A scientist converts the linear NRCS values of the pixels of a SAR image into a

Question

A scientist converts the linear NRCS values of the pixels of a SAR image into a grayscale image with 256 gray levels, such that an NRCS of 0.0 is mapped to a gray level of 0 (black) and an NRCS of 1.0 is mapped to a gray level of 255 (white). It turns out that features in an ocean area in the image look very dark, at gray levels from just 6 to 18, while features in a land area show up at gray levels from 150 to 220. a) To what gray level ranges will the ocean features and land features be mapped if the NRCS values are converted to dB before grayscaling? Assume that the grayscaling is done such that an NRCS of -20.0 dB is mapped to 0 (black) and an NRCS of 0.0 dB is mapped to 255 (white). 2.5%] b) The scientist realizes that thermal noise of the radar has increased the detected linear NRCS values by an amount of 0.01 on average. She tries to correct the data for this effect by subtracting 0.01 from each original pixel value. To what gray level ranges will the land and ocean features be mapped now (in the linear image and in the dB image) if the grayscaling and the conversion to dB is done in the same way as before? Please make sure to compute this for the linear image and for the dB image and discuss the results. [2.5%] Always explain how you obtain your results. Note that only 256 gray levels from 0 to 255 exist, so your results must be integer values within that range.

Explanation / Answer

a) linear transformation is needed to convert the scale

liner trnsformation formula,

dB – dBmin = (LI –LImin ) * [(dBmax – dBmin) / (LImax - LImin)] where LI =Linear image greyscale number

dB – (-20)= (LI – 0 ) * [(0 – -20) / (255 - 0)]

dB = -20 + LI*(20/255) …………… (i)

Now, putting the greyscale value in equation (i), we can get dB value of the corresponding.

for ocean and land, we can calculate in dB

Type

Linear image

dB

Ocean minimum

6

-19.52941176

Ocean maximum

18

-18.58823529

Land minimum

150

-8.235294118

Land maximum

220

-2.745098039

     Thus, ocean value is -19.52 to -18.59 in linear image and land value is -8.23 to -2.74 in dB.

b)

LI range/dB range = (LImax - LImin)/ (dBmax – dBmin)

Linear image range = 0.01 * (255/20) = 0.1275

Type

Linear image

Corrected Linear image

Final Linear image with truncation

dB

Corrected dB

Ocean minimum

6

5.8725

6

-19.52941176

-19.53941176

Ocean maximum

18

17.8725

18

-18.58823529

-18.59823529

Land minimum

150

149.8725

150

-8.235294118

-8.245294118

Land maximum

220

219.8725

220

-2.745098039

-2.755098039

Linear image greyscale will be same for ocean and land digital values, nut in NRSC db will change for those values. In greyscale, values are rounded up.

Type

Linear image

dB

Ocean minimum

6

-19.52941176

Ocean maximum

18

-18.58823529

Land minimum

150

-8.235294118

Land maximum

220

-2.745098039

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