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View Planning for Multi-Stage Object Reconstruction
Scott, William; Roth, Gerhard; Rivest, J.F.
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View Planning for Multi-Stage Object
Reconstruction *
Scott, W., Roth, G., Rivest, J.F.
June 2001
* published in Vision Interface 2001. pp 64-71, Ottawa, Ontario, Canada. June 2001.
NRC 45870.
Copyright 2001 by
National Research Council of Canada
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Fine
Model
✲ ✘ ✺❆✬✫ ❁❼ ❶❆ ✙✦✘ ✱ ✴✦✚ ✺✫❶✥✮✫ ✙ ✱ ⑥ ✚✴ ✫ ✮ ❇✘ ✫✾❽ ✙ ✚ ✰✰ ✘ ✰✺ ✦ ✫ ✤✭✰ ✘ ④❆✫ ✴✩✴ ✫✫ ❹ ❁❁ ❺ ✩ ❹ ❾❺ ✢ ✲ ✫✾✛✥✮✫ ✙ ✱ ⑥ ✚✴ ✫ ✮ ✚ ✷✷✬✥ ✚ ✤✭✫ ✴ ✦ ✥ ✦ ✭✫ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✷✬✥⑥ ✙ ✫✛ ❊ ❇ ❽❽❋✭ ✚✵ ✫ ✚ ✷✷✫ ✚ ✬✫ ✮ ✘ ✰ ✦ ✭✫ ✙✘✦ ✫✬ ✚✦ ❆✬✫✢ ❈ ✰ ✫⑧✤✫✷ ✦✘ ✥✰ ✘ ✴ ③✚ ✬⑥✥⑧ ✚ ✰✮ ✪ ✥ ✦✦✴ ✤✭ ✙✘ ✤✭ ❹ ❁❿❺ ✾✭✥ ✘ ✰ ✦ ✬✥ ✱ ✮❆✤✫ ✮ ✚ ✛✥✮✫ ✙ ✱ ⑥ ✚✴ ✫ ✮✤✥✰✤✫✷ ✦ ✸ ✥✬ ✘ ✰ ✴ ✷✫ ✤ ✦✘ ✥✰❆ ✴✘ ✰✺✛✫ ✚ ✱ ✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✛ ✚✦ ✬ ✘ ✤✫ ✴ ✢ ✣❆⑥ ✴ ✫ ④❆✫✰ ✦✙ ✼ ✩ ✣✤✥ ✦✦ ✫ ✦ ✚✙ ❹ ❾❺ ✘ ✰ ✦ ✬✥ ✱ ✮❆✤✫ ✮ ✚ ✤✥✰✤✫✷ ✦✩ ✦ ✭✫ ❶✥✮ ✘➀ ✫ ✮ ❶✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ❶ ✚✦ ✬ ✘ ⑧ ❊ ⑤❶❋ ✚✙ ✺✥✬ ✘✦ ✭✛ ✩ ✸ ✥✬ ✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫ ✱ ✥✬ ✘ ✫✰ ✦ ✫ ✮ ✵✘ ✫✾ ✷ ✙ ✚ ✰ ✱ ✰ ✘ ✰✺ ✸ ✥✬ ✚ ❆ ✦ ✥✛ ✚✦ ✫ ✮ ✛✥✮✫ ✙ ✚ ✤④❆ ✘ ✴✘✦✘ ✥✰✢ ➁➂➃ ➄➅ ➃➆➇➈➉➂ ➊ ➅ ➃➋➂➈➌➂ ➍ ✬✫ ✤✥✰ ✴✦ ✬❆✤ ✦✘ ✥✰ ✾ ✚✴ ✮✫ ➀ ✰✫ ✮ ✚✴ ✛✥✮✫ ✙ ✚ ✤④❆ ✘ ✱ ✴✘✦✘ ✥✰ ⑥ ✚✴ ✫ ✮ ✥✰ ✚ ✴ ✫ ✦ ✥ ✸ ✫⑧✷ ✙✘ ✤ ✘✦ ④❆ ✚✙✘✦ ✼ ✬✫ ④❆ ✘ ✬✫✛✫✰ ✦✴ ✫⑧✷✬✫ ✴✴ ✫ ✮ ✘ ✰ ✚ ➆ ➅➍ ➂ ➎ ➏ ➐➂➉➋ ➑ ➉➇➌➋ ➅ ➈✢ ➒✰ ✚ ✮✮ ✘✦✘ ✥✰ ✦ ✥ ✚✙✙ ✱ ✚✴ ✷✫ ✤ ✦ ✤✥ ✵ ✫✬ ✚ ✺✫ ✩ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ④❆ ✚✙✘✦ ✼ ✬✫ ④❆ ✘ ✬✫✛✫✰ ✦✴ ✚ ✬✫ ✴ ✷✫ ✤ ✘➀ ✫ ✮ ✘ ✰ ✦ ✫✬✛ ✴ ✥ ✸ ✷✬✫ ✤ ✘ ✴✘ ✥✰ ✚ ✰✮ ✴✚ ✛✷ ✙✘ ✰✺✮✫✰ ✱ ✴✘✦ ✼✢ ③ ✭ ✘ ✴ ✘ ✴ ✷✬✫ ✴ ✫✰ ✦✙ ✼ ✦ ✭✫ ✥✰ ✙ ✼ ⑩ ✰✥✾✰ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✚ ✷✷✬✥ ✚ ✤✭ ✦ ✥ ✘ ✰✤✥✬✷✥✬ ✚✦ ✫ ✴ ✷✫ ✤ ✘➀ ✤✥⑥ ⑦ ✫ ✤ ✦✘✵ ✫✬✫ ✤✥✰ ✴✦ ✬❆✤ ✱ ✦✘ ✥✰✤✬ ✘✦ ✫✬ ✘ ✚ ⑥✫✼✥✰✮ ✚✙✙ ✱ ✚✴ ✷✫ ✤ ✦ ✤✥ ✵ ✫✬ ✚ ✺✫✢ ➒ ✙✙ ❆ ✴✦ ✬ ✚✦ ✫ ✮ ✚✦ ✲ ✘ ✺❆✬✫ ❁✩ ✦ ✭✫ ✤✥✰✤✫✷ ✦ ✘ ✰ ✵ ✥ ✙✵ ✫ ✴ ✚ ✛✥✮✫ ✙ ✱ ⑥ ✚✴ ✫ ✮ ✩ ✛❆ ✙✦✘ ✱ ✴✦ ✫✷✷✬✥✤✫ ✴✴ ✥ ✸ ✷✬✥✺✬✫ ✴✴✘✵ ✫✬✫ ➀ ✰✫ ✱ ✛✫✰ ✦✩ ✴ ✫✷ ✚ ✬ ✚✦✘ ✰✺ ✫⑧✷ ✙ ✥✬ ✚✦✘ ✥✰ ✸ ✬✥✛✷✬✫ ✤ ✘ ✴✘ ✥✰✛✫ ✚✴ ❆✬✫ ✱ ✛✫✰ ✦ ✢ ✜ ✚ ✷ ✘ ✮ ✩ ✷✬✫✷✬✥✺✬ ✚ ✛✛✫ ✮ ✴ ✤✫✰✫✫⑧✷ ✙ ✥✬ ✚✦✘ ✥✰ ✷✬✥ ✱ ✮❆✤✫ ✴✚ ✷✥ ✙ ✼✺✥✰ ✚✙ ✛✫ ✴ ✭ ➃ ➅ ➓➔ → ➆ ➅➍ ➂ ➎✩ ✚ ✰ ✚ ✷✷✬✥⑧ ✘ ✛ ✚ ✱ ✦✘ ✥✰ ✥ ✸ ✥⑥ ⑦ ✫ ✤ ✦ ✺✫✥✛✫ ✦ ✬✼✢ ❂ ✫⑧ ✦✩ ✦ ✭✫ ✬✥❆✺✭ ✛✥✮✫ ✙ ✘ ✴ ✮✫ ✤ ✘ ✛ ✚✦ ✫ ✮ ✦ ✥ ✚✴✚ ✛✷ ✙✘ ✰✺✬✫ ✴ ✥ ✙ ❆ ✦✘ ✥✰ ⑦ ❆ ✴✦ ✚ ✮✫ ④❆ ✚✦ ✫ ✸ ✥✬ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✱ ✦ ✭✫ ✙ ✫ ✵ ✫ ✙ ⑥✫ ✘ ✰✺✫⑧✷✫✬ ✘ ✛✫✰ ✦✚✙✙ ✼✮✫ ✦ ✫✬ ✱ ✛ ✘ ✰✫ ✮✢ ③ ✭✫ ✬✥❆✺✭ ✛✥✮✫ ✙ ✘ ✴ ✦ ✭✫✰ ❆ ✴ ✫ ✮ ✦ ✥ ✮✫ ✵ ✫ ✙ ✥✷ ✚ ✵✘ ✫✾✷ ✙ ✚ ✰ ✸ ✥✬ ✚✴ ❆⑥ ✴ ✫ ④❆✫✰ ✦ ✴✦✚ ✺✫✥ ✸ ✷✬✫ ✤ ✘ ✴✘ ✥✰✛✫ ✚✴ ❆✬✫ ✱ ✛✫✰ ✦ ✘ ✰ ✤✥✛✷ ✙✘ ✚ ✰✤✫✾ ✘✦ ✭ ✦ ✭✫✛✥✮✫ ✙✴ ✷✫ ✤ ✘➀ ✤ ✚✦✘ ✥✰✢ ❈✴ ✚ ✰ ✚ ✮✮ ✘✦✘ ✥✰ ✚✙ ✛✫ ✚✴ ❆✬✫ ✦ ✥✬✫ ✮❆✤✫ ✤✥✛✷❆ ✦✚✦✘ ✥✰ ✚✙ ✤✥✛✷ ✙ ✫⑧ ✘✦ ✼ ✩ ✦ ✭✫ ✬✥❆✺✭ ✛✥✮✫ ✙ ✛ ✚ ✼ ⑥✫ ✴ ✫✺✛✫✰ ✦ ✫ ✮ ✚ ❆Fine Model
Rough Model
Recon Task
* Generate VPs
* Compute MM
* Find NBVs
Model Spec
Env Spec
NBV List
Fine Modeling Stage
View Plan Generation
View Plan Execution &
Model Building
Imaging System
* Scan
* Register
* Integrate
Rough Model
Acquisition Stage
✲ ✘ ✺❆✬✫ ❿❼ ✲ ✘ ✰✫❶✥✮✫ ✙✘ ✰✺❽✬✥✤✫ ✴✴ ✦ ✥✛ ✚✦✘ ✤ ✚✙✙ ✼ ✥✬ ✛ ✚ ✰❆ ✚✙✙ ✼ ✘ ✰ ✦ ✥ ✚ ✴ ✫ ✦ ✥ ✸ ✷ ✚✦ ✤✭✫ ✴ ⑥ ✚✴ ✫ ✮ ✥✰ ✦ ✭✫ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺ ✤✭ ✚✙✙ ✫✰✺✫✷✬✫ ✴ ✫✰ ✦ ✫ ✮⑥✼✮ ✘ ✫✬✫✰ ✦ ✴ ❆✬ ✸✚ ✤✫ ✸ ✫ ✚✦ ❆✬✫ ✴ ✢ ✲ ✥✬✫⑧ ✚ ✛✷ ✙ ✫ ✩ ✤ ✚✵✘✦✘ ✫ ✴✚ ✬✫✷ ✚ ✬ ✦✘ ✤❆ ✙ ✚ ✬ ✙ ✼ ✮ ✘⑨ ✤❆ ✙✦ ✦ ✥ ✘ ✛ ✚ ✺✫✮❆✫ ✦ ✥ ✴ ✭ ✚ ✮✥✾✫ ✫ ✤ ✦✴ ✢ ❈ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙ ✱ ✘✦ ✼✛ ✚✦ ✬ ✘ ⑧ ✁ ✘ ✴ ✤✥✛✷❆ ✦ ✫ ✮ ✸ ✥✬ ✫ ✚ ✤✭ ✴ ✫✺✛✫✰ ✦ ✫ ✮✬✫✺ ✘ ✥✰✢ ❸ ✼✤✥✰ ✵ ✫✰ ✦✘ ✥✰ ✩ ✬✥✾ ✴ ✤✥✬✬✫ ✴ ✷✥✰✮ ✦ ✥ ✴ ❆✬ ✸✚ ✤✫✷✥ ✘ ✰ ✦✴✚ ✰✮ ✤✥ ✙ ❆✛✰ ✴ ✦ ✥ ✵✘ ✫✾✷✥ ✘ ✰ ✦✴ ✢ ✲ ✥✬ ✘ ✰ ✴ ✷✫ ✤ ✦✘ ✥✰ ✩✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙ ✰✥ ✦ ✥✰ ✙ ✼✫⑧ ✘ ✴✦✴ ⑥❆ ✦ ✘ ✴ ✮✫ ➀ ✰✫ ✮ ✘ ✰✤✥✰ ✴✘ ✮✫✬ ✚ ⑥ ✙ ✫✮✫ ✦✚✘✙ ✢ ➒✰✥⑥ ⑦ ✫ ✤ ✦ ✬✫ ✤✥✰ ✴✦ ✬❆✤ ✱ ✦✘ ✥✰ ✩ ✥✰ ✦ ✭✫ ✥ ✦ ✭✫✬ ✭ ✚ ✰✮ ✩ ✾✫ ✰✫✫ ✮ ✦ ✥ ✤✬✫ ✚✦ ✫ ✚ ✬✥❆✺✭ ✛✥✮✫ ✙ ④❆ ✘ ✤ ⑩✙ ✼ ✾ ✘✦ ✭✥❆ ✦ ✙ ✚ ⑥✥✬ ✘ ✥❆ ✴ ✥✰ ✱ ✙✘ ✰✫ ✷✬✥✤✫ ✮❆✬✫ ✴ ✢ ③ ✭✫ ✘ ✴✴ ❆✫ ✦ ✭✫✰ ✩ ✘ ✴ ✭✥✾✬✥❆✺✭✤ ✚ ✰ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙ ⑥✫ ✚ ✰✮ ✼✫ ✦ ✬✫ ✙✘ ✚ ⑥ ✙ ✼ ✺❆ ✘ ✮✫ ✷✬✫ ✤ ✘ ✴ ✫ ⑤ ✶ ✺✫✥✛✫ ✦ ✬ ✘ ✤ ✴ ✫✰ ✴✘ ✰✺ ✚ ✰✮✛✥✮✫ ✙✘ ✰✺✂ ✄ ☎ ✆✝✞ ❑ ②✟ ✞ ✉❏▲ ✠ ✡✈✉☛ ☞①❑▲❏②✈✉ ✌✍ ✎ ✏✑ ✒✓ ✔ ✕✖ ✗✗ ✑ ✗✘ ✔✙✚✛✒ ✜✜ ③ ✭✫ ✤❆✬✬✫✰ ✦ ✾✥✬ ⑩ ✤✥✰✤✫✰ ✦ ✬ ✚✦ ✫ ✴ ✥✰ ✦ ✭✫ ➀ ✰✫ ✛✥✮✫ ✙✘ ✰✺ ✬✫ ✤✥✰ ✴✦ ✬❆✤ ✦✘ ✥✰ ✴✦✚ ✺✫ ✴ ✭✥✾✰ ✘ ✰ ✛✥✬✫✮✫ ✦✚✘✙✚✦ ✲ ✘ ✺❆✬✫ ❿ ✢ ③ ✭✫✷✬✥✤✫ ✴✴✘ ✰✷❆ ✦✴✚ ✬✫ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙ ✷ ✙ ❆ ✴✚ ✛✥✮✫ ✙ ✴ ✷✫ ✤ ✘➀ ✤ ✚✦✘ ✥✰ ✚ ✰✮ ✘ ✛ ✚ ✺ ✘ ✰✺ ✫✰ ✵✘ ✬✥✰✛✫✰ ✦ ✴ ✷✫ ✤ ✘➀ ✤ ✚✦✘ ✥✰✢ ③ ✭✫ ✛✥✮✫ ✙ ✴ ✷✫ ✤ ✘➀ ✤ ✚✦✘ ✥✰ ✮✫ ➀ ✰✫ ✴ ✬✫ ✤✥✰ ✴✦ ✬❆✤ ✦✘ ✥✰ ✺✥ ✚✙ ✴ ❊ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ✷✬✫ ✤ ✘ ✴✘ ✥✰ ✚ ✰✮ ✴✚ ✛✷ ✙✘ ✰✺✮✫✰ ✴✘✦ ✼❋ ✚✴ ✾✫ ✙✙ ✚✴ ✤✥✰ ➀ ✺❆✬ ✚ ⑥ ✙ ✫ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✷ ✚ ✬ ✚ ✛✫ ✦ ✫✬ ✴ ✢ ③ ✭✫ ✫✰ ✱ ✵✘ ✬✥✰✛✫✰ ✦ ✴ ✷✫ ✤ ✘➀ ✤ ✚ ✦ ✘ ✥✰ ✮✫ ➀ ✰✫ ✴⑩ ✫✼✷ ✚ ✬ ✚ ✛✫ ✦ ✫✬ ✴✘ ✰ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬ ✚ ✰✮✷✥ ✴✘ ✦ ✘ ✥✰ ✘ ✰✺ ✴ ✼ ✴ ✦ ✫✛✛✥✮✫ ✙ ✴ ✢ ③ ✭✫✛ ✚✘ ✰ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✦ ✚✴⑩ ✴✚ ✦✦ ✭ ✘ ✴ ✴ ✦ ✚ ✺✫ ✚ ✬✫ ✦ ✥✺✫✰✫✬ ✚ ✦ ✫✤ ✚ ✰✮ ✘ ✮ ✚ ✦ ✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦✴✩ ✤✥✛✷❆ ✦ ✫ ✚ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✛ ✚✦ ✬ ✘ ⑧ ✚ ✰✮ ✴ ✫ ✱ ✙ ✫ ✤ ✦✦ ✭✫✰✫⑧ ✦ ✱ ⑥✫ ✴✦ ✱ ✵✘ ✫✾ ✙✘ ✴✦ ✢ ③ ✭ ✚✦✵✘ ✫✾✷ ✙ ✚ ✰ ✘ ✴ ✴ ✫✰ ✦✦ ✥ ✦ ✭✫✷✭✼ ✴✘ ✤ ✚✙✘ ✛ ✚ ✺ ✘ ✰✺ ✴ ✼ ✴✦ ✫✛ ✦ ✥⑥✫✫⑧✫ ✤❆ ✦ ✫ ✮✢ ✌✍✌ ✢ ✣ ✤✒✙ ✑✥ ✒ ✗ ✦ ✖✕ ✔✙✚✛✒ ✜✜ ③ ✭✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✚✙ ✷✬✥✤✫ ✮❆✬✫ ✸ ✥ ✙✙ ✥✾✫ ✮ ✘ ✰ ✦ ✭ ✘ ✴ ✾✥✬ ⑩ ❊ ✲ ✘ ✺❆✬✫ ⑤❋✫✛✷ ✙ ✥✼ ✴ ✦ ✭✫ ✴ ✫ ✴✦ ✫✷ ✴ ✘ ✰ ✚ ✤ ✙ ✥ ✴ ✫ ✮ ✙ ✥✥✷ ✷✬✥ ✱ ✤✫ ✴✴ ✾ ✘✦ ✭ ✴ ✼✰ ✦ ✭✫ ✦✘ ✤✮ ✚✦✚ ✦ ✥✫⑧✷ ✙ ✥✬✫ ✦ ✭✫ ✘ ✛✷ ✚ ✤ ✦ ✥ ✸ ✬✥❆✺✭ ✛✥✮✫ ✙ ✮✫ ✤ ✘ ✛ ✚✦✘ ✥✰ ✚ ✰✮✫✬✬✥✬ ✴ ✥✰ ✵✘ ✫✾✷ ✙ ✚ ✰④❆ ✚✙✘✦ ✼✢ ❈Fine Model
* Decimate
* Add Noise
Rough Model
Recon Task
* Generate VPs
* Compute MM
* Find NBVs
Model Spec
Env Spec
NBV List
Estimated
Composite
Measurability
View Plan
Generation
View Plan
Verification
Recon Task
* Compute
Measurability
Verified
Composite
Measurability
✲ ✘ ✺❆✬✫⑤ ❼ ✹ ⑧✷✫✬ ✘ ✛✫✰ ✦✚✙ ❽✬✥✤✫ ✴✴ ✭ ✘ ✺✭ ✮✫✰ ✴✘ ✦ ✼ ✛✫ ✴ ✭ ✴ ❆✤✭ ✚✴ ✦ ✭✫ ✫⑧ ✚ ✛✷ ✙ ✫ ✚ ✦ ✲ ✘ ✺❆✬✫ ✧ ✴ ✫✬ ✵ ✫ ✴✚✴✚✴ ❆✬✬✥✺ ✚ ✦ ✫ ➀ ✰✫✛✥✮✫ ✙ ✢ ③ ✭✫ ➀ ✰✫✛✥✮✫ ✙✘ ✴ ✮✫ ✤ ✱ ✘ ✛ ✚✦ ✫ ✮ ✦ ✥✤✬✫ ✚✦ ✫✤✥ ✚ ✬ ✴ ✫✬✬✥❆✺✭✛✥✮✫ ✙ ✴✚✦ ✷✬✥✺✬✫ ✴✴✘✵ ✫ ✙ ✼ ✙ ✥✾✫✬ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦✘ ✫ ✴✩ ✚✸✦ ✫✬ ✾✭ ✘ ✤✭ ✴ ❆✬ ✸✚ ✤✫ ✰✥ ✘ ✴ ✫ ✘ ✴ ✚ ✮✮✫ ✮✢ ❈ ✰✫⑧ ✚ ✛✷ ✙ ✫✥ ✸✚ ✤✥ ✚ ✬ ✴ ✫ ✙ ✼ ✱ ✴✚ ✛✷ ✙ ✫ ✮ ✩ ✰✥ ✘ ✴ ✼✬✥❆✺✭ ✛✥✮✫ ✙✘ ✴ ✴ ✭✥✾✰ ✚✦ ✲ ✘ ✺❆✬✫ ❄ ✢ ③ ✭✫✬✥❆✺✭ ✛✥✮✫ ✙ ✮✬ ✘✵ ✫ ✴ ✦ ✭✫ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺✷✬✥✤✫ ✴✴✩✘ ✰✤ ✙ ❆✮ ✘ ✰✺ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✺✫✰✫✬ ✱ ✚✦✘ ✥✰ ✩ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✫ ✴✦✘ ✛ ✚✦✘ ✥✰ ✚ ✰✮ ❂❸❇✙✘ ✴✦ ✮✫ ✦ ✫✬✛ ✘ ✱ ✰ ✚✦✘ ✥✰⑥✼✛✫ ✚ ✰ ✴ ✥ ✸✚ ✺✬✫✫ ✮✼ ✴ ✫ ✚ ✬ ✤✭ ✴ ✫ ✦ ✤✥ ✵ ✫✬ ✘ ✰✺ ✚✙ ✺✥ ✱ ✬ ✘✦ ✭✛✢ ✽✦ ✭✫✬ ✘ ✰✷❆ ✦✴✘ ✰✤ ✙ ❆✮✫ ✘ ✛ ✚ ✺ ✘ ✰✺ ✫✰ ✵✘ ✬✥✰✛✫✰ ✦ ✚ ✰✮ ✛✥✮✫ ✙✴ ✷✫ ✤ ✘➀ ✤ ✚✦✘ ✥✰ ✴ ✢ ③ ✭✫✬✫ ✴ ❆ ✙✦✘ ✰✺ ✵✘ ✫✾✷ ✙ ✚ ✰ ✴✚ ✬✫✫⑧ ✱ ✫ ✤❆ ✦ ✫ ✮ ✚ ✺ ✚✘ ✰ ✴✦ ✦ ✭✫✷ ✚ ✬✫✰ ✦ ➀ ✰✫✛✥✮✫ ✙✩ ✤ ✙ ✥ ✴✘ ✰✺ ✦ ✭✫ ✙ ✥✥✷ ✦ ✥✷✬✥ ✵✘ ✮✫ ✵ ✫✬ ✘➀ ✫ ✮✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✢ ✌✍★ ✩ ✒ ✗✜✚✙ ✪✚✫✒✕ ③ ✭✫ ✴ ✫✰ ✴ ✥✬ ✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫ ✛✥✮✫ ✙ ✫✛⑥✫ ✮✮✫ ✮ ✘ ✰ ✦ ✭✫ ⑤❶ ✴ ✼ ✴✦ ✫✛ ✘ ✴ ✬✫ ✚✴ ✥✰ ✚ ⑥ ✙ ✼ ✤✥✛✷✬✫✭✫✰ ✴✘✵ ✫✢ ✣✫ ✵ ✫✬ ✚✙ ✺✫✰✫✬ ✘ ✤ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✛✫ ✤✭ ✚ ✰ ✘ ✴ ✛ ✴ ✚ ✰✮ ✦ ✭✫ ✘ ✬ ✚✴✴ ✥✤ ✘ ✚✦ ✫ ✮ ✸ ✬❆ ✴✦ ❆✛ ✴ ✭ ✚ ✷✫ ✴✚ ✬✫✮✫ ➀ ✰✫ ✮ ✚ ✰✮✷ ✚ ✬ ✚ ✛✫ ✦ ✫✬ ✘✬ ✫ ✮ ✘ ✰ ✦ ✫✬✛ ✴ ✥ ✸➀ ✫ ✙ ✮ ✥ ✸✵✘ ✫✾ ✩ ✴ ✤ ✚ ✰ ✙ ✫✰✺ ✦ ✭ ✩ ✛ ✘ ✰ ✘ ✛❆✛ ✚ ✰✮✛ ✚ ⑧ ✘ ✛❆✛✬ ✚ ✰✺✫ ✴ ✢ ③ ✭✫ ✤ ✚ ✛✫✬ ✚ ✘ ✴ ✛✥✮✫ ✙ ✫ ✮ ✚✴ ✚ ⑥ ✘ ✱ ✴✦✚✦✘ ✤ ✴ ✫✰ ✴ ✥✬ ✾ ✘✦ ✭ ✚ ✴ ✷✫ ✤ ✘➀ ✫ ✮ ✥✷ ✦✘ ✤ ✚✙ ⑥ ✚✴ ✫ ✙✘ ✰✫✭✢ ➒✛ ✚ ✺✫ ✴✘✬ ✫ ✚ ✰✮ ✥ ✦ ✭✫✬✷ ✚ ✱ ✬ ✚ ✛✫ ✦ ✫✬ ✴✚ ✬✫✥✷ ✦✘ ✥✰ ✚✙✙ ✼✬✫ ✤✥✰ ➀ ✺❆✬ ✚ ⑥ ✙ ✫✢ ❇✘ ✫✾✷✥ ✘ ✰ ✦✴✚ ✬✫ ✦ ✬✫ ✚✦ ✫ ✮ ✚✴ ✺✫✰✫✬ ✚✙✘✬ ✫ ✮ ✵✘ ✫✾✷✥ ✘ ✰ ✦✴ ❊ ✮✯✰ ✱ ❋ ✩ ✤✥✰ ✴✘ ✴✦✘ ✰✺✥ ✸ ✴ ✫✰ ✴ ✥✬✷✥ ✴ ✫ ✮ ✚ ✰✮ ✚✴ ✫ ✦ ✥ ✸ ✤✥✰ ✦ ✬✥ ✙✙ ✚ ⑥ ✙ ✫ ✴ ✫✰ ✴ ✥✬✷ ✚ ✬ ✚ ✛✫ ✱ ✦ ✫✬ ✴ ✰ ✱ ✢ ③ ✭❆ ✴ ✫ ✚ ✤✭ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✭ ✚✴✚ ✰ ✚✴✴ ✥✤ ✘ ✚✦ ✫ ✮ ✴ ✫✰ ✴ ✥✬ ✤✥✰ ➀ ✺❆✬ ✚✦✘ ✥✰✢ ③ ✭ ✘ ✴ ❆✰✬✫ ✴✦ ✬ ✘ ✤ ✦ ✫ ✮ ✚ ✷✷✬✥ ✚ ✤✭ ✦ ✥ ✵✘ ✫✾ ✱ ✷✥ ✘ ✰ ✦ ✺✫✰✫✬ ✚✦✘ ✥✰ ✤✥✰ ✦ ✬ ✚✴✦✴ ✾ ✘✦ ✭ ✵✘ ✫✾ ✘ ✰✺ ✤✥✰ ✴✦ ✬ ✚✘ ✰ ✦✴ ✲✳✴ ✵✶✷✸✵✹✺✵ ✻ ✼ ✸✵ ✴ ✽ ✹ ✼ ✺✾✿ ✽ ✴ ✵✵ ✼ ✵❀ ✴ ✿✿❁✸ ✴ ✷ ❂ ✺❃❄✺✹✺✵❃✸❅✺✸ ❆ ✻❂ ✺❅✸❃ ✻ ❃✸✿ ❂✼ ❃ ✻ ✼ ✷ ✴ ✻ ✺❇❄ ✻ ❁✺ ✴ ✻ ✻❂ ✺❁ ✴ ✵❀✺✷ ✴ ❅✺❁ ✴✴ ❃ ✴ ✿✸ ✼ ✵ ✻ ❃✺✵❃✸❁ ✴ ✵❇ ✻❂ ❈❃ ❆✴ ✼✽ ✻ ✸ ✻ ✴❉ ✺ ✼ ✵ ✻ ✸ ✴ ✷✷✸❈✵ ✻ ✸✵✺✸ ❆ ✼✻ ❃ ❅✸❃ ✻✼ ❅✿✸❁ ✻ ✴ ✵ ✻ ❂ ✴✴ ✻ ✺❁ ✼ ❃ ✻ ✼ ✷❃❊❃ ❂ ✴ ❇✸✾✺ ❋ ✺✷ ✻ ❃●✲ ✘ ✺❆✬✫✧ ❼ ✿✚✵✘✦ ✼ ✲ ✘ ✰✫❶✥✮✫ ✙ ✲ ✘ ✺❆✬✫ ❄❼ ❂ ✥ ✘ ✴ ✼ ✿✚✵✘✦ ✼ ✜✥❆✺✭❶✥✮✫ ✙ ✤✥✛✛✥✰ ✙ ✼ ✚ ✷✷ ✙✘ ✫ ✮ ✘ ✰ ✦ ✭✫ ✙✘ ✦ ✫✬ ✚ ✦ ❆✬✫ ✩ ✴ ❆✤✭ ✚✴ ✦ ✭✫❆ ✴ ✫✥ ✸ ✵✘ ✫✾ ✴ ✷✭✫✬✫ ✴✁ ✢ ✗ ✭ ✘✙ ✫✥❆✬ ✷✥ ✴✘ ✦ ✘ ✥✰ ✘ ✰✺ ✴ ✼ ✴ ✦ ✫✛ ✛✥✮✫ ✙ ✘ ✰✤✥✬✷✥✬ ✚ ✦ ✫ ✴ ✫✬✬✥✬✷ ✚ ✬ ✚ ✛✫ ✦ ✫✬ ✴ ✩ ✘ ✦ ✘ ✴ ✤✥✰ ✴✘ ✮✫✬✫ ✮✫✬✬✥✬ ✱ ✸ ✬✫✫ ✸ ✥✬ ✦ ✭✫✫⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✷✬✫ ✴ ✫✰ ✦ ✫ ✮✭✫✬✫✢ ❶✥ ✴✦✘ ✛✷✥✬ ✦✚ ✰ ✦✙ ✼ ✩ ✚✴ ✫✰ ✴ ✥✬✺✫✥✛✫ ✦ ✬ ✘ ✤✰✥ ✘ ✴ ✫✛✥✮✫ ✙✘ ✴ ✘ ✰✤✥✬✷✥✬ ✚✦ ✫ ✮ ⑥ ✚✴ ✫ ✮ ✥✰ ✬ ✚ ✰✺✫✤ ✚ ✛✫✬ ✚ ✤ ✚✙✘ ⑥✬ ✚✦✘ ✥✰ ✮ ✚✦✚ ❹ ❿❺ ✩ ❹⑤ ❺ ✩ ❹✧ ❺ ✢ ③ ✭✫ ✰✥ ✘ ✴ ✫ ✛✥✮✫ ✙ ✫ ✴✦✘ ✛ ✚✦ ✫ ✴ ✴✦✚✦✘ ✴✦✘ ✤ ✴ ✥ ✸ ✦ ✭✫✬✫ ✴✘ ✮❆ ✚✙ ✬ ✚ ✰✮✥✛✰✥ ✘ ✴ ✫✬✫✛ ✚✘ ✰ ✘ ✰✺ ✚✸✦ ✫✬✤ ✚✙✘ ⑥✬ ✚✦✘ ✥✰✢ ✗ ✫ ❆ ✴ ✫ ✦ ✭✫ ✴✦✚ ✰✮ ✚ ✬ ✮ ✤✥✰ ✵ ✫✰ ✦✘ ✥✰ ✸ ✥✬ ✦ ✭✫ ✬ ✚ ✰✺✫ ✤ ✚ ✛ ✱ ✫✬ ✚ ✤✥✥✬ ✮ ✘ ✰ ✚✦ ✫ ✸ ✬ ✚ ✛✫ ✥ ✸ ✬✫ ✸ ✫✬✫✰✤✫ ❼ ✦ ✭✫ ⑧ ✩ ✼ ✚ ✰✮ ✰✫✺ ✱ ✚✦✘✵ ✫ ✬ ✱ ✚ ⑧✫ ✴ ✚ ✬✫✷ ✚ ✬ ✚✙✙ ✫ ✙ ✦ ✥ ✦ ✭✫ ✙ ✚✴ ✫✬ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✷ ✙ ✚ ✰✫ ✩ ✤ ✚ ✛✫✬ ✚ ✥✷ ✦✘ ✤ ✚✙ ⑥ ✚✴ ✫ ✙✘ ✰✫ ✚ ✰✮✤ ✚ ✛✫✬ ✚ ⑥✥✬✫ ✴✘ ✺✭ ✦✩ ✬✫ ✴ ✷✫ ✤ ✱ ✦✘✵ ✫ ✙ ✼✢ ✣✫✰ ✴ ✥✬✺✫✥✛✫ ✦ ✬ ✘ ✤✰✥ ✘ ✴ ✫✫ ✫ ✤ ✦✴ ✚ ✬✫✛✥✮✫ ✙ ✫ ✮ ✚✴ ✸ ✥ ✙✙ ✥✾ ✴✩ ✾✭✫✬✫✄☎✂ ✯✄✆✯✂ ✄✝✂ ✚ ✬✫ ✦ ✭✫ ✴✦✚ ✰✮ ✚ ✬ ✮✮✫ ✵✘ ✚✦✘ ✥✰✫ ✴ ✱ ✦✘ ✛ ✚✦ ✫ ✮✰✥ ✘ ✴ ✫✤✥✛✷✥✰✫✰ ✦✴✚✙ ✥✰✺ ✦ ✭✫✬✫ ✴ ✷✫ ✤ ✦✘✵ ✫ ✴ ✫✰ ✴ ✥✬ ✚ ⑧✫ ✴✩ ✰✥ ✘ ✴ ✫ ✤✥✫ ⑨ ✤ ✘ ✫✰ ✦✴ ❊✞ ☎✯ ✞ ✆✯ ✞ ✝❋ ✚ ✬✫ ✮✫✬ ✘✵ ✫ ✮ ✸ ✬✥✛ ✤ ✚✙✘ ⑥✬ ✚✦✘ ✥✰✮ ✚✦✚✚ ✰✮ ✬✘ ✴ ✬ ✚ ✰✺✫ ✚✙ ✥✰✺ ✦ ✭✫✤ ✚ ✛✫✬ ✚ ⑥✥✬✫ ✱ ✴✘ ✺✭ ✦ ✢ ➒✰ ✦ ✭ ✘ ✴➀ ✬ ✴✦ ✥✬ ✮✫✬✛✥✮✫ ✙✩ ✥ ✱ ✮ ✘ ✚ ✺✥✰ ✚✙ ✰✥ ✘ ✴ ✫✤✥ ✱ ✵✚ ✬ ✘ ✚ ✰✤✫✛ ✚✦ ✬ ✘ ⑧✫ ✙ ✫✛✫✰ ✦✴✚ ✬✫✤✥✰ ✴✘ ✮✫✬✫ ✮ ✴ ✫ ✤✥✰✮ ✚ ✬✼✫ ✸ ✱ ✸ ✫ ✤ ✦✴✘ ✺✰✥✬✫ ✮ ✸ ✥✬ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺✷❆✬✷✥ ✴ ✫ ✴ ✢ ✂ ✄☎ ✟ ✞ ☎✠ ✂ ✄✆ ✟ ✞ ✆✠ ✂ ✄✝ ✟ ✞ ✝✠✡ ❊ ❁ ❋ ❈✴ ✰✥ ✘ ✴ ✫ ✚✙ ✥✰✺ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬ ⑥✥✬✫ ✴✘ ✺✭ ✦ ✷✬✫ ✮✥✛ ✘ ✰ ✚✦ ✫ ✴ ✚ ✰✮ ✴ ✛ ✚✙✙ ✫✬✬✥✬ ✴✦✚ ✰✺✫✰ ✦✘ ✚✙ ✦ ✥ ✦ ✭✫ ✴ ❆✬ ✸✚ ✤✫ ✚ ✬✫✥ ✸ ✮✫⑥ ✚✦ ✚ ⑥ ✙ ✫ ✴✘ ✺✰ ✤ ✚ ✰✤✫ ✩ ✾✫❆ ✴ ✫✂ ✄✝ ✚✴✚✴ ❆✬✬✥✺ ✚✦ ✫ ✥✬✛✫ ✚✴ ❆✬✫ ✱ ✛✫✰ ✦ ✷✬✫ ✤ ✘ ✴✘ ✥✰✢ ❈ ✮✮ ✘✦✘ ✥✰ ✚✙✙ ✼ ✩ ✫ ✴✦✘ ✛ ✚✦ ✫ ✮ ✴ ✫✰ ✴ ✥✬ ✰✥ ✘ ✴ ✫ ✘ ✴ ✛✥✮ ✘➀ ✫ ✮ ⑥✼ ✚ ✰ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✚✙✙ ✼ ✱ ⑥ ✚✴ ✫ ✮✺✬ ✚✬✘ ✰✺ ✚ ✰✺ ✙ ✫ ✛✥✮✫ ✙ ✸ ✥✬ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬ ⑧ ✱ ✬ ✚ ✰✮ ✼ ✱ ✬ ✷ ✙ ✚ ✰✫ ✴ ✢ ➒✰✤ ✘ ✮✫✰✤✫ ✚ ✰✺ ✙ ✫✫ ✫ ✤ ✦ ✴✚ ✬✫✛✥ ✴ ✦ ✰✥ ✦ ✘ ✤✫ ✚ ⑥ ✙ ✫ ✘ ✰ ✦ ✭✫✷ ✙ ✚ ✰✫✥ ✸ ✦ ✬ ✘ ✚ ✰ ✱ ✺❆ ✙ ✚ ✦ ✘ ✥✰ ✱ ✦ ✭ ✚ ✦ ✘ ✴ ✩✦ ✭✫✼ ✬ ✱ ✷ ✙ ✚ ✰✫ ✩ ✾✭✫✬✫ ✦ ✭✫✼ ✺✫✰✫✬ ✚✙✙ ✼ ✸ ✥ ✙✙ ✥✾ ✚ ✰ ✘ ✰ ✵ ✫✬ ✴ ✫✤✥ ✴✘ ✰✫✬✫ ✙ ✚✦✘ ✥✰ ✴ ✭ ✘ ✷❆✷ ✦ ✥ ✚ ✤❆ ✦ ✱ ✥ ✚ ✰ ✱ ✺ ✙ ✫☛✆✝✢ ③ ✭✫✬✫ ✘ ✴ ✰✥✰✥ ✦✘ ✤✫ ✚ ⑥ ✙ ✫ ✘ ✰✤ ✙✘ ✰ ✚✦✘ ✥✰✫ ✫ ✤ ✦ ✘ ✰ ✦ ✭✫ ✴ ✤ ✚ ✰✰ ✘ ✰✺✷ ✙ ✚ ✰✫❆✷ ✦ ✥ ✚ ✤❆ ✦ ✱ ✥ ✚ ✰✺ ✙ ✫☛☎✝ ✚✦ ✾✭ ✘ ✤✭✷✥ ✘ ✰ ✦ ✦ ✭✫ ✬✫ ✤✫ ✘✵ ✫ ✮ ✫✰✫✬✺✼✮✬✥✷ ✴ ⑥✫ ✙ ✥✾ ✦ ✭✬✫ ✴ ✭✥ ✙ ✮✢ ③ ✭❆ ✴✩ ✾✫ ✛✥✮ ✘✸ ✼ ✦ ✭✫ ✫ ✴✦✘ ✛ ✚✦ ✫ ✮ ✷✬✫ ✤ ✘ ✴✘ ✥✰ ✥⑥ ✦✚✘ ✰✫ ✮ ✸ ✬✥✛ ✹ ④❆ ✚ ✱ ✦✘ ✥✰ ❁ ⑥✼ ✦ ✭✫ ✸ ✥ ✙✙ ✥✾ ✘ ✰✺ ✩ ✾✭✫✬✫☞ ✌ ❊✍ ❋ ✘ ✴ ✦ ✭✫ ✘ ✰ ✵ ✫✬ ✴ ✫❆✰ ✘✦ ✴✦ ✫✷ ✸ ❆✰✤ ✦✘ ✥✰ ✩ ❊ ☞ ✌ ❊ ✍ ❋ ✟ ❁✎ ☞ ❊✍ ❋ ❋ ❼ ✂ ✄✝ ✟ ✞ ✝✠✡ ✤✥ ✴❊ ✍ ✆✝❋☞ ✌ ❊ ✍ ✆✝ ✎ ☛✆✝❋☞ ✌ ❊✍ ☎✝ ✎ ☛☎✝❋ ❊❿ ❋ ✗ ✭ ✘✙ ✫ ✺✬ ✚✬✘ ✰✺ ✚ ✰✺ ✙ ✫ ✫ ✫ ✤ ✦✴ ✚ ✬✫ ✸ ✬✫ ④❆✫✰ ✦✙ ✼ ✛✥✮ ✱ ✫ ✙ ✫ ✮ ✘ ✰ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✚✙ ✺✥✬ ✘✦ ✭✛ ✴ ❊ ❹ ❁ ❺ ✩ ❹ ❄❺ ✩ ❹ ❁❿❺ ❋ ✩✦ ✭✫✼ ✭ ✚✵ ✫⑥✫✫✰ ✦ ✬✫ ✚✦ ✫ ✮ ✴ ❆⑥ ⑦ ✫ ✤ ✦✘✵ ✫ ✙ ✼✬ ✚✦ ✭✫✬ ✦ ✭ ✚ ✰✥⑥ ⑦ ✫ ✤ ✦✘✵ ✫ ✙ ✼✢ ③ ✭ ✚✦✘ ✴✩✙ ✥✾✺✬ ✚✬✘ ✰✺ ✚ ✰✺ ✙ ✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦✴✚ ✬✫✺ ✘✵ ✫✰✷✬✫ ✸ ✫✬ ✱ ✫✰✤✫✥ ✵ ✫✬✭ ✘ ✺✭✺✬ ✚✬✘ ✰✺ ✚ ✰✺ ✙ ✫ ✴✩ ✬ ✚✦ ✭✫✬ ✦ ✭ ✚ ✰✫ ✵✚✙ ❆ ✚✦✘ ✰✺ ✦ ✭✫✥⑥ ⑦ ✫ ✤ ✦✘✵ ✫✫ ✫ ✤ ✦✴ ✥ ✸ ✺✬ ✚✬✘ ✰✺ ✚ ✰✺ ✙ ✫✥✰✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ④❆ ✚✙✘✦ ✼ ✩ ✴ ❆✤✭ ✚✴ ✷✬✫ ✤ ✘ ✴✘ ✥✰ ✚ ✰✮ ✴✚ ✛✷ ✙✘ ✰✺✮✫✰ ✴✘✦ ✼✢ ✌✍✏ ✪✒✖ ✜✑✙✖✒ ✑ ✕ ✑✦ ✓ ✗ ✫ ❆ ✴ ✫ ✴ ✫ ✵ ✫✬ ✚✙ ✵✚ ✬ ✘ ✚ ✰ ✦✴ ✥ ✸ ✦ ✭✫ ✦ ✫✬✛ ➆➂➇ ➏ ➓➃➇✔➋ ➎ ➋➌✕✢ ✹✚ ✤✭ ➆➂➇ ➏ ➓➃➇✔➋ ➎ ➋➌✕➆➇➌➃➋✖➂ ➎ ➂➆➂➈➌✗✌✘ ✘ ✴✚ ⑥ ✘ ✰ ✚ ✬✼✫ ✴ ✱ ✦✘ ✛ ✚✦ ✫ ✥ ✸ ✦ ✭✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✥ ✸ ✚ ✴✘ ✰✺ ✙ ✫ ✴ ❆✬ ✸✚ ✤✫ ✷✥ ✘ ✰ ✦ ✙ ✌ ✥✰ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙ ✸ ✬✥✛ ✚✴✘ ✰✺ ✙ ✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✮ ✘ ❹ ❾❺ ✢ ③ ✭✫ ✫ ✴✦✘ ✛ ✚✦ ✫ ✴ ✫✬ ✵ ✫ ✴ ✦ ✥ ✷✬✫ ✮ ✘ ✤ ✦ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✬✫ ✴ ❆ ✙✦✴ ✚✦ ✚ ✭ ✘ ✺✭✫✬ ✴✚ ✛✷ ✙✘ ✰✺✮✫✰ ✴✘✦ ✼✾ ✘✦ ✭ ✦ ✭✫ ✬✫ ✚✙✴ ✫✰ ✴ ✥✬ ✩ ✬✫ ✚✙ ✥⑥ ✱ ⑦ ✫ ✤ ✦ ✚ ✰✮ ✬✫ ✚✙ ✘ ✛ ✚ ✺ ✘ ✰✺ ✫✰ ✵✘ ✬✥✰✛✫✰ ✦ ✢ ③ ✥ ⑥✫ ✛✫ ✚✴ ❆✬ ✱ ✚ ⑥ ✙ ✫ ✩ ✚✙✙ ✛✥✮✫ ✙✴ ✷✫ ✤ ✘➀ ✤ ✚✦✘ ✥✰✬✫ ④❆ ✘ ✬✫✛✫✰ ✦✴ ✛❆ ✴✦ ⑥✫✛✫ ✦ ✚✦ ✦ ✭ ✚✦✴ ❆✬ ✸✚ ✤✫✷✥ ✘ ✰ ✦ ✸ ✥✬ ✦ ✭ ✚✦ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✢ ✣✷✫ ✤ ✘➀ ✤ ✚✙✙ ✼ ✩ ✦ ✭✫ ✴ ❆✬ ✸✚ ✤✫ ✷✥ ✘ ✰ ✦ ✛❆ ✴✦✸✚✙✙ ✾ ✘✦ ✭ ✘ ✰ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬ ✸ ✬❆ ✴✦ ❆✛ ✸ ✥✬ ✦ ✭ ✚✦✵✘ ✫✾✷✥ ✘ ✰ ✦✩✦ ✭✫ ✴ ❆✬ ✸✚ ✤✫✷✥ ✘ ✰ ✦ ✛❆ ✴✦ ⑥✫ ✙ ✥✤ ✚✙✙ ✼ ✵✘ ✴✘ ⑥ ✙ ✫ ✦ ✥ ✦ ✭✫ ✥✷ ✦✘ ✤ ✚✙ ✴ ✥❆✬ ✤✫ ✚ ✰✮ ✬✫ ✤✫ ✘✵ ✫✬ ✩ ✚ ✰✮ ✫ ✴✦✘ ✱ ✛ ✚✦ ✫ ✮ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ✷✬✫ ✤ ✘ ✴✘ ✥✰ ✚ ✰✮ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦ ✼ ✛❆ ✴✦ ✛✫✫ ✦ ✦ ✭✫ ✴ ✷✫ ✤ ✘➀ ✫ ✮ ✬✫ ④❆ ✘ ✬✫✛✫✰ ✦ ✢ ✽ ❆✬ ✛✫ ✚✴ ❆✬ ✚ ✱ ⑥ ✘✙✘✦ ✼✛ ✚✦ ✬ ✘ ✤✫ ✴✚ ✬✫⑥ ✘ ✰ ✚ ✬✼✢ ❈ ✰ ✚✙ ✥✺❆✫ ✸ ✥✬✛ ✴ ✤ ✚ ✰ ✚✙ ✴ ✥⑥✫ ✮✫ ➀ ✰✫ ✮✢ ③ ✭✫ ➆➂➇ ➏ ➓➃➇✔➋ ➎ ➋➌✕ ➅➄ ➇ ➏ ➋➈➔ ➎ ➂ ✚➋➂✛➐ ➅ ➋➈➌ ✗ ❊ ✮ ✘ ❋ ✥✬ ✩ ✫ ④❆ ✘✵✚✙ ✫✰ ✦✙ ✼ ✚ ✰ ✘ ✛ ✚ ✺✫ ✩ ✘ ✴ ✦ ✭✫ ✬ ✚✦✘ ✥✥ ✸ ✦ ✭✫ ✴ ❆✬ ✸✚ ✤✫✤✥ ✵ ✱ ✫✬ ✚ ✺✫✥ ✸ ✦ ✭ ✚✦✵✘ ✫✾✷✥ ✘ ✰ ✦ ✜✢ ✘ ✜ ✬✫ ✙ ✚✦✘✵ ✫ ✦ ✥ ✦ ✭✫ ✴✘✬ ✫✥ ✸ ✦ ✭✫ ✴ ❆✬ ✸✚ ✤✫ ✷ ✚✦ ✤✭ ✚✴ ✚ ✾✭✥ ✙ ✫ ✜✢ ✜ ✢ ③ ✭✫ ✴ ✫ ✦ ✢ ✘ ✥ ✸ ✴ ❆✬ ✸✚ ✤✫ ✫ ✙ ✫✛✫✰ ✦✴ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✙ ✫ ⑥✼ ✚ ✴✘ ✰✺ ✙ ✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✮✘ ✘ ✴ ✮✫ ✱ ➀ ✰✫ ✮⑥✼ ✦ ✭✫✤✥✬✬✫ ✴ ✷✥✰✮ ✘ ✰✺ ✤✥ ✙ ❆✛✰ ✵ ✫ ✤ ✦ ✥✬ ✁ ✣✤✘ ✥ ✸ ✦ ✭✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✛ ✚✦ ✬ ✘ ⑧✢ ✗ ❊ ✮ ✘ ❋✟ ✜✢ ✘ ✜ ✜ ✢ ✜ ❊ ⑤❋
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
-8.5
-8
-7.5
-7
-6.5
-6
-5.5
-5
-4.5
-4
Measurability
Relative Sampling Density: den_rel = log_2 ( den_RM / den_FM )
VERIFIED MEASURABILITY vs. RELATIVE SAMPLING DENSITY
Target: Cavity
VP_Algorithm = VARIABLE
Spec = ( 50,2 )
Env = ( LS-M, CMM )
FM = 4225 samples
D/W = 0.1
D/W = 0.2
D/W = 0.3
D/W = 0.5
D/W = 0.7
D/W = 1.0
✲ ✘ ✺❆✬✫ ❃❼ ❇ ✫✬ ✘➀ ✫ ✮ ❶✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✵ ✴ ✢ ✜✫ ✙ ✚✦✘✵ ✫ ✣ ✚ ✛ ✱ ✷ ✙✘ ✰✺ ✶ ✫✰ ✴✘✦ ✼ ③ ✭✫ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺ ✚✙ ✺✥✬ ✘✦ ✭✛✥✷✫✬ ✚✦ ✫ ✴ ✥✰ ➂ ➏ ➌➋➆➇➌➂ ➍ ➆➂➇ ➏ ➓➃➇✔➋ ➎ ➋➌✕ ✥ ✸ ✚ ✴✘ ✰✺ ✙ ✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✥✬ ✴ ✫ ✦✴ ✥ ✸ ✵✘ ✫✾ ✱ ✷✥ ✘ ✰ ✦✴ ✢ ✗ ✭✫✰ ✦ ✭✫✬✫ ✴ ❆ ✙✦✘ ✰✺ ❂❸❇✙✘ ✴✦✘ ✴ ✫⑧✫ ✤❆ ✦ ✫ ✮⑥✼ ✚ ✬✫ ✚✙✴ ✫✰ ✴ ✥✬ ✚ ✺ ✚✘ ✰ ✴✦ ✦ ✭✫✬✫ ✚✙ ✥⑥ ⑦ ✫ ✤ ✦ ✥✬⑥✼ ✚✴ ✫✰ ✴ ✥✬✛✥✮✫ ✙ ✚ ✺ ✚✘ ✰ ✴✦ ✚✴✘ ✛❆ ✙ ✚✦ ✫ ✮ ➀ ✰✫ ✛✥✮✫ ✙ ✩✦ ✭✫ ✬✫ ✴ ❆ ✙✦ ✘ ✴ ✚➂➃➋ ➑ ➂ ➍ ➆➂➇ ➏ ➓➃➇✔➋ ➎ ➋➌✕✢ ✲ ✘ ✰ ✚✙✙ ✼ ✩ ✦ ✭✫ ✦ ✫✬✛ ➉ ➅ ➆➐ ➅➏ ➋➌➂ ➆➂➇ ➏ ➓➃➇ ➊ ✔➋ ➎ ➋➌✕ ✾ ✘✙✙ ⑥✫ ❆ ✴ ✫ ✮ ✾ ✘✦ ✭ ⑥✥ ✦ ✭ ✫ ✴✦✘ ✛ ✚✦ ✫ ✮ ✚ ✰✮ ✵ ✫✬ ✘➀ ✫ ✮ ✬✫ ✴ ❆ ✙✦✴ ✦ ✥✮✫ ➀ ✰✫ ✦ ✭✫✰✫ ✦ ✤✥ ✵ ✫✬ ✚ ✺✫✥ ✸ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✴ ✫ ✦✴ ✢ ✌✍ ✢ ✣ ✤✒✙ ✑✥ ✒ ✗ ✦ ✜ ✹ ⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✾✫✬✫ ✤✥✰✮❆✤ ✦ ✫ ✮ ✾ ✘✦ ✭ ✴ ✼✰ ✦ ✭✫ ✦✘ ✤ ✤ ✚✵✘✦ ✼ ✷ ✚✦ ✤✭✫ ✴ ✥ ✸ ✵✚ ✬ ✘ ✥❆ ✴ ✴ ✭ ✚ ✷✫ ✴ ✚✴ ✬✫✷✬✫ ✴ ✫✰ ✦✚✦✘✵ ✫ ✥ ✸ ✚ ✮ ✘✸ ✱ ➀ ✤❆ ✙✦ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✤✭ ✚✙✙ ✫✰✺✫✢ ③ ✭✫ ✷✬ ✘ ✰✤ ✘ ✷ ✚✙ ✘ ✰✷❆ ✦ ✷ ✚ ✬ ✚ ✛✫ ✦ ✫✬ ✴✚ ✬✫ ✦ ✭✫ ✴✘✬ ✫✥ ✸ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙ ✬✫ ✙ ✚✦✘✵ ✫ ✦ ✥ ✦ ✭✫✥⑥ ⑦ ✫ ✤ ✦✘✵ ✫ ➀ ✰✫✛✥✮✫ ✙ ✫⑧✷✬✫ ✴✴ ✫ ✮ ✘ ✰ ✦ ✫✬✛ ✴ ✥ ✸ ✬✫ ✙ ✚✦✘✵ ✫ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦ ✼ ✩✦ ✭✫ ✙ ✫ ✵ ✫ ✙ ✥ ✸ ✬✥❆✺✭ ✛✥✮✫ ✙ ✺✫✥✛✫ ✦ ✬ ✘ ✤ ✴ ❆✬ ✸✚ ✤✫✰✥ ✘ ✴ ✫ ✚ ✰✮ ✦ ✭✫ ✴ ✭ ✚ ✷✫✥ ✸ ✦ ✭✫ ✦✚ ✬✺✫ ✦ ✴ ❆✬ ✸✚ ✤✫✷ ✚✦ ✤✭✢ ✲ ✥✬ ✥❆ ✦ ✷❆ ✦ ✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫✛✫ ✚✴ ❆✬✫ ✴✩ ✾✫ ✫⑧ ✚ ✛ ✘ ✰✫ ✤✥✛ ✱ ✷✥ ✴✘✦ ✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✚ ✤✭ ✘ ✫ ✵ ✫ ✮ ❆✷✥✰ ✫⑧✫ ✤❆ ✦✘ ✥✰ ✥ ✸ ✦ ✭✫ ❂❸❇ ✙✘ ✴✦✩ ➉➓➆➓ ➎ ➇➌➋✚➂ ➆➂➇ ➏ ➓➃➇✔➋ ➎ ➋➌✕ ✚✴ ✚ ✸ ❆✰✤ ✦✘ ✥✰ ✥ ✸ ✦ ✭✫✰❆✛⑥✫✬✥ ✸ ✵✘ ✫✾ ✴ ✮❆✬ ✘ ✰✺ ✦ ✭✫✫⑧✫ ✤❆ ✦✘ ✥✰✥ ✸ ✦ ✭✫ ❂❸❇ ✙✘ ✴✦✩✴✘✬ ✫✥ ✸ ✦ ✭✫✺✫✰✫✬ ✚✦ ✫ ✮ ❂❸❇ ✙✘ ✴✦✚ ✰✮✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✫ ✴✦✘ ✛ ✚✦✘ ✥✰ ✫✬✬✥✬✢ ❶✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✫ ✴✦✘ ✛ ✚✦✘ ✥✰✫✬✬✥✬ ❊ ✦ ✭✫ ✮ ✘ ✫✬✫✰✤✫ ⑥✫ ✦ ✾✫✫✰ ✫ ✴✦✘ ✛ ✚✦ ✫ ✮ ✚ ✰✮ ✵ ✫✬ ✘➀ ✫ ✮ ✤✥✛✷✥ ✴✘✦ ✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘ ✦ ✼❋ ✘ ✴✚ ✰ ✘ ✰✮ ✘ ✤ ✚ ✦ ✥✬✥ ✸ ✦ ✭✫ ✬✫ ✙✘ ✚ ⑥ ✘✙✘ ✦ ✼✥ ✸ ✦ ✭✫ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺✷✬✥✤✫ ✴✴ ✢ ✁ ✂ ✞ ✈ ✟ ✞ ❏❑ ✄ ▲✉✇ ☎ ✞ ✠▲❏② ✆✞ ✝ ▲ ✟ ✞ ✝ ✠②✉☞ ✟ ✞ ✉ ■ ②❏ ✄ ✣✭ ✚ ✮✥✾✫ ✫ ✤ ✦✴ ✘ ✰ ✴ ❆✬ ✸✚ ✤✫✤✥✰✤ ✚✵✘✦✘ ✫ ✴ ✷✬✫ ✴ ✫✰ ✦ ✚ ✛ ✚⑦ ✥✬ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✷✬✥⑥ ✙ ✫✛ ✚ ✰✮ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✤✭ ✚✙✙ ✫✰✺✫✾✭✫✰1
2
3
4
5
6
7
8
9
10
-8.5
-8
-7.5
-7
-6.5
-6
-5.5
-5
-4.5
-4
NBV List Size
Relative Sampling Density: den_rel = log_2 ( den_RM / den_FM )
NBV LIST SIZE vs. RELATIVE SAMPLING DENSITY
Target: Cavity
VP_Algorithm = VARIABLE
Spec = ( 50,2 )
