Теория пары снимков

16

Теория пары снимков

1. Формулы связи координат точек местности и их изображений на тереопаре
снимков (прямая фотограмметрическая засечка)

На рис.1 показана стереопара снимков Р1 и Р2, на которых точка местности
М изобразилась соответственно в точках m1 и m2. Будем считать, что
элементы внутреннего и внешнего ориентирования снимков известны.

picscalex100010009000003540000000000120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02200220011200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffe0000000c60100000b00000026060f000c004d61746854797065
000050000a00000026060f000a00ffffffff010000000000030000000000 Рис.1 .

Выведем формулы связи координат точек местности и координат их
изображений на стереопаре снимков.

Из рис.1 следует, что векторы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определяют соответственно положение точки местности М и центра
проекции S1 снимка Р1 относительно начала системы координат объекта
OXYZ. Вектор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 определяет положение
центра проекции S2 снимка Р2 относительно центра проекции S1.

Векторы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 определяют положение точек m1 и М относительно центра проекции S1.
Векторы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 определяют положение точек m2 и М относительно центра проекции S2.

Из рис.1 следует, что
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 (1 )

Так как векторы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 коллинеарны, то
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 ; ( 2)

где N – скаляр.

С учетом ( 2) выражение (1.8.1) будет иметь вид
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. ( 3)

В координатной форме выражение (1.7.3) будет иметь вид

picscalex1000100090000038d0200000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c024007000e1200000026060f001a00ffffffff00001000
0000c0ffffffb8ffffffc00d0000f80600000b00000026060f000c004d61746854797065
0000a00110000000fb0280fe0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320ab2051d0d01000000f70008000000320a42041d0d0100
0000f70008000000320ad2021d0d01000000f70008000000320aa8061d0d01000000f800
08000000320adc011d0d01000000f60008000000320ab205880a01000000e70008000000
320a4204880a01000000e70008000000320ad202880a01000000e70008000000320aa806
880a01000000e80008000000320adc01880a01000000e60008000000320a2a06550c0100
0000a20008000000320aea03850c01000000a20008000000320aaa016d0c01000000a200
08000000320a00043d08010000002b0008000000320a80055f0701000000f70008000000
320a10045f0701000000f70008000000320aa0025f0701000000f70008000000320ada06
5f0701000000f80008000000320aaa015f0701000000f60008000000320a80054c040100
0000e70008000000320a10044c0401000000e70008000000320aa0024c0401000000e700
08000000320ada064c0401000000e80008000000320aaa014c0401000000e60008000000
320a00042103010000003d0008000000320ab2052b0201000000f70008000000320a4204
2b0201000000f70008000000320ad2022b0201000000f70008000000320aa8062b020100
0000f80008000000320adc012b0201000000f60008000000320ab2052e0001000000e700
08000000320a42042e0001000000e70008000000320ad2022e0001000000e70008000000
320aa8062e0001000000e80008000000320adc012e0001000000e60017000000fb0220ff
0000000000009001000000cc0402001054696d6573204e657720526f6d616e2043797200
cce1040000002d01010004000000f001000008000000320aa006510c0100000031000800
0000320a6004510c01000000310008000000320a2002690c01000000310008000000320a
a006230601000000530008000000320a6004230601000000530008000000320a20023b06
01000000530017000000fb0280fe0000000000009001000000cc0402001054696d657320
4e657720526f6d616e2043797200cce1040000002d01000004000000f001010008000000
320a4006660b010000005a0008000000320a0004600b01000000590008000000320ac001
480b01000000580008000000320a00046f09010000004e0008000000320a40062a050100
00005a0008000000320a0004240501000000590008000000320ac0010c05010000005800
08000000320a40060c01010000005a0008000000320a0004ee0001000000590008000000
320ac001ee0001000000580017000000fb0260ff0000000000009001000000cc04020010
54696d6573204e657720526f6d616e2043797200cce1040000002d01010004000000f001
000008000000320ad806930601000000310008000000320a980493060100000031000800
0000320a5802ab060100000031000a00000026060f000a00ffffffff0100000000001000
0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
000004000000f0010100030000000000 ; ( 4)

где X1’,Y1’,Z1’ –координаты вектора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 в системе
координат объекта OXYZ.
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.

