Correction

Remote Sensing Examination - 2015-2016The 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 :

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1 Multiple choices questionsQuestion 1

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

λ

Refl

ectanc

e

Spectral Plot

s1s2s3s4

In figure Spectral plot, the specta corresponding to grass is

4 2 3 1

Correction

Question 2Figure 2

0 100 200 300 400 500 600 700 800

0

100

200

300

400

500

600

7001.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

0.25

0 100 200 300 400 500 600 700 800

0

100

200

300

400

500

600

7000.36

0.30

0.24

0.18

0.12

0.06

0.00

0.06

1 2

0 100 200 300 400 500 600 700 800

0

100

200

300

400

500

600

7001.2

0.8

0.4

0.0

0.4

0.8

1.2

0 100 200 300 400 500 600 700 800

0

100

200

300

400

500

600

7000.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

3 4From images in Figure 2, which image correspdonds to the computation of NDVI?

3 2 4 1

Question 3λ (µm) 0.45-0.52 0.52-0.60 0.63-0.69 0.76-0.90

x 777 817 413 849From the above pixel x, its NDVI value is:

2.89449 0.02689 0.36638 0.34547

Question 4A 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 0.76-0.90x 0.8 0.2 0.1 0.0

In a “true color” composition, the pixel will be:

green black blue red

Correction

Question 5 For a Gaussian mixture model, where the x ∈ R10 and C = 5, the number of parameters to estimateis:

50 329 55 325

Question 6The satellite Quickbird acquires images with 4 spectral bands where pixels have size of 2.5 meters per side. Theseimages are

Panchromatic Hyperspectral Multispectral Color

2 PCA-Based regularizationThe Tikhonov optimization problem for the estimation of the inverse of the covariance matrix of class i is :

Âi = minAi

[∥∥∥Σ̂iAi − I∥∥∥2 + ‖ΓiAi‖2] (1)with Σ̂i the empirical covariance matrix of class i and Γi a matrix that gives preference to some solution. In thiswork, we will consider a particular form Γi:

Γi = QiΨiQti with Ψi = diag

0, . . . , 0︸ ︷︷ ︸p

,+∞, . . . ,+∞︸ ︷︷ ︸d−p

where Qi = [qi1, . . . ,qid] is the orthonormal matrix of eigenvectors of Σ̂i, qi1 (resp. qid) is the eigenvectorcorresponding to the largest (resp. lowest) eigenvalue and p ∈ {1, . . . , d}.

Correction

Question 7 Prove that Ai can be written is terms of eigenvector/eigenvalue of Σ̂i and p in the following form:

Âi =p∑

j=1λ−1ij qijq

tij = Q̃iΛ̃

−1i Q̃ti.

Write Q̃i and Λ̃i. f p j Part reserved to the corrector

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Question 8 Compute the condition number associated to the inverse problem (25).f j Part reserved to the corrector

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Correction

Question 9 Implement the regularization with matlab (training, cross_validation and testing). Ap-ply it on the hyperspectral data sets : plot the overall accuracy in function of the parameter using thecross-validation technique and select the optimal value of p. Provide matlab files to run your program.

f p j Part reserved to the corrector

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3 Enhance Vegetation IndexThe NDVI is known to saturate and some authors prefer to use another index to assess vegetation. The EnhanceVegetation 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

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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