Env = ( LS-M, CMM )
FM = 4225 samples
D/W = 0.1
D/W = 0.2
D/W = 0.3
D/W = 0.5
D/W = 0.7
D/W = 1.0
✲ ✘ ✺❆✬✫ ❻❼ ❂❸❇ ✠✘ ✴✦ ✣ ✘✬ ✫ ✵ ✴ ✢ ✜✫ ✙ ✚✦✘✵ ✫✣ ✚ ✛✷ ✙✘ ✰✺ ✶ ✫✰ ✱ ✴✘✦ ✼ ✘ ✛ ✚ ✺ ✘ ✰✺✾ ✘✦ ✭ ✚ ⑥ ✘ ✱ ✴✦✚✦✘ ✤ ✴ ✫✰ ✴ ✥✬✢ ③ ✭✫ ✘ ✛ ✚ ✺ ✘ ✰✺✺✫✥✛✫ ✦ ✬✼ ✘ ✴ ✮✫ ✦ ✫✬✛ ✘ ✰✫ ✮⑥✼ ✦ ✾✥ ⑩ ✫✼✷ ✚ ✬ ✚ ✛✫ ✦ ✫✬ ✴❼ ✦ ✭✫✥✷ ✦✘ ✤ ✚✙ ⑥ ✚✴ ✫ ✱ ✙✘ ✰✫ ✚ ✰✮ ✦ ✭✫ ✴ ✤ ✚ ✰✰ ✘ ✰✺✬ ✚ ✰✺✫✢ ③ ✭✫ ➀ ✬ ✴✦ ✘ ✴ ➀ ⑧✫ ✮ ✾✭ ✘✙ ✫ ✦ ✭✫ ✴ ✫ ✤✥✰✮ ✘ ✴✵✚ ✬ ✘ ✚ ⑥ ✙ ✫✢ ➒ ✦ ✘ ✴ ✮✫ ✴✘ ✬ ✚ ⑥ ✙ ✫ ✦ ✥✛ ✘ ✰ ✘ ✛ ✘✬ ✫ ✦ ✭✫ ✙ ✚✦✦ ✫✬ ✚✴ ✺✫✥✛✫ ✦ ✬ ✘ ✤✰✥ ✘ ✴ ✫ ✘ ✰✤✬✫ ✚✴ ✫ ✴ ④❆ ✚ ✮✬ ✚✦✘ ✤ ✚✙✙ ✼✾ ✘✦ ✭ ✬ ✚ ✰✺✫✢ ✿ ✥✰ ✴ ✫ ④❆✫✰ ✦✙ ✼ ✩ ✴ ✤ ✚ ✰ ✴ ✚ ✬✫ ✰✥✬✛ ✚✙✙ ✼ ✦✚⑩ ✫✰ ✤ ✙ ✥ ✴ ✫ ✦ ✥ ✦ ✭✫ ✛ ✘ ✰ ✘ ✛❆✛✬ ✚ ✰✺✫✢ ③ ✭✫ ✴ ✫✰ ✴ ✥✬✛✥✮✫ ✙ ✫ ✮ ✘ ✰ ✦ ✭✫ ✴ ✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✭ ✚✴✚ ✰ ✥✷ ✦✘ ✤ ✚✙ ⑥ ✚✴ ✫ ✙✘ ✰✫✥ ✸ ❁ ❾❉ ✗✗ ✚ ✰✮ ✚ ✛ ✘ ✰ ✘ ✛❆✛ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✬ ✚ ✰✺✫✥ ✸ ❁ ✧ ❿ ✗✗ ✱ ✬✫✷✬✫ ✴ ✫✰ ✦✚✦✘✵ ✫ ✺✫✥✛✫ ✦ ✬✼ ✸ ✥✬ ✚ ✛ ✘ ✮ ✱ ✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫✬ ✚ ✰✺✫✤ ✚ ✛✫✬ ✚ ✢➒✰ ✦ ✭ ✘ ✴ ✴ ✫ ✤ ✦✘ ✥✰✾✫✫⑧ ✚ ✛ ✘ ✰✫ ✦ ✭✫ ✘ ✛✷ ✚ ✤ ✦ ✥ ✸✦✚ ✬✺✫ ✦ ✴ ✭ ✚ ✷✫ ✚ ✰✮✬✫ ✙ ✱ ✚✦✘✵ ✫ ✴✚ ✛✷ ✙✘ ✰✺✮✫✰ ✴✘✦ ✼ ✥✰ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫✢ ✹ ⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✾✫✬✫ ✤✥✰✮❆✤ ✦ ✫ ✮ ✾ ✘✦ ✭ ✚✵✚ ✬ ✘ ✫ ✦ ✼ ✥ ✸ ✤ ✚✵ ✱ ✘✦ ✼ ✴ ✭ ✚ ✷✫ ✴ ✚ ✰✮ ✬✥❆✺✭ ✛✥✮✫ ✙ ✚ ✷✷✬✥⑧ ✘ ✛ ✚✦✘ ✥✰ ✴ ✢ ✲ ✘ ✺❆✬✫ ❃ ✷ ✙ ✥ ✦✴ ✵ ✫✬ ✘➀ ✫ ✮ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✚✴ ✚ ✸ ❆✰✤ ✦✘ ✥✰ ✥ ✸ ✬✥❆✺✭ ✛✥✮✫ ✙ ✦ ✥ ➀ ✰✫ ✛✥✮✫ ✙ ✬✫ ✙ ✚✦✘✵ ✫ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦ ✼✡ ✡ ☛☞✌ ✸ ✥✬ ✚ ✤ ✚✵✘✦ ✼ ✦✚ ✬✺✫ ✦ ✥ ✵ ✫✬ ✚ ✬ ✚ ✰✺✫✥ ✸ ✺✫✥✛✫ ✦ ✬✼✫⑧✷✬✫ ✴✴ ✫ ✮ ✘ ✰ ✦ ✫✬✛ ✴ ✥ ✸ ✮✫✷ ✦ ✭ ✱ ✦ ✥ ✱ ✾ ✘ ✮ ✦ ✭ ✬ ✚ ✦ ✘ ✥ ✍✎ ✏ ✢ ➒✰ ✺✫✰✫✬ ✚✙ ✩ ✾✫ ✾✥❆ ✙ ✮ ✚ ✰ ✦ ✘ ✤ ✘ ✷ ✚ ✦ ✫ ✫✰✤✥❆✰ ✦ ✫✬ ✘ ✰✺ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✚ ✰✮ ✵✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺✮ ✘⑨ ✤❆ ✙✦ ✼ ✸ ✥✬✍✎ ✏ ✑❉✒❄✸ ✥✬ ✚✴ ✫✰ ✴ ✥✬✾ ✘✦ ✭ ✚ ✬✫ ✙ ✚✦✘✵ ✫ ✙ ✼ ✙ ✥✰✺ ✥✷ ✦✘ ✤ ✚✙ ⑥ ✚✴ ✫ ✙✘ ✰✫ ✴ ❆✤✭ ✚✴ ✦ ✭✫ ✥✰✫ ✛✥✮ ✱ ✫ ✙ ✫ ✮ ✘ ✰ ✦ ✭✫ ✴ ✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✢ ❈✴ ✫⑧✷✫ ✤ ✦ ✫ ✮ ✩ ✾✫ ✥⑥ ✴ ✫✬ ✵ ✫ ✦ ✭ ✚✦ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✘ ✛✷✬✥ ✵ ✫ ✴ ✾ ✘✦ ✭ ✘ ✰✤✬✫ ✚✴✘ ✰✺ ✡ ☛☞✌ ✚✴✚ ✤✥✰ ✴ ✫ ④❆✫✰✤✫ ✥ ✸ ✚ ⑥✫ ✦✦ ✫✬ ✤ ✚ ✰✮ ✘ ✮ ✚✦ ✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✴ ✫ ✦ ✚ ✰✮ ✭ ✘ ✺✭✫✬ ➀ ✮✫ ✙✘✦ ✼✬✥❆✺✭✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫✬✫✷✬✫ ✴ ✫✰ ✦✚✦✘ ✥✰✢ ➒✰ ✥❆✬ ✚✙ ✺✥✬ ✘✦ ✭✛ ✩ ✮ ✘ ✴ ✤✬✫ ✦✘✬ ✚✦✘ ✥✰ ✙ ✫ ✵ ✫ ✙ ✴ ✘ ✰ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✚ ✰✮ ✥⑥ ⑦ ✫ ✤ ✦ ✴ ❆✬ ✸✚ ✤✫ ✴ ✷ ✚ ✤✫ ✚ ✬✫ ✬✫ ✙ ✚✦ ✫ ✮✢ ✲ ❆✬ ✦ ✭✫✬ ✩ ✛✫ ✚✴ ❆✬ ✚ ✱ ⑥ ✘✙✘✦ ✼ ✘ ✴ ✬✫ ✮❆✤✫ ✮ ✾ ✘✦ ✭ ✘ ✰✤✬✫ ✚✴✘ ✰✺ ✺✫✥✛✫ ✦ ✬ ✘ ✤✮ ✘⑨ ✤❆ ✙✦ ✼ ✩ ✚✙✦ ✭✥❆✺✭✰✥ ✦ ✚✙ ✾ ✚ ✼ ✴✘ ✰ ✚ ✤✥✛✷ ✙ ✫ ✦ ✫ ✙ ✼ ✷✬✫ ✮ ✘ ✤ ✦✚ ⑥ ✙ ✫ ✸✚✴ ✭ ✱ ✘ ✥✰✢ ✪ ✥✥✮ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✬✫ ✴ ❆ ✙✦✴ ✚ ✬✫ ✚ ✤✭ ✘ ✫ ✵ ✫ ✮ ❆✷ ✦ ✥ ✍✎ ✏ ✓ ❉✒❻ ⑥❆ ✦ ✮✬✥✷✥ ✴ ✭ ✚ ✬✷ ✙ ✼ ✸ ✥✬ ✵ ✫✬✼✮✫✫✷✤ ✚✵✘✦✘ ✫ ✴ ✔✕ ✺ ✽✴ ✻ ✼ ✹✺ ❃ ✴ ❅✿ ✽✼ ✵❀ ❇✺✵❃ ✼✻ ✶ ✼ ❃ ❇✺ ✖ ✵✺❇ ✴ ❃ ✽ ✸❀ ✔ ✸ ❆ ✻❂ ✺ ❁ ✴ ✻ ✼ ✸ ✗ ✺ ✻ ✾✺✺✵ ✻❂ ✺❃ ✴ ✽✼ ✵❀❇✺✵❃ ✼✻ ❆ ✻❂ ✺❁✸❈❀ ❂ ✴ ✵❇ ✖ ✵✺❅✸❇✺ ✽ ❃●0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1
2
3
4
5
6
7
8
9
10
Measurability
NBV List Viewpoint
VERIFIED MEASURABILITY PROGRESSION BY NEXT-BEST-VIEW
Target: Cavity
VP_Algorithm = VARIABLE
Spec = ( 50,2 )
Env = ( LS-M, CMM )
den_rel = - 4.0
D/W = 0.1
D/W = 0.2
D/W = 0.3
D/W = 0.5
D/W = 0.7
D/W = 1.0
✲ ✘ ✺❆✬✫ ❾❼ ❇ ✫✬ ✘➀ ✫ ✮ ❶✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ❽✬✥✺✬✫ ✴✴✘ ✥✰ ✾ ✘✦ ✭ ❂❸❇ ✣✫ ✙ ✫ ✤ ✦✘ ✥✰ ✚ ✬✥❆✰✮✍✎ ✏ ✓ ❁ ✒❉ ✢ ③ ✭✫ ✴ ✫ ✤✥✰✮ ⑩ ✫✼✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫ ✘ ✰✮ ✘ ✤ ✚✦ ✥✬ ✘ ✴ ✦ ✭✫ ✴✘✬ ✫✥ ✸ ✦ ✭✫ ❂❸❇ ✙✘ ✴✦ ✢ ❈ ✰ ✚ ✷✷✬✥⑧ ✘ ✛ ✚✦ ✫ ✘ ✰✮ ✘ ✤ ✚✦ ✥✬✥ ✸ ✦ ✭✫ ✰❆✛ ✱ ⑥✫✬ ✥ ✸ ✵✘ ✫✾ ✴ ✬✫ ④❆ ✘ ✬✫ ✮ ✸ ✥✬ ✚ ✷ ✚✦ ✤✭ ❹ ❺ ✘ ✴ ✷✬✥ ✵✘ ✮✫ ✮ ⑥✼ ✁ ✂✄☎ ✾✭✫✬✫ ✦ ✭✫ ✸ ✥✥ ✦ ✷✬ ✘ ✰ ✦ ✬ ✚✦✘ ✥✂✄ ✟✆ ✝ ✎✆ ✞ ✩✦ ✭✫✷ ✚✦ ✤✭ ✸ ✥✥ ✦ ✷✬ ✘ ✰ ✦ ✆ ✝ ✘ ✴ ✦ ✭✫ ✷ ✚✦ ✤✭ ✚ ✬✫ ✚ ✚ ✰✮ ✴ ✫✰ ✴ ✥✬ ✸ ✥✥ ✦ ✷✬ ✘ ✰ ✦ ✆ ✞ ✘ ✴ ✦ ✭✫ ✸ ✬❆ ✴✦ ❆✛ ✤✬✥ ✴✴ ✱ ✴ ✫ ✤ ✦✘ ✥✰ ✚✙ ✚ ✬✫ ✚✚✦ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬✟ ✴ ✥✷ ✦✘ ✛ ✚✙ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✬ ✚ ✰✺✫✢ ✗✘✦ ✭ ✂✄ ✟ ❉✒❄❄✩ ✦ ✭✫ ✤ ✚✵✘✦ ✼ ✦✚ ✬✺✫ ✦ ❆ ✴ ✫ ✮ ✘ ✰ ✦ ✭✫ ✴ ✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✤✥❆ ✙ ✮ ⑥✫ ✛✫ ✚✴ ❆✬✫ ✮ ⑥✼ ✚✴✘ ✰✺ ✙ ✫ ✵✘ ✫✾ ✚✦✙ ✥✾✍✎ ✏ ✩ ✾✭ ✘ ✤✭ ✘ ✴ ✤✥✰ ➀ ✬✛✫ ✮⑥✼ ✦ ✭✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✚✙ ✮ ✚✦✚ ✢ ❈✴ ✦ ✭✫ ✤ ✚✵✘✦ ✼ ✮✫✷ ✚ ✬ ✦✴ ✸ ✬✥✛ ✷ ✙ ✚ ✰ ✚ ✬ ✘✦ ✼ ✩ ✲ ✘ ✺❆✬✫ ❻ ✮✫✛✥✰ ✴✦ ✬ ✚✦ ✫ ✴ ✦ ✭ ✚✦ ✦ ✾✥ ✵✘ ✫✾ ✴ ✚ ✬✫ ✴ ✥✥✰ ✰✫ ✤✫ ✴✴✚ ✬✼ ✦ ✥ ✤ ✚ ✷ ✦ ❆✬✫ ✦ ✭✫ ✺✫✥✛✫ ✦ ✬✼✢ ❈✴ ✸ ✫✾ ✚✴ ✦ ✭✬✫✫ ✵✘ ✫✾ ✴✚ ✬✫ ✴ ❆ ⑨ ✤ ✘ ✫✰ ✦✦ ✥✛✫ ✚✴ ❆✬✫ ✚✙✙ ⑥❆ ✦✦ ✭✫✛✥ ✴✦ ✫⑧ ✦ ✬✫✛✫ ✴ ✭ ✚ ✷✫ ✴ ✢ ➒✰ ✦ ✭✫ ✴ ✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✴✩ ✦ ✭✫ ❂❸❇ ✙✘ ✴✦ ✴✘✬ ✫✾ ✚✴ ✤ ✚ ✷✷✫ ✮ ✚ ✦✦ ✫✰ ✵✘ ✫✾ ✴ ✢ ✲ ✘ ✺❆✬✫ ❾ ✴ ✭✥✾ ✴ ✦ ✭✫ ✷✬✥✺✬✫ ✴✴ ✥ ✸ ✵ ✫✬ ✘➀ ✫ ✮ ✤❆✛❆ ✙ ✚ ✦ ✘✵ ✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘ ✦ ✼✾ ✘ ✦ ✭ ✴ ❆✤✤✫ ✴✴✘✵ ✫ ✵✘ ✫✾ ✴✸ ✬✥✛ ✦ ✭✫ ❂❸❇✙✘ ✴ ✦ ✸ ✥✬✥✰✫✬✥❆✺✭✛✥✮✫ ✙ ✴✘✬ ✫✢ ❇✘ ✫✾✷✥ ✘ ✰ ✦✴ ✺✫✰✫✬ ✚✦ ✫ ✮ ✸ ✬✥✛ ✦ ✭✫ ✬✥❆✺✭ ✛✥✮✫ ✙ ✚ ✬✫ ✴ ✫ ✙ ✫ ✤ ✦ ✫ ✮ ⑥✼ ✚ ✺✬✫✫ ✮✼ ✴ ✫ ✦ ✤✥ ✵ ✫✬ ✱ ✘ ✰✺ ✚✙ ✺✥✬ ✘✦ ✭✛✥✰ ✦ ✭✫⑥ ✚✴✘ ✴ ✥ ✸ ✮✫ ✤ ✙✘ ✰ ✘ ✰✺❆ ✦✘✙✘✦ ✼✢ ❈ ✤ ✦ ❆ ✚✙ ✴ ✤ ✚ ✰✰ ✘ ✰✺✬✫ ✴ ❆ ✙✦✴ ✛ ✚ ✼ ✵✚ ✬✼ ✴✙✘ ✺✭ ✦✙ ✼✢ ❇ ✫✬ ✘➀ ✫ ✮✛✫ ✚✴ ❆✬ ✚ ✱ ⑥ ✘✙✘✦ ✼✷✬✥✺✬✫ ✴✴✘ ✥✰ ✘ ✴ ✛✥✰✥ ✦ ✥✰ ✘ ✤ ✩ ❆ ✴ ❆ ✚✙✙ ✼⑥❆ ✦ ✰✥ ✦ ✚✙ ✾ ✚ ✼ ✴ ✘ ✰ ✮✫ ✤✬✫ ✚✴✘ ✰✺ ✘ ✰✤✬✫✛✫✰ ✦✴ ✮❆✫ ✦ ✥ ✛ ✘ ✰✥✬ ✫✬✬✥✬ ✴ ✘ ✰ ✦ ✭✫ ✷✬✫ ✮ ✘ ✤ ✦✘ ✥✰ ✷✬✥✤✫ ✴✴ ✢ ✲ ❆✬ ✦ ✭✫✬ ✩ ✚✙ ✛✥ ✴✦ ✚✙✙ ✸ ✫ ✚✴✘ ⑥ ✙ ✫✛✫ ✚ ✱ ✴ ❆✬✫✛✫✰ ✦ ✘ ✴✚ ✤✭ ✘ ✫ ✵ ✫ ✮ ✘ ✰ ✚✵ ✫✬✼ ✴ ✛ ✚✙✙ ✰❆✛⑥✫✬✥ ✸✵✘ ✫✾ ✴✩ ✦ ✼✷ ✘ ✤ ✚✙✙ ✼ ✥✰✫ ✦ ✥ ✸ ✥❆✬ ✸ ✥✬✛✥ ✴✦✴ ✭ ✚ ✷✫ ✴ ✢ ✲ ✥✬ ✦ ✭✫✮✫✫✷✫ ✴✦ ✤ ✚✵✘✦✘ ✫ ✴✩ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✺ ✚✘ ✰ ✴ ⑥✫✼✥✰✮ ✦ ✭ ✘ ✴ ✰❆✛⑥✫✬ ✚ ✬✫ ✛ ✚ ✬✺ ✘ ✰ ✚✙ ✢ ❈ ✰ ✹ ⑧ ✦ ✫✰✮✫ ✮ ✪✚ ❆ ✴✴✘ ✚ ✰➒✛ ✚ ✺✫ ❊✹ ✪ ➒❋ ✵✘ ✫✾✥ ✸ ✦ ✭✫✮ ✘ ✴ ✱ ✦ ✬ ✘ ⑥❆ ✦✘ ✥✰ ✥ ✸ ✴ ❆✬ ✸✚ ✤✫ ✰✥✬✛ ✚✙ ✴ ✸ ✥✬ ✦ ✭✫ ✵ ✫✬✼ ✮✫✫✷ ✛✫ ✴ ✭ ❊ ✍✎ ✏ ✟ ❁ ✒❉ ❋ ❆ ✴ ✫ ✮ ✘ ✰ ✦ ✭✫ ✫⑧✷✫✬ ✘ ✛✫✰ ✦ ✚✦ ✘ ✺❆✬✫ ❾ ✘ ✴-80
-60
-40
-20
0
20
40
60
80
-150
-100
-50
0
50
100
150
Latitude (Degrees)
Longitude (Degrees)
MESH EGI (MERCATOR PROJECTION)
Mesh vertex normals
✲ ✘ ✺❆✬✫ ❼ ❶✫ ✴ ✭ ✹ ⑧ ✦ ✫✰✮✫ ✮ ✪✚ ❆ ✴✴✘ ✚ ✰➒✛ ✚ ✺✫ ✴ ✭✥✾✰ ✚✦ ✲ ✘ ✺❆✬✫ ✘ ✰ ❶✫✬ ✤ ✚✦ ✥✬✷✬✥ ⑦ ✫ ✤ ✦✘ ✥✰ ✸ ✥✬✛ ✚✦✠ ✢ ➒✰ ✦ ✭✫ ✷ ✚ ✬ ✦✘ ✤❆ ✙ ✚ ✬ ✦ ✫ ✴✦ ✺✫✥✛✫ ✦ ✬✼✫⑧ ✚ ✛ ✘ ✰✫ ✮ ✭✫✬✫ ✩ ✾✫ ✰✥ ✦ ✫ ✦ ✭ ✚✦ ✦ ✭✫✛✫ ✴ ✭ ✹✪ ➒✫⑧✭ ✘ ⑥ ✘✦✴✚ ✰❆✰✫ ✵ ✫✰✥✬ ✘ ✫✰ ✦✚✦✘ ✥✰✮✫✰ ✱ ✴✘✦ ✼✢ ③ ✭✫ ✴ ❆✬ ✸✚ ✤✫ ✰✥✬✛ ✚✙ ✥✬ ✘ ✫✰ ✦✚✦✘ ✥✰ ✮ ✘ ✴✦ ✬ ✘ ⑥❆ ✦✘ ✥✰ ✸ ✥✬ ✦ ✭ ✘ ✴ ✴ ✭ ✚ ✷✫ ✸✚✙✙ ✴ ✘ ✰ ✦ ✥ ✦ ✭✬✫✫✮ ✘ ✴✦✘ ✰✤ ✦ ✮✫✰ ✴✘✦ ✼ ✬ ✥✰✫ ✴❼ ❊ ❁ ❋ ✚ ✭✫ ✚✵ ✼✤✥✰✤✫✰ ✦ ✬ ✚✦✘ ✥✰ ✘ ✰ ✦ ✭✫✤✫✰ ✦ ✫✬✤✥✬✬✫ ✴ ✷✥✰✮ ✘ ✰✺ ✦ ✥ ✰✫ ✚ ✬ ✙ ✼ ✡ ✚✦ ✚ ✰✮ ✙ ✥✾ ✤❆✬ ✵✚✦ ❆✬✫ ✚ ✬✫ ✚✴ ✚ ✬✥❆✰✮ ✦ ✭✫ ✤ ✚✵ ✱ ✘✦ ✼ ✬ ✘ ✛ ✚ ✰✮ ✚✦ ✘✦✴ ⑥✥ ✦✦ ✥✛ ✩ ❊❿ ❋ ✚ ✰✥ ✦ ✭✫✬ ✭ ✘ ✺✭ ✮✫✰ ✴✘✦ ✼ ✮✥❆✺✭✰❆ ✦ ✱ ✴ ✭ ✚ ✷✫ ✮ ✬ ✥✰✫ ✚ ✬✥❆✰✮ ✦ ✭✫ ✷✫✬ ✘ ✷✭✫✬✼ ✥ ✸ ✦ ✭✫ ✹✪ ➒ ✷ ✙ ✥ ✦ ✤✥✬✬✫ ✴ ✷✥✰✮ ✘ ✰✺ ✦ ✥ ✙ ✥✾✤❆✬ ✵✚✦ ❆✬✫ ✚ ✬✫ ✚✴ ✥✰ ✦ ✭✫ ✤ ✚✵✘✦ ✼✾ ✚✙✙ ✴✩✚ ✰✮ ❊ ⑤❋ ✚ ✰ ✘ ✰ ✦ ✫✬ ✵ ✫✰ ✘ ✰✺ ✙ ✥✾✮✫✰ ✴✘✦ ✼ ✬ ✥✰✫ ✤✥✬✬✫ ✴ ✷✥✰✮ ✘ ✰✺ ✦ ✥✭ ✘ ✺✭ ✤❆✬ ✵✚✦ ❆✬✫✬✫✺ ✘ ✥✰ ✴ ✰✫ ✚ ✬ ✦ ✭✫✤ ✚✵ ✱ ✘✦ ✼ ✙✘ ✷ ✚ ✰✮ ⑥✥ ✦✦ ✥✛✢ ✲ ✘ ✺❆✬✫ ❁ ❉ ✷✬✫ ✴ ✫✰ ✦✴✚ ✰ ✹ ✪ ➒ ✵✘ ✫✾✥ ✸ ✦ ✭✫ ✚ ⑧ ✘ ✴ ✤✥✛✷✥ ✱ ✰✫✰ ✦ ✥ ✸ ✦ ✭✫ ❂❸❇✵✘ ✫✾✷✥ ✘ ✰ ✦ ✙✘ ✴✦ ✺✫✰✫✬ ✚✦ ✫ ✮ ✸ ✥✬ ✦ ✭ ✘ ✴✦✚ ✬ ✱ ✺✫ ✦ ✢ ❈✴ ✫⑧✷✫ ✤ ✦ ✫ ✮ ✩ ❂❸❇✙✘ ✴ ✦ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✴✚ ✬✫ ✴✘ ✦ ❆ ✚ ✦ ✫ ✮✥✰ ✦ ✭✫✥✷✷✥ ✴✘ ✦ ✫ ✴✘ ✮✫✥ ✸ ✦ ✭✫ ✹ ✪ ➒ ✴ ✷✭✫✬✫ ✦ ✥ ✦ ✭✫ ✦ ✚ ✬✺✫ ✦ ✴ ❆✬ ✱ ✸✚ ✤✫✢ ❸ ✥ ✦ ✭ ✦ ✭✫ ❂❸❇✙✘ ✴ ✦ ✚ ✰✮ ✘ ✦ ✴ ✰✫✺ ✚ ✦ ✘✵ ✫✛ ✘ ✬✬✥✬ ✘ ✛ ✚ ✺✫ ✚ ✬✫✮ ✘ ✴ ✷ ✙ ✚ ✼✫ ✮ ✸ ✥✬✤✥✬✬✫ ✙ ✚✦✘ ✥✰✾ ✘✦ ✭ ✦ ✭✫✛✫ ✴ ✭✢ ③ ✭✫ ❂❸❇ ✴ ✫ ✙ ✫ ✤ ✦✘ ✥✰ ✴ ✫ ④❆✫✰✤✫ ✘✙✙ ❆ ✴✦ ✬ ✚✦ ✫ ✴ ✭✥✾ ✦ ✭✫ ✚✙ ✺✥✬ ✘✦ ✭✛✛ ✚ ⑧ ✱ ✘ ✛ ✘✬ ✫ ✴ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ⑥✼ ➀ ✬ ✴✦✦✚⑩✘ ✰✺ ✴ ✤ ✚ ✰ ✴✸ ✬✥✛ ✦ ✭✫✷✫ ✱ ✬ ✘ ✷✭✫✬✼ ✘ ✰✥✬ ✮✫✬ ✦ ✥✤ ✚ ✷ ✦ ❆✬✫ ✙ ✚ ✬✺✫ ✴ ❆✬ ✸✚ ✤✫ ✚ ✬✫ ✚✴ ✰✫ ✚ ✬ ✦ ✭✫ ✬ ✘ ✛✢ ❶✫ ✚✴ ❆✬✫✛✫✰ ✦ ✬✫ ✦ ❆✬✰ ✴ ✮ ✘ ✛ ✘ ✰ ✘ ✴ ✭ ✾ ✘✦ ✭ ✴ ❆⑥ ✴ ✫ ④❆✫✰ ✦ ✵✘ ✫✾✷✥ ✘ ✰ ✦✴ ✤ ✙ ❆ ✴✦ ✫✬ ✘ ✰✺ ✚ ⑥✥❆ ✦ ✦ ✭✫ ✤ ✚✵✘✦ ✼ ✮✫✷ ✦ ✭ ✚ ⑧ ✘ ✴ ✚✴ ✦ ✭✫ ✚✙ ✺✥✬ ✘✦ ✭✛ ✚✦✦ ✫✛✷ ✦✴ ✴ ✛ ✚✙✙ ✺ ✚✘ ✰ ✴ ✘ ✰ ✦ ✭✫ ✸ ❆✬ ✦ ✭✫✬✫ ✴✦ ✮✫✷ ✦ ✭ ✴ ✥ ✸ ✦ ✭✫ ✤ ✚✵✘✦ ✼✢ ➒✰ ✴ ❆✛✛ ✚ ✬✼ ✩ ✦ ✭✫ ✬✫ ✙ ✚✦✘✵ ✫ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦ ✼ ✙ ✫ ✵ ✫ ✙ ✡ ☛☞✌ ✮✫ ✦ ✫✬✛ ✘ ✰✫ ✴ ✮ ✘ ✴ ✤✬✫ ✦✘✬ ✚✦✘ ✥✰ ✘ ✰ ✦ ✫✬ ✵✚✙ ✴✘ ✰ ⑥✥ ✦ ✭ ✬✥❆✺✭ ☛☞ ✵✌✍ ✎ ✿❁✸ ✏ ✺✷ ✻ ✼ ✸✵❅ ✴ ✿❃ ✻❂ ✺✸❁ ✼ ✺✵ ✻ ✴ ✻ ✼ ✸✵✸ ❆✑✒ ✹✺✷ ✻ ✸❁❃✓❃❈✷ ❂ ✴ ❃❃❈❁ ❆✴ ✷✺✵✸❁❅ ✴✽ ❃ ✴ ✵❇ ✻❂ ✺❃✺✵❃✸❁ ✗ ✸❁✺❃ ✼ ❀ ❂✻ ✷✸❅✿✸✵✺✵ ✻ ✸ ❆ ✹ ✼ ✺✾❊ ✿✸ ✼ ✵ ✻ ✸❁ ✼✺✵✻ ✴ ✻ ✼ ✸✵✔ ✻ ✸ ✻❂ ✺ ✷✸❁❁✺❃✿✸✵❇✼ ✵❀✿✸ ✼ ✵ ✻ ✸✵ ✴ ❈✵ ✼✻ ❃✿ ❂ ✺❁✺● ✕❂✼✽ ✺ ✴✳ ✺❁✷ ✴ ✻ ✸❁✿❁✸ ✏ ✺✷ ✻ ✼ ✸✵❃❈ ❋ ✺❁❃ ❆ ❁✸❅✾✺ ✽✽❉ ✵✸✾✵❇ ✼ ❃ ✻ ✸❁ ✻ ✼ ✸✵❃ ✼ ✵ ✻❂ ✺✿✸ ✽ ✴ ❁❁✺❀ ✼ ✸✵❃❄ ✻❂ ✺✿❁✸ ✏ ✺✷ ✻ ✼ ✸✵✿❁✸✹ ✼ ❇✺❃ ✴ ❃ ✼ ❅✿ ✽ ✺ ✴ ✽✽ ❊ ✴ ❃✿✺✷ ✻ ✿❁✺❃✺✵ ✻ ✴ ✻ ✼ ✸✵ ✴ ✵❇ ✻❂ ✺✿✸ ✽✴ ❁ ✴ ✵❇ ✍❁✺✺✵ ✼ ✷ ❂ ✴ ✖✺❃✷ ✴ ✵ ✗ ✺❃✺ ✽ ✺✷ ✻ ✺❇ ✻ ✸❅ ✼ ✵ ✼ ❅ ✼✗ ✺❇ ✼ ❃ ✻ ✸❁ ✻ ✼ ✸✵●
