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1
2. Thermal and Hyperspectral Sensing
遙感探測Remote Sensing
國立成功大學測量及空間資訊學系
王驥魁
2
Thermal imagingTABI-1800, 11:30 pm, GSD 15 cmNatural gas processing facility and power plantAlberta, Canada
chimney
Plume of hot gas
chimney(not in use)
underground pipe
3
Thermal imaging• Not dependent on reflected solar radiation• Can be operated at any time of the day or night• Operated in 3 – 5 μm or 8 – 14 μm due to
atmospheric effect• Detectors must be cooled to very low temperature
for maximum sensitivityType Abbreviation Useful Spectral Range
Mercury-doped germanium ( 汞摻鍺 )
Ge:Hg 3 – 14 μm
Indium antimonide( 銻化銦 )
InSb 3 – 5 μm
Mercury cadmium telluride ( 汞碲化鎘 )
HgCdTe (MCT), or “trimetal” 3 – 14 μm
4
Thermal radiation principles
Object with temperature
Internal temperature (kinetic temperature)
Thermal detectorRadiant temperature
(external temperature)
5
Blackbody radiation
6
Radiation from real materials• All real materials emit only a fraction of the energy
emitted from a blackbody at the equivalent temperature.
• Emissivity
• Emissivity can vary with wavelength• Emissivity can even vary with temperature
depending on the material
𝜀 ( λ )= radiant exitanceof anoject at a giventemperatureradiant exitance of a blackbody at the same temperature
0<𝜀 ( λ )<1
7
Radiation from real materials
• Graybody has an emissivity less than 1 but is constant at all wavelengths
• The emissivity of selective radiator is a function of wavelength
8
Radiation from real materials
Water is very close a blackbody in 6 – 14 μm range.
9
Variations of emissivity• Material• Condition and
arrangement of the materials
• Dry soil (0.95) vs. wet soil (0.92)
• Loose soil vs. compacted soil
• Individual tree leaves (0.96) vs tree crowns (0.98)
Material Typical Average Emissivity over 8 -14 μm
Clear water 0.98 - 0.99Wet snow 0.98 - 0.99Human skin 0.97 - 0.99Rough ice 0.97 - 0.98Healthy green vegetation 0.96 - 0.99Wet soil 0.95 - 0.98Asphaltic concrete 0.94 - 0.97Brick 0.93 - 0.94Wood 0.93 - 0.94Basaltic rock 0.92 - 0.96Dry mineral soil 0.92 - 0.94Portland cement concrete 0.90 - 0.94Paint 0.90 - 0.96Dry vegetation 0.88 - 0.94Dry snow 0.85 - 0.90Granitic rock 0.83 - 0.87Glass 0.77 - 0.81Sheet iron (rusted) 0.63 - 0.70Polished metals 0.16 - 0.21Aluminum foil 0.03 - 0.07Highly polished gold 0.02 - 0.03
10
Consideration of spectral range for thermal data• The ambient temperature of earth surface is normally about
.• This results a peak emission at approximately 9.7 μm.• Hence, most thermal sensors perform at 8 – 14 μm range.• Although it’s a fact that the emissivity of objects can vary in 8
– 14 μ m, for broad band detectors, the objects are assumed as graybody.
• Cautions should be exercised when conducting inter-data comparison.within-band emissivity of materials in 10.5 – 11.5 μm sensed by
NOAA AVHRR is not the same as those in 10.4 – 12.5 μm sensed by Landsat TM band 6.
• The 3 – 5 μm range is useful for forest fire mapping.
11
Atmospheric effects• Within given atmospheric window
• atmospheric absorption and scattering tend to make the signals from ground objects appear colder than they are
• atmospheric emission tends to make objects appear warmer than they are
12
Interaction of thermal radiation with terrain elements
For Krichhoff radiation law, the spectral emissivity of an object equals its spectral absorptance, i.e., “good absorbers are good emitters”, .
In remote sensing applications, we assume all objects are opaque to thermal radiation.
The higher an objects’ reflectance, the lower its emissivity; vice versa.
13
Interaction of thermal radiation with terrain elements• Water has negligibly low reflectance in thermal IR
(TIR), so its emissivity is essential 1 for that spectral range.
• Sheet metal is highly reflective of thermal energy, so it has an emissivity much less than 1.
• So, the thermal measurement of real materials.
• How to obtain the kinetic temperature from radiant temperature?
