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Chapter 4 Image Enhancement in the Frequency Domain

4.1??. ?????????????????????????????sin?/?cos??(??4.1),??????????,??????????(Fourier series)???????????(????????????)???????????????sin?/?cos????????????????????????(Fourier transform)?. . ??????????????:????????????????,?????????????????(??),?????????????????????????,????????????????????

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Chapter 4 Image Enhancement in the Frequency Domain

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    2. 4.1?? ???????????????????????? ?????sin?/?cos??(??4.1),???????? ??,??????????(Fourier series)? ??????????(????????????)?? ?????????????sin?/?cos??????? ?????????????????(Fourier transform) ?

    3. ??????????????:????????? ???????,???????????????? ?(??),???????????????????? ?????,?????????????????? ??????????????????????

    4. 4.2???????????? 4.2.1 ????????????? ?????? ????? (4.2-1) ?? ?? ,????????????? ?? (4.2-1) ?????????????(Fourier transform pair)

    5. ????????????? ? (4.2-3) ??????????? (4.2-4)

    6. ????????????, ? ???????? (4.2-5) ???????(discrete Fourier transform, DFT)???? ???????? ?? ,?????DFT??????: (4.2-6)

    7. ??????????? ??????????? ?????(??)???????? ? ??(4.2-5)?? ,??? ???? ???,? ?? ??????????? ??? ?????????????(?????4.6???)? ?????????????????

    8. Eulers?? (4.2-7) ??(4.2-5),? (4.2-8) ?????????????????? ?? ????????( ??)????????(frequency domain)?

    9. ????,?(4.2-5)?(4.2-8)???????????? ??????,???????: (4.2-9) ?? (4.2-10) ??????????(magnitude)???(spectrum),? (4.2-11) ????(phase angle)?????(angle spectrum)?

    10. ?(4.2-10)?(4.2-11)??, ? ??? ??? ???????????????????????? ?(power spectrum),???????????: (4.2-12) ????(spectrum density)?????????????

    11. ??4.1:?????????????? ??4.2?????????(1)?? ???????? ??,????????????(2)???????? ,??????????????

    12. ?(4.2-5)???????,?? ,?? ,????????????? ????????? ?????????? ?? ?????? ? ????????(????), ????????? ???? (???? ??) ? ?? ????

    13. ????? ?,????? ?? ? ?? (4.2-13) ??? ???,?????????????? (4.2-14) ?? ?? ? ??????? (4.2-15)

    14. 4.2.2???DFT????? ?? ?????(??) ????????? ???? (4.2-16) ?? ??,?? ,????????? (4.2-17) ??

    15. (4.2-16)?(4.2-17)??????????(DFT)???? ? ???(transform)?????(frequency variable),? ? ???(spatial)?????(image variable)? ?????????? ?????????: (4.2-18) (4.2-19) (4.2-20) ?? ? ????????

    16. ???????????????????????? ? (4.2-21) ?? ??????????,????? ?????????[?? ]?? ? ? ????2-D?DFT??? ?????,???? ???????????(frequency rectangle)????? ???????????,???? ????

    17. ? ????(4.2-16)?? (4.2-22) ??????? ????????,?? ?????,?????????????????? ???

    18. ?? ???,???????????? (4.2-23) ???*????????????????????? (4.2-24) ??????????????? ??????,????????????????: (4.2-25) (4.2-26)

    19. ??4.2:?????????????? ???????20X40?????????512X512?? ????,???????,??????????? ?? ???????4.3(b)??(????????? ??????????)

    20. 4.2.3??????? ??????????: ????(4.2-16)???, ??????? ?? ??,????????????????????? ?????,?????????????????? ???????????????????????? ??????? ?????????????? ???????????,???????????? ???????????????????????? ????????,????

    21. ??4.3:??????????,????????? ? ?4.4(a)????????????????????? ??,??2500???????????? ??? ???????????????????????? ????????????????

    22. ??????????: ??????????????????????: 1.?????? ?????,?(4.2-21)????? ?? 2.?? ,??(1)?????DFT? 3.?????? ?? ? 4.??(3)?????DFT? 5.??(4)??????? 6.? ??(5)????

    23. ?????[??????(filter transfer function)? ??????]?????????????????, ????????? ?????????,??????????? (4.2-27) ????, ?????,???????????? ??????,?????, ?????????? ? ????????,???????????? (zero-phase-shift)????

    24. ?????????? ??????????? ?: (4.2-28) ???????????????? ?????? ??????