Найдем значение N, входящее в выражение ( 4). Из рис.1 следует, что

picscalex100010009000003270100000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600200081200000026060f001a00ffffffff00001000
0000c0ffffffa8ffffffc0070000080200000b00000026060f000c004d61746854797065
0000500017000000fb0280fe0000000000009001000000cc0402001054696d6573204e65
7720526f6d616e2043797200cc83040000002d01000008000000320ac001c80601000000
420008000000320ac001ae0301000000520008000000320ac0013a000100000052001700
0000fb0220ff0000000000009001000000cc0402001054696d6573204e657720526f6d61
6e2043797200cc83040000002d01010004000000f001000008000000320a2002ca040100
0000310008000000320a20026f0101000000320011000000fb0280fe0000000000009001
00000002040200104d542045787472610002040000002d01000004000000f00101000800
0000320a7600f20601000000720008000000320a7600e70301000000720008000000320a
7600730001000000720010000000fb0280fe000000000000900100000002000200105379
6d626f6c0002040000002d01010004000000f001000008000000320ac001a80501000000
2d0008000000320ac0017602010000003d000a00000026060f000a00ffffffff01000000
000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc0400
00002d01000004000000f0010100030000000000;

или с учетом (2)

picscalex1000100090000031f0100000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600260081200000026060f001a00ffffffff00001000
0000c0ffffffa8ffffff20080000080200000b00000026060f000c004d61746854797065
0000500017000000fb0280fe0000000000009001000000cc0402001054696d6573204e65
7720526f6d616e2043797200cc83040000002d01000008000000320ac0012e0701000000
420008000000320ac001ba03020000004e7208000000320ac0013a000100000052001700
0000fb0220ff0000000000009001000000cc0402001054696d6573204e657720526f6d61
6e2043797200cc83040000002d01010004000000f001000008000000320a200230050100
0000310008000000320a20026f0101000000320011000000fb0280fe0000000000009001
00000002040200104d542045787472610002040000002d01000004000000f00101000800
0000320a7600580701000000720008000000320a7600730001000000720010000000fb02
80fe0000000000009001000000020002001053796d626f6c0002040000002d0101000400
0000f001000008000000320ac0010e06010000002d0008000000320ac001760201000000
3d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000
bc02000000cc0102022253797374656d00cc040000002d01000004000000f00101000300
00000000. ( 5)

Так как векторы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 коллинеарны, то их векторное произведение
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 . ( 6)

С учетом (5) выражение ( 6) можно представить в виде
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;

Или

picscalex100010009000003cf0100000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c026002a00b1200000026060f001a00ffffffff00001000
0000c0ffffffa8ffffff600b0000080200000b00000026060f000c004d61746854797065
0000500010000000fb0205fedd00000000009001000000020002001053796d626f6c0002
040000002d01000008000000320abe01650101000000280010000000fb0205fedd000000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320abe01470501000000290010000000fb0273fddd0000000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320abf01
3f0701000000280010000000fb0273fddd00000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320abf010f0b010000002900
17000000fb0220ff0000000000009001000000cc0402001054696d6573204e657720526f
6d616e2043797200cccc040000002d01000004000000f001010008000000320a20025c0a
01000000320008000000320a2002940401000000320008000000320a20023f0201000000
310017000000fb0280fe0000000000009001000000cc0402001054696d6573204e657720
526f6d616e2043797200cccc040000002d01010004000000f001000008000000320ac001
f30901000000720008000000320ac001a10701000000420008000000320ac0012b040100
0000720008000000320ac001ef0101000000720008000000320ac0014600010000004e00
11000000fb0280fe000000000000900100000002040200104d5420457874726100020400
00002d01000004000000f001010008000000320ac400e70901000000720008000000320a
7600cb0701000000720008000000320ac4001f0401000000720008000000320ac400e301
01000000720010000000fb0280fe0000000000009001000000020002001053796d626f6c
0002040000002d01010004000000f001000008000000320ac001cd0801000000b4000800
0000320ac0010b06010000003d0008000000320ac001050301000000b4000a0000002606
0f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc0102
022253797374656d00cc040000002d01000004000000f0010100030000000000 . ( 7)

В координатной форме выражение (7) имеет вид
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или
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 , ( 8),

где:

picscalex100010009000003e00000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c026002c0031200000026060f001a00ffffffff00001000
0000c0ffffffb4ffffff80030000140200000b00000026060f000c004d61746854797065
0000500017000000fb0280fe0000000000009001000000cc0402001054696d6573204e65
7720526f6d616e2043797200cc83040000002d01000008000000320ac001b60201000000
6b0008000000320ac0012602010000002c0008000000320ac001b701010000006a000800
0000320ac001e800010000002c0008000000320ac001550001000000690011000000fb02
80fe000000000000900100000002040200104d542045787472610002040000002d010100
04000000f001000008000000320a6a00cb0201000000720008000000320a6a007e010100
0000720008000000320a6a0040000100000072000a00000026060f000a00ffffffff0100
0000000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc
040000002d01000004000000f0010100030000000000- орты, совпадающие с осями
координат X,Y,Z системы координат объекта OXYZ;

