1、第七講：遙感(yogn)數(shù)據(jù)預(yù)處理 幾何糾正共五十八頁(yè)幾何(j h)糾正 遙感影像一般需要經(jīng)過幾何糾正的預(yù)處理去除像元的幾何畸變，使像元回到正確的平面位置(wi zhi) (x,y) 上； 遙感影像經(jīng)過幾何糾正后，可以和其它專題信息（GIS）進(jìn)行復(fù)合分析； 從經(jīng)過幾何糾正的遙感影像上可以提取正確的距離、面積和方位信息共五十八頁(yè) 內(nèi)部(nib)和外部幾何誤差. 系統(tǒng)誤差和隨機(jī)誤差 幾何(j h)誤差的類型 共五十八頁(yè)內(nèi)部幾何誤差（Internal geometric errors） 是由遙感系統(tǒng)本身以及遙感系統(tǒng)成像過程中與地球自轉(zhuǎn)和地球曲率效應(yīng)(xioyng)相結(jié)合而產(chǎn)生的幾何誤差。內(nèi)部幾何誤差

2、一般屬于系統(tǒng)誤差（可預(yù)測(cè)的誤差）。這種誤差可以通過傳感器發(fā)射前或飛行過程中傳感器系統(tǒng)與地球的相關(guān)幾何特征預(yù)測(cè)。如： 由地球自轉(zhuǎn)引起的圖像歪斜 掃描系統(tǒng)引起的像元對(duì)應(yīng)的地面實(shí)際大小的變化, 掃描系統(tǒng)引起的地形水平位移內(nèi)部幾何(j h)誤差 共五十八頁(yè)地球自轉(zhuǎn)引起(ynq)的影像歪斜 太陽(yáng)同步的對(duì)地觀測(cè)(gunc)微星一般沿著固定的軌道運(yùn)行。在從北到南的降軌模式時(shí)獲取圖像。 地球從西向東每24小時(shí)自轉(zhuǎn)一周。 衛(wèi)星從北向南飛行時(shí)，地球同時(shí)自西向東旋轉(zhuǎn)，造成圖像歪斜 共五十八頁(yè)a) Landsat satellites 4, 5, and 7 are in a Sun-synchronous orbi

3、t with an angle of inclination of 98.2. The Earth rotates on its axis from west to east as imagery is collected. b) Pixels in three hypothetical scans (consisting of 16 lines each) of Landsat TM data. While the matrix (raster) may look correct, it actually contains systematic geometric distortion ca

4、used by the angular velocity of the satellite in its descending orbital path in conjunction with the surface velocity of the Earth as it rotates on its axis while collecting a frame of imagery. c) The result of adjusting (deskewing) the original Landsat TM data to the west to compensate for Earth ro

5、tation effects. Landsats 4, 5, and 7 use a bidirectional cross-track scanning mirror.圖像(t xin)歪斜 共五十八頁(yè)掃描(somio)系統(tǒng)引起的地面實(shí)際分辨率大小的變化 衛(wèi)星遙感的掃描系統(tǒng)一般在幾百公里的高度，只需偏離星下點(diǎn)很小的角度來獲取數(shù)據(jù)，因此可以減小掃描系統(tǒng)引起的幾何誤差(wch)； 航空遙感系統(tǒng)只是在幾公里的高空飛行，因此掃描系統(tǒng)的總視場(chǎng)角可以達(dá)到70左右，這樣就容易引起幾何上的畸變共五十八頁(yè)The ground resolution cell size along a single across

6、-track scan is a function of a) the distance from the aircraft to the observation where H is the altitude of the aircraft above ground level (AGL) at nadir and H sec f off-nadir; b) the instantaneous-field-of-view of the sensor, b, measured in radians; and c) the scan angle off-nadir, f. Pixels off-

7、nadir have semi-major and semi-minor axes (diameters) that define the resolution cell size. The total field of view of one scan line is q. One-dimensional relief displacement and tangential scale distortion occur in the direction perpendicular to the line of flight and parallel with a line scan.共五十八