    25. ??????????????????????? ????,??????????????????? ??????????????????????,? ????????????????

    26. ??????????: ??????????????????,??(4.2-22) ?,???????? ??,???????? ??????????????,? (4.2-29) ???????????? ??,?????? ???????????

    27. ?????????????(notch filter),????? ???????(notch)?????,??????? ?4.4(a)???????4.6?,??????????? ?????????,?????????????? ???(???????????,???????,? ??????????,????????????, ??????)

    28. ??????????????????,????? ???,?????????: *?????:????,????????????? *?????:????,????????????? ?4.7?????4.4(a)??????????????? ????????,??????????????? ?????????????????????4.8?

    29. 4.2.4?????????????? ???????????????????(convolution theorem),??? ?????,????: (4.2-30) (?????????)

    30. ? ? ???????? (4.2-31) ???????????????????????? ? ?? (4.2-32)

    31. ????? ???? ????(impulse function) ??? ,?????????: (4.2-33) ???? ??? ???????? ????,????? ?,?????? ?

    32. ?(3.2-33)???,???????????????? ??????????,????????(sifting property)??? (4.2-34) ??(4.2-16)?,????????????????? ?????: (4.2-35)

    33. ??? ,???(4.2-30)?????? (4.2-36) ????? (4.2-37)

    34. ????????????,??????????? ??????,???????????????,? ?,?????????????????????? ?? ????????????????????????

    35. ???????????????,???????? ??????,????????????????? ?????? ? ????,? (4.2-38) ?? ?????????,??????????? ?: (4.2-39)

    36. ??????????????????????: ??(??????)??????,??????? ????? ???????,? ?? ,??? ,? ??????? ( ??????) ??????????4.9?

    37. ???????????????????????? ?,????????????: (4.2-40) (4.2-41) ?? ???????????4.9(b)?4.9(d)?

    38. 4.3????????? ????????????,??????????? ?? (4.3-1) ?? ???????????? ???? ????????,??????????? ? ?????????????: (1)???(????) (2)????(??????) (3)?????(????)

    39. 4.3.1??????? ????????????: (4.3-2) ?? ??????????? ????????????? ,??????? ,?(4.2-21),?????????? ,?? ?? ???????????? (4.3-3)

    40. ?4.10???? ?(a)??????(b)????? ??(c)????? ?????????????? (cutoff frequency),?? ??4.10?????? (??:??????????????????)

    41. ???????????????????????? ???????? ??? (4.3-4) ?? ?(4.2-20)??,????????,??? ??????????? ???? ?????? (4.3-5) ???????????? ????

    42. ??4.4:??DFT??????????????? ?4.11???????????,?????????5 ?15 ?30 ?80??230???????4.12,???? ??????????????? ???4.12(c)?(e)??????(ringing)??,???? ????????,????????

    43. ?????????????????,?????? ?????,????????????????ILPF ?????? ???? ?????: ????????? ???? ??????????????? ????

    44. ????? ???????????????? ????,??4.13(c),???????? ??????? ???,??????4.13(d)? ???????????????????????? ??

    45. 4.3.2????????? ????? ?????? ??????????? ???????: (4.3-6) ?? ?(4.3-3)????

    46. ??4.5:????????? ????4.15?,?? ,???????????? ????

    47. ????????????????,??????? ???????,???????????????? ???????,??4.16??? ????,???BLPF?????????????? ????????????

    48. 4.3.3??????? ????????(GLPF)?(4.2.4)??????,??? ???(?4.17)??: (4.3-7) ??????????,??? ,? ??? ?????????: (4.3-8) ??(4.3-7)?(4.3-8)????????,??????? ????

    49. ??4.6:?????? ?4.18????(4.3-8)??GLPF????4.18(a)???? ,?? ???4.11(b)?????????,??4.15? ????GLPF?????????????BLPF??? ??,??GLPF???????BLPF???????? ????????????

    50. 4.3.4????????? ???????????????,????,??? ????????????: ???????,????????? ????????? ????????????

    51. ???????,????????: ?4.19??????????????,??????? ????????????,??????????? ???????????????????????? ????????

    52. ????????: ????????????????????,??? ????????????,?4.20????????? ??,?????????,?????,????? ????

    53. ???????????: ?4.21???????????,?????????? ??(VHRR)??,?????????????,?? ???????????????????????? ??????????,???????

    54. 4.4????????? ???????????????????????? ,?????????????????????,? ????????????????(high-pass filtering) ????? ???????????????????????? ?: (4.4-1) ??????; ???????