BX, BY, BZ, X1’, Y1’, Z1’, X1’, Y1’, Z1’ – координаты векторов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 в системе
координат объекта OXYZ.
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 ,

где i – номер снимка, а
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. (9)

Так как векторы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 коллинеарны ( так как векторы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 компланарны), значение N можно
найти как отношение их модулей, то есть
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 ; (10)

В координатной форме выражение (10) с учетом (8) имеет вид
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; (11)

У коллинеарных векторов отношение их координат равно отношению их
модулей, поэтому можно записать, что:

picscalex1000100090000033a05000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02200de0201200000026060f001a00ffffffff000010000000c0ffffff
a8ffffffa0200000c80c00000b00000026060f000c004d61746854797065000020030800
0000fa0200001000000000000000040000002d0100000500000014021402260305000000
130214029c0a1c000000fb0205fee300000000009001000000020002001053796d626f6c
007740000000c80e0ae21643c7771f43c77720c0c97700003000040000002d0101000800
0000320a72022b1d0100000028791c000000fb0205fee300000000009001000000020002
001053796d626f6c007740000000d70e0abc1643c7771f43c77720c0c977000030000400
00002d01020004000000f001010008000000320a7202651f010000002979050000001402
8006260305000000130280065a0b050000001402ec0a2603050000001302ec0a040b1c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01010004000000f00102000900
0000320a4c0b2a1e040000002e31342908000000320a4c0be81d01000000203108000000
320a4c0b761d0100000028310b000000320a4c0be21a0700000020202020202020030c00
0000320a4c0b22170a000000202020202020202020200c000000320a4c0b62130a000000
202020202020202020200c000000320a4c0ba20f0a000000202020202020202020200c00
0000320a4c0be20b0a0000002020202020202020202008000000320a4c0ba60b01000000
2e2008000000320a4c0b040b02000000202009000000320ae0063e1e040000002e313329
08000000320ae006fc1d01000000203108000000320ae0068a1d0100000028310b000000
320ae006f61a0700000020202020202020030c000000320ae00636170a00000020202020
2020202020200c000000320ae00676130a000000202020202020202020200c000000320a
e006b60f0a000000202020202020202020200c000000320ae006f60b0a00000020202020
20202020202008000000320ae006a20b010000003b2008000000320ae0065a0b01000000
202008000000320a7402d91d02000000313208000000320a7402a91d0100000020320b00
0000320a7402981a0700000020202020202020030c000000320a7402d8160a0000002020
20202020202020200c000000320a740218130a000000202020202020202020200c000000
320a7402580f0a000000202020202020202020200c000000320a7402980b0a0000002020
202020202020202008000000320a7402440b010000003b2008000000320a74029c0a0200
000020201c000000fb0220ff0000000000009001000000000402001054696d6573204e65
7720526f6d616e001643c7771f43c77720c0c97700003000040000002d01020004000000
f001010008000000320adc0c130a01000000312008000000320adc0c0309010000003220
08000000320adc0cd00501000000322008000000320adc0cb80401000000312008000000
320ab60a5f0a01000000322008000000320ab60aa50501000000322008000000320a7008
860a01000000312008000000320a70082e0901000000322008000000320a7008fb050100
0000322008000000320a70089b0401000000312008000000320a4a06b50a010000003220
08000000320a4a06ed0501000000322008000000320a04049d0901000000312008000000
320a0404450801000000322008000000320a04049c0501000000322008000000320a0404
3c0401000000312008000000320ade01f70901000000322008000000320ade01b9050100
000032201c000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e001643c7771f43c77720c0c97700003000040000002d01010004000000
f001020008000000320a7c0c6a0901000000592008000000320a7c0ced07010000005820
08000000320a7c0c0e0501000000592008000000320a7c0cbb0301000000582008000000
320a560a490901000000582008000000320a560ab00701000000422008000000320a560a
e30401000000592008000000320a560a4c0301000000422008000000320a4c0b4c000100
00004e2008000000320a1008b309010000005a2008000000320a10081808010000005820
08000000320a10080f05010000005a2008000000320a10089e0301000000582008000000
320aea059f0901000000582008000000320aea05f80701000000422008000000320aea05
0105010000005a2008000000320aea054c0301000000422008000000320ae0064c000100
00004e2008000000320aa403ca08010000005a2008000000320aa4038307010000005920
08000000320aa403b004010000005a2008000000320aa403930301000000592008000000
320a7e01350901000000592008000000320a7e01c40701000000422008000000320a7e01
cd04010000005a2008000000320a7e014c0301000000422008000000320a74024c000100
00004e201c000000fb0220ff0000000000009001010000000402001054696d6573204e65
7720526f6d616e001643c7771f43c77720c0c97700003000040000002d01020004000000
f001010008000000320ab60a820801000000592008000000320ab60a3d04010000005820
08000000320a4a06db08010000005a2008000000320a4a063d0401000000582008000000
320ade01a708010000005a2008000000320ade011e040100000059201c000000fb0280fe
0000000000009001000000020002001053796d626f6c007740000000c80e0ae51643c777
1f43c77720c0c97700003000040000002d01010004000000f001020008000000320a660c
680a01000000a22008000000320a660c0f0901000000a22008000000320a7c0caf060100
00002d2008000000320a660c0c0601000000a22008000000320a660cdd0401000000a220
08000000320a400a6b0a01000000a22008000000320a560a8406010000002d2008000000
320a400ae10501000000a22008000000320a4c0be001010000003d2008000000320afa07
ab0a01000000a22008000000320afa073a0901000000a22008000000320a1008da060100
00002d2008000000320afa07070601000000a22008000000320afa07c00401000000a220
08000000320ad405c10a01000000a22008000000320aea05cc06010000002d2008000000
320ad405f90501000000a22008000000320ae006e001010000003d2008000000320a8e03
c20901000000a22008000000320a8e03810801000000a22008000000320aa4037b060100
00002d2008000000320a8e03a80501000000a22008000000320a8e03910401000000a220
08000000320a6801330a01000000a22008000000320a7e019806010000002d2008000000
320a6801c50501000000a22008000000320a7402e001010000003d200a00000026060f00
0a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc01020222
53797374656d000000000a0021008a010000000002000000fcf312002942c77704000000
2d01020004000000f0010100030000000000

