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ﺍﺭﺍﺋﻪ ﺭﻭﺷﻲ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺑﺎ ﺩﻭﺭﺑﻴﻦ ﺑﺎ ﺍﺳﺘ
Page 1
ﺍﺭﺍﺋﻪ ﺭﻭﺷﻲ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺑﺎ ﺩﻭﺭﺑﻴﻦ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ
ﻣﻬﺪﻱ ﻣﻴﺮﺯﺍﺑﻜﻲ
١
ﻭ ﻋﻠﻲ ﺁﻗﺎﮔﻞ ﺯﺍﺩﻩ
٢
ﺩﺍﻧﺸﺠﻮﻱ ﻛﺎﺭﺷﻨﺎﺳﻲ ﺍﺭﺷﺪ ﻛﺎﻣﭙﻴﻮﺗﺮ
-
ﺩﺍﻧﺸﮕﺎﻩ ﺁﺯﺍﺩ ﺍﺳﻼﻣﻲ ﻭﺍﺣﺪ ﺟﻨﻮﺏ ﺗﻬﺮﺍﻥ
Email : Mirzabaki@yahoo.com
ﺩﺍﻧﺸﻴﺎﺭ ﮔﺮﻭﻩ ﻣﻬﻨﺪﺳﻲ ﺑﺮﻕ
ﺩﺍﻧﺸﻜﺪﻩ ﻓﻨﻲ ﺩﺍﻧﺸﮕﺎﻩ
ﺗﺒﺮﻳﺰ
ﭼﻜﻴﺪﻩ
ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺿﻤﻦ ﺑﺮﺭﺳﻲ ﺭﻭﺷﻬﺎﻱ ﻣﺨﺘﻠﻒ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ، ﺭﻭﺷﻲ ﺑﺮﺍﻱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻓﺎﺻﻠـﻪ ﺷﻲﺀ ﺍﺯ ﺩﻭﺭﺑﻴﻦ
(
ﻋﻤﻖ ﺻﺤﻨﻪ
)
ﺗﻮﺳﻂ ﻳﻚ ﺩﻭﺭﺑﻴﻦ ﺍﺭﺍﺋﻪ ﻣﻲ ﺷﻮﺩ
.
ﺭﻭﺵ ﭘﻴﺸﻨﻬﺎﺩﻱ
ﺑﺮ ﺍﺳﺎﺱ ﻓﺮﻣﻮﻝ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ ﺍﺳﺖ
.
ﺑﺮﺍﻱ ﭘﻴـﺪﺍ ﻛﺮﺩﻥ ﭘﺎﺭﺍﻣﺘﺮﻫـﺎﻱ ﺗﺎﺑﻊ ﺩﺭﻭﻧﻴﺎﺏ ، ﻳﻚ ﻣﺠﻤﻮﻋﻪ ﺧﻄﻮﻁ ﺑﺎ ﻓﺎﺻﻠـﻪ ﻣﺸﺨﺺ ﺍﺯ ﺩﻭﺭﺑﻴﻦ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ
ﻗﺮﺍﺭ ﻣﻲ ﮔﻴﺮﻧــﺪ ﻭ ﺳﭙﺲ ﻓﺎﺻﻠﻪ ﺗﺼﻮﻳﺮ ﻫﺮ ﺧﻂ
ﺩﺭ ﻋﻜﺲ ﺑﺮﺩﺍﺷﺘﻪ ﺷﺪﻩ ﺍﺯ ﻟﺒﻪ ﭘﺎﺋﻴﻦ ﺗﺼﻮﻳﺮ
(
ﺑﻪ ﻋﻨﻮﺍﻥ ﻧﻘﻄﻪ ﻣﺮﺟﻊ
)
ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ
.
ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺮﺍﻱ ﺭﻭﺵ ﭘﻴﺸﻨﻬﺎﺩﻱ ﮔﻮﻳﺎﻱ ﺩﻗﺖ ﺑﺎﻻ ﻭ ﺣﺠﻢ ﻋﻤﻠﻴﺎﺕ ﻛﻢ ﻧﺴﺒﺖ ﺑﻪ ﺭﻭﺷﻬﺎﻱ
ﻣﻮﺭﺩ ﺑﺤﺚ ﺍﺳﺖ
.
ﻭﺍﮊﮔﺎﻥ ﻛﻠﻴﺪﻱ
:
ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺑﺎ ﺩﻭﺭﺑﻴﻦ ، ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ
ﻣﻘﺪﻣﻪ
ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﻳﺎ ﺗﺸﺨﻴﺺ ﻋﻤﻖ ﺑﻪ ﻛﻤﻚ ﺩﻭﺭﺑﻴﻦ ﺩﺍﺭﺍﻱ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﻣﺘﻨﻮﻋﻲ ﺩﺭ ﺻﻨﺎﻳــﻊ ﺩﻓﺎﻋﻲ ، ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺭﻭﺑﺎﺗﻬﺎ ، ﻫﺪﺍﻳﺖ ﻭ ﻛﻨﺘﺮﻝ
ﻣﺴﻴﺮ ﻭﺳﺎﻳﻂ ﻧﻘﻠﻴﻪ ، ﺟﻬﺖ ﻳﺎﺑﻲ ﻭ ﻧﻈﺎﻳﺮ ﺁﻥ ﻣﻲ ﺑﺎﺷﺪ
.
ﺍﻳﻦ ﻣﺴﺄﻟﻪ ﺍﺯ ﺩﻳﺪﮔﺎﻫﻬﺎﻱ ﻣﺨﺘﻠﻔﻲ ﺑﺮﺭﺳﻲ ﺷﺪﻩ ﻭ ﻣﻘﺎﻻﺕ ﻣﺘﻌﺪﺩﻱ ﺩﺭ ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺍﺭﺍﺋﻪ ﮔﺮﺩﻳﺪﻩ ﺍﻧﺪ
.
ﺭﻭﺷﻬﺎﻳﻲ ﻛﻪ ﺗﺎﻛﻨﻮﻥ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﻧﺪ ،
ﻫﻤﮕﻲ ﺑﻪ ﭼﻨﺪ ﺩﺳﺘﻪ ﻛﻠﻲ ﻗﺎﺑﻞ ﺗﻘﺴﻴﻢ ﻫﺴﺘﻨﺪ
:
ﺩﺳﺘﻪ ﺍﻭﻝ ، ﻛﻠﻴﻪ ﺭﻭﺷﻬﺎﻳﻲ ﺭﺍ ﺷﺎﻣﻞ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺑﺮ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺩﻭ ﺩﻭﺭﺑﻴﻦ ﺗﺄﻛﻴﺪ ﺩﺍﺭﻧﺪ
.
ﺍﻳﻦ ﺩﺳﺘﻪ ﺟ
ﺰﻭ ﻗﺪﻳﻤﻲ ﺗﺮﻳﻦ ﺗﺤﻘﻴﻘﺎﺕ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﺩﺭ ﺍﻳﻦ
ﺧﺼﻮﺹ ﻫﺴﺘﻨﺪ ﻭ ﺍﻣﺮﻭﺯﻩ ﺟﺰ ﺩﺭ ﻣﻮﺍﺭﺩﻱ ﻛﻪ ﺑﻪ ﻓﻴﺰﻳﻮﻟﻮﮊﻱ ﭼﺸﻢ ﺍﻧﺴﺎﻥ ﻣﺮﺑﻮﻁ ﻣﻴﺸﻮﺩ ، ﺍﺳﺘﻔﺎﺩﻩ ﭼﻨﺪﺍﻧﻲ ﻧﺪﺍﺭﻧﺪ
.