8、頁(yè)Ground Swath Width航跡交叉(across-track)掃描系統(tǒng)的地面(dmin)幅寬（ ground swath width） 是掃描鏡完全掃過一次覆蓋的地面條帶的寬度。航跡交叉掃描系統(tǒng)的地面幅寬是傳感器總視場(chǎng)角q和傳感器高度H的函數(shù)。其計(jì)算公式為：共五十八頁(yè)地面(dmin)幅寬90 總視場(chǎng)角的航跡交叉(jioch)掃描系統(tǒng)在6000 m 高度的地面幅寬為：共五十八頁(yè)掃描系統(tǒng)造成(zo chn)的一維地形位移 航跡交叉掃描系統(tǒng)會(huì)導(dǎo)致地形位移。對(duì)每個(gè)掃描線，地形位移發(fā)生在垂直與飛行線的方向； 在星下點(diǎn)位置，掃描系統(tǒng)垂直向下看，水桶表現(xiàn)為一個(gè) 圓，但在偏離星下點(diǎn)的位置，就會(huì)發(fā)生

9、水平位移； 目標(biāo)(mbio)物里局部地形越高，目標(biāo)(mbio)物的頂部離星下點(diǎn)越遠(yuǎn)，一維地形位移量越大共五十八頁(yè)a) Hypothetical perspective geometry of a vertical aerial photograph obtained over level terrain. Four 50-ft-tall tanks are distributed throughout the landscape and experience varying degrees of radial relief displacement the farther they are f

10、rom the principal point (PP). b) Across-track scanning system introduces one-dimensional relief displacement perpendicular to the line of flight and tangential scale distortion and compression the farther the object is from nadir. Linear features trending across the terrain are often recorded with s

11、-shaped or sigmoid curvature characteristics due to tangential scale distortion and image compression.共五十八頁(yè)掃描系統(tǒng)正切(zhngqi)比例尺畸變（ Tangential Scale Distortion） 在航跡交叉掃描系統(tǒng)的成像過程中，掃描鏡是以常速轉(zhuǎn)動(dòng)的。由于靠近星下點(diǎn)的目標(biāo)比偏離星下點(diǎn)的目標(biāo)離掃描鏡更近，而掃描鏡在以常速轉(zhuǎn)動(dòng)，因此在每條掃描線上，星下點(diǎn)的像元在掃描線方向的大小比偏離星下點(diǎn)（影像邊緣）的小。這對(duì)水平于掃描線的目標(biāo)實(shí)際上是一種“壓縮(y su)”效應(yīng)。距離星下點(diǎn)越遠(yuǎn)，比

12、例尺壓縮(y su)效應(yīng)越明顯。這種效應(yīng)叫做“”正切比例尺壓縮(y su)。 總體特征：接近星下點(diǎn)的目標(biāo)表現(xiàn)為正常形狀；遠(yuǎn)離星下點(diǎn)的目標(biāo)被壓縮，其現(xiàn)狀發(fā)生畸變。 正切比例尺畸變導(dǎo)致線形特征目標(biāo)（如道路等）呈現(xiàn)s-shape or sigmoid distortion ；但對(duì)于平行于或垂直于飛行線的線形目標(biāo)，則不會(huì)出現(xiàn)這種情況。共五十八頁(yè)a) Hypothetical perspective geometry of a vertical aerial photograph obtained over level terrain. Four 50-ft-tall tanks are distrib

13、uted throughout the landscape and experience varying degrees of radial relief displacement the farther they are from the principal point (PP). b) Across-track scanning system introduces one-dimensional relief displacement perpendicular to the line of flight and tangential scale distortion and compre

14、ssion the farther the object is from nadir. Linear features trending across the terrain are often recorded with s-shaped or sigmoid curvature characteristics due to tangential scale distortion and image compression.共五十八頁(yè)外部(wib)幾何誤差（External geometric errors ）外部幾何誤差一般由隨時(shí)空發(fā)生變化的外部因素引起。引起遙感影像外部幾何誤差的主要因素