Таким образом, если известны элементы внутреннего и внешнего
ориентирования стереопары снимков и измерены на этих снимках координаты
соответственных точек x1,y1 и x2,y2, то сначала надо определить по одной
из формул ( 12)-( 14) значение скаляра N, а затем по формуле ( 4)
вычислить координаты точки местности X,Y,Z.

2. Формулы связи координат точек местности и координат их изображений на
стереопаре снимков идеального случая съемки

В идеальном случае съемки угловые элементы ориентирования снимков
стереопары 1=1=1=2=2=2=0, а базис фотографирования параллелен оси Х
системы координат объекта OXYZ.

В этом случае координаты базиса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будут равны BX=B,
BY=BZ=O (B-модуль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).

Примем, что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, то есть начало системы координат объекта
OXYZ совмещено с точкой S1), f1=f2=f, a x0i=y0i=0.

Так как угловые элементы ориентирования снимков равны нулю, то
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,

а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,

где i – номер снимка.

При этом выражение (1 .13) примет вид
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 , (1)

а выражение (1 .4), которое мы представим в виде
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будет иметь вид
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, (2)

а с учетом ( 1)
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 . (3)

Так как из третьего уравнения выражения (3) следует, что

picscalex100010009000003f00000000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02200480051200000026060f001a00ffffffff00001000
0000c0ffffffb8ffffff40050000d80300000b00000026060f000c004d61746854797065
0000e00009000000fa02000010000000000000002200040000002d010000050000001402
000240000500000013020002580105000000140200021004050000001302000234051700
0000fb0280fe0000000000009001000000cc0402001054696d6573204e657720526f6d61
6e2043797200cc83040000002d01010008000000320a8c03450401000000700008000000
320a6e012a0401000000420008000000320a8c03720001000000660008000000320a6e01
6000010000005a0010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01020004000000f001010008000000320a60020203010000002d00
08000000320a6002ca01010000003d000a00000026060f000a00ffffffff010000000000
10000000fb021000070000000000bc02000000cc0102022253797374656d00cc04000000
2d01010004000000f0010200030000000000,

то формулы связи координат (3) можно представить в виде
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(4)

3. Определение координат точек местности по стереопаре снимков методом
двойной обратной фотограмметрической засечки

Для определения координат точек местности по стереопаре снимков методом
прямой фотограмметрической засечки необходимо, чтобы были известны
элементы внешнего ориентирования снимков. В большинстве случаев практики
их значения не известны. В этом случае определение координат точек
местности по стереопаре снимков выполняют методом двойной обратной
фотограмметрической засечки.