ﺍﺳﺎﺱ ﺍﻳﻦ ﺭﻭﺷﻬﺎ ﺑﺪﻳﻦ ﮔﻮﻧﻪ
ﻣﻲ ﺑﺎﺷﺪ ﻛﻪ ﺩﻭ ﺩﻭﺭﺑﻴﻦ ﺭﻭﻱ ﻳﻚ ﺧﻂ ﺗﺮﺍﺯ ﺍﻓﻘﻲ ﺩﺭ ﻓﺎﺻﻠﻪ ﻣﻌﻴﻨﻲ ﺍﺯ ﻳﻜﺪﻳﮕﺮ ﻗﺮﺍﺭ ﻣﻲ ﮔﻴﺮﻧﺪ ﻭ ﺭﻭﻱ ﺟﺴﻢ ﻣﻮﺭﺩ ﻧ
ﻈﺮ ﻣﺘﻤﺮﻛﺰ ﻣﻲ ﺷﻮﻧﺪ
.
ﺳﭙﺲ
ﻣﻴﺰﺍﻥ ﺯﺍﻭﻳﻪ ﺍﻧﺤﺮﺍﻑ ﺩﻭﺭﺑﻴﻨﻬﺎ ﺍﺯ ﺧﻂ ﻭﺍﺻﻞ ﺑﻴﻦ ﺁﻧﻬﺎ ﺗﻮﺳﻂ ﻣﻜﺎﻧﻴﺰﻣﻲ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﮔﺮﺩﺩ ﻭ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﻭﺷﻬﺎﻱ ﻣﺜﻠﺜﺎﺗﻲ ﻓﺎﺻﻠﻪ ﻋﻤﻮﺩﻱ ﺟﺴﻢ
ﺗﺎ ﺧﻂ ﻭﺍﺻﻞ ﺩﻭ ﺩﻭﺭﺑﻴﻦ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ
.
ﻣﻬﻤﺘﺮﻳﻦ ﻣﺸﻜﻞ ﺍﻳﻦ ﺭﻭﺷﻬﺎ ﻧﻴﺎﺯ ﺩﺍﺷﺘﻦ ﺑﻪ ﺣﺮﻛﺖ ﻣﻜﺎﻧﻴﻜﻲ ﺩﻭﺭﺑﻴﻨﻬﺎ ﺑﺮﺍﻱ ﺗﻤﺮ
ﻛﺰ ﺭﻭﻱ ﺟﺴﻢ ﺍﺳﺖ
.
ﺍﺯ ﻣﻌﺎﻳﺐ ﺩﻳﮕﺮ ﺍﻳﻦ ﺭﻭﺷﻬﺎ ، ﻭﺍﺑﺴﺘﮕﻲ
ﺑﻪ ﺩﻭ ﺩﻭﺭﺑﻴﻦ ﻣﻲ ﺑﺎﺷﺪ ﻛﻪ ﺍﻭﻻ ﻫﺰﻳﻨﻪ ﺑﻴﺸﺘﺮﻱ ﺭﺍ ﻣﻲ ﻃﻠﺒﺪ ﻭ ﺛﺎﻧﻴﺎ ﺩﺭ ﺻﻮﺭﺕ ﺑﺮﻭﺯ ﺧﺮﺍﺑﻲ ﺑﺮﺍﻱ ﻳﻜﻲ ﺍﺯ ﺁﻧﻬﺎ ، ﺳﻴﺴﺘﻢ ﺑﻪ ﻛﻠﻲ ﺍﺯ ﻛﺎﺭ ﻣﻲ ﺍﻓﺘﺪ
.
ﺩﺳﺘﻪ ﺩﻭﻡ ﺭﻭﺷﻬﺎﻱ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺑﺮ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ﺩﻭﺭﺑﻴﻦ ﺗﺎﻛﻴﺪ ﺩﺍﺭﻧﺪ
.
ﺩﺭ ﺍﻳﻦ ﺭﻭﺷﻬﺎ
ﺍﺳﺎﺱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﺑﺮ ﻣﻴﺰﺍﻥ ﺗﻐﻴﻴﺮ ﺍﻧﺪﺍﺯﻩ ﺗﺼﻮﻳﺮ ﺷﻲﺀ
ﻣﻮﺭﺩ ﻧﻈﺮ ﺑﺮ ﺍﺛﺮ ﺣﺮﻛﺖ ﺩﻭﺭﺑﻴﻦ ﺑﻪ ﺍﻧﺪﺍﺯﻩ ﻣﻌﻠﻮﻡ ﻣﻲ ﺑﺎﺷﺪ
[١]
.
ﺍﻳﻦ ﺭﻭﺵ ﺩﻭ ﻣﺸﻜﻞ ﻋﻤﺪﻩ ﺩﺍﺭﺩ
:
ﻧﺨﺴﺖ ﺍﻳﻨﻜﻪ ﺑﺎﻳﺪ ﺍﻧﺪﺍﺯﻩ ﻭﺍﻗﻌﻲ ﺷﻲﺀ ﻣﻮﺭﺩ ﻧﻈﺮ ﺭﺍ ﻛﻪ ﻗﺮﺍﺭ ﺍﺳﺖ ﻓﺎﺻﻠﻪ ﺁﻥ ﺍﺯ ﺩﻭﺭﺑﻴﻦ ﻣﺤﺎﺳﺒﻪ ﺷﻮﺩ ،
ﺑﺪﺍﻧﻴﻢ
.
ﺩﻭﻡ ﺍﻳﻨﻜﻪ ﺩﺍﻧﺴﺘﻦ ﻓﺎﺻ
ﻠﻪ ﻛﺎﻧﻮﻧﻲ ﻟﻨﺰ ﻋﺪﺳﻲ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﺍﻟﺰﺍﻣﻲ ﻣﻲ ﺑﺎﺷﺪ
.
ﻳﻌﻨﻲ ﺍﻳﻦ ﺭﻭﺵ ﺑﻪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺩﻭﺭﺑﻴﻦ ﻭﺍﺑﺴﺘﻪ ﺍﺳﺖ
.
ﺩﻭﻣﻴﻦ ﮐﻨﻔﺮﺍﻧﺲ ﻣﺎﺷﻴﻦ ﺑﻴﻨﺎﻳﯽ ﻭ ﭘﺮﺩﺍﺯﺵ ﺗﺼﻮﻳﺮ
The Second Conference On Machine
ﺍﻳﺮﺍﻥ
Vision, Image Processing &
ﺗﻬﺮﺍﻥ
_
ﺑﻬﻤﻦ ﻣﺎﻩ
۱۳۸۱
(Applications (MVIP 2003
Tehran-Feb.2003

Page 2
ﺩﺳﺘﻪ ﺳﻮﻡ ﺍﺯ ﺭﻭﺷﻬﺎﻱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻓﺎﺻﻠﻪ ﺑﺎ ﺩﻭﺭﺑﻴﻦ ﺩﺭ ﻣﻮﺍﺭﺩﻱ ﻛﻪ ﺷﻲﺀ ﻣﻮﺭﺩ ﻧﻈﺮ ﻣﺘﺤﺮﻙ ﺑﺎﺷﺪ ﺑﻪ ﻛﺎﺭ ﺑﺮﺩﻩ ﻣﻲ ﺷﻮﻧﺪ ﻭ ﺩﺭ ﺍﻳﻦ ﺩﺳﺘﻪ ﺍﺯ
ﺭﻭﺷﻬﺎ ، ﺩﻭﺭﺑﻴﻦ ﺩﺭ ﻣﻜﺎﻧﻲ ﺛﺎﺑﺖ ﻗﺮﺍﺭ ﺩ
ﺍﺩﻩ ﻣﻲ ﺷﻮﺩ
.
