Correction
Remote Sensing Examination - 2015-2016 The QCM’s responses are to indicate by shading in black or blue ink ( → ) the boxes corresponding to your answers. There is only one correct answer for each question: • Good answer : +1 • Bad answer : -0.5 • No answer : 0 To untick a box checked by mistake, take care to erase the contents of this box (do not surround another answer, etc.), otherwise it will be considered as checked.
Name : ...................................................................................................... ......................................................................................................
1
Multiple choices questions
Question 1 Spectral Plot 1
s1 s2 s3 s4
Reflectance
0.8 0.6 0.4 0.2 0
0.5
1
1.5
2
2.5
λ In figure Spectral plot, the specta corresponding to grass is 4
2
3
1
Correction
Question 2 Figure 2
0
0
0.25
100
0.00
200
0.25 0.50
300
0.75
400
0.06
100
0.00 200
0.06
300
0.12
400
0.18
500
0.24
600
0.30
1.00 500
1.25 1.50
600 700 0
1.75 100
200
300
400
500
600
700
800
1
0
700 0
0.36 100
200
300
400
500
600
700
800
2
0
0.8
100
1.2
100
200
0.8
200
0.4
300
0.4
300
0.2
400
0.0
400
0.0
500
0.4
500
600
0.8
600
1.2
700 0
700 0
100
200
300
400
500
600
700
800
0.6
0.2 0.4 0.6 100
200
300
400
500
600
700
800
3 4 From images in Figure 2, which image correspdonds to the computation of NDVI? 3
2
4
1
Question 3 λ (µm)
0.45-0.52
x 777 From the above pixel x, its NDVI value is: 2.89449
0.52-0.60
0.63-0.69
0.76-0.90
817
413
849
0.02689
0.36638
0.34547
Question 4 A given pixel x has the following reflectance values in the visble and near-infra read: λ (µm) 0.45-0.52 0.52-0.60 0.63-0.69 0.76-0.90 x 0.8 In a “true color” composition, the pixel will be: green
black
0.2
0.1
blue
0.0
red
Correction
Question 5 is:
For a Gaussian mixture model, where the x ∈ R10 and C = 5, the number of parameters to estimate
50
329
55
325
Question 6 The satellite Quickbird acquires images with 4 spectral bands where pixels have size of 2.5 meters per side. These images are Panchromatic
2
Hyperspectral
Multispectral
Color
PCA-Based regularization
The Tikhonov optimization problem for the estimation of the inverse of the covariance matrix of class i is :
2
ˆ 2 ˆ Ai = min Σi Ai − I + kΓi Ai k Ai
(1)
ˆ i the empirical covariance matrix of class i and Γi a matrix that gives preference to some solution. In this with Σ work, we will consider a particular form Γi : Γi = Qi Ψi Qti with Ψi = diag 0, . . . , 0, +∞, . . . , +∞ | {z } | {z } p
d−p
ˆ i , qi1 (resp. qid ) is the eigenvector where Qi = [qi1 , . . . , qid ] is the orthonormal matrix of eigenvectors of Σ corresponding to the largest (resp. lowest) eigenvalue and p ∈ {1, . . . , d}.
Correction
ˆ i and p in the following form: Prove that Ai can be written is terms of eigenvector/eigenvalue of Σ
Question 7
ˆi = A
p X
t ˜ ˜ −1 ˜ t λ−1 ij qij qij = Qi Λi Qi .
j=1
˜ i and Λ ˜ i. Write Q
f
j Part reserved to the corrector
p
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Question
8
Compute
the
condition
number
associated
to
the f
inverse
problem
(25).
j Part reserved to the corrector
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Correction
Question 9 Implement the regularization with matlab (training, cross_validation and testing). Apply it on the hyperspectral data sets : plot the overall accuracy in function of the parameter using the cross-validation technique and select the optimal value of p. Provide matlab files to run your program. f
p
j Part reserved to the corrector
................................................................................................................
3
Enhance Vegetation Index
The NDVI is known to saturate and some authors prefer to use another index to assess vegetation. The Enhance Vegetation Index (EVI) is widely used, it is computed as EV I(x) =
2.5(x[ir] − x[r]) x[ir] + 6x[r] − 7.5x[b] + 1
Question 10 Write a matlab function that takes as input parameters the multispectral image, and the band numbers corresponding to the near-infra red, red and blue channels, respectively. f
p
j Part reserved to the corrector
................................................................................................................
Question 11
Apply this function on the image fabas, and threshold the EVI to extract the vegetated areas.
Report the treshold used below. Explain your choice.
f
p
j Part reserved to the corrector
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Correction