𝑀=𝜀𝜎 𝑇 4
14
Diurnal temperature variation
Quasi-equilibrium(the change rate of temperature is small) High-contrast Cooling
Thermal crossover(no radiant temperature difference exists between two materials)
Variation of temperature (maximum, minimum, range, time of maximum and minimum)
15
Thermal properties• Thermal conductivity
• A measure of the rate at which heat passes through a material• EX. Heat passes though metals much faster than though rocks.
• Thermal capacity• Determines how well a material stores head.• EX. Water has a very high thermal capacity compared to other material
types.
• Thermal inertia• A measure of the response of a material to temperature changes.• It increases with an increase in material conductivity, capacity, and
density.• In general, materials with high thermal inertia have more uniform
surface temperatures thoughtout the day and night than material of low thermal inertia.
16
Thermal image (qualitative use)
Middleton, WisconsinFlying height 600 m, IFOV 5 mrad
Daytime (pm 2:40) Nighttime (pm 9:50)
Lake (warmer than surroundings)
Pond (warmer than surroundings)
HighTemperatureLow
Residential area (no thermal shadow at night)
Thermal “shadows” are created by trees due to cooler temperature.
Pavements are warmer than surroundings at both day and night
17
Thermal image (qualitative use)
AM 9:40An ephemeral glacial lakeMiddleton, WisconsinFlying height 600 m, IFOV 5 mrad
HighTemperatureLow
Lake beach ridge(fine sandy loam, 細砂壤土 )
Sod farm( 草皮農場 )
Bare soil
Trees
Lakebed soil(silt loam 粉砂壤土 )
18
Thermal image (qualitative use)
A cattle ranch, Middleton, WisconsinFlying height 600 m, IFOV 5 mrad HighTemperatureLow
PM 9:50 AM 1:45
cows
sheet metal roof
19
Thermal image (qualitative use)
DaytimeQuantico, VirginiaIFOV 0.25 mrad, GSD ~0.3 m HighTemperatureLow
cows
shadow?
20
Thermal image (qualitative use)
PM 1:50Oak Creek Power Plant, WisconsinFlying height 800 m, IFOV 2.5 mrad HighTemperatureLow
windPlume of cooling water
Lake Michigan
21
Thermal image (qualitative use)
AM 2:00, -4°C (air)Iowa CityFlying height 460 m, IFOV 1 mrad
HighTemperatureLow
Wind-blown snow pattern on the ground
Building heat loss
22
Thermal image (qualitative use)
R: band 5 (red)G: band 3 (green)B: band 2 (blue)
R: band 12 (thermal IR)G: band 9 (mid-IR)B: band 10 (mid-IR)
Zaca FireSanta Barbara, CaliforniaAutonomous Modular Sensor (AMS), NASA Ikhana UAV
active fire
burned over area
23
Radiometric calibration of thermal images and temperature mapping• When quantified temperature results are required, the
calibration procedure is a must.• Two most commonly used calibration methods
• Internal blackbody source referencing• Air-to-ground correlation
• It is possible to estimate the surface temperature from the thermal image based on theoretical atmospheric models with the knowledge of the atmospheric condition (i.e., temperature, pressure, CO2 concentration) when the thermal image was collected.
24
Internal blackbody source referencing
25
Air-to-ground correlation
Regression fitting:
system response parametersemissivity at point of measurement
kinetic temperature at point of measurement
26
FLIR systems(not the company name)
• Forward-looking infrared (FLIR)• Compared to traditional system that are 1-D-array- or
scanning-based system, which requires the movement of the platform and post-processing for image generation.
• 2D array for real-time application
http://media4.s-nbcnews.com/j/MSNBC/Components/Photo/_new/900501-airport-thermal-hmed2p.grid-6x2.jpg
https://upload.wikimedia.org/wikipedia/commons/a/ab/Flickr_-_Official_U.S._Navy_Imagery_-_Alleged_drug_traffickers_are_arrested_by_Colombian_naval_forces..jpg
http://www.guncopter.com/images/gallery/uh-1n.jpg
27
FLIR images
Thermal shadow?Different level of liquid in each tank.
