Graph Theory & Applications. Boundaries Using Graphs. Graph Search. Find the route that minimizes. cost

Transcription

1 Graph Thory & Appliations Bounaris Using Graphs Fin th rout that minimizs osts Fin th ritial path in a projt Fin th optimal borr aroun a rgion Fin loop an no quations or analog iruit analysis p q ost H Lowst ost ours whn p = H an q = 0 W want to in optimal rak gs with loation an orintation suh that: p q Whit is on th rit Blak is on th lt Bounaris Using Graphs Graph Sarh

2 Graph Sarh Graph Sarh Cost Funtions or Bounaris Strngth o g Dirtion o g Bounary urvatur Proximity to approximat bounary loation Othr a priori inormation Graph Sarh Huristis Th minimum ost o a path throu no n is th sum o two trms: r n g n h n I ĥ (n) = 0 or ĥ (n) = h(n), thn th minimum ost rsult is guarant I ĥ (n) nvr ovrstimats th minimum ost btwn any two nos, thn minimum ost rsult is also guarant (Vry har to in an ĥ (n) that satisis this rquirmnt) I ĥ (n) somtims ovrstimats th ost, thn minimum ost solution not guarant, but algorithm is astr ĥ (n) is bas on huristis an uat guss us to sp up an algorithm A goo hoi or ĥ (n) will sp up algorithm by ruing th numbr o nos that must b xpan 7

3 Thrsholing Global Thrsholing Simpl global thrsholing usually will only work in spial ass: Goo ontrast btwn bakgroun an objts Controll liting Evn i thr is goo ontrast btwn objts an bakgroun, unvn illumination tns to smar th histogram, rsulting in ovrlap btwn objt an bakgroun pixl valus I thr is ompliat strutur in th objts an/or bakgroun, thr may b no lar sparation in pixl valus 9 0 Itrativ Algorithm or Thrsholing Slt an initial stimat or thrshol T Sgmnt th imag using T Th imag pixls will b sgmnt into two sts G an G 3 Calulat th avrag gray lvls, µ an µ, o G an G 4 Comput a nw thrshol: T Aaptiv (Spatially Varying) Thrsholing Suivi th imag into subimags Apply thrsholing to iniviual subimags N to tst or subimags that ar ntirly objt or ntirly bakgroun: Unimoal vs bimoal histogram Varian Can also us moving winow or ovrlapping subimags 5 Rpat stps throu 4 until onvrgn is aquat

4 Combination o Eg Dttion an Thrsholing Eg Dttion & Thrsholing Exampl Prorm g ttion an orm histogram o all non-g pixls Histogram o non-g pixls shoul hav bttr sparation btwn mos than histogram o all pixls in th imag Sgmnt all non-g pixls into objt an bakgroun Classiy g pixls bas on sign o th Laplaian Original Atr Sobl g ttor Atr thrsholing 3 4 Rgion Bas Sgmntation Th sgmntation pross partitions th imag into n isjoint rgions, { R, R,, R n } () H(R i ) = TRUE or i =,,, n () H(R i R j ) = FALSE or i j H an b a untion o avrag gray lvl irn btwn max an min gray lvls varian o gray lvls smoothnss o bounary masurs o txtur siz o rgion Rgion mrging algorithm: Rgion Mrging Prorm initial sgmntation o imag into many small rgions satisying () Choos any pair o ajant rgions, R p an R q 3Mrg R p an R q i H(R p R q ) = TRUE 4Rpat an 3 until () is satisi N initial sgmntation: Us ovrly snsitiv thrsholing or g ttion Start with x, 4x4, or x rgions W n to b l to trmin an trak ajany Final rsult may pn on th orr in whih rgions ar mrg 5

5 Rgion Splitting Rgion Splitting Exampl Rgion splitting algorithm: Start with th ntir imag as on rgion I any rgion os not satisy (), split it into our subrgions 3 Rpat until all rgions satisy () Rsulting sgmntation may not satisy () Sgmntation an b rprsnt by a quatr ata strutur Chkrboar ailur mo 7 Rgion Split an Mrg Rgion split an mrg algorithm: Follow th rgion splitting algorithm, orming th quatr ata strutur Examin ajant rgions on irnt branhs o th quatr ata strutur, an ollow th rgion mrging algorithm Post-prossing: Mrg rgions smallr than a givn siz Contour rlaxation Apply imag unrstaning analysis o rlationships btwn rgions 9