Решение задачи по этому методу выполняется в следующей
последовательности:

1. Определяют элементы взаимного ориентирования снимков. Пять элементов
взаимного ориентирования снимков определяют взаимную угловую ориентацию
стереопары снимков и базиса фотографирования. Для их определения
необходимо измерить не менее пяти соответственных точек на стереопаре
снимков;

2. Строят фотограмметрическую модель объекта по измеренным на стереопаре
снимков координатам изображений соответственных точек и значениям
элементов взаимного ориентирования снимков. Построенная модель подобна
сфотографированному объекту, но имеет произвольный масштаб и произвольно
расположена и ориентирована относительно системы координат объекта;

3. Определяют элементы внешнего ориентирования фотограмметрической
модели по опорным точкам. Эти семь элементов определяют масштаб модели,
ее положение и ориентацию относительно системы координат объекта. Для их
определения достаточно трех опорных точек, не лежащих на одной прямой.
По значениям элементов внешнего ориентирования фотограмметрической
модели и элементов взаимного ориентирования можно определить элементы
внешнего ориентирования стереопары снимков;

4. По координатам точек, определенных в системе координат модели, и
элементам внешнего ориентирования модели определяют координаты точек в
системе координат объекта.

4. Условие, уравнения и элементы взаимного ориентирования снимков

На рис. 1 представлена стереопара снимков Р1 и Р2 в положении, которое
они занимали в момент фотографирования.

Любая пара соответственных лучей в этом случае пересекается в точке М
местности и лежит в плоскости, проходящей через базис фотографирования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(баз
исной плоскости).

Очевидно, что в этом случае векторы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, лежащие в
базисной плоскости, компланарны.

Рис. 1

Как известно из аналитической геометрии, смешанное произведение
компланарных векторов равно нулю.
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. ( .1)

Условие компланарности в координатной форме имеет вид:
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 . ( 2)

В уравнении ( 2)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координаты векторов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 в системе
координат фотограмметрической модели ОМХМYMZM, в общем случае
произвольно расположенной и ориентированной.

В дальнейшем эту систему координат будем называть просто системой
координат модели.

Условие ( 2) связывает между собой только направления векторов и
выполняется при любых значениях их модулей. Поэтому значение модуля
вектора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можн
о выбрать произвольно. Направление вектора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опре
деляется двумя независимыми величинами. В качестве этих величин можно
выбрать координаты bz и bу вектора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,
коллинеарного вектору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,
задав величину координаты bx произвольно.

В частном случае величину bx можно выбрать равной 1.

При этом направление вектора
picscalex100010009000003b00000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000280011200000026060f001a00ffffffff00001000
0000c0ffffffa8ffffff40010000a80100000b00000026060f000c004d61746854797065
0000200017000000fb0280fe0000000000009001000000cc0402001054696d6573204e65
7720526f6d616e2043797200cc83040000002d01000008000000320ac0013a0001000000
c20011000000fb0280fe000000000000900100000002040200104d542045787472610002
040000002d01010004000000f001000008000000320a760064000100000072000a000000
26060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc
0102022253797374656d00cc040000002d01000004000000f0010100030000000000буду
т определять величины:
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 и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 .

Выражение (2) в этом случае будет иметь вид:
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 ( 3)

В уравнении (3)
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,

где i – номер снимка, а А’1 – ортогональная матрица, элементы aij
которой являются функциями угловых элементов ориентирования i-го снимка
i’,i’,i’ относительно системы координат модели ОМХМYMZM.

В выражении (3), которое является уравнением взаимного ориентирования в
общем виде, куда кроме координат соответственных точек, измеренных на
стереопаре снимков, и элементов внутреннего ориентирования входят 8
параметров by, bz, 1’, 1’, 1’, 2’, 2’, 2’, которые определяют угловую
ориентацию базиса фотографирования и стереопары снимков относительно
системы координат модели ОМХМYMZM.

Причем параметры 1’ и 2’ определяют поворот снимков стерепары вокруг оси
ХМ, параметры bz, 1’, 2‘ – поворот базиса фотографирования и стереопары
снимков вокруг оси YM, а параметры by, 1’, 2 ‘ – поворот базиса
фотографирования и стереопары снимков вокруг оси ZM.

Однако, из этих 8 параметров только 5 определяют взаимную угловую
ориентацию базиса фотографирования и стереопары снимков.

Условие (3) выполняется при любой ориентации системы координат модели
ОМХМYMZM. Следовательно, ее можно ориентировать таким образом, чтобы 3
из 8 параметров стали равны нулю.