ﻓﺮﺁﻳﻨﺪ ﻛﺎﺭ ﺑﺪﻳﻦ ﮔﻮﻧﻪ ﺍﺳﺖ ﻛﻪ ﺍﺑﺘﺪﺍ ﺷﻲﺀ ﻣﺘﺤﺮﻙ ﺑﺮ ﺍﺳﺎﺱ ﭼﻬﺎﺭ ﻭﻳﮋﮔﻲ ﺣﺪﺍﻛﺜﺮ ﺳﺮﻋﺖ ،
ﺗﻐﻴﻴﺮﺍﺕ ﺟﺰﺋﻲ ﺳﺮﻋﺖ ، ﻫﻤﺴﺎﻧﻲ ﺣﺮﻛﺖ ﻭ ﭘﻴﻮﺳﺘﮕﻲ ﺣﺮﻛﺖ ﺷﻨﺎﺳﺎﻳﻲ ﻣﻲ ﺷﻮﺩ ﻭ ﺳﭙﺲ ﺑﺎ ﺭﻭﺷﻲ ﻓﺎﺻﻠﻪ ﺷﻲﺀ ﻣﺘﺤﺮﻙ ﺭﺍ ﻣﺤﺎﺳﺒﻪ
ﻣﻲ ﻛﻨﺪ
[٢]
.
ﺩﺭ ﺍﻳﻦ ﺭﻭﺵ ﻣﻮﻗﻌﻴﺘﻬﺎﻱ ﻣﺨﺘﻠﻒ ﺷﻲﺀ ﻣﻮﺭﺩ
ﻧﻈﺮ ﺩﺭ ﺩﻧﺒﺎﻟﻪ ﺗﺼﺎﻭﻳﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺗﻌﻴﻴﻦ ﻣﻲ ﺷﻮﺩ ﻭ ﻋﻤﻖ ﻧﺴﺒﻲ ﻫﺪﻑ ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﻛﻨﺪ
ﺍﺯ .
ﻣﺸﻜﻼﺕ ﺍﻳﻦ ﺭﻭﺵ ﻣﻴﺘﻮﺍﻥ ﺣﺠﻢ ﺯﻳﺎﺩ ﻋﻤﻠﻴﺎﺕ ﻣﺤﺎﺳﺒﺎﺗﻲ ﺭﺍ ﻣﻄﺮﺡ ﻧﻤﻮﺩ
.
ﺩﺳﺘﻪ ﭼﻬﺎﺭﻡ ﺭﻭﺷﻬﺎﻳﻲ ﻫﺴﺘﻨﺪ ﻛﻪ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﻳﺎ ﻋﻤﻖ ﺍﺯ ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﺗﺼﺎﻭﻳﺮ ﺑﺮﺩﺍﺷﺘﻪ ﺷﺪﻩ ﺑﺎ ﻳﻚ ﺩﻭﺭﺑﻴﻦ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﻛﻨﻨ
ﺪ ﻛﻪ ﺑﺮ
ﺍﺳﺎﺱ ﻣﺪﻝ ﮊﺋﻮﻣﺘﺮﻳﻜﻲ ﻣﻮﻗﻌﻴﺖ ﺟﺴﻢ ﻭ ﺩﻭﺭﺑﻴﻦ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﻧﺪ
[٣]
.
ﺩﺭ ﺍﻳﻦ ﺭﻭﺷﻬﺎ ﻧﻴﺰ ﻫﻤﻮﺍﺭﻩ ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺼﻮﺭﺕ ﺗﻘﺮﻳﺒﻲ ﺧﻮﺍﻫﻨﺪ ﺑﻮﺩ ﻭ ﻭﺟﻮﺩ ﻓﺮﺿﻬﺎﻱ ﭘﻴﺸﻨﻬﺎﺩﻱ ، ﻫﻢ ﺳﺒﺐ ﺗﻘﺮﻳﺒﻲ ﺑﻮﺩﻥ ﻧﺘﺎﻳﺞ
ﻣﻲ ﺷﻮﺩ ﻭ ﻫﻢ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺁﻥ ﺭﺍ ﺑﺮﺍﻱ ﺍﺟﺴﺎﻡ ﻣﻮﺟﻮﺩ ﺩﺭ ﻓﻮﺍﺻﻞ ﻧﺰﺩﻳﻚ ﺑﻪ ﺩﻭﺭ
ﺑﻴﻦ ﻏﻴﺮﻋﻤﻠﻲ ﻣﻲ ﺳﺎﺯﺩ
.
ﺩﺳﺘﻪ ﭘﻨﺠﻢ ﺍﺯ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﻣﻮﺟﻮﺩ ، ﻳﺎﻓﺘﻦ ﻋﻤﻖ ﺗﺼﻮﻳﺮ
(
ﻓﺎﺻﻠﻪ ﺟﺴﻢ ﺍﺯ ﺩﻭﺭﺑﻴﻦ
)
ﺭﺍ ﺑﻪ ﻛﻤﻚ ﻟﺒﻪ ﻫﺎﻱ ﻣﺤﻮ ﻳﺎ ﻛﺪﺭ ﺗﺼﻮﻳﺮ ﭘﻴﺸﻨﻬﺎﺩ
ﻣﻲ ﻛﻨﻨﺪ
[٤].
ﻗﺎﻟﺐ ﺍﺻﻠﻲ ﺍﻳﻦ ﺭﻭﻳﻜﺮﺩ ﺑﺪﻳﻦ ﮔﻮﻧﻪ ﺍﺳﺖ
:
ﺗﺼﻮﻳﺮ ﻣﺸﺎﻫﺪﻩ ﺷﺪﻩ ﺍﺯ ﻳﻚ ﺟﺴﻢ ﺑﻪ ﺻﻮﺭﺕ ﻧﺘﻴﺠﻪ ﻛﺎﻧﻮﻭﻟﻮﺷﻦ ﺗﺼﻮﻳﺮ ﻭﺍ
ﺿﺢ ﺟﺴﻢ ﻭ
ﻳﻚ ﺗﺎﺑﻊ
Point Spread
ﻣﺪﻟﺴﺎﺯﻱ ﻣﻲ ﺷﻮﺩ
.
ﺍﻳﻦ ﺗﺎﺑﻊ ﺑﻪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺩﻭﺭﺑﻴﻦ ﻭ ﻓﺎﺻﻠﻪ ﺟﺴﻢ ﺗﺎ ﺩﻭﺭﺑﻴﻦ ﻭﺍﺑﺴﺘﻪ ﺍﺳﺖ
.
ﺑﺎ ﺗﻘﺎﺭﻥ ﻣﺤﻮﺭﻱ ﺣﺎﺻﻞ ،
ﻳﻚ ﺗﺎﺑﻊ
Line Spread
ﻛﻪ ﻣﻄﺎﺑﻖ ﺑﺎ ﺗﺎﺑﻊ ﻣﻮﺭﺩ ﻧﻈﺮ ﻣﺎ ﺑﺎﺷﺪ ﺍﺯ ﻳﻚ ﻟﺒﻪ ﭘﻠﻪ ﺍﻱ ﻣﺤﻮ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ
.
ﺣﺎﻝ ﻣﻴﺰﺍﻥ ﭘﺮﺍﻛﻨﺪﮔﻲ ﺍﺯ ﺗﺎﺑﻊ
Line
Spread
ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺍﻳﻦ ﭘﺮﺍﻛﻨﺪﮔﻲ ﺑﺎ ﻋﻜﺲ ﻓﺎﺻﻠﻪ ، ﻧﺴﺒﺖ ﺧﻄﻲ ﺩﺍﺭﺩ
.