28
多光譜影像表示法 影像描述空間
灰值
水 植物
水
植物 土壤
土壤
1 波段灰值
波段
灰值
2 2 1
可運用三種描述空間:影像空間 (Image Space) 、光譜空間 (Spectral Space) 、及特徵空間 (Feature Space) 來表現多光譜影像的特性
影像空間 光譜空間 特徵空間
多光譜影像表示法
29
以影像方式展現光譜在空間上之差異,常運用三原色表示三個不同波段之反應值,稱為假色影像 (Pseudo-color Image)
波段一波段二波段三波段四波段五
多光譜影像RGB
假色影像
RGB
影像空間 Image Space
05/01/2023 30
多光譜影像表示法 光譜空間 Spectral Space
在光譜空間,每一個像元所涵蓋地物之光譜反應值為波長的函數,表現像元之光譜變化
波段區間水體像元
反應值DN
植物像元波段區間反應值
DN
05/01/2023 31
多光譜影像表示法 特徵空間 Feature Space
將每個量測波段當成一個特徵變量,形成特徵空間。特徵空間的一個座標點 ( 或稱特徵向量 ) 對應到光譜空間為一條光譜曲線,而對應到影像空間則為一個像元band
col
row
灰值
1 2
1
2
水植物
水
植物土壤
土壤
波段灰值
波段灰值 特徵向量
特徵空間
特徵點
05/01/2023 32
多光譜影像表示法 特徵空間點散佈圖 Scatter Plot
每個像元的反應值在特徵空間形成一個特徵點,展繪一區域的影像即形成散佈的點群圖,稱為點散佈圖。由於特徵空間是多維度的,無法直接展繪,通常以三角陣列之二維點位分佈圖來表現像元值變化的情形。二維點位分佈圖是一種投影後的點位分佈。也可利用透視或動畫檢視三個波段之量測值分佈情形
band2
band1
band4band3band2
band32D Scatter Plots
3D Scatter Plots
05/01/2023 33
影像統計量 直方圖 Histogram
2 2
1 222
2 25 55
55 5
1 1 2 2 5 5 51 1 14
44
444
2
443
43 3 33 33
33 3
3 33 3
3
機率%
灰值
10
30
20
40
1 2 3 4 5
統計影像中各灰值出現之機率 ( 頻率 / 總像元數 ) ,並繪成直條統計圖形式 (Bar chart)
NDNcounthistDN )(
05/01/2023 34
影像統計量 統計量 Statistics
ModeMedian
Mean
Mode : 頻率最高值Median : 中值Mean ( ): 平均值 Variance ( ): 變異數
Variance
NDNN
ii
1
NDNN
ii
1
22 )(
Histogram
灰值1 2 3 4 5
機率密度函數圖 PDF
灰值
機率密度%
機率%
10
30
20
40
05/01/2023 35
影像統計量 特徵向量數學式
Band 2Band 1
Band 3
i
i
i
DNDNDN
3
2
1
05/01/2023 36
影像統計量 統計量計算式
Band 1
Band
2
1σ11
σ22
N
bnbnmbmmn
kkk
k
DNDNN
Cov1
1
111 1 ,
N
bbkk
Tk DN
N 121
1 , Mean vector
Covariance
2
Band 2
Band
3
2σ22
σ33
3σ12
σ23
等機率橢圓
05/01/2023 37
影像統計量 相關矩陣 Correlation Matrix
21
11 ,
1
1
1
1
mn
nnmmmnmn
k
k
R
1mn
1mn
10 mn
01 mn
nnmmmn ,0
nnmmmn ,0
05/01/2023 38
影像統計量 相關矩陣 Correlation Matrix
21
11 ,
1
1
1
1
mn
nnmmmnmn
k
k
R
1mn
1mn
10 mn
01 mn
nnmmmn ,0
nnmmmn ,0
05/01/2023 39
影像統計量Correlati
onBand
1Band
2Band
3Band
4Band
5Band
6Band
7
Band1 1 Band2
0.962
1
Band3
0.919
0.966
1
Band4
0.267
0.366
0.434
1
Band5
0.518
0.617
0.714
0.821
1
Band6
0.462
0.508
0.565
0.413
0.610
1
Band7
0.743
0.813
0.883
0.629
0.918
0.668
1