15、是成像是傳感器平臺(tái)的姿態(tài)(zti)和位置，包括： 高度 變化 姿態(tài) 變化 (滾動(dòng)，仰伏).共五十八頁(yè)高度(god)變化理想狀態(tài)下，遙感系統(tǒng)在離地面固定的高度飛行，以保證整個(gè)航跡上影像(yn xin)比例尺一致。 如果飛行過程中飛機(jī)航高發(fā)生變化，影像(yn xin)的比例尺就會(huì)發(fā)生變化. The diameter of the spot size on the ground (D; the nominal spatial resolution) is a function of the instantaneous-field-of-view (b) and the altitude above

16、ground level (H) of the sensor system, i.e.,共五十八頁(yè)a) Geometric modification in imagery may be introduced by changes in the aircraft or satellite platform altitude above ground level (AGL) at the time of data collection. Increasing altitude results in smaller-scale imagery while decreasing altitude re

17、sults in larger-scale imagery. b) Geometric modification may also be introduced by aircraft or spacecraft changes in attitude, including roll, pitch, and yaw. An aircraft flies in the x-direction. Roll occurs when the aircraft or spacecraft fuselage maintains directional stability but the wings move

18、 up or down, i.e. they rotate about the x-axis angle (omega: w). Pitch occurs when the wings are stable but the fuselage nose or tail moves up or down, i.e., they rotate about the y-axis angle (phi: f). Yaw occurs when the wings remain parallel but the fuselage is forced by wind to be oriented some

19、angle to the left or right of the intended line of flight, i.e., it rotates about the z-axis angle (kappa: k). Thus, the plane flies straight but all remote sensor data are displaced by k. Remote sensing data often are distorted due to a combination of changes in altitude and attitude (roll, pitch,

20、and yaw).共五十八頁(yè)姿態(tài)(zti)變化 衛(wèi)星遙感平臺(tái)的姿態(tài)相對(duì)比較穩(wěn)定，因?yàn)樗艽髿馔牧骱惋L(fēng)的影響比較小。對(duì)于航空遙感平臺(tái)，由于受許多外部因素的作用，會(huì)隨機(jī)發(fā)生各種姿態(tài)的變化，包括 滾動(dòng)（ roll）, 仰伏（pitch, and yaw）等。因此遙感系統(tǒng)一般都配備特別的姿態(tài)穩(wěn)定系統(tǒng)來穩(wěn)定傳感器的姿態(tài)。 由于傳感器姿態(tài)變化導(dǎo)致的遙感影像的幾何誤差只能通過(tnggu)地面控制點(diǎn)進(jìn)行糾正。共五十八頁(yè)a) Geometric modification in imagery may be introduced by changes in the aircraft or satellite p

21、latform altitude above ground level (AGL) at the time of data collection. Increasing altitude results in smaller-scale imagery while decreasing altitude results in larger-scale imagery. b) Geometric modification may also be introduced by aircraft or spacecraft changes in attitude, including roll, pi

22、tch, and yaw. An aircraft flies in the x-direction. Roll occurs when the aircraft or spacecraft fuselage maintains directional stability but the wings move up or down, i.e. they rotate about the x-axis angle (omega: w). Pitch occurs when the wings are stable but the fuselage nose or tail moves up or

23、 down, i.e., they rotate about the y-axis angle (phi: f). Yaw occurs when the wings remain parallel but the fuselage is forced by wind to be oriented some angle to the left or right of the intended line of flight, i.e., it rotates about the z-axis angle (kappa: k). Thus, the plane flies straight but