ﺛﺎﺑﺘﻬﺎﻱ ﺍﻳﻦ ﺭﺍﺑﻄﻪ ﺧﻄﻲ ﺍﺯ ﺭﻭﺍﻝ ﺳﺎﺩﻩ ﻛﺎﻟﻴﺒﺮﺍﺳﻴﻮﻥ ﺩﻭﺭﺑﻴﻦ
ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﻧﺪ
.
ﺳﭙﺲ ﺑﺎ ﻣﺤﺎﺳﺒﻪ ﻣﻴﺰﺍﻥ ﭘﺮﺍﻛﻨﺪﮔﻲ ، ﻓﺎﺻﻠﻪ ﺟﺴﻢ ﺍﺯ ﻳﻚ ﺭﺍﺑﻄﻪ ﺧﻄﻲ ﺑﺪﺳﺖ ﺧﻮﺍﻫﺪ ﺁﻣﺪ
.
ﻋﻤﺪﻩ ﺗﺮﻳﻦ ﻣﺸﻜﻞ ﺍﻳﻦ ﺭﻭﺵ ﻧﻴﺰ ﺣﺠﻢ ﻋﻤﻠﻴﺎﺕ ﺑﺎﻻﻳ
ﻲ ﺍﺳﺖ ﻛﻪ ﺟﻬﺖ ﻳﺎﻓﺘﻦ ﺩﻭ ﺗﺎﺑﻊ ﻓﻮﻕ ﺍﻟﺬﻛﺮ ﻣﻮﺭﺩ ﻧﻴﺎﺯ ﻣﻲ ﺑﺎﺷﺪ ﻭ ﺑﻌﻼﻭﻩ ﺑﻪ ﺩﻟﻴﻞ
ﻣﺎﻫﻴﺖ ﺗﻘﺮﻳﺒﻲ ﻋﻤﻠﻴﺎﺕ ، ﻧﺘﻴﺠﻪ ﺣﺎﺻﻞ ﺩﺍﺭﺍﻱ ﺗﻘﺮﻳﺐ ﺧﻮﺍﻫﺪ ﺑﻮﺩ
.
ﺩﺭ
ﺩﺳﺘﻪ ﺷﺸﻢ ﺍﺯ ﺭﻭﺵ ﻫﺎﻱ ﻣﻮﺟﻮﺩ ، ﻋﻼﻭﻩ ﺑﺮ ﺩﻭﺭﺑﻴﻦ ، ﺍﺑﺰﺍﺭ ﻛﻤﻜﻲ ﺩﻳﮕﺮﻱ ﻧﻴﺰ ﺩﺭ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﺟﺴﻢ ﻣﻮﺭﺩ ﻧﻈﺮ، ﻧﻘﺶ ﺍﻳﻔﺎ ﻣﻲ ﻛﻨﻨﺪ
ﺍﺯ .
ﺟﻤﻠﻪ ﺍﻳﻦ ﺍﺑﺰﺍﺭ ﻛﻤﻜﻲ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﻣﻮﺭﺩﻱ ﺍﺷﺎﺭﻩ ﻛﺮﺩ ﻛﻪ ﺩﺭ ﺁﻥ ﻳﻚ ﻣﻨﺒﻊ ﻧﻘﻄﻪ ﺍﻱ ﻟﻴﺰﺭﻱ ﺑﺎ ﺳﻪ ﻋﺪﺩ
LED
ﻛﻪ ﺭﻭﻱ ﻣﺤﻮﺭ ﻧﻮﺭﻱ ﺁﻥ ﻗﺮﺍﺭ
ﺩﺍﺭﻧﺪ ، ﺑﺼﻮﺭﺕ ﻳﻚ ﻣﺠﻤﻮﻋﻪ ﺭﻭﻱ ﻳﻚ ﻣﻴﻠﻪ ﻣﺪﺍﺩﻱ ﺷﻜﻞ ﺗﻌﺒﻴﻪ ﺷﺪﻩ ﺍﻧﺪ
[
٥]
.
ﻣﻬﻤﺘﺮﻳﻦ ﻋﻴﺐ ﺍﻳﻦ ﺭﻭﺵ ﻧﻴﺰ ﺩﺭ ﺍﻳﻦ ﺍﺳﺖ ﻛﻪ ﺍﻭﻻ ﺍﺯ ﺍﺑﺰﺍﺭ ﻛﻤﻜﻲ ﺩﻳﮕﺮﻱ ﻏﻴﺮ ﺍ
ﺯ ﺩﻭﺭﺑﻴﻦ ﺩﺭ ﺍﻣﺮ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ ﻭ ﺛﺎﻧﻴﺎ ﺑﺎﻳﺪ ﺍﺯ
ﻧﻮﻉ ﻭﻳﮋﻩ ﺍﻱ ﺍﺯ ﺩﻭﺭﺑﻴﻦ
( CCD )
ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩ
.
ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺭﻭﺷﻲ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﺷﻲﺀ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ﺩﻭﺭﺑﻴﻦ ﺍﺭﺍﺋﻪ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺍﺯ ﺳﺎﺩﮔﻲ ﺧﺎﺹ ﻭ ﺩﻗﺖ ﻗﺎﺑﻞ ﻗﺒﻮﻟﻲ ﺑﺮﺧﻮﺭﺩﺍﺭ
ﻣﻲ ﺑﺎﺷﺪ
.
ﺍﺳﺎﺱ ﺍﻳﻦ ﺭﻭﺵ ، ﺍﺳﺘﻔﺎ
ﺩﻩ ﺍﺯ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ ﺍﺳﺖ
.
ﺭﻭﺵ ﭘﻴﺸﻨﻬﺎﺩﻱ
ﺩﺭ ﺑﺨﺶ ﻗﺒﻠﻲ ﻣﺮﻭﺭﻱ ﻛﻠﻲ ﺑﺮ ﺍﻧﻮﺍﻉ ﺭﻭﺷﻬﺎﻱ ﻣﻮﺟﻮﺩ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺑﻪ ﻛﻤﻚ ﺩﻭﺭﺑﻴﻦ ﺩﺍﺷﺘﻴﻢ
.
ﺩﺭ ﺍﻳﻦ ﻗﺴﻤﺖ ﺑﻪ ﺑﻴﺎﻥ ﺍﻳﺪﻩ ﺟﺪﻳﺪﻱ ﺩﺭ ﺍﻳﻦ
ﺯﻣﻴﻨﻪ ﺧﻮﺍﻫﻴﻢ ﭘﺮﺩﺍﺧﺖ
.
ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺧﺎﺻﻴﺖ ﭘﺮﺳﭙﻜﺘﻴﻮ ﻣﻲ ﺩﺍﻧﻴﻢ ﻛﻪ ﺧﻄﻮﻁ ﻣﻮﺍﺯﻱ ﻣﺘﺴﺎﻭﻱ ﺍﻟﻔﺎﺻﻠﻪ ، ﻫﺮ
ﭼﻪ ﺍﺯ ﻣﻨﻈﺮ ﺩﻭﺭﺑﻴﻦ ﺩﻭﺭﺗﺮ ﺑﺎﺷﻨﺪ ، ﺍﺯ
ﺩﻳﺪ ﻧﺎﻇﺮ ﺩﺍﺭﺍﻱ ﻓﺎﺻﻠﻪ ﻛﻤﺘﺮﻱ ﻫﺴﺘﻨﺪ
.
ﻣﺎ ﺍﺯ ﺍﻳﻦ ﺍﺻﻞ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﺑﻬﺮﻩ ﻣﻲ ﺟﻮﻳﻴﻢ
.