1 2 3 4 5 6 71234567
05/01/2023 40
Band1 Band2 Band3 Band4
Band5 Band6 Band71 2 3 4 5 6 7
1234567
05/01/2023 41
波譜轉換與特徵萃取 波譜轉換 Spectral Transformation
將原影像波段之量測值以某種函數重新組合成新的波段稱為波譜轉換
nDN
DNDN
2
1
DN 則波譜轉換為 DNf
DN
若組合函數為線性函數則稱為波譜的線性轉換:
nnnn
n
c
cDN
ww
wwCDNW
1
1
111
DN
05/01/2023 42
波譜轉換與特徵萃取波譜轉換事實上是將原波譜特徵重新選取或組合成新的特徵,因此又稱為特徵萃取。遙測常用的特徵萃取方式有:波段選取:從原波段中選擇出應用波段波段線性組合:波譜的線性轉換波段非線性組合:波譜的非線性轉換
特徵萃取 Feature Extraction
05/01/2023 43
波譜轉換與特徵萃取利用影像統計方法計算得的相關矩陣,顯示波段資訊的相關性,高相關的兩波段表示含有高度重複的資訊。因此,從原波段中只要選其中較為獨立的波段,即可獲得相近的資訊。
波段選取 Feature Selection
05/01/2023 44
波譜轉換與特徵萃取 主要成分分析 Principal Components Analysis, PCA
PCA 是一種波譜正交轉換,轉換後的特徵為不相關,即其 Covariance 為對角線矩陣或其相關矩陣為單位矩陣。轉換後影像之 Variances 將從大排到小,具愈大 Variance 的影像包含愈多光譜資訊,依 Variance 大小排序成主要成份影像
Band 1
Band
2 σ11
σ22
PC 轉換在特徵空間為旋轉至等機率橢圓 ( 球 ) 之主軸的轉換,以 2-band 影像為例
First PCSecond PC
θ
05/01/2023 45
波譜轉換與特徵萃取 PCA 之計算
PCA 轉換後之主要成分影像間為獨立不相關,即其 Cov 之非對角元素皆為零,可應用特徵值 (Eigenvalue) 計算之理論,將 Cov 對角線化 (Diagonalization) ,即ECov
kkkk
k
00
0000
2
1
1
111
轉換後
ECov
kkk
PC
00
0000
ˆ00
0000
2
1
2
22
11
即
05/01/2023 46
波譜轉換與特徵萃取 PCA 之計算
Cov E V Cov V
DN
DNV
DN
DN
PCT
I
N
T
n
1
也就是說我們可利用 Cov 求出 Eigenvalues 及 Eigenvectors 進而運用左式求得 Principal components
PC 影像所對應之 Eigenvalue 愈大代表所含的光譜資訊量愈多,因此我們常取前面幾張含資訊量較大的 PC 影像取代原影像,以增加分析或判讀之效率
由於 Cov 為二次矩陣 (Quadratic matrix) 因此其 Eigenvalues 個數與矩陣之階數相同且皆為實數,而且其 Eigenvactor matrix 為正交矩陣 (Orthogonal matrix) ,若 V 為 Eigenvector matrix 則
05/01/2023 47
PC1 PC2 PC3
05/01/2023 48
波譜轉換與特徵萃取 比率影像 Ratio Image
將兩個不同波段間對應的像元值取比率而得之影像,是一種非線性的波譜轉換。可利用比率影像減少同類地物因陰影或照明情況的不同所造成的差異,亦可應用地表物對某些光譜之反射率的差異強調某些地物光譜變化的特徵,如近紅外光影像與紅光影像之比可強調健康植物之區域 Band A Band B Ratio
落葉-陽 48 50 0.96
陰 18 19 0.95
針葉-陽 31 45 0.69
陰 11 16 0.69
05/01/2023 49
波譜轉換與特徵萃取 植物指標影像 Vegetation Index Image採用比率影像的概念,將多光譜影像組合成反應植物量的影像,稱為植物指標影像。實作上是運用植物對紅光及近紅外光反射的差異來突顯植物的影像,常用的組成法有:
RVIDNDN
NIR
R
Ratio Vegetation Index (RVI)
Normalized Difference Vegetation Index (NDVI)
NDVIDN DNDN DN
NIR R
NIR R
Transformed Vegetation Index (TVI) TVI
DN DNDN DN
NIR R
NIR R
0 5
12
.