24、 all remote sensor data are displaced by k. Remote sensing data often are distorted due to a combination of changes in altitude and attitude (roll, pitch, and yaw).共五十八頁(yè)幾何校正(jiozhng)方法共五十八頁(yè)地面(dmin)控制點(diǎn)由于遙感平臺(tái)高度和姿態(tài)變化導(dǎo)致的幾何誤差可以通過地面控制點(diǎn)結(jié)合一定的數(shù)學(xué)模型進(jìn)行糾正。地面控制點(diǎn)（ground control point ,GCP) 是一個(gè)在遙感影像上或地圖上容易識(shí)別的點(diǎn)所對(duì)應(yīng)的地

25、面的實(shí)際位置。進(jìn)行幾何糾正時(shí)，必須同時(shí)(tngsh)獲取地面控制點(diǎn)的兩套坐標(biāo)對(duì)： 影像坐標(biāo)（image coordinates）， 在圖像上用 i 行和 j 列表示； 地圖坐標(biāo)（map coordinates ）(e.g., x,y measured in degrees of latitude and longitude, feet in a state plane coordinate system, or meters in a Universal Transverse Mercator projection). 通過對(duì)多個(gè)GCP的坐標(biāo)對(duì) (i,j and x,y) from many

26、GCPs (e.g., 20) 進(jìn)行最小二乘擬合，就可以得到不同坐標(biāo)之間的幾何變換系數(shù)（ geometric transformation coefficients）. 通過這個(gè)變換系數(shù)就可以將整個(gè)影像糾正到正確的地理或投影坐標(biāo)中去。共五十八頁(yè)地面(dmin)控制點(diǎn)的獲取在將遙感影像糾正到標(biāo)準(zhǔn)地圖坐標(biāo)時(shí)，地面控制點(diǎn)一般從以下途徑獲取： 紙質(zhì)平面地圖（hard-copy planimetric maps ）(e.g., U.S.G.S. 7.5-minute 1:24,000-scale topographic maps) 數(shù)字平面地圖（digital planimetric maps ）(e.

27、g., the U.S.G.S. digital 7.5-minute topographic map series) where GCP coordinates are extracted directly from the digital map on the screen;數(shù)字正射影像（ digital orthophotoquads ）：這種影像已經(jīng)結(jié)果(ji gu)正射幾何糾正 (e.g., U.S.G.S. digital orthophoto quarter quadrangles DOQQ); 全球定位系統(tǒng)（global positioning system (GPS) ins

28、truments）共五十八頁(yè)幾何糾正(jizhng)類型用戶得到的遙感影像一般已經(jīng)經(jīng)過系統(tǒng)幾何誤差的糾正。用戶一般關(guān)心的是隨機(jī)誤差的糾正。遙感影像幾何糾正一般有兩類： 影像到地圖的糾正（image-to-map rectification） 影像到影像的配準(zhǔn)（ image-to-image registration）一般需要在幾何糾正的同時(shí)，把遙感影像同時(shí)投影到標(biāo)準(zhǔn)(biozhn)的地圖坐標(biāo)系中，以便綜合分析和應(yīng)用，因此，需要首先進(jìn)行影像到地圖的糾正；但是，一旦有了結(jié)果幾何糾正的標(biāo)準(zhǔn)影像，也可以通過影像到影像的配準(zhǔn)來實(shí)現(xiàn)新的遙感影像的幾何糾正共五十八頁(yè)影像到地圖(dt)的糾正 影像到地圖的糾正

29、（Image-to-map rectification）：如果(rgu)需要從影像中量測(cè)面積、方向和距離，必須進(jìn)行影像到地圖的糾正。 影像到地圖的糾正不一定能夠完全糾正地形導(dǎo)致的一維位移；影像到地圖的糾正涉及到在影像上選取GCP(行和列)以及地圖上相應(yīng)點(diǎn)的坐標(biāo)共五十八頁(yè)a) U.S. Geological Survey 7.5-minute 1:24,000-scale topographic map of Charleston, SC, with three ground control points identified (13, 14, and 16). The GCP map coor