ﺭﻭﺵ ﭘﻴﺸﻨﻬﺎﺩﻱ ﺍﺯ ﺩﻭ ﻓﺎﺯ ﺗﺸﻜﻴﻞ ﺷﺪﻩ ﺍﺳﺖ
:
ﻣﺮﺣﻠﻪ ﺍﻭﻝ ﻣﺤﺎﺳﺒﻪ ﻳﻚ ﺗﺎﺑﻊ ﺩﺭﻭﻧﻴﺎﺏ ﺑﺮ ﺍﺳﺎﺱ ﺍﺭﺗﻔﺎﻉ ﻭ ﺯﺍﻭﻳﻪ ﺩﻭﺭﺑﻴﻦ ﻧﺴﺒﺖ ﺑﻪ ﺧﻂ ﺍﻓﻖ
ﻣﻲ ﺑﺎﺷﺪ
.
ﻣﺮﺣﻠﻪ ﺩﻭ
ﻡ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺎﺑﻊ ﺩﻭﺭﻧﻴﺎﺏ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﺟﺴﻢ ﺩﻟﺨﻮﺍﻩ ﻧﺴﺒﺖ ﺑﻪ ﺩﻭﺭﺑﻴﻦ ﻣﻲ ﺑﺎﺷﺪ
.
ﺩﺭ ﻣﺮﺣﻠﻪ ﺍﻭﻝ ﻳﺎ
ﻣﺮﺣﻠﻪ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ، ﺭﻭﺵ ﻛﺎﺭ ﺑﺪﻳﻦ ﮔﻮﻧﻪ ﺍﺳﺖ ﻛﻪ ﺍﺑﺘﺪﺍ ﺩﻭﺭﺑﻴﻦ ﺭﺍ ﺩﺭ ﺍﺭﺗﻔﺎﻉ ﻭ ﺯﺍﻭﻳﻪ ﺛﺎﺑﺘﻲ ﻧﺴﺒﺖ ﺑﻪ ﺳﻄﺢ ﺍﻓﻖ ﻗﺮﺍﺭ ﻣﻲ ﺩﻫﻴﻢ
.
ﺳﭙﺲ ﺩﺭ ﺍﻳﻦ
ﻭﺿﻌﻴﺖ ﺍﺯ ﺧﻄﻮﻁ ﻣﺘﺴﺎﻭﻱ ﺍﻟ
ﻔﺎﺻﻠﻪ ﺍﻱ ﻛﻪ ﺑﺎ ﻓﺎﺻﻠﻪ ﻣﻌﻠﻮﻣﻲ ﺭﻭﻱ ﻳﻚ ﺳﻄﺢ ﻳﻜﻨﻮﺍﺧﺖ ﻋﻤﻮﺩ ﺑﺮ ﺍﻣﺘﺪﺍﺩ ﻣﺤﻮﺭ ﻧﻮﺭﻱ ﺩﻭﺭﺑﻴﻦ ﺗﺮﺳﻴﻢ ﺷﺪﻩ ﺍﻧﺪ ،
ﺗﺼﻮﻳﺮﻱ ﺩﺭﻳﺎﻓﺖ ﻣﻲ ﮔﺮﺩﺩ
.
ﺑﻌﺪ ﺍﺯ ﺁﻥ ﺟﺪﻭﻟﻲ ﺗﺸﻜﻴﻞ ﻣﻲ ﮔﺮﺩﺩ ﻛﻪ ﺳﺘﻮﻥ ﺍﻭﻝ ﺁﻥ ، ﻓﺎﺻﻠﻪ ﺗﺼﻮﻳﺮ ﻫﺮ ﺧﻂ ﺩﺭ ﻋﻜﺲ ﺑﺮﺩﺍﺷﺘﻪ ﺷﺪﻩ ﺍﺯ ﻟﺒﻪ ﭘﺎﺋﻴﻦ

Page 3
ﺗﺼﻮﻳﺮ ﺑﺮﺣﺴﺐ ﭘﻴﻜﺴﻞ
(
ﺑﻪ ﻋﻨﻮﺍﻥ ﻧﻘﻄﻪ ﻣﺮﺟﻊ
)
ﺑﻮﺩﻩ ﻭ ﺳﺘﻮﻥ ﺩﻭﻡ ﺁﻥ ، ﻓﺎﺻﻠﻪ ﻭﺍﻗﻌﻲ ﺧﻂ ﺍﺯ ﺩﻭﺭﺑﻴﻦ ﺑﺮ ﺣﺴﺐ ﻭﺍﺣﺪ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻃﻮﻝ
(
ﻣﺜﻼ
ﺳﺎﻧﺘﻴﻤﺘﺮ
)
ﻣﻲ ﺑﺎﺷﺪ
.
ﺣﺎﻝ ﺑﻪ ﻛﻤﻚ ﺍﻳﻦ ﺟﺪﻭﻝ ﻭ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﻭﺵ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ
[٦]
، ﭼﻨﺪ ﺟﻤﻠﻪ ﺍﻱ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻛﻪ ﺑﻌﻨﻮﺍﻥ ﺗﺎﺑﻊ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﻫﺮ ﻧﻘﻄﻪ
ﺩﻟﺨﻮﺍﻩ ﺑﺎ ﺩﻭﺭﺑﻴﻦ ﺑﻪ ﻛﺎﺭ ﺧﻮﺍ
ﻫﺪ ﺭﻓﺖ ، ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ
:
(
)
(
)
,)(
)()(
)(
,
,
i
j
n
jioi
i
n
jioi
n
oj
j
j
xx
xx
xLj
xLxf
xf
=
=
=
=
=
¦
π
π
)١(
ﻛﻪ
x
ﻓﺎﺻﻠﻪ ﺗﺼﻮﻳﺮ ﻧﻘﻄﻪ ﻣﻮﺭﺩ ﻧﻈﺮ ﺩﻟﺨﻮﺍﻩ ﺑﺮﺍﻱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻓﺎﺻﻠﻪ ﺍﺯ ﻧﻘﻄﻪ ﻣﺮﺟﻊ ﺑﺮ ﺣﺴﺐ ﭘﻴﻜﺴﻞ ﻭ
n
ﺗﻌﺪﺍﺩ ﺧﻄﻮ
ﻁ ﺗﺮﺳﻴﻢ ﺷﺪﻩ ﺩﺭ ﻣﺤﻴﻂ
ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﺍﺳﺖ
.
ﻋﻠﺖ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﻭﺵ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ ﺍﻳﻨﺴﺖ ﻛﻪ
:
ﺍﻭﻻ ﻋﻨﺎﺻﺮ ﺳﺘﻮﻥ ﺍﻭﻝ ﺟﺪﻭﻝ ﻣﺎ ﻣﺘﺴﺎﻭﻱ ﺍﻟﻔﺎﺻﻠﻪ ﻧﻴﺴﺘﻨﺪ
.
ﺛﺎﻧﻴﺎ ﺧﻄﺎﻱ ﺍﻳﻦ ﺭﻭﺵ ﺑﺎ
ﻣﺸﺘﻖ
n+1
ﺍﻡ ﺗﺎﺑﻊ ﺩﺭﻭﻧﻴﺎﺏ ﻓﻮﻕ ﺍﻟﺬﻛﺮ ﻣﺘﻨﺎﺳﺐ ﺍﺳﺖ
.
ﺑﺪﻳﻬﻲ ﺍﺳﺖ ﻛﻪ ﻫﺮ ﭼﻪ ﻣﻘﺪﺍﺭ
n
(
ﺗﻌﺪﺍﺩ ﺧﻄﻮﻁ ﺗﺮﺳﻴ
ﻢ ﺷﺪﻩ ﺩﺭ ﻣﺤﻴﻂ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ
)
ﺑﻴﺸﺘﺮ ﺷﻮﺩ ، ﺩﻗﺖ ﺗﺎﺑﻊ ﻣﻮﺭﺩ ﺑﺤﺚ ﻧﻴﺰ ﺑﺎﻻ ﺧﻮﺍﻫﺪ ﺭﻓﺖ
.
