Where can I find tables or database reporting Minnaert Constant values (used for topographic correction of remote sensing images) for different type of soils?
Hi Varun,
Thank you for your answer.
I implanted a software (in IDL) for atmospheric (based on MODTRAN) and topographic corrections. This software includes a module for the compute of the Minnaert constant. I applied the procedure to an HYPERION image and obtained the Minnaert constant for different type of soils.
Now, I’m looking for literature values of Minnaert constant to make comparisons with the values tha I obtained.
Thank you again
My original answer seems to have disappeared so posting again below:
Hi Sergio,
I am not aware of a look up table for Minnaert correction constants (k). Since the value of k is dependent on terrain properties(slope and aspect), solar azimuth and solar zenith angle (the later two depend on time the image was captured), my guess is you will be hard pressed to find a comprehensive look up table (there are just too many combinations to deal with).
But, you might be best served by carrying out the topographic correction by developing your own constant/s, as is usually done.
What you need to do this is:
1. the image you want to apply the correction to. If you are using images from sources such as LandSat, the image meta-data will contain values for solar azimuth and solar zenith angle.
2. A digital elevation model (DEM) of the same region as the image, from which you will derive terrain slope and aspect, which then feed into the equation for the illumination model as explained below.
The basic method for a Minnaert correction to get a corrected image is carried out using the following equation:
(corrected image) = (input image) * [cos(z) / cos(i)] ^k
where:
k = Minnaert constant
z = solar zenith angle
cos_i = cosine of the illumination model and is calculated as:
cos_i = cos(s) * cos(z) + sin(s) * sin(z) * cos(a - o)
where:
s = terrain slope
z = solar zenith angle
a = solar azimuth angle
o = terrain aspect angle
To estimate k and feed into the first equation you need to run the following regression:
ln(input image) = ln(corrected image) - k ln[cos_i/cos(z)]
The output of this regression will estimate a constant for ln(corrected image) and k. This k value is then fed into the first equation.
The method above results in a single Minnaert constant which is then applied over the entire image. However, there are published arguments that a 'global minnaert constant' may not always provide satisfactory results. To address this there are some pixel based methods such as Lu. et al. 2008 (https://www.researchgate.net/publication/235244169_Pixel-based_Minnaert_Correction_Method_for_Reducing_Topographic_Effects_on_the_Landsat_7_ETM_Image?ev=srch_pub&_sg=uznRr3hjSuO6uD709Qjl4%2B3kJgQXWTBEn%2FQuEwCqyJ3Z4YLNe%2BXz0xPYtHX5pLJU_TM1KaGJVyey3Oh5L%2BW35vb%2BcXjzq4ew1wNroGNlvY7zdD71KXrE2%2B%2FWdYz%2BQbX96).
Lastly, there are some readily implemented correction procedures offered by different software (some more comprehensive than others). I have used GRASS and ENVI to carry out Minnaert corrections. Have a look at their help pages or user forums to get more details:
1. http://grass.osgeo.org/grass65/manuals/i.topo.corr.html
2. http://www.exelisvis.com/Support/Forums/tabid/184/forumid/6/postid/5797/scope/posts/Default.aspx
Hope this helps
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