05/01/2023 50
影像分類 Image Classification 基本概念多光譜影像分類是依據像元之多光譜資料將像元分群集,並對應到地物類別。依分類方法是否需要訓練資料可分成監督式 及非監督式 兩種類型:監督式分類 (Supervised Classification) :事先指定各地物類之樣本區,稱為訓練區 (Training area) ,而以訓練區之光譜資料為樣本,設定分類之準則將整幅影像分類非監督式分類 (Unsupervised Classification) :先單純依據像元之光譜資料,將像元分群集 (Cluster) ,而後再分析各 Cluster 之光譜資料判讀其相應之地物類別
05/01/2023 51
影像分類 Image Classification 監督式分類訓練區將訓練區之像元展繪在特徵空間,同物類像元因為光譜特徵相似會聚集在一起,如右圖。監督式分類原理即分析計算訓練區像元在特徵空間之分布的統計參數,如中值、範圍及變異量等,而後利用這些參數決定其他像元的類別。
Band i
Band
j
WW
W
WW
W W
W
W W
W
UU
U
U
U
U
U
U
UU
U
UU U
U
U
U
UU
SS
SSS
SS
SS
CC
C
C
CCCCC
C
HHH
H
H HHHH
H
H
H
H
HH
HH
FF
F
FF
F
F
F
FF
FFF
F F
F
05/01/2023 52
影像分類 Image Classification最短距離分類法 Minimum-Distance-to-Mean classifier
由各訓練區之群集區域計算得其中值,而後計算欲分類像元之光譜值與各中值距離,以最短距離決定其類別
Band i
Band
j
WW
W
WW
W W
W
W W
W
UU
U
U
U
U
U
U
UU
U
UU U
U
U
U
UU
SS
SSS
SS
SS
CC
C
C
CCCCC
C
HHH
H
H HHHH
H
H
H
H
HH
HH
FF
F
FF
F
F
F
FF
FFF
F F
F此分類法只考慮群集分佈中心,未考量群集分佈的散佈情形
05/01/2023 53
影像分類 Image Classification平行體分類法 Parallelpiped classifier
由各訓練區之群集分佈區域之外包平行體劃定類別範圍,而以欲分類像元之光譜特徵所在之位置決定其類別
Band i
Band
j
WW
W
WW
W W
W
W W
W
UU
U
U
U
U
U
U
UU
U
UU U
U
U
U
UU
SS
SSS
SS
SS
CC
C
C
CCCCC
C
HHH
H
H HHHH
H
H
H
H
HH
HH
FF
F
FF
F
F
F
FF
FFF
F F
F
同時考慮了群集分佈中心及散佈,但外包平行體只是群集散佈情形初步的描述,而且常有重疊情形,會產生分類上的困擾
05/01/2023 54
影像分類 Image Classification高斯最似分類法 Gaussian Maximum Likelihood classifier
假設訓練區之群集為高斯正常分佈,應用 Maximum Likelihood 理論決定群集分佈之參數,如此則可依 Bayes Theorem 計算欲分類之像元值屬於各群集之機率,而以最高機率決定其所屬之類別
Band i
Band
j
WW
W
WW
W W
W
W W
W
UU
U
U
U
U
U
U
UU
U
UU U
U
U
U
UU
SS
SSS
SS
SS
CC
C
C
CCCCC
C
HHH
H
H HHHH
H
H
H
H
HH
HH
FF
F
FF
F
F
F
FF
FFF
F F
F
等機率線無上述兩種分類法之缺點,是為目前最常用的分類法
05/01/2023 55
影像分類 Image Classification訓練處理之意義訓練處理的品質決定分類的成效,雖分類階段可以高度地自動化,但訓練階段有賴專業的遙測判讀員綜合參考資料及影像區域之地理性質,以分析出訓練資料訓練處理之最終目的是要從影像中組合出一組可以用來描述影像中各地物類別之光譜樣本的統計量,訓練資料必須具代表性且完整, 也就是說所有的光譜類別都必須具有足夠代表性的統計量
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影像分類 Image Classification訓練區選取在訓練區之選取上,我們通常以互動式在螢幕上選取多邊形訓練區域,亦可用指定種子像元的方式,再依其鄰近相似光譜之像元擴充成訓練區初步選完訓練區之後,須檢視各組訓練資料之分佈情形,以及各組資料間在光譜上之區分性,若分佈情形及區分性不良則須增加或重選訓練區
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影像分類 Image Classification訓練區檢視分析光譜樣本直方圖分析:繪出訓練類別各波段之直方圖,檢視單一類別之分佈情形,或同時比較多個訓練類別之區分性群集區分性量化分析:以統計參數表示類別之區分性訓練資料自我分類之分析:以訓練資料本身先試做分類,而後檢視其分類結果之確性互動式漸進分類:利用電腦彩色顯圖技術,以互動方式暸解各訓練樣本之分佈情形或初步分類之結果代表區域分類:先初步選擇一個較具代表性之少量訓練資料進行分類,以此初步分類結果檢視並修飾訓練區,最後以此分類結果為訓練資料進行全區之分類
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影像分類 Image Classification非監督式分類法常用的群集法為“ K-means” ( 其改進方法稱為 ISODATA) ,先由分析者給予群集數,而後於特徵空間任意設置同數目之群集中心,而計算每一點與各群集中心之距離,以最短距離決定像元之群集,分群後則依新的群集來計算中心,再進行分群計算,一直做到群集中心不變為止