30、dinates are measured in meters easting (x) and northing (y) in a Universal Transverse Mercator projection. b) Unrectified 11/09/82 Landsat TM band 4 image with the three ground control points identified. The image GCP coordinates are measured in rows and columns.共五十八頁(yè)影像(yn xin)到影像(yn xin)的配準(zhǔn) 影像到影像的配

31、準(zhǔn)（Image-to-image registration）是一個(gè)通過位移和旋轉(zhuǎn)等過程，使具有相同地理區(qū)域的遙感(yogn)影像在空間位置上一致，以保證相同區(qū)域?qū)?yīng)的要素在兩幅配準(zhǔn)的影像上處于相同的位置 這種配準(zhǔn)用于當(dāng)遙感影像中的像元不必有地圖投影的唯一x,y 坐標(biāo)。比如，當(dāng)我們只想了解不同日期獲取的某一區(qū)域的影像中是否發(fā)生了某種變化時(shí)共五十八頁(yè)影像(yn xin)糾正/配準(zhǔn)的混合方法圖像糾正和配準(zhǔn)實(shí)際上基于同樣的圖像處理原理。其差別在于影像到地圖的糾正中，參考圖是一個(gè)具有標(biāo)準(zhǔn)(biozhn)地圖投影的地圖，而在影像之間配準(zhǔn)時(shí)參考圖是另一幅影像. 如果將一幅經(jīng)過影像到地圖糾正過的影像作為參考圖

32、，那么任何影像和這幅影像配準(zhǔn)后都會(huì)繼承該影像中的幾何誤差。因此，在對(duì)影像絕對(duì)位置精度要求比較高的應(yīng)用中，一般都是用影像到地圖的糾正。但是，當(dāng)進(jìn)行兩個(gè)或多個(gè)時(shí)段間遙感影像的變化檢測(cè)時(shí)，一般選擇混合的糾正/配準(zhǔn)方法。共五十八頁(yè)a) Previously rectified Landsat TM band 4 data obtained on November 9, 1982, resampled to 30 30 m pixels using nearest-neighbor resampling logic and a UTM map projection. b) Unrectified Oct

33、ober 14, 1987, Landsat TM band 4 data to be registered to the rectified 1982 Landsat scene. 圖像到圖像的混合(hnh)糾正 共五十八頁(yè)影像(yn xin)到地圖的幾何糾正將遙感影像(yn xin)糾正到地圖坐標(biāo)系涉及兩個(gè)基本操作: 空間插值（Spatial interpolation） 亮度插值（Intensity interpolation）共五十八頁(yè)空間(kngjin)插值（spatial interpolation） 在幾何糾正過程中，輸入像元的坐標(biāo)(行和列號(hào)，用x,y表示) 與地圖中同名點(diǎn)的地圖

34、坐標(biāo)(x,y) 間的幾何關(guān)系必須建立； 這個(gè)(zh ge)關(guān)系通過若干GCP點(diǎn)對(duì)來實(shí)現(xiàn)； 通過這個(gè)坐標(biāo)變化關(guān)系，就可以用糾正前輸入影像(x,y)點(diǎn)的像元來填充相應(yīng)的糾正后輸出影像相應(yīng)(x,y)點(diǎn) 的像元。這個(gè)過程叫做空間插值.共五十八頁(yè)亮度(lingd)插值（intensity interpolation）空間插值后，必須確定每個(gè)像元的亮度值。不過，經(jīng)過幾何糾正(jizhng)后，很難存在糾正(jizhng)前和糾正(jizhng)后對(duì)應(yīng)像元間像元值的一一對(duì)應(yīng)關(guān)系。在坐標(biāo)變換后輸出圖像中的像元對(duì)應(yīng)的位置在糾正(jizhng)前的圖像中不一定正好處于某一個(gè)完整的行列坐標(biāo)點(diǎn)上。所以必須有一個(gè)確定幾