    55. ???????????????????????, ?4.22???????,?4.23??????????? ????

    56. 4.4.1??????? ????????????(IHPF)???: (4.4-2) ?? ??????????????,?????? ?????????,????ILPF???????? ???????

    57. ???(a)????????????????, ???????,??(c)?????????????

    58. 4.4.2????????? ?????????????????: (4.4-3) ?4.22???????BHPF????????? BLPF??ILPF?????,?????4.24??4.25? ??????????????????,????? ???????????,?????????

    59. 4.4.3??????? ???????????: (4.4-4)

    60. 4.4.4????????? ???? (4.4-5) ?? (4.4-6) ???????????? (4.4-7)

    61. ???????????????????????? ? (4.4-8) ????????????(?? ),?????? ??????? (4.4-9)

    62. ? ????????????????? ????? (4.4-10) (4.4-11) ?4.27?????????????

    63. ??????????????????????? (4.4-12) ???????????,??(4.4-8)??????? ???? ?????? ,?????????????????: (4.4-13)

    64. ??4.7:????????????? ?4.28(a)??3.40(a)????,??(4.4-12)????? ?????4.28(d),??????????????? ????????,??????????????? ?

    65. 4.4.5?????????????????? ???????????????????,???? ???????????,??????????(high- boost filtering)????????(unsharp masking)??? ???? ????:??????????????????? ????? (4.4-14) ???????? ????? ????? ??:

    66. ?????????? (4.4-16) ????(4.4-14)?,???? (4.4-17) ??????????????????? ? =1,??????????????????? ? >1,???????????

    67. ??? (4.4-18) ???(4.4-1)??,???????????????? ???? (4.4-19) ?? ?

    68. ??4.8:?????????? ???4.29(c)(d)?????(4.4-17)?? ?

    69. ???????????????????????? ?,???????????????,?????? ??(high-frequency emphasis)???,???????? ?? (4.4-20) ?? ? ?????0.25?0.5???? ? ?????1.5?2.0??????(4.4-19)?,????? ?,????????????? ,?????,????????

    70. ??4.9:?????? ?4.30(a)?????????????X???,??? ??????,???4.30(c)???????????? ???????????,???????????? ????,??????????,???????? ?,??????4.30(d)?,??????????? ?????????????????

    71. 4.5???? ?2.3.4????????????????????? ????,??????????????????? ??,????????????? ????? ?????????: (4.5-1) ?????????

    72. ?????? (4.5-2) ? (4.5-3) ? (4.5-4) ?? ??? ????? ?

    73. ??????????? ??? (4.5-5) ???????? (4.5-6) ???(4.5-7)?(4.5-8)??(4.5-9)?

    74. ??,?? ????????????,??? (??)????????????,?? ?? (4.5-10) ?? (4.5-11) (4.5-12) ????????????

    75. ???????????4.31?,?????????? ??(homomorphic system)??????,?????? ???(4.5-4)??????????????,???? ?????(homomorphic filter function) ???? ?????????

    76. ???? ????:?????? ????? ????:???? ????? ???????????? ??,??????? ,?????????? ?????????????? ? ?????? >1? <1,??????4.32?????????? (?????????????)

    77. ???,???????????????????, ????????(?? ??? ??????? ???) (4.3-3)

    78. ??4.10:??????? ?????,????????????????,? ?,?4.33(a)?????????????????,? ?????4.33(b)?

    79. 4.6?? 4.6.1???????????????? ?? ?????????? (4.6-1) (4.6-2) ????????????

    80. ?? ?,? ?(4.6-1)??? (4.6-3) (4.6-4)

    81. 2. ???????? ???????? (4.6-5) (4.6-6) (??????????????,??????) ??,?? ? ??? (4.6-7) (4.6-8)

    82. ?? ??????? ? ???? ? ?????,? ,? ????????????,?? ??? ?????????

    83. 4. ????????? ????????????????: (4.6-10) ????????? (4.6-11) ?????4.2????,???????? (4.6-12) ??????????????? (4.6-13)

    84. ?4.34(a)?????????,??????? ?????????(4.6-10)?(4.6-13)?????? ,??????? ?????? ?? ?,??????????????????,??? ?4.34(a)??(b),???? ??? ???????,?4.34(c)????????,???? ?????,?????????4.34(d)?

    85. 5. ???? (4.2-16)??????????????????? ? (4.6-14) ?? (4.6-15)

    86. ????????,??????????????? ????,??????????????????? ?????????,????????4.35?? (?????????????)