ﻳﻌﻨﻲ
:
)(
max
1 x
f
R
n
n
+
)٢(
ﻣﺮﺣﻠﻪ ﺩﻭﻡ ﻛﺎﺭ ﺑﺪﻳﻦ ﮔﻮﻧﻪ ﺍﺳﺖ ﻛﻪ ﺍﮔﺮ ﺟﺴﻤﻲ ﺭﺍ ﻣﻘﺎﺑﻞ ﺩﻭﺭﺑﻴﻦ ﻗﺮﺍﺭ ﺩﻫﻴﻢ ،
(
ﺑﻪ ﺷﺮﻁ ﺁﻧﻜﻪ ﺍ
ﺭﺗﻔﺎﻉ ﻭ ﺯﺍﻭﻳﻪ ﺩﻭﺭﺑﻴﻦ ﻧﺴﺒﺖ ﺑﻪ ﻣﺤﻴﻂ
ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﺗﻐﻴﻴﺮ ﻧﻜﺮﺩﻩ ﺑﺎﺷﺪ
)
، ﺍﻳﻦ ﺍﻟﮕﻮﺭﻳﺘﻢ ﻓﺎﺻﻠﻪ ﺗﺼﻮﻳﺮ ﻟﺒﻪ ﭘﺎﺋﻴﻨﻲ
ﺟﺴﻢ ﺭﺍ
(
ﻛﻪ ﺩﺭ ﻭﺍﻗﻊ ﻧﺰﺩﻳﻜﺘﺮﻳﻦ ﻟﺒﻪ ﺟﺴﻢ ﻧﺴﺒﺖ ﺑﻪ ﺩﻭﺭﺑﻴﻦ ﺩﺭ ﻣﺤﻴﻂ
ﻭﺍﻗﻌﻲ ﻣﻲ ﺑﺎﺷﺪ
)
، ﻧﺴﺒﺖ ﺑﻪ ﻟﺒﻪ ﭘﺎﺋـﻴﻦ ﺗﺼـﻮﻳﺮ
(
ﻧﻘﻄﻪ ﻣﺮﺟﻊ
)
ﺑﺮ ﺣﺴﺐ ﭘﻴﻜﺴﻞ ﺷﻤﺎﺭﺵ ﻛﺮﺩﻩ ﻭ ﺁﻧﺮﺍ ﺑﻪ
ﻋﻨﻮﺍﻥ ﭘﺎﺭﺍﻣﺘﺮ
x
ﺑﺮﺍﻱ ﺗﺎﺑﻊ ﺩﺭﻭﻧﻴﺎﺏ
ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ ﻣﻲ ﺩﻫﻴﻢ
.
ﻣﻘﺪﺍﺭ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ﺗﻮﺳﻂ ﺗﺎﺑﻊ ، ﻓﺎﺻﻠﻪ ﻭﺍﻗﻌﻲ ﺟﺴﻢ ﺗﺎ ﺩﻭﺭﺑﻴﻦ ﻣﻲ ﺑﺎﺷﺪ
.
ﺍﻳﻦ ﺭﻭﺵ ﺍﺯ ﭼﻨﺪ ﺩﻳﺪﮔﺎﻩ ﻧﺴﺒﺖ ﺑﻪ ﺭﻭﺷﻬﺎﻱ ﻗﺒﻠﻲ ﻣﺰﻳﺖ ﺩﺍﺭﺩ
:
ﺍﻟﻒ
)
ﺗﻨﻬﺎ ﺍﺯ ﻳﻚ ﺩﻭﺭﺑﻴﻦ ﺑﺮﺍﻱ ﺍﺭﺯﻳﺎﺑﻲ ﻓﺎﺻﻠﻪ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ
.
)ﺏ
ﻫﻴﭽﮕﻮﻧﻪ ﻭﺍﺑﺴﺘﮕﻲ ﻣﺴﺘﻘﻴﻤﻲ ﺑﻪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺩﻭﺭﺑﻴﻦ ﻧﻈﻴﺮ ﻓﺎﺻﻠﻪ ﻛﺎﻧﻮﻧﻲ ﻟﻨﺰ ﺁﻥ ﻧﺪﺍﺭﺩ
.
)ﺝ
ﻣﺤﺎﺳﺒﺎﺕ ﺁﻥ ﻧﺴﺒﺖ ﺑﻪ ﺭﻭﺷﻬﺎﻱ ﺩﻳﮕﺮ ﺑﺴﻴﺎﺭ ﺳﺎﺩﻩ ﺗﺮ ﺍﺳﺖ
.
)ﺩ
ﻧﻴﺎﺯ ﺑﻪ ﻫﻴﭽﮕﻮﻧﻪ ﺍﺑﺰﺍﺭ ﻛﻤﻜﻲ ﺍﺿﺎﻓﻲ ﺑﺮﺍﻱ ﺑﺮ ﺁﻭﺭﺩ ﻓﺎﺻﻠﻪ
(
ﻧﻈﻴﺮ ﻣﻨﺒﻊ ﻟﻴﺰﺭﻱ
)
ﻧﺪﺍﺭﺩ
.
)ﻩ
ﭼﻮﻥ ﺣﺠﻢ ﻋﻤﻠﻴﺎﺕ ﻭ ﻣﺤﺎﺳﺒﺎﺕ ﺁﻥ ﻫﻤ
ﻮﺍﺭﻩ ﺛﺎﺑﺖ ﺑﻮﺩﻩ ﻭ ﺩﺭ ﺑﺎﺯﺓ ﺯﻣﺎﻧﻲ ﻣﺸﺨﺺ ﻭ ﺛﺎﺑﺘﻲ ﻗﺎﺑﻞ ﺍﻧﺠﺎﻡ ﺍﺳﺖ، ﻟﺬﺍ ﺩﺭ ﺍﻣﻮﺭﻱ ﻛﻪ ﺩﺭ ﺁﻥ ﺯﻣﺎﻥ
ﭘﺎﺳﺦ ﺳﻴﺴﺘﻢ ﺩﺍﺭﺍﻱ ﺍﻫﻤﻴﺖ ﻣﻲ ﺑﺎﺷﺪ، ﻗﺎﺑﻞ ﺍﻋﺘﻤﺎﺩ ﺧﻮﺍﻫﺪ ﺑﻮﺩ
.
)ﻭ
ﺩﺭﺻﺪ ﺧﻄﺎﻱ ﺍﻳﻦ ﺭﻭﺵ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﻧﻘﺎﻃﻲ ﻛﻪ ﺩﺭ ﺩﺍﻣﻨﻪ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﻗﺮﺍﺭ ﺩﺍﺭﻧﺪ ، ﺑﺴﻴﺎﺭ ﻧﺎﭼﻴﺰ ﺍﺳﺖ
.