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分類精度評估誤差距陣 Error Matrix應用已知類別之參考資料,或稱地真資料 (Ground Truth) 評估分類的正確率,最普遍的評估方法是用 Error Matrix (Confusion Matrix or Contingency Table) 來表示分類錯誤之情形
Reference Data (Known Cover Types)
W S F U C H Row Total W 480 0 5 0 0 0 485 S 0 52 0 20 0 0 72 F 0 0 313 40 0 0 353 U 0 16 0 126 0 0 142 C 0 0 0 38 342 79 459 H 0 0 38 24 60 359 481 Cl
assif
icatio
n Da
ta
Col. Total 480 68 356 248 402 438 1992
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分類精度評估正確率 Correctness正確分類之比率,顯示於 Error Matrix 中之對角元素,其整體的正確率以整體精度 (Overall Accuracy, OA) 表示之
整體精度正確分類之像元數
總像元數
%841992)35934212631352480(OA
某類別沒被認出來之比率,顯示於 Error Matrix 中之各行,遺漏率決定生產者精度 (Producer’s Accuracy)
生產者精度某類別正確分類之像元數
某類別之總像元數
遺漏率 Omission
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分類精度評估誤認率 Commission某分類為誤認之比率,顯示於 Error Matrix 中之各列,誤認率決定使用者精度 (User’s Accuracy)
使用者精度某分類為正確之像元數
某分類之總像元數
Producer’s Accuracy User’s Accuracy
W=480/480=100% W=480/485=99%
S=52/68=76% S=52/72=87%
F=313/356=88% F=313/353=87%
U=126/248=51% U=126/142=89%
C=342/402=85% C=342/459=74%
H=359/438=82% H=359/481=75%
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分類精度評估 指標 Kappa index從整體精度的評估來看,隨機分類也可獲得某種程度的正確率。較公平的評估是把預期的隨機分類正確率當成比較的基準,所以 指標是用來衡量分類結果到底比隨機分類好多少的量化指標。 指標同時考量 Error Matrix 中對角及非對角元素而得之統計指標,其估值 (k hat) 之定義為̂
agreement chance-1agreement chance-accuracy observedˆ
Observed accuracy (OA) 為觀測得之整體精度Chance agreement (CA) 則為預期的隨機分類正確率
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分類精度評估隨機分類正確率Reference Data (Known Cover Types)
W S F U C H Row Total
W 480*485 68*485 356*485 248*485 402*485 438*485 485
S 480*72 68*72 356*72 248*72 402*72 438*72 72
F 480*353 68*353 356*353 248*353 402*353 438*353 353
U 480*142 68*142 356*142 248*142 402*142 438*142 142
C 480*459 68*459 356*459 248*459 402*459 438*459 459
H 480*481 68*481 356*481 248*481 402*481 438*481 481 Clas
sifica
tion
Data
Col. Total 480 68 356 248 402 438 1992
21
N
xxr
iii
)(
total grandentries diagonal of sumagreement chance
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分類精度評估
793776
1674
1992
1
1
r
iii
r
iii
xx
x
N
)(
Reference Data (Known Cover Types)
W S F U C H Row Total W 480 0 5 0 0 0 485 S 0 52 0 20 0 0 72 F 0 0 313 40 0 0 353 U 0 16 0 126 0 0 142 C 0 0 0 38 342 79 459 H 0 0 38 24 60 359 481 Cl
assif
icatio
n Da
ta
Col. Total 480 68 356 248 402 438 1992
84.019921674OA
%..
..CA-1CA-OAˆ 80800
2001200840
計算結果
2001992793776 2 .CA