    87. 4.6.2?????????????????? ?????????,?????????????? ???????,????4.2.1???????: (4.6-16) (4.6-17) ??(4.6-17)??????????? ?? (4.6-18)

    88. ?(4.6-16)?(4.6-18)??????,? ?????? ????????????????? ??, ???????????? ? ???? (4.6-19) ??????????????,? ? ?? ??(????),?????????????,??? ???????

    89. ???????????,? ???????? ???,??????4.35?????,??????? ?? ???????????? ????? ,?? ?????????,???????,? ???4.2.1?4.2.2????,??????????? ???,??????????????

    90. 4.6.3???????:????? ?4.2.4????,???????,???????? ??????????,????????????? ???????,????????????? ?4.36?????????,????????4.2-30? ???????????: (4.6-20)

    91. ??(a)~(e)??????????,????????? ?????,???????????(f)~(j)????? ??????????,????????????? ????? ??4.36(j)???,??[0,100]?[400,500]??4.36(e)? ???,????????,??????????? ????,????????? ????? ???????,?????????

    92. ????????,?? ??? ?? ??? ?,??????????????,??????? ??,?? ,????????(extended)??? (padded)????? (4.6-21) (4.6-22)

    93. ?????? ,???????????, ??4.36???????,????????? (wraparound error)? ?? ??????? ??????? ??4.37?????????( ),?? ?

    94. ?????????????????,?????? ???? ???? ,??? ????? ??? ?? ??? ,?: (4.6-23) (4.6-24) ? (4.6-25) (4.6-26)

    95. ????????????,??????????? ???????????????????????, ??????????,????????????? ?????????????,????????,? ?????4.38,??(a)?????????,???? ????,?(b)(c)??????

    96. ????????? ???,????????? ?????????,?????????? ???????????????????????, ???????????????????????, ?????????????????,?????? ?????????????

    97. ?4.39???????4.12(c)???????????? ??(?????????)?

    98. ?4.40?????????????????????? ??,??4.39??????4.12(a)????????? ?????4.40,???????????

    99. 4.6.4????????? ?4.2.4???????,????4.6.3??????? ?,??,??????????(correlation)???? ????? ??? ????? ? ?????? ??? : (4.6-27) ?? (4.6-28) (4.6-29)

    100. ?????? ? ?????? (4.6-30) ?? ? ?????,??????????(??), ?? ??????(4.6-27)?????????? ?????,?????????????????? ???,???? ???????

    101. ??????????????,????????? ?????(correlation theorem): (4.6-31) (4.6-32) ????????????

    102. ??????????????,????????? ??????????(matching)? ?????????? ????(template)? ???????? ????????????? ??,????? ????,??? ? ??????????????????

    103. ???(cross correlation):????,???????? ??? ???(autocorrelation):???????? ?????,???????,? (4.6-33) (4.6-34)

    104. ??4.11:???? ?4.41(a)???(b)???,???????????? ???(c)(d),?????????(e)???????(f) ??,???????????????????

    105. 4.6.5???????????? ????????????????????4.1?,? ??????????????????????

    106. 4.6.6??????? DFT??????????????????????? ???(FFT),?(4.2-5)????? ???????? ??,?? ??????/????,?FFT? ????????????? ?????FFT???????????????? (successive doubling method)? (4.6-35) ?? (4.6-36)

    107. ? ???????: (4.6-37) ?? ??????,?? (4.6-38) ?? ????????? (4.6-39)

    108. ??? (4.6-40) ??? (4.6-41) (4.6-42)

    109. ??(4.6-40)???? (4.6-43) ??? ,???? (4.6-44)

    110. ?????????,?? ??????????? ?????????????,?(4.6-43)?(4.6-44)? ?? ????????(4.6-41)?(4.6-42)????? ? ????,????(4.6-43)??? ? ????????(4.6-44)???

    111. ??????????????,? ? ??? ??????????? ? ??1????2??? ??4????8??? ??12????24???

    112. ???????FFT???????: (4.6-45) (4.6-46) ?? ???? (4.6-47) (4.6-48)

    113. FFT????DFT???????????? (4.6-49) ???? ,??????? ???(4.6-49): (4.6-50) ????4.42?????? ????????

    114. 4.6.7?????????? ???????????????????????? ,???????????????? ?,??? ??????? ???????,?????? ????? (???)?DFT,????DFT?????? ??????????FFT?????4.35?4.6.2??? ?????????

    115. ??

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