ﺍﺯ ﻣﺤﺪﻭ
ﺩﻳﺘﻬﺎﻱ ﺍﻳﻦ ﺭﻭﺵ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﻭﺍﺑﺴﺘﮕﻲ ﺁﻥ ﺑﻪ ﺍﺭﺗﻔﺎﻉ ﻭ ﺯﺍﻭﻳﻪ ﺩﻭﺭﺑﻴﻦ ﻧﺴﺒﺖ ﺑﻪ ﺍﻓﻖ ﺍﺷﺎﺭﻩ ﻧﻤﻮﺩ ، ﺑﻪ ﻧﺤﻮﻱ ﻛﻪ ﺍﮔﺮ ﻳﻚ ﻳﺎ ﻫﺮ ﺩﻭ
ﭘﺎﺭﺍﻣﺘﺮ ﺗﻐﻴﻴﺮ ﻛﻨﺪ ، ﻧﻴﺎﺯ ﺑﻪ ﮔﺬﺭﺍﻧﺪﻥ ﻣﺠﺪﺩ ﻣﺮﺣﻠﻪ ﺍﻭﻝ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﺗﺎﺑﻊ ﺩﺭﻭﻧﻴﺎﺏ ﺧﻮﺍﻫﺪ ﺑﻮﺩ
.
ﻫﻤﭽﻨﻴﻦ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﺭﻭﺵ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ
ﻓﺎﺻﻠﻪ ﻧﻘﺎﻃﻲ ﻛﻪ ﺧﺎﺭ
ﺝ ﺍﺯ ﺩﺍﻣﻨﻪ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﻗﺮﺍﺭ ﺩﺍﺭﻧﺪ ، ﻏﻴﺮ ﻋﻤﻠﻲ ﺍﺳﺖ
.
ﻧﺘﺎﻳﺞ ﻳﻚ ﺁﺯﻣﺎﻳﺶ ﺑﺮﺍﻱ ﺭﻭﺵ ﺍﺭﺍﺋﻪ ﺷﺪﻩ
ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ، ﺭﻭﻱ ﻳﻚ ﺳﻄﺢ ﻳﻜﻨﻮﺍﺧﺖ ﺧﻄﻮﻃﻲ ﻣﻮﺍﺯﻱ ﺑﻪ ﻓﺎﺻﻠﻪ
٥
ﺳﺎﻧﺘﻴﻤﺘﺮ ﺗﺮﺳﻴﻢ ﺷﺪﻧﺪ
.
ﺳﭙﺲ ﺩﻭﺭﺑﻴﻦ ﺩﺭ ﺍﺭﺗﻔﺎﻉ
٤٥
ﺳﺎﻧﺘﻴﻤﺘﺮﻱ ﻭ
ﺑﺎ ﺯﺍﻭﻳﻪ
٣٠
ﺩﺭﺟﻪ ﻧﺴﺒﺖ ﺑﻪ ﺧﻂ ﺍﻓﻖ ﻣﺴﺘﻘﺮ ﺷﺪ
.
ﺑﺮ ﺍﺳﺎﺱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻓﺎﺻﻠﻪ ﺗﺼﺎﻭﻳﺮ ﺍﻳﻦ ﺧﻄﻮﻁ ﻧﺴﺒﺖ ﺑﻪ ﻣﺒﺪﺍ ﻣﻘﺎﻳﺴﻪ ﺍﻓﻘﻲ
(
ﻟﺒﻪ ﭘﺎﻳﻴﻨﻲ ﺗﺼﻮﻳﺮ
)
ﺑﺮ ﺣﺴﺐ ﭘﻴﻜﺴﻞ ﻭ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻓﺎﺻﻠﻪ
ﻭﺍﻗﻌﻲ ﺁﻧﻬﺎ ﺑﺮ ﺣﺴﺐ ﺳﺎﻧﺘﻴﻤﺘﺮ ﺍﺯ ﺩﻭﺭﺑﻴﻦ ﺩﺭ ﻣﺤﻴﻂ ﻣﻮﺭﺩ ﺁﺯﻣﺎﻳﺶ ، ﺟﺪﻭﻝ ﺷﻤﺎﺭﻩ
١
ﺣﺎﺻﻞ ﮔﺮﺩﻳﺪ
.
ﺟﺪﻭﻝ ﺷﻤﺎﺭﻩ
X
:
ﺗﻌﺪﺍﺩ ﭘﻴﻜﺴﻞ ﺷﻤﺎﺭﺵ ﺷﺪﻩ
Y
:
ﻓﺎﺻﻠﻪ ﻭﺍﻗﻌﻲ ﺍﺯ ﺩﻭﺭﺑﻴﻦ
)
X
٣٤
٦٤
٩٢
١١٤
١٣٦
١٥٥
١٧٣
١٨٩
٢٠٤
٢١٨
٢٣٢
٢٤٥
٢٥٧
٢٦٨
٢٧٩
٢٨٨
٢٩٧
٣٠٤
٣١١
٣١٩
Y
٥
١٠
١٥
٢٠
٢٥
٣٠
٣٥
٤٠
٤٥
٥٠
٥٥
٦٠
٦٥
٧٠
٧٥
٨٠
٨٥
٩٠
٩٥
١٠٠

Page 4
ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺟﺪﻭﻝ ﺍﺳﺘﺨﺮﺍﺝ ﺷﺪﻩ ﻭ ﺑﺎ ﺑﻬﺮﻩ ﮔﻴﺮﻱ ﺍﺯ ﻓﺮﻣﻮﻝ ﺩﺭﻭﻧﻴﺎﺑﻲ ﻻﮔﺮﺍﻧﮋ ، ﺗ
ﺎﺑﻌﻲ ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﺍﺳﺘﺨﺮﺍﺝ ﮔﺮﺩﻳﺪ
.
ﺳﭙﺲ ﻓﺎﺻﻠﻪ
ﭼﻨﺪ ﻧﻘﻄﻪ ﺗﺼﺎﺩﻓﻲ ﺭﻭﻱ ﻳﻚ ﺳﻄﺢ ﺍﺯ ﺩﻭﺭﺑﻴﻦ ﺑﻪ ﻛﻤﻚ ﺍﻳﻦ ﺗﺎﺑﻊ ﻣﺤﺎﺳﺒﻪ ﮔﺮﺩﻳﺪ ﻛﻪ ﺩﺭ ﺟﺪﻭﻝ ﺷﻤﺎﺭﻩ
٢
ﻓﺎﺻﻠﻪ ﻭﺍﻗﻌﻲ ﻭ ﻓﺎﺻﻠﻪ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ
ﺟﻬﺖ ﻣﻘﺎﻳﺴﻪ ﺍﺭﺍﺋﻪ ﮔﺮﺩﻳﺪﻩ ﺍﻧﺪ
.
ﺟﺪﻭﻝ ﺷﻤﺎﺭﻩ
٢
ﻓﺎﺻﻠﻪ ﺩﺭ ﺗﺼﻮﻳﺮ
(
ﭘﻴﻜﺴﻞ
)
١٧٦
٢٤٧
٢٩٩
ﻓﺎﺻﻠﻪ ﻣﺤﺎﺳﺒ
ﻪ ﺷﺪﻩ
(
Cm
)
٥٣
/
٣٦
٧٨
/
٦٠
١٨
/
٨٦
ﻓﺎﺻﻠﻪ ﻭﺍﻗﻌﻲ ﺑﺎ ﺩﻭﺭﺑﻴﻦ
(
Cm
)
٣٦
٦٠
٨٥
ﺧﻄﺎﻱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ
(
ﺩﺭ ﺻﺪ
)
%
٠٨
٠/
%
٢٠
٠/
%
٤٤
٠/
ﻫﻤﺎﻧﮕﻮﻧﻪ ﻛﻪ ﺩﺭ ﺟﺪﻭﻝ ﺷﻤﺎﺭﻩ
٢
ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ ، ﺍﻳﻦ ﺭﻭﺵ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﻧﻘﺎﻃﻲ ﻛﻪ ﺩﺭ ﺩﺍﻣﻨﻪ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﻗﺮﺍﺭ ﺩﺍﺭﻧﺪ ، ﺑﺎ ﺩﻗﺖ
ﺑﺎﻻﻳﻲ ﻋﻤﻞ ﻣﻲ ﻛﻨﺪ
.