Очевидно, что в общем случае можно сделать равным нулю только один из
параметров, входящих в три группы параметров:

– 1’, 2’;

– bz, 1’, 2‘;

– by, 1’, 2’.

–

Таким образом, в качестве элементов взаимного ориентирования можно
выбрать любую комбинацию из восьми параметров by, bz, 1’, 1’, 1’, 2’,
2’, 2’, кроме комбинаций, в которые одновременно входят две тройки
параметров bz, 1’, 2‘ и by, 1’, 2’, а также пара параметров 1’ и 2’.

Рассмотрим наиболее распространенные системы элементов взаимного
ориентирования:

Система 1’, 1’, 2’, 2’, 2’. Если принять при этом, что by=bz= 1’=0, то
уравнение (3) имеет вид:
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. ( 4)

Система by, bz, 2’, 2’, 2’. Если при этом принять, что 1’= 1’= 1’ =0, то
уравнение (3) будет иметь вид:
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 ; ( 5)

так как
picscalex104010009000003860100000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c020007c00c1200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffff800c0000a60600000b00000026060f000c004d61746854797065
0000900110000000fb0280fe0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a9205e80b01000000f70008000000320a2204e80b0100
0000f70008000000320ab202e80b01000000f70008000000320a8806e80b01000000f800
08000000320abc01e80b01000000f60008000000320a92050c0601000000e70008000000
320a22040c0601000000e70008000000320ab2020c0601000000e70008000000320a8806
0c0601000000e80008000000320abc010c0601000000e60008000000320ae003e0040100
00003d0008000000320ae0035202010000003d0008000000320aca03600101000000a200
17000000fb0280fe0000000000009001000000cc0402001054696d6573204e657720526f
6d616e2043797200cca7040000002d01010004000000f001000008000000320a2006070b
01000000310008000000320a2006e80801000000300008000000320a2006c60601000000
300008000000320ae0030a0b01000000300008000000320ae003e5080100000031000800
0000320ae003c60601000000300008000000320aa0010a0b01000000300008000000320a
a001e80801000000300008000000320aa001c30601000000310008000000320ae0038a03
01000000450008000000320ae0033a0001000000410017000000fb0220ff000000000000
9001000000cc0402001054696d6573204e657720526f6d616e2043797200cca704000000
2d01000004000000f001010008000000320a40045c010100000031000a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01010004000000f0010000030000000000.

Комментарий. 3 оставшихся из 8 параметров после выбора 5 элементов
взаимного ориентирования задают ориентацию системы координат модели
ОМХМYMZM. Например, выбрав систему элементов взаимного ориентирования
by, bz, 2’, 2’, 2’ и приняв, что 1’= 1’= 1’ =0, мы таким образом задаем
систему координат модели ОМХМYMZM, которой параллельны осям x, y, z
системы координат первого снимка стереопары S1x1y1z1. В общем случае
значения трех параметров можно задавать произвольно.

5. Определение элементов взаимного ориентирования

Для определения элементов взаимного ориентирования в качестве исходного
используют уравнения взаимного ориентирования ( 4.3)
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.

Каждая точка, измеренная на стереопаре снимков, позволяет составить одно
уравнение (4.3), в которое, помимо измеренных координат точек на
стереопаре снимков, элементов внутреннего ориентирования и трех
параметров, задающих ориентацию системы координат модели, входят 5
неизвестных элементов взаимного ориентирования.

Очевидно, что для определения элементов взаимного ориентирования
необходимо измерить на стереопаре снимков не менее 5 точек.

В качестве примера рассмотрим определение элементов взаимного
ориентирования by, bz, 2’, 2’, 2’.

В связи с тем, что уравнения ( 4.3) не линейны, их предварительно
приводят к линейному виду и переходят к уравнению поправок:
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 . ( 1)

В уравнении поправок коэффициенты ai частные производные от функции (
4.3) по соответствующим аргументам, а ?– свободный член.

Значения коэффициентов аi в уравнении ( 1) вычисляют по следующим
известным значениям:

– измеренным координатам точек на стереопаре снимков – хi, yi;

– элементам внутреннего ориентирования снимков fi, x0i, y0i;

– 3 параметрам, задающим ориентацию системы координат модели (в нашем
случае 1’, 1’, 1’) и приближенным значениям элементов взаимного
ориентирования.

Свободный член ? вычисляется по формуле ( 4.3) таким же образом.

Полученную систему уравнений поправок решают методом приближений, а в
случае, если измерено более 5 точек по методу наименьших квадратов (под
условием VTPV=min). В результате решения находят значения элементов
взаимного ориентирования.