35、何糾正(jizhng)后輸出影像的像元值的過程。這個(gè)過程叫做亮度插值共五十八頁(yè)利用坐標(biāo)(zubio)變換進(jìn)行空間插值影像到地圖的糾正（ Image-to-map rectification ）需要通過用一個(gè)多項(xiàng)式，利用最小二乘方法擬合糾正前和糾正后GCP的坐標(biāo)，來建立兩個(gè)坐標(biāo)系之間的變換關(guān)系。使用幾次多項(xiàng)式取決于遙感影像幾何畸變的性質(zhì)、GCP的數(shù)量，以及有無(wú)地形(dxng)一維位移等。共五十八頁(yè)Concept of how different-order transformations fit a hypothetical surface illustrated in cross-sectio

36、n. a) Original observations. b) First-order linear transformation fits a plane to the data. c) Second-order quadratic fit. d) Third-order cubic fit.共五十八頁(yè)NASA ATLAS near-infrared image of Lake Murray, SC, obtained on October 7, 1997, at a spatial resolution of 2 2 m. The image was rectified using a s

37、econd-order polynomial to adjust for the significant geometric distortion in the original dataset caused by the aircraft drifting off course during data collection.共五十八頁(yè)利用(lyng)坐標(biāo)變換進(jìn)行空間插值一般來說，如果對(duì)一個(gè)相對(duì)小的區(qū)域（如1/4景Landsat TM scene ）的中等幾何(j h)畸變，一階，六個(gè)參數(shù)的仿射（線性）變換（ affine (linear) transformation ） 就足夠。這類變換可

38、以糾正遙感影像的六類幾何畸變： x和 y坐標(biāo)的平移 x and y坐標(biāo)的比例尺變化 歪斜 旋轉(zhuǎn)共五十八頁(yè)坐標(biāo)變換(binhun)：輸入到輸出的映射Input-to-Output (Forward) Mappingx 和 y 輸出的經(jīng)過糾正后的影像的位置 ， x 和 y 為原始(yunsh)的輸入影像的位置. 這個(gè)方程表達(dá)的是輸入到輸出（ input-to-output,）的映射關(guān)系，也叫前向映射（ forward-mapping）。共五十八頁(yè)a) The logic of filling a rectified output matrix with values from an unrecti

39、fied input image matrix using input-to-output (forward) mapping logic. b) The logic of filling a rectified output matrix with values from an unrectified input image matrix using output-to-input (inverse) mapping logic and nearest-neighbor resampling. Output-to-input inverse mapping logic is the pref

40、erred methodology because it results in a rectified output matrix with values at every pixel location.共五十八頁(yè)坐標(biāo)變換：輸入到輸出(shch)的映射Input-to-Output (Forward) MappingForward mapping logic works well if we are rectifying the location of discrete coordinates found along a linear feature such as a road in a v

41、ector map. In fact, cartographic mapping and geographic information systems typically rectify vector data using forward mapping logic. However, when we are trying to fill a rectified output grid (matrix) with values from an unrectified input image, forward mapping logic does not work well. The basic

42、 problem is that the six coefficients may require that value 15 from the x , y location 2,3 in the input image be located at a floating point location in the output image at x,y = 5,3.5, as shown. The output x,y location does not fall exactly on an integer x and y output map coordinate. In fact, usi

43、ng forward mapping logic can result in output matrix pixels with no output value. This is a serious condition and one that reduces the utility of the remote sensor data for useful applications. For this reason, most remotely sensed data are geometrically rectified using output-to-input or inverse ma

44、pping logic.共五十八頁(yè)坐標(biāo)變換:輸出到輸入(shr)（反向）映射Output-to-Input (Inverse) Mapping輸出到輸入（Output-to-input） 或反向映射（ inverse mapping ）的表達(dá)式如下:x 和 y 為糾正后輸出影像的位置, x and y 為對(duì)應(yīng)的糾正前原始輸入影像的位置。糾正后的輸出影像的像元按照 x (column) 和 y (row) 系統(tǒng)(xtng)的排列。 共五十八頁(yè)a) The logic of filling a rectified output matrix with values from an unrectif