ﺍﻣﺎ ﺩﺭ ﺧﺎﺭﺝ ﺍﺯ ﺍﻳﻦ ﻣﺤﺪﻭﺩﻩ ، ﺩﻗﺖ ﻣﺤﺎﺳﺒﻪ ﺍﻓﺖ ﭘﻴﺪﺍ ﻣﻲ ﻛﻨﺪ ﻭ ﻋﻤﻼ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﺭﻭﺵ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻓﺎﺻﻠﻪ ﻧﻘﺎﻃﻲ
ﺩﺭ ﺧﺎﺭﺝ ﺍﺯ ﺩﺍﻣﻨﻪ ﻣﺰﺑﻮﺭ ﻏﻴﺮﻋﻤﻠﻲ ﺧﻮﺍﻫﺪ ﺑﻮﺩ
.
ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻭﻳﮋﮔﻴﻬﺎﻱ ﺭﻭﺵ ﺫﻛﺮ ﺷﺪﻩ ، ﺍﺯ ﺁﻥ ﻣﻲ ﺗﻮﺍﻥ ﺩﺭ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﻛﻪ ﺩﺭ ﺑﺮﺩ ﻣ
ﺤﺪﻭﺩﻱ ﻋﻤﻞ ﻣﻲ ﻛﻨﻨﺪ ، ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩ
.
ﻣﺜﻼ ﺍﮔﺮ ﻗﺮﺍﺭ ﺑﺎﺷﺪ ﻛﻪ ﺳﻴﺴﺘﻤﻲ ﺗﺪﺍﻓﻌﻲ ﻃﺮﺍﺣﻲ ﺷﻮﺩ ﻛﻪ ﺩﺭ ﻣﻘﺎﺑﻞ ﺍﺷﻴﺎﺀ ﻣﺘﺤﺮﻛﻲ ﻛﻪ ﺩﺭ ﻣﺤﺪﻭﺩﻩ ﻣﻌﻴﻨﻲ ﻗﺮﺍﺭ ﻣﻲ ﮔﻴﺮﻧﺪ ، ﻭﺍﻛﻨﺶ ﻧﺸﺎﻥ ﺩﻫﺪ ،
ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﺭﻭﺵ ﻣﻨﺎﺳﺐ ﺧﻮﺍﻫﺪ ﺑﻮﺩ
.
ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﺭﻭﺵ ﻣﺤﺪﻭﺩﻳﺘﻲ ﺍﺯ ﻧﻈﺮ ﺑﻌﺪ ﻭ ﻋﻤﻖ ﻧﺪﺍﺭﺩ ﻭ ﺑﺮﺍﻱ
ﻫﺮ ﺑﺎﺯﻩ ﺍﻱ ﻗﺎﺑﻞ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺳﺖ ، ﺗﻨﻬﺎ ﺑﺎﻳﺪ ﺑﻪ ﺍﻳﻦ ﻧﻜﺘﻪ ﺗﻮﺟﻪ ﺩﺍﺷﺖ ﻛﻪ
ﻣﺤﻴﻂ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﺭﺍ ﻣﺘﻨﺎﺳﺐ ﺑﺎ ﺑﺎﺯﻩ ﻣﺬﻛﻮﺭ ﺗﻨﻈﻴﻢ ﻧﻤﻮﺩ
.
ﺑﺪﻳﻦ ﮔﻮﻧﻪ ﻛﻪ ﺧﻄﻮﻁ ﻣﺤﻴﻂ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﺷﻮﻧﺪ ﻛﻪ ﺗﻤﺎﻣﻲ ﺍﻳﻦ
ﺣﻴﻄﻪ ﺭﺍ ﭘﻮﺷﺶ ﺩﻫﻨﺪ
.
ﻃﺒﻴﻌﻲ ﺍﺳﺖ ﻫﺮﭼﻪ ﺗﻌﺪﺍﺩ ﺍﻳﻦ ﻧﻘﺎﻁ ﺑﻴﺸﺘﺮ ﺷﻮﺩ ، ﺩﻗ
ﺖ ﻣﺤﺎﺳﺒﺎﺕ ﻧﻴﺰ ﺑﺎﻻﺗﺮ ﺧﻮﺍﻫﺪ ﺭﻓﺖ
.
ﻧﺘﻴﺠﻪ ﮔﻴﺮﻱ
ﺭﻭﺷﻲ ﻛﻪ ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﻣﻌﺮﻓﻲ ﮔﺮﺩﻳﺪ ، ﺍﺯ ﺟﻬﺎﺕ ﻣﺨﺘﻠﻔﻲ ﻧﻈﻴﺮ ﺳﺎﺩﮔﻲ ، ﺩﻗﺖ ، ﻋﺪﻡ ﻧﻴﺎﺯ ﺑﻪ ﺍﺑﺰﺍﺭ ﻛﻤﻜﻲ ﻭ ﻋﺪﻡ ﻭﺍﺑﺴﺘﮕﻲ ﺑﻪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ
ﺩﻭﺭﺑﻴﻦ ﺩﺍﺭﺍﻱ ﻣﺰﻳﺖ ﻫﺎﻳﻲ ﻧﺴﺒﺖ ﺑﻪ ﺭﻭﺷﻬﺎﻱ ﻗﺒﻠﻲ ﻣﻲ ﺑﺎﺷﺪ
.
ﺍﺯ ﻣﺤﺪﻭﺩﻳﺖ
ﻫﺎﻱ ﺍﻳﻦ ﺭﻭﺵ ﻣﻲ ﺗﻮﺍﻥ
ﺑﻪ ﻭﺍﺑﺴﺘﮕﻲ ﺁﻥ ﺑﻪ ﺍﺭﺗﻔﺎﻉ ﻭ ﺯﺍﻭﻳﻪ ﺩﻭﺭﺑﻴﻦ
ﻭ ﻧﻴﺰ ﺩﺍﻣﻨﻪ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻭﻟﻴﻪ ﺍﺷﺎﺭﻩ ﻛﺮﺩ
.
ﺍﻳﻦ ﺭﻭﺵ ﺑﺮﺍﻱ ﻛﺎﺭﺑﺮﺩﻫﺎﻳﻲ ﻛﻪ ﺩﺭ ﺁﻥ ﻓﺎﺻﻠﻪ ﻳﺎﺑﻲ ﺩﺭ ﺑﺎﺯﺓ ﻣﺤﺪﻭﺩ ﻭ ﺑﺎ ﺩﻗﺖ ﺑﺎﻻ ﻣﻮﺭﺩ ﻧﻴﺎﺯ ﺍﺳﺖ ، ﻣﻔﻴﺪ ﻭ ﻛﺎﺭﺍ ﺧﻮﺍﻫﺪ ﺑﻮﺩ
.
ﻣﻨﺎﺑﻊ ﻭ ﻣﺮﺍﺟﻊ
,”1] N. Yamaguti , Sh. Oe and K. Terada , “A Method of Distance Measurement by Using Monocular Camera]
The 36th .SICE Annual Conference , 1997
2] H. Guo and Y. Lu , “Depth Detection of Targets in a Monocular Image Sequence” , 18]th Digital Avionic
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.Intelligent Vehicles Symposium , 2000
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.International Conference on Computer Vision and Pattern Recognition , 1988
, “5] M. Takatsuka and et al. , “Low-Cost Interactive Active Monocular Range Finder]
.IEEE Computer Society Conference on Computer Vision and Pattern Recognition , 1999
, “6] J.M. Mathews , “Numerical Methods for Mathematics, Science and Engineering]
.printice-Hall, 1992