Критерием, по которому принимается решение о завершении итерраций, могут
являться величины поправок к определяемым неизвестным или величины
остаточных поперечных параллаксов, которые для каждой измеренной точки
вычисляются по формулам:
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 ; ( 2)

где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.

Величина qост представляет собой разность ординат измеренных точек на
стереопаре снимков, приведенных к идеальному случаю съемки, то есть
q=y1-y2.

Необходимо отметить, что при отсутствии ошибок построения снимка и
ошибок измерений величина q должна быть равна 0.

При определении элементов взаимного ориентирования оптимальным вариантом
считается измерение 12-18 точек на стереопаре снимков, расположенных
парами или тройками в 6 стандартных зонах (рис. 1).

Рис. 1

– главная точка снимка

– стандартно расположенная зона

В этом случае получается наиболее точное и надежное определение
элементов взаимного ориентирования и появляется возможность локализации
грубых измерений.

6. Построение фотограмметрической модели

Построение фотограмметрической модели заключается в определении
координат точек объекта по измеренным на стереопаре снимков координатам
их изображений в системе координат модели ОМХМYMZM.

Определение координат точек модели производится по формулам прямой
фотограмметрической засечки (см. раздел 1).

При этом координаты центра проекции S принимаются произвольными (обычно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).
Также произвольно (но не равной 0) выбирается величина ВХ. В большинстве
случаев практики величину ВХ принимают равной:
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;

где b – базис фотографирования в масштабе снимка,

m – знаменатель масштаба снимка.

Остальные значения элементов внешнего ориентирования определяют по 8
параметрам by, bz, 1’, 1’, 1’, 2’, 2’, 2’, 5 из которых являются
элементами взаимного ориентирования, а 3 определяют ориентацию системы
координат модели.

При этом
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.

Например, если были определены элементы взаимного ориентирования 1’, 1’,
2’, 2’, 2’ и при этом величины параметров by, bz, 1’ были приняты
равными нулю (by=bz=1’=0), то BY=BZ=0, 1=0, 1=1’, 1=1’, 2=2’, 2=2’,
2=2’.

Если были определены элементы взаимного ориентирования by, bz, 2’, 2’,
2’, а величины параметров 1’, 1’, 1’ были приняты равными нулю (1’= 1’=
1’=0), то
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.

7. Внешнее ориентирование модели. Элементы внешнего ориентирования
модели

Рис. 1

На рис.1: OXYZ – система координат объекта, ОМХМYMZM – система координат
фотограмметрической модели , А – точка объекта ,АМ -точка
фотограмметрической модели, соответствующая точке А объекта .

Векторы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определяют положение начала системы координат модели ОМХМYMZM и точки А
местности относительно начала системы координат объекта OXYZ.

Векторы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 определяют соответственно
положение точек АМ и А относительно системы координат
фотограмметрической модели.

Из рис. 1 следует, что
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 . ( 1)

Векторы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коллинеарны, поэтому
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 ; ( 2)

где t – знаменатель масштаба модели.

С учетом ( 2) выражение ( 1) имеет вид:

picscalex1000100090000032d0100000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c028002e0091200000026060f001a00ffffffff00001000
0000c0ffffffb9ffffffa0090000390200000b00000026060f000c004d61746854797065
0000600012000000fb0280fe0000000000009001000000cc04020020417269616c204379
7200cc00040000002d01000008000000320ac0011c0901000000740008000000320ac001
290701000000520008000000320ac001d00301000000520008000000320ac00122000100
0000520012000000fb0220ff0000000000009001000000cc04020020417269616c204379
7200cc00040000002d01010004000000f001000008000000320a20024d08010000004d00
08000000320a2002fb0401000000300008000000320a2002570101000000410011000000
fb0280fe000000000000900100000002040200104d542045787472610002040000002d01
000004000000f001010008000000320a65006d0701000000720008000000320a65001404
01000000720008000000320a6500660001000000720010000000fb0280fe000000000000
9001000000020002001053796d626f6c0002040000002d01010004000000f00100000800
0000320ac0010906010000002b0008000000320ac0019f02010000003d000a0000002606
0f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc0102
022253797374656d00cc040000002d01000004000000f0010100030000000000 ; ( .3)

В координатной форме выражение ( 3) имеет вид:
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 ; ( 4)

Или
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 . ( .5)

В выражениях ( 4) и ( 5):

X, Y, Z – координаты точки объекта в системе координат объекта;

ХМ, YM, ZM – координаты соответствующей точки модели в системе координат
фотограмметрической модели;

АМ – матрица преобразования координат, элементы aij которой являются
функциями углов М, М, М, определяющих ориентацию системы координат
модели относительно системы координат объекта;

t – знаменатель масштаба модели.

