The entropy as a measure of the performance of a vegetation index. A pilot study using ALOS digital images
George Skianis(1) and Konstantinos Nikolakopoulos(2)
(1) University of Athens, Panepistimiopolis, 15784 Zografou, Athens, Greece
(2) Institute of Geology & Mineral Exploration (IGME), 20, Chrysoupoleos str., 15127 Melissia Athens, Greece
In recent research studies (Vaiopoulos et.al. 2004, Skianis et. al. 2007a, b) it has been shown that probability theory may helping assessing the performance of various vegetation indices. Introducing proper distributions, we have pointed out that the histogram of the image of the quite often used NDVI vegetation index, for example, may be described by the following distribution g(u):
g(u) = 4λ(1-u2)/[ λ(1+u)2+(1-u)2]2 (1)
u is the ratio of the tonality at the Near Infrared Band to that at the Red Band. λ is the ratio of the tonality variance at the Red Band to that at the Near Infrared Band.
The magnitude of the entropy of the image histogram may be useful in assessing the performance of the vegetation index. If the entropy is high, the histogram is broad, the image contrast is big and different land cover types are expected to be more clearly expressed. A low entropy means a not good tonality contrast, which may imply difficulties in recognizing targets of interest.
The entropy H of the image may be defined by:
H = ∫R g(u).ln[g(u)]du (2)
R is the range of u. In the case of the NDVI vegetation index, R is the range [-1, 1]. For other vegetation indices, it may be different.
In the present paper the integral of relation (2) is numerically calculated, in order to study the behavior of the entropy H of the NDVI, as well as other indices. It is pointed out that H depends on λ, or, in other words, on the standard deviations of the Near Infrared and Red Channels. It is possible, however, to increase the entropy and improve the tonality contrast, by modifying properly the expression for the NDVI.
These theoretical predictions were compared with real data obtained by ALOS digital images, in order to test the validity of the proposed methodological approach. The results and conclusions of this paper may be useful in mapping the land cover of an area using satellite imagery.
Vaiopoulos, D. A., Skianis, G. A., Nikolakopoulos, K., 2004 : The contribution of probability theory in assessing the efficiency of two frequently used vegetation indices. International Journal of Remote Sensing, 25(20), 4219-4236.
Skianis G., Vaiopoulos D., and Nikolakopoulos K., 2007a: A Comparative Study of the Performance of the NDVI, the TVI and the SAVI Vegetation Indices over burnt areas, using probability theory and spatial analysis techniques. Proceedings of the 6th International Workshop of the EARSeL Special Interest Group on Forest Fires, 27-29 September 2007, Thessaloniki-Greece, 142-145.
Skianis, G. Aim., Vaiopoulos, D., Nikolakopoulos, K., 2007b: A Probabilistic Approach to the Problem of Assessing the Efficiency of the Transformed Vegetation Index. Int. J. Sus. Dev. Plann. 2(4), 461-480.