45、ied input image matrix using input-to-output (forward) mapping logic. b) The logic of filling a rectified output matrix with values from an unrectified input image matrix using output-to-input (inverse) mapping logic and nearest-neighbor resampling. Output-to-input inverse mapping logic is the prefe

46、rred methodology because it results in a rectified output matrix with values at every pixel location.共五十八頁(yè)Spatial Interpolation LogicThe goal is to fill a matrix that is in a standard map projection with the appropriate values from a non-planimetric image.共五十八頁(yè)計(jì)算反向映射(yngsh)方程的均方更誤差（ Root-Mean-Square

47、d Error ，RMSE）用GCP建立的坐標(biāo)間的關(guān)系求出六個(gè)變換系數(shù)來模擬原始影像的幾何畸變后，就可以用反向映射關(guān)系確定每個(gè)輸出像元對(duì)應(yīng)的原始影像像元的位置。但是，在利用六個(gè)變換系數(shù)對(duì)這個(gè)圖像繼續(xù)糾正之前，首先需要評(píng)價(jià)六個(gè)變換系數(shù)（變換方程）對(duì)原始影像幾何畸變的描述(mio sh)精度.一般通過計(jì)算每對(duì)控制點(diǎn)的均方更誤差（ root-mean-square error ,RMSE ）來評(píng)價(jià)。共五十八頁(yè)RMSEwhere:xorig and yorig are are the original row and column coordinates of the GCP in the image

48、 and x and y are the computed or estimated coordinates in the original image when we utilize the six coefficients. Basically, the closer these paired values are to one another, the more accurate the algorithm (and its coefficients). The square root of the squared deviations represents a measure of t

49、he accuracy of each GCP. By computing RMSerror for all GCPs, it is possible to (1) see which GCPs contribute the greatest error, and 2) sum all the RMSerror. 共五十八頁(yè)RMSE在幾何糾正過程中，一般不會(huì)將所有選取的GCP都用于確定糾正方程中六個(gè)變換系數(shù)和常數(shù)項(xiàng)，而是用一個(gè)迭代的過程。首先，用所有的GCP計(jì)算出變換系數(shù)和常數(shù)項(xiàng)，通過計(jì)算每個(gè)GCP的RMSE，然后刪除RMSE最大的GCP，用剩下(shn xi)的GCP再計(jì)算變換系數(shù)和RMSE

50、。如此迭代，直到RMSE達(dá)到用戶確定的閾值(e.g., 1 pixel error in the x-direction and 1 pixel error in the y-direction)共五十八頁(yè)Characteristics of Ground Control Points Point NumberOrder of Points DeletedEasting on MapX1Northing on MapY1X pixelY PixelTotal RMS error after this point deleted1125971203,627,0501501850.50129597

51、,6803,627,8001661650.663.201601,7003,632,580283128.542Total RMS error with all 20 GCPs used:11.016If we delete GCP #20, the RMSE will be 8.452 共五十八頁(yè)亮度(lingd)插值（Intensity Interpolation）經(jīng)過坐標(biāo)變換后，需要 提取原始影像中x,y 位置的亮度值，賦予(fy)對(duì)應(yīng)的糾正后影像中 x,y 坐標(biāo)位置。由于經(jīng)過反向映射后，規(guī)則排列的糾正后的影像的坐標(biāo)x,y 對(duì)應(yīng)的原始影像中的位置x,y 為浮點(diǎn)數(shù)（非整數(shù)），因此不能直接確定x,y 位置的像元值。這時(shí)需要通過亮度插值方法確定。亮度插值方法包括： 最近鄰插值（nearest neighbor）雙線性插值 （bilinear interpolation ）立方卷積（cubic convolution）這個(gè)過程一般也叫做重采樣（ resampling）共五十八頁(yè)最近(zujn)鄰重采樣（Nearest-Neighbor Resampling） 將最接近位置(wi zhi)x, y 坐標(biāo)的像元值賦予對(duì)