7 параметров: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 – называют элементами внешнего ориентирования модели.

8. Определение элементов внешнего ориентирования модели по опорным
точкам

Для определения элементов внешнего ориентирования модели по опорным
точкам в качестве исходных используют уравнения ( 7.5), которые
представим в виде:
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 . ( 1)

Каждая планово-высотная опорная точка (X,Y,Z) позволяет составить 3
уравнения ( 1), в которых неизвестными являются 7 элементов внешнего
ориентирования модели. Каждая плановая опорная точка (X,Y) позволяет
составить два первых уравнения из выражения ( 1), а каждая высотная
опорная точка (Z) – третье уравнение из выражения ( 1).

Для определения элементов внешнего ориентирования модели необходимо
составить систему не менее чем из 7 уравнений. Очевидно, что для этого
необходимо иметь не менее двух планово-высотных и одной высотной опорной
точки. Задачу можно также решить, если иметь две плановые и три высотные
опорные точки.

Так как уравнения ( 1) не линейны, их приводят к линейному виду и
переходят к уравнениям поправок.
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 . ( 2)

В уравнении поправок:

ai, bi, ci – частные производные от уравнений ( 1) по соответствующим
переменным ;

?X, ?Y, ?Z – свободные члены.

Значения коэффициентов уравнений поправок ai, bi, ci вычисляют по
известным значениям координат ХМ, YM, ZM и X, Y, Z и приближенным
значениям неизвестных. Значения свободных членов ?X, ?Y, ?Z вычисляют
таким же образом по формулам ( .1).

Полученную таким образом систему уравнений поправок решают методом
последовательных приближений. Если количество уравнений поправок в
системе больше семи, то ее решают по методу наименьших квадратов (под
условием VTPV=min).

9. Определение элементов внешнего ориентирования снимков стереопары

По элементам внешнего ориентирования модели и элементам взаимного
ориентирования можно определить элементы внешнего ориентирования снимков
стереопары.

Линейные элементы внешнего ориентирования снимков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 определяют по формулам:
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 ; ( 1)

в которых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 – координаты центра проекции i-го снимка стереопары в системе
координат модели.

Угловые элементы внешнего ориентирования снимков i, i, i определяют в
следующей последовательности:

1. Сначала получают матрицу преобразования координат i-го снимка
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; ( 2)

АМ – матрица, в которой элементы aij вычисляют по угловым элементам
внешнего ориентирования модели М, М, М ;

Ai’ – матрица, в которой элементы aij вычисляют по угловым элементам
взаимного ориентирования i-го снимка i’, i’, i’.

2. Затем по элементам aij матрицы Ai вычисляют угловые элементы внешнего
ориентирования i-го снимка стереопары:
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 .

10. Точность определения координат точек объекта по стереопаре снимков

Для предрасчета точности определения координат точек местности по
стереопаре аэрофотоснимков, учитывая, что углы наклона снимков не
превышают 1°- 3°, а базис фотографирования практически горизонтален,
воспользуемся формулами связи координат точек местности и координат их
изображений на стереопаре снимков идеального случая съемки ( 2.4):
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 . ( 2.4)

Сначала получим среднюю квадратическую ошибку определения высоты точки Z
местности. Для этого продифференцируем третью формулу выражения (1.8.4)
по аргументу р.
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 .

Заменим величину р на b – базис в масштабе снимка.

Рис.1

На рис.1 О1и О2 – главные точки снимка.

В результате получим
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 .

Перейдя к средним квадратическим ошибкам получим формулу:
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 . ( 1)

Для получения средних квадратических ошибок определения координат Х и Y
точки местности продифференцируем первые две формулы выражения (1.8.4)
по аргументам x, y, Z и перейдем к средним квадратическим ошибкам.

В результате получим
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 . ( 2)

В качестве примера вычислим величины mX, mY и mZ точек местности,
определенных по стереопаре снимков масштаба 1:5000, полученной АФА с f
=150 мм и форматом кадра 23х23 см, с продольным перекрытием 60%.

Будем считать, что на стереопаре снимков точки были измерены с ошибками
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 .

В этом случае высота фотографирования
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;

а базис фотографирования в масштабе снимка
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 .

Средние квадратические ошибки определения координат точки местности,
вычисленные по формулам ( 1) и ( 2) будут равны:
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.

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