-80
-60
-40
-20
0
20
40
60
80
-150
-100
-50
0
50
100
150
Latitude (Degrees)
Longitude (Degrees)
NBV LIST EGI (MERCATOR PROJECTION)
1
2
3
4
5
6
7
8
9
10
NBVs
NBVs (neg)
✲ ✘ ✺❆✬✫ ❁ ❉ ❼ ❂❸❇✠✘ ✴✦ ✹ ⑧ ✦ ✫✰✮✫ ✮ ✪✚ ❆ ✴✴✘ ✚ ✰➒✛ ✚ ✺✫ ✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫ ✴ ✷ ✚ ✤✫ ✚ ✰✮ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✴ ✷ ✚ ✤✫✢ ➒✰✤✬✫ ✚✴ ✱ ✘ ✰✺ ✴ ✭ ✚ ✷✫✤✥✛✷ ✙ ✫⑧ ✘✦ ✼✮✫✛ ✚ ✰✮ ✴✚ ✭ ✘ ✺✭✫✬✬✫ ✙ ✚✦✘✵ ✫ ✴✚ ✛ ✱ ✷ ✙✘ ✰✺✮✫✰ ✴✘✦ ✼ ✚ ✰✮ ✵✘ ✤✫ ✱ ✵ ✫✬ ✴✚✩ ⑥❆ ✦✦ ✭✫✬✫ ✙ ✚✦✘ ✥✰ ✴ ✭ ✘ ✷ ✘ ✰⑤ ✶ ✴ ✷ ✚ ✤✫ ✘ ✴ ✰✥ ✦ ✚✴ ✴✘ ✛✷ ✙ ✫ ✚✴ ✦ ✭✫ ✤✥✰ ✵ ✫✰ ✦✘ ✥✰ ✚✙ ✴✚ ✛✷ ✙✘ ✰✺ ✦ ✭✫✥✬✫✛ ✸ ✥✬ ❁✶ ✤✥✛✛❆✰ ✘ ✤ ✚✦✘ ✥✰ ✴✘ ✺✰ ✚✙ ✴ ✢ ✽ ❆✬ ✫⑧✷✫✬ ✘ ✱ ✛✫✰ ✦✴✴ ✭✥✾ ✦ ✭ ✚✦✚✴✚ ✛✷ ✙✘ ✰✺ ✙ ✫ ✵ ✫ ✙ ✥ ✸ ✡ ☛☞✌ ✓✎❄ ✷✬✥ ✵✘ ✮✫ ✴ ✺✥✥✮✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✷✬✫ ✮ ✘ ✤ ✦✘ ✥✰ ✸ ✥✬✤✥✰✤ ✚✵ ✫ ✴ ✭ ✚ ✷✫ ✴✩ ✦ ✭✫ ✛✥ ✴✦ ✮ ✘⑨ ✤❆ ✙✦✴ ✤ ✚ ✰✰ ✘ ✰✺✤✭ ✚✙✙ ✫✰✺✫ ✩ ✸ ✥✬ ✴ ✤ ✚ ✰✰ ✘ ✰✺✺✫✥✛✫ ✱ ✦ ✬ ✘ ✫ ✴ ✬✫✷✬✫ ✴ ✫✰ ✦✚✦✘✵ ✫ ✥ ✸ ✤✥✰ ✦ ✫✛✷✥✬ ✚ ✬✼ ✬ ✚ ✰✺✫ ✤ ✚ ✛✫✬ ✚✴ ✢ ✠ ✥✾✫✬ ✡ ☛☞✌ ✘ ✴✴ ❆ ✘✦✚ ⑥ ✙ ✫ ✸ ✥✬ ✴✘ ✛✷ ✙ ✫✬ ✴ ✭ ✚ ✷✫ ✴ ✢ ✲ ❆✬ ✦ ✭✫✬ ✩ ✸ ✥✬ ✦ ✼✷ ✘ ✤ ✚✙ ✴ ❆✬ ✸✚ ✤✫✷ ✚✦ ✤✭✫ ✴✚ ✰✮ ✘ ✛ ✚ ✺ ✘ ✰✺✺✫✥✛✫ ✦ ✬ ✘ ✫ ✴✩ ✛✥ ✴✦ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✤✥ ✵ ✫✬ ✚ ✺✫ ✚ ✰✮ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ✘ ✴✚ ✤✭ ✘ ✫ ✵ ✫ ✮✾ ✘ ✦ ✭ ✚✵ ✫✬✼ ✴ ✛ ✚✙✙ ✰❆✛⑥✫✬✥ ✸✴ ✤ ✚ ✰ ✴❊✵✘ ✫✾ ✴ ❋✢ ☎✈ ① ☞ ✁ ✂ ✈✇ ✞ ✠ ☎❑❑✈❑ ■ ❸ ✼✮✫ ➀ ✰ ✘✦✘ ✥✰ ✩✦ ✭✫✬✥❆✺✭ ✛✥✮✫ ✙✘ ✰✺✷✬✥✤✫ ✴✴✘ ✴✘ ✰ ✦ ✫✰✮✫ ✮ ✦ ✥✫⑧✫ ✤❆ ✦ ✫④❆ ✘ ✤ ⑩✙ ✼✾ ✘✦ ✭ ✙✘ ✛ ✘✦ ✫ ✮ ✚ ✷✬ ✘ ✥✬ ✘⑩ ✰✥✾ ✙ ✫ ✮✺✫ ✚ ✰✮ ✾ ✘✦ ✭✥❆ ✦ ✫ ✙ ✚ ⑥✥✬ ✚✦ ✫✫⑧✷✫✬ ✘ ✛✫✰ ✦✚✙ ✴ ✫ ✦ ❆✷✢ ③ ✭✫✬✫ ✸ ✥✬✫ ✩ ✾✫ ✤ ✚ ✰ ✫⑧✷✫ ✤ ✦ ✬✥❆✺✭ ✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ✫✬✬✥✬ ✦ ✥ ⑥✫ ✛❆✤✭ ✭ ✘ ✺✭✫✬ ✦ ✭ ✚ ✰ ✴ ✷✫ ✤ ✘➀ ✫ ✮ ✸ ✥✬ ✦ ✭✫ ✦✚ ✬✺✫ ✦ ➀ ✰✫ ✛✥✮✫ ✙ ✢ ✣❆✤✭ ✫✬✬✥✬ ✴✚ ✬✫ ✘ ✰ ✚ ✮✮ ✘✦✘ ✥✰ ✦ ✥ ✦ ✭✫ ✘ ✰ ✦ ✫✰ ✦✘ ✥✰ ✚✙ ✴ ✷ ✚ ✬ ✴ ✫ ✴✚ ✛✷ ✙✘ ✰✺ ✚✦ ✦ ✭ ✘ ✴✴✦✚ ✺✫✥ ✸ ✦ ✭✫✬✫ ✤✥✰ ✴✦ ✬❆✤ ✦✘ ✥✰✷✬✥ ✱ ✤✫ ✴✴ ✢ ③ ✭ ✘ ✴✴ ✫ ✤ ✦✘ ✥✰ ✚ ✮✮✬✫ ✴✴ ✫ ✴ ✦ ✭✫ ✘ ✛✷ ✚ ✤ ✦ ✥ ✸ ✬✥❆✺✭✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫✫✬✬✥✬ ✴ ✥✰ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫✢ ❇✘ ✫✾ ✷ ✙ ✚ ✰✰ ✘ ✰✺ ✚✙ ✺✥✬ ✘✦ ✭✛ ✴ ✸✚✵ ✥❆✬ ✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ✺✫ ✱ ✥✛✫ ✦ ✬✼ ✚✙ ✥✰✺ ✦ ✭✫ ✙ ✥✤ ✚✙✴ ❆✬ ✸✚ ✤✫✰✥✬✛ ✚✙ ✢ ③ ✭✫✺✫✥✛✫ ✦ ✬ ✘ ✤ ✰✥ ✘ ✴ ✫✤✥✛✷✥✰✫✰ ✦ ✚✙ ✥✰✺ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬⑥✥✬✫ ✴✘ ✺✭ ✦ ✺✬✫ ✚✦✙ ✼ ✫⑧ ✱ ✤✫✫ ✮ ✴ ✦ ✬ ✚ ✰ ✴✵ ✫✬ ✴ ✫✛✫ ✚✴ ❆✬✫✛✫✰ ✦ ✫✬✬✥✬✢ ✄✫✰✤✫✾✫ ✴ ✫ ✙ ✫ ✤ ✦ ✚ ✴✘ ✛✷ ✙ ✫ ✛✥✮✫ ✙ ✸ ✥✬ ✬✥❆✺✭ ✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫ ✫✬✬✥✬ ⑥ ✚✴ ✫ ✮ ✥✰ ✚ ✰✥ ✘ ✴ ✫✤✥✛✷✥✰✫✰ ✦ ✚✙ ✥✰✺ ✦ ✭✫ ✙ ✥✤ ✚✙ ✴ ❆✬ ✸✚ ✤✫✰✥✬✛ ✚✙ ✢ ③ ✭✫✛✥✮✫ ✙ ✫ ✮✰✥ ✘ ✴ ✫ ✘ ✴✚✬ ✫✬✥✛✫ ✚ ✰✷✬✥✤✫ ✴✴ ✾ ✘✦ ✭ ✚✴✦✚ ✰ ✱ ✮ ✚ ✬ ✮ ✮✫ ✵✘ ✚✦✘ ✥✰ ✄☛☎ ✫⑧✷✬✫ ✴✴ ✫ ✮ ✚✴✚ ✷✫✬ ✤✫✰ ✦✚ ✺✫✥ ✸ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬✟ ✴ ✛ ✘ ✰ ✘ ✛❆✛ ✬ ✚ ✰✺✫✢ ➒✰ ✦ ✭✫ ✷✬✫ ✴ ✫✰ ✦ ✾✥✬ ⑩ ✾✫ ✮✥0.94
0.95
0.96
0.97
0.98
0.99
1
-6
-5.5
-5
-4.5
-4
Measurability
Relative Sampling Density: den_rel = log_2 ( den_RM / den_FM )
MEASURABILITY IMPACT OF ROUGH MODEL ERROR
Target: Cavity
VP_Algorithm = VARIABLE
Spec = ( 50,2 )
Env = ( LS-M, CMM )
FM = 4225 samples
D/W = 0.5
sigma_noise = 2.0%
sigma_noise = 0.5%
sigma_noise = 0.0%
✲ ✘ ✺❆✬✫ ❁❁❼ ❶✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ➒✛✷ ✚ ✤ ✦ ✥ ✸ ✜✥❆✺✭ ❶✥✮✫ ✙ ✹ ✬ ✱ ✬✥✬1
1.5
2
2.5
3
3.5
4
4.5
-6
-5.5
-5
-4.5
-4
NBV List Size
Relative Sampling Density: den_rel = log_2 ( den_RM / den_FM )
NBV LIST SIZE IMPACT OF ROUGH MODEL ERROR
Target: Cavity
VP_Algorithm = VARIABLE
Spec = ( 50,2 )
Env = ( LS-M, CMM )
FM = 4225 samples
D/W = 0.5
sigma_noise = 2.0%
sigma_noise = 0.5%
sigma_noise = 0.0%
✲ ✘ ✺❆✬✫ ❁❿❼ ❂❸❇ ✠✘ ✴✦ ✣ ✘✬ ✫ ➒✛✷ ✚ ✤ ✦ ✥ ✸ ✜✥❆✺✭ ❶✥✮✫ ✙ ✹ ✬✬✥✬ ✰✥ ✦ ✚ ✮✮✬✫ ✴✴ ✥❆ ✦✙✘ ✫✬ ✴✩ ✫ ✮✺✫✫ ✫ ✤ ✦✴✩ ✤✥✬✰✫✬✬✫✡✫ ✤ ✦✘ ✥✰ ✴ ✥✬ ✮✼✰ ✚ ✛ ✘ ✤✬ ✚ ✰✺✫ ✙✘ ✛ ✘✦✚✦✘ ✥✰ ✴ ✢ ③ ✾✥ ✴ ✫ ✦✴ ✥ ✸ ✫⑧✷✫✬ ✘ ✛✫✰ ✦✴ ✾✫✬✫✤✥✰✮❆✤ ✦ ✫ ✮✥✰ ✚ ✤ ✚✵✘✦ ✼ ✦ ✫ ✴✦✦✚ ✬✺✫ ✦ ✥ ✸ ✛✥✮✫✬ ✚✦ ✫ ✙ ✼ ✮ ✘⑨ ✤❆ ✙✦✴ ✭ ✚ ✷✫ ❊ ✍✎ ✏ ✟ ❉✒❄ ❋ ✸ ✥✬ ✚ ✬ ✚ ✰✺✫✥ ✸ ✬✫ ✙ ✚✦✘✵ ✫ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦✘ ✫ ✴ ❆ ✴✘ ✰✺ ✚ ✬ ✚ ✰ ✱ ✮✥✛ ✰✥ ✘ ✴ ✫ ✺✫✰✫✬ ✚✦ ✥✬ ✴ ✫ ✦ ✚✦ ✄☛☎ ✟ ❉✒❉❿✆ ☎✌✝ ✚ ✰✮ ✄☛☎ ✟ ❉✒❉❉❄✆ ☎✌✝ ✢ ③ ✭✫ ➀ ✬ ✴✦ ✰✥ ✘ ✴ ✫ ✙ ✫ ✵ ✫ ✙✘ ✴ ④❆ ✘✦ ✫ ✭ ✘ ✺✭ ❊ ✘ ✢✫✢ ✓ ❿✒❾ ✗✗ ✸ ✥✬ ✦ ✭✫ ✴ ✫✰ ✴ ✥✬ ❆ ✴ ✫ ✮ ✘ ✰ ✦ ✭✫ ✴ ✫ ✫⑧✷✫✬ ✘ ✱ ✛✫✰ ✦✴ ❋ ✴ ❆✤✭ ✦ ✭ ✚✦✘✦ ✺ ✘✵ ✫ ✴ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙✚ ✰✥ ✦✘ ✤✫ ✚ ⑥ ✙ ✼ ✤✬❆✛⑥ ✙ ✫ ✮ ✴ ✭ ✚ ✷✫ ❊ ✲ ✘ ✺❆✬✫ ❄ ❋✢ ✲ ✘ ✺❆✬✫ ✴ ❁❁ ✚ ✰✮ ❁❿✴ ✭✥✾ ✦ ✭✫ ✘ ✛✷ ✚ ✤ ✦ ✥✰ ✵ ✫✬ ✘➀ ✫ ✮✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✚ ✰✮ ✦ ✭✫ ✴✘✬ ✫✥ ✸ ✦ ✭✫ ❂❸❇✙✘ ✴✦ ✥ ✸✚ ✰✥ ✘ ✴ ✼✬✥❆✺✭✛✥✮✫ ✙✘ ✰✤✥✛✷ ✚ ✬ ✘ ✴ ✥✰ ✦ ✥ ✦ ✭✫ ✰✥ ✘ ✴ ✫ ✙ ✫ ✴✴ ✤ ✚✴ ✫✞✢ ③ ✭✫✰✥ ✘ ✴ ✼✮ ✚✦✚✘ ✴ ✷✬✫ ✴ ✫✰ ✦ ✫ ✮ ✚✴✚✵ ✫✬ ✚ ✺✫ ✟✠ ✸ ✻ ✺ ✻❂✴ ✻ ✻❂ ✺❇ ✴ ✻ ✴ ❆ ✸❁✡☛☞✌✍✎✍✍✏ ✑☞✒✓ ✼ ❃ ✴ ❁ ✻ ✼✖ ✷ ✼ ✴✽✽ ✶❃✺✿❊ ✴✴ ✻ ✺❇❃ ✽✼ ❀ ❂✻✽ ✻ ✻❂ ✺ ✼ ❀ ❂✻ ❆ ❁✺ ✴ ❇ ✴ ✗✼✽✼✻ ✶●❆✫ ✷❆ ✥✬✛✰❆ ✥✰✫ ✺✛ ✰✮ ✬ ✮✮✫ ✥✰✢ ✿ ✥✰ ✦ ✬ ✚ ✬✼ ✦ ✥ ✾✭ ✚✦ ✛ ✘ ✺✭ ✦ ✘ ✰ ✘✦✘ ✚✙✙ ✼ ⑥✫ ✫⑧✷✫ ✤ ✦ ✫ ✮ ✩ ✾✫ ➀ ✰✮ ✦ ✭ ✚✦ ✬✥❆✺✭✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫✫✬✬✥✬ ✴ ✭ ✚✵ ✫ ✚ ✬✫ ✙ ✚✦✘✵ ✫ ✙ ✼ ✛ ✘ ✰✥✬ ✘ ✛✷ ✚ ✤ ✦ ✥✰✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✢➒✰ ✴ ✥✛✫✤ ✚✴ ✫ ✴✩ ✦ ✭✫ ✘ ✰ ✱ ✷❆ ✦ ✫✬✬✥✬ ✴✚ ✤ ✦ ❆ ✚✙✙ ✼✬✫ ✴ ❆ ✙ ✦ ✘ ✰ ✚ ✰ ✘ ✛✷✬✥ ✵ ✫ ✮✥❆ ✦ ✷❆ ✦ ✢ ③ ✭✫ ✬✫ ✚✴ ✥✰ ✴✸ ✥✬ ✦ ✭ ✘ ✴ ✷✭✫✰✥✛✫✰ ✚ ✤ ✚ ✰ ⑥✫ ✸ ✥❆✰✮ ✘ ✰ ✦ ✭✫ ✘ ✛ ✱ ✷ ✚ ✤ ✦ ✥✰ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✺✫✰✫✬ ✚✦✘ ✥✰✢ ✜ ✚ ✰✮✥✛ ✴ ❆✬ ✸✚ ✤✫✫✬✬✥✬ ✴ ✘ ✰ ✦ ✬✥✮❆✤✫ ✚ ✮ ✘✦ ✭✫✬ ✘ ✰✺ ✁ ✫ ✫ ✤ ✦ ✥✰ ✴ ❆✬ ✸✚ ✤✫ ✰✥✬✛ ✚✙ ✫ ✴ ✱ ✦✘ ✛ ✚✦✘ ✥✰✢ ✶ ❆✬ ✘ ✰✺ ✦ ✭✫ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✺✫✰✫✬ ✚✦✘ ✥✰ ✷✬✥✤✫ ✴✴✩ ✦ ✭ ✘ ✴ ✘ ✰ ✦ ❆✬✰ ✬ ✚ ✰✮✥✛ ✘✬ ✫ ✴ ✦ ✭✫ ✮ ✘ ✴✦ ✬ ✘ ⑥❆ ✦✘ ✥✰ ✥ ✸ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✷✥ ✴✘✦✘ ✥✰ ✴✚✴ ✾✫ ✙✙ ✚✴ ✦ ✭✫ ✚ ⑧ ✘ ✴ ✤✥✛✷✥✰✫✰ ✦ ✥ ✸ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✥✬ ✘ ✫✰ ✦✚✦✘ ✥✰✢ ③ ✭✫ ✦ ✾ ✘ ✴✦ ✤✥✛✷✥✰✫✰ ✦ ✥ ✸ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✥✬ ✘ ✱ ✫✰ ✦✚✦✘ ✥✰ ❊ ✬✥ ✦✚✦✘ ✥✰ ✚ ⑥✥❆ ✦ ✦ ✭✫✤ ✚ ✛✫✬ ✚ ⑥✥✬✫ ✴✘ ✺✭ ✦ ❋ ✘ ✴ ✫ ✴ ✱ ✴ ✫✰ ✦✘ ✚✙✙ ✼ ❆✰✤✭ ✚ ✰✺✫ ✮ ✚✴ ✘✦ ✘ ✴ ✴ ✫ ✦ ✘ ✰ ✬✫ ✸ ✫✬✫✰✤✫ ✦ ✥ ✺ ✙ ✥⑥ ✚✙ ✴ ✭ ✚ ✷✫ ✤✭ ✚ ✬ ✚ ✤ ✦ ✫✬ ✘ ✴✦✘ ✤ ✴ ✢ ③ ✭✫ ✰✫ ✦ ✬✫ ✴ ❆ ✙✦ ✥ ✸ ✛✥✮✫ ✴✦ ✙ ✫ ✵ ✱ ✫ ✙ ✴ ✥ ✸ ✬✥❆✺✭✛✥✮✫ ✙ ✴ ❆✬ ✸✚ ✤✫✫✬✬✥✬ ✘ ✴ ✚ ✬ ✚ ✰✮✥✛ ✘✬ ✫ ✮ ✚ ✰✮ ✷✥ ✴✴✘ ⑥ ✙ ✼ ✛✥✬✫❆✰ ✘✸ ✥✬✛ ✴✚ ✛✷ ✙✘ ✰✺✥ ✸ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✴ ✷ ✚ ✤✫✢ ✗ ✫✤ ✚ ✰✤✥✰✤ ✙ ❆✮✫ ✦ ✭ ✚✦ ✬✫ ✚✴ ✥✰ ✚ ⑥ ✙ ✫✬✥❆✺✭✛✥✮✫ ✙ ✬ ✚ ✰ ✱ ✮✥✛ ✴ ❆✬ ✸✚ ✤✫✫✬✬✥✬ ✴ ✭ ✚✵ ✫ ✦ ✭✫ ✸ ✥ ✙✙ ✥✾ ✘ ✰✺✫ ✫ ✤ ✦✴❼ ❶✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✫ ✴✦✘ ✛ ✚✦ ✫❆✰✤✫✬ ✦✚✘ ✰ ✦ ✼ ✘ ✴✴✙✘ ✺✭ ✦✙ ✼ ✘ ✰ ✱ ✤✬✫ ✚✴ ✫ ✮ ⑥❆ ✦ ✚✵ ✫✬ ✚ ✺✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✘ ✴ ✙ ✚ ✬✺✫ ✙ ✼ ❆✰ ✱ ✤✭ ✚ ✰✺✫ ✮✢ ✽ ✰ ✚✵ ✫✬ ✚ ✺✫ ✩✦ ✭✫✬✫ ✘ ✴✚✴✙✘ ✺✭ ✦ ✘ ✰✤✬✫ ✚✴ ✫ ✘ ✰ ❂❸❇✙✘ ✴✦ ✴✘✬ ✫✢ ③ ✭ ✘ ✴ ✚ ✮✮ ✘✦✘ ✥✰ ✚✙ ✴ ✤ ✚ ✰✰ ✘ ✰✺ ✤✥ ✴✦ ✘ ✴ ✥ ✴ ✫ ✦ ⑥✼ ✘ ✰✤✬✫ ✚✴ ✫ ✮✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✬✥⑥❆ ✴✦ ✰✫ ✴✴ ✦ ✥✥ ✦ ✭✫✬✫✬✬✥✬ ✴ ✥❆✬ ✤✫ ✴✸ ✬✥✛ ✚ ✛✥✬✫ ✫⑧ ✦ ✫✰ ✴✘✵ ✫ ✤✥ ✵ ✫✬ ✘ ✰✺ ✥ ✸ ✵✘ ✫✾ ✱ ✷✥ ✘ ✰ ✦ ✴ ✷ ✚ ✤✫✢ ✁ ✝ ①✟✟▲❑ ✄ ▲✉✇ ✡✈✉▼ ✠① ■ ②✈✉ ■ ➒ ✦ ✘ ✴ ✘ ✰ ✴✦ ✬❆✤ ✦✘✵ ✫ ✦ ✥ ✫⑧ ✚ ✛ ✘ ✰✫ ✚ ✤ ✦ ❆ ✚✙ ✵ ✫✬ ✴ ❆ ✴ ✫ ✴✦✘ ✛ ✚✦ ✫ ✮ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫✢ ✲ ✘ ✺❆✬✫ ❁ ⑤ ✴ ✭✥✾ ✴ ✤✥✛ ✱ ✷✥ ✴✘✦ ✫ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✫ ✴✦✘ ✛ ✚✦ ✫ ✮ ✚✦ ✦ ✭✫ ✬✥❆✺✭ ✛✥✮✫ ✙ ✵✘ ✫✾✷✥ ✘ ✰ ✦ ✺✫✰✫✬ ✚✦✘ ✥✰ ✴✦✚ ✺✫ ✚✴ ✚ ✸ ❆✰✤ ✦✘ ✥✰ ✥ ✸ ✤ ✚✵✘✦ ✼ ✴ ✭ ✚ ✷✫ ✚ ✰✮ ✬✫ ✙ ✚✦✘✵ ✫ ✴✚ ✛✷ ✙✘ ✰✺ ✮✫✰ ✴✘✦ ✼✢ ❈ ✦ ✦ ✭✫ ✬✥❆✺✭ ✛✥✮✫ ✙✙ ✫ ✵ ✫ ✙✩ ✦ ✭✫✫ ✴✦✘ ✛ ✚✦✘ ✥✰✷✬✥✤✫ ✴✴✘ ✴ ④❆ ✘✦ ✫✥✷ ✦✘ ✛ ✘ ✴✦✘ ✤ ✩ ✷✬✫ ✮ ✘ ✤ ✦ ✘ ✰✺ ✰✫ ✚ ✬ ✷✫✬ ✸ ✫ ✤ ✦ ✚ ✤✭ ✘ ✫ ✵ ✫✛✫✰ ✦ ✥ ✸ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘ ✦ ✼ ✺✥ ✚✙ ✴✸ ✥✬ ✚✙✙ ⑥❆ ✦✦ ✭✫✛✥ ✴ ✦ ✫⑧ ✦ ✬✫✛✫✤ ✚✵✘ ✦ ✘ ✫ ✴ ✢ ✲ ✘ ✺❆✬✫ ❁ ✧ ✷✬✫ ✴ ✫✰ ✦ ✴ ✦ ✭✫ ✚ ✤ ✦ ❆ ✚✙ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘ ✦ ✼ ✚ ✤✭ ✘ ✫ ✵ ✫ ✮ ✺ ✘✵ ✫✰ ✦ ✭✫ ❂❸❇ ✙✘ ✴✦ ✺✫✰✫✬ ✚✦ ✫ ✮ ✸ ✬✥✛ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙ ✢ ❂ ✥ ✦ ✾ ✘✦ ✭ ✱ ✴✦✚ ✰✮ ✘ ✰✺ ✦ ✭✫ ✥✷ ✦✘ ✛ ✘ ✴✦✘ ✤ ✰ ✚✦ ❆✬✫ ✥ ✸ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼ ✫ ✴✦✘ ✱ ✛ ✚✦✘ ✥✰ ✚✦ ✦ ✭✫✬✥❆✺✭✛✥✮✫ ✙✙ ✫ ✵ ✫ ✙✩ ✾✫✰✥ ✦ ✫ ✦ ✭ ✚✦ ✦ ✭✫ ✚ ✤ ✱ ✦ ❆ ✚✙ ✷✫✬ ✸ ✥✬✛ ✚ ✰✤✫ ✚ ✤✭ ✘ ✫ ✵ ✫ ✮ ✘ ✴ ✵ ✫✬✼ ✺✥✥✮ ✩ ✷ ✚ ✬ ✦✘ ✤❆ ✙ ✚ ✬ ✙ ✼ ✸ ✥✬ ✡ ☛☞✌ ✂ ✎❄ ✢ ③ ✭✫✰✫ ✦ ✛✫ ✚✴ ❆✬ ✚ ⑥ ✘✙✘✦ ✼✫ ✴✦✘ ✛ ✚✦✘ ✥✰✫✬✬✥✬ ✘ ✴ ✷✬✫ ✴ ✫✰ ✦ ✫ ✮ ✘ ✰ ✲ ✘ ✺❆✬✫ ❁❄ ✢ ③ ✭✫ ✸ ✥✬✫✺✥ ✘ ✰✺ ✴ ❆✺✺✫ ✴✦✴ ✦ ✭ ✚✦ ✚ ✬✥❆✺✭ ✛✥✮✫ ✙ ✬✫✷✬✫ ✴ ✫✰ ✦✚✦✘ ✥✰ ✥ ✸ ✚ ⑥✥❆ ✦ ❿❄❉ ✦ ✬ ✘ ✚ ✰✺ ✙ ✫ ✴ ✾ ✘✙✙ ✷✬✥ ✵✘ ✮✫✺✥✥✮ ✵✘ ✫✾✷ ✙ ✚ ✰✰ ✘ ✰✺ ✬✫ ✴ ❆ ✙✦✴✸ ✥✬ ➀ ✰✫✛✥✮✫ ✙ ✚ ✤④❆ ✘ ✴✘✦✘ ✥✰✥ ✸ ✚✴ ✫✺✛✫✰ ✦ ✥ ✸ ✚ ⑥✥❆ ✦ ❾✩ ❉❉❉ ✦ ✬ ✘ ✚ ✰✺ ✙ ✫ ✴ ✢ ③ ✭✫ ✤✥✛✷ ✙ ✫⑧ ✘✦ ✼ ✥ ✸ ✦ ✭✫ ⑤❶ ✚✙ ✺✥✬ ✘✦ ✭✛ ✘ ✴ ✄❊ ☎✆✡❋ ✩ ✾✭✫✬✫☎ ✟ ✜✝ ✜ ✚ ✰✮ ✆ ✟ ✜ ✢ ✜ ✚ ✬✫ ✦ ✭✫ ✴✘✬ ✫ ✴ ✥ ✸ ✦ ✭✫ ✵✘ ✫✾ ✱ ✷✥ ✘ ✰ ✦ ✚ ✰✮ ✴ ❆✬ ✸✚ ✤✫✷✥ ✘ ✰ ✦ ✴ ✫ ✦✴✩ ✬✫ ✴ ✷✫ ✤ ✦✘✵ ✫ ✙ ✼✢ ❈ ⑩ ✫✼ ✸ ✫ ✚ ✱ ✦ ✸ ✦ ✚✙ ✘✦ ✘ ✴✴ ✚✴ ✴✚ ✙✘ ✘ ✴ ✸✚ ✚
