRiê0Ä>ÇYÃt½2Éʼvíq¾¥Ä>»mÈt»m¸‡Çf¾m¿>Éν2½ÑËIÅ ‚Ó=¸l¿4½t¾m½2¸Y»m¸fÉ×¾m¿4ÃJ̧èbèjÒ ½zq¾m¸fĊ»¥ÖÝÆƒ¿>¿>Çl½2¸lŒ¼¹Ó=ìt»m¿DÄq»mÁ í éž ;@¿4;7¾b;T¿IÛ êT¸f¾m¼J· ÉÍÒ ¾mà ¬ÄqÌÎÈ2Á§¸YÏjìT»b¿>Çf¾mÉÎÄq½–èj½tÆpÄ>»mÁr¿D¾mÉÊÄ>½®Û G»mÄzÇl¸f¸ŠÅtÉν2Ë>,¼ Éμ¥È2¿>ÌÎÉ ÜŠ¿4¾mÉÎÄq½ ¿4Ӓ޽ѺTÒ¯2Å ¾mî ÉÎÁrÒ)ÒR¿>éžÌÎî¯ÍÖ|ÈtÌ×Å0ÇYî»mÃ2ÉÎÅ2¿>ÇYÃwÉο4½2ºt¸Š¿4¾m¿4½ÑÉÎÈI½2ÅJË.¿>ӒÓ|½ÑÒRÅI¸lÙ¼¥Ã2ӒÒA¸lÓ|Ò)¼lÛ2·¹ÉÊè½t¸lÄq¸lÌÎÉØz½2Ï9¼¥·ízÖ;¸lÉÎÉμ¥½tÈÑ¿>¼v½2¿4¾mÌΟlÉÊÜlÉν®¿4逾mÒ ÉÎÒ ¯Äq½B)Þ¯Òîž= êTÓ|ÉÎËqzÉθY½2Û ¾mËr1É = 뮿>¸f½Ñ»¥ÅIT»bÒ¿>ӒÉν Ò ¸ŠÒ¿4Ó|ÌÍÏ[¾mÉÎÉÎÌ Á§Î¸f¸» Õ2—ÇŠ¿4¿4È2¾mÌ®ÉÎÄ>êA½wÒ î¸lÌÎËqÇbí0Ä4»mÔ6É͸f¾m»¥Ã2¾)Á§¿4¼ ½ÑÅÐÓ|ÉÎÇYÃ2¿>¸l)Ì ž¿4»mÌÊ¿4½ÑÅRÒ2ê0Èt»mØg¸fրÄ>Æ WÄqÌÍÖTËqÄ>½Ñ¿>Ì®ê0Èt»¥Æu¿4Çl¸‚ê0ÉÎÁ§º2ÌÎÉÍÏ ÈtӒ¼¥ÉÎÒ ½2žË ¿4z»mÈÑÌÊ¿4¿>½ÑÅTÅ=»mÉο4ǂ½Ñ¸fÅ »¥»m—Ä4»ÒÑêAÁ§Ò ¸Y¾¥»m¸lÉÊÇbÇfíT¼lÔ6Û2¸Yè »¥¾ŠÛÑê0ÉÎÁ§º2Éʼ¥ÌÎÈ2ÉÍÆp¿>ÖTÌÎÉÎÉ ½2܊¿4ˀ¾m¼¥ÉÎÄ>ÈT½ »¥Æu¿4= Çl¸l¼)TÛÀ` É;mÃ|Çl Ä>ÌÊÄ4; »¿>½ÑÅr¾m¸fÚ0¾mÈt»m¸ ¿4½2È2ÇlË>¸ È2î ¸l¼ ¾¥¾¥‡»mÉÎÒ Ô2ÈTÄq¾m¸lº2¼lº6Ût¸>è Ò ¸fÀ ÉÎÈѼ¥ÈÑ¿>¿4ÅTÌÊ»mÉÎÉÎ܊ǯ¿D¾mÓ|ÉÎÄq¸f½¾¥»mÉÎ= Ç ÆƒÄ40»iÛ êT> ÉÎÁ§º2TÌÎÉÍÒ ÆpÖTÉν2˞Ó|¸l¼¥Ã2¸l¼—À`É;mç2º6¸Š¿D»¥Ï

 



        ! #" $

  C 



, +&?& @1% &?&'A B

D

 



% '&)(

+*

/.10  32453687:9   $';  $$" !

)-

E

F

4G ?H

I

K &?(

 *L

>

 '

JG3G G

C 'A +*

ML

I -QR&)(

G

H

MN

-

?&

,I

SH

PO

'@

UT

V

P-

C @)('A C (

 @W

4G I

YG G3G

 ('  BW

-

)

[-

\-



F

 &W



JG3G G

Q L

X%I

'& &)(

Suggest Documents