​Comparison of RGB Indices used for Vegetation Studies based on Structured Similarity Index (SSIM)

Remote sensing methods are receiving more and more attention during vegetation studies, thanks to the rapid development of drones. The use of indices created using different bands of the electromagnetic spectrum is currently a common practice in agriculture e.g. normalized vegetation index (NDVI), for which, in addition to the red (R), green (G) and blue (B) bands, in different infrared (IR) ranges used bands are used. In addition, there are many indices in the literature that can only be calculated from the red, green, blue (RGB) bands and are used for different purposes. The aim of our work was to objectively compare and group the RGB indices found in the literature (37 pcs) using an objective mathematical method (structured similarity index; SSIM), as a result of which we classified the individual RGB indices into groups that give the same result. To do this, we calculated the 37 RGB indexes on a test image, and then compared the resulting images in pairs using the structural similarity index method. As a result, 28 of the 37 indexes examined could be narrowed down to 7 groups - that is, the indexes belonging to the groups are the same - while the remaining 9 indexes showed no similarity with any other index.

Nowadays, with the help of drones, we can not only take detailed, high-resolution shots but also evaluate the shots using the methods used in image processing. In the present case, these represent the various filters (noise, color, edge, etc.) on the one hand, and the indices calculated from the spectrum bands on the other. The use of indices is currently common practice in agriculture; however, these indices use bands used in different infrared ranges in addition to the RGB (red, green, blue) bands. In addition, there are several indices containing only RGB bands, the most common purpose of which is to create indices formed using only RGB bands like the results of the Normalized Vegetation Index (NDVI) and Normalized Difference Red Edge Index (NDRE) indices formed using the more expensive infrared bands (Near Infrared, RedEdge).

The aim of our work is to objectively compare and group the most common RGB indices (37 pcs) currently found in the literature. Of course, it is not our goal to process all the indices that can be found in the literature, since new indices are always being created, which are usually specific to a specific plant culture. The most important question is how many groups they can be classified into, using an objective mathematical method, as well as which RGB indexes each group contains, so which indexes give almost the same result. We did not aim to examine the applicability of the indices, i.e. to what vegetation they were applied, and what is the interpretation of the results of the given index. Considering the various plant cultures, we didn't have the opportunity to do so. We wanted to use a purely mathematical method to compare the indices and draw attention to possible redundancies.

As a first step, we collected the most important RGB indices found in the literature, which are as follows (Table 1).

The test image used for the RGB indices (Figure 1) was taken in JPG picture file format with a DJI Mavic Mini rotary-wing quadcopter drone, in Vértes mountains, Hungary. The recording shows low and higher vegetation, shade, a barren dirt road, and white limestone piles, so the recording provides a good opportunity to test the indices. The parameters of the camera used for recording are as follows. Sensor type 1/2.3" CMOS (Complementary Metal-Oxide Semiconductor sensor), effective pixel 12 Megabyte, image size 4000 x 3000 pixels, viewing angle 83°, focal length 24 mm and aperture f/2.8.

To find out which band carries the most information, we calculated the Shannon’s entropy of each band [1,2] (Table 2).

So, those indexes that contain the band with the highest entropy give the right result (differentiate the vegetation sufficiently [3,4].

Table 2 contains the values calculated according to the reference [5,6] for the self-similar (Spectral Fractal Dimension) image structure. All of this is important for higher-order image processing processes, information security analysis [3,7,8], and for the investigation of the effect of image sensor noise on the image structure [9,10].

From the RGB bands of the recording shown in Figure 1, we calculated the individual indices with the Quantum GIS (QGIS) software based on the formulas shown in Table 1, and then each index image was created in two file formats. As a first step, we created a "false color" image; with the same colour scale for each index, where the red color represents the negative or 0 value, while the blue color represents the more positive values. This way you can easily compare the completed index images. As a second step, the index image was saved as a grayscale image since the mathematical method for objective comparison only handles grayscale JPG images.

The pairwise comparison of the index images was done based on the structural similarity index [11], which results in a value between -1 and +1, where -1 represents the complete difference between the two images, while + 1 for a complete match. The comparisons were made in the Python Programming Language with the "scikit-image" program package, which also includes the SSIM method [12].

As a result of the comparisons, we obtained a similarity matrix, which gives the pairwise similarity value of each index. We considered only indices with a pairwise SSIM value ≥ 0.9 to be the same. Based on the values of the similarity matrix, the following indices show complete agreement (the formulas are the same, so SSIM = 1):

• ExG = GCC (for the exact name of the indexes see Table 1.)
• GLI = VDVI
• GRVI = MPRI, NDI, NGRDI, VIgreen (of course these indices are also the same)
• IKAW = SI

During the examination of further similarities, we obtained 7 groups (Table 3) in which the SSIM value of the indices is 1.0 > x ≥ 0.9.

Out of the 37 indexes, 28 indexes are included in the above 7 groups. From these groups, we selected one characteristic index that best characterizes the given group (by visual comparison), these are MGRVI, RGBVI, GCC, MVARI, GLI, VEG, and TGI. The remaining 9 indices can be considered unique, i.e. not like any other index, they are: BGI, BI, ExB, GR, HUE, RCC, PRI, vNDVI, and WI.

Thus, as a result, the 38 indexes can be considered a total of 16 different indexes, which are as follows: BGI, BI, ExB, GCC, GLI, GR, HUE, MGRVI, MVARI, RCC, RGBVI, RGI (same as PRI), TGI, VEG, vNDVI, WI (Figure 2).

Based on the examination of the most common 37 RGB indices found in the literature using the objective similarity method, we can therefore speak of 16 independent indices. It is important to emphasize that this does not mean that redundant indexes are unnecessary, but only that during image data processing, we can even use several indexes to answer a question, which will probably give a similar result. During the comparisons, we ignored the original applicability of the given indices, that is, on what type of vegetation they were first used. However, when solving the given problem, this aspect must also be considered before the index is selected.

Further investigation can be performed on several types of vegetation and the 16 types of indices can be interpreted. But perhaps the most important question is which index gives the most similar results to the NDVI index, as this could reduce the use of multispectral cameras during vegetation surveys with unmanned aerial vehicles (UAVs).

So far, we have not found works of a similar nature and purpose in the literature that is, where indexes were compared using an objective statistical method. The comparison of the vegetation indices was only aimed at which RGB indices give similar results as the multispectral (MS) indices, tested on a specific type of vegetation [13-18]. The present work does not examine the similarity of the RGB and MS indices on a specific vegetation, but independently of the vegetation, namely in an objective statistical manner. Thus, the results are most likely true for most vegetation.

Future developments include the creation of an open image database suitable for the presented SSIM-based comparative studies based on various aspects (UAVs, recording parameters, image sensor devices and types, image file formats, vegetation types, and vegetation periods). Thus, based on the various aspects above, we will be able to objectively compare the pictures. Hopefully, we will be able to report on their results soon.

Project no. TKP2021-NVA-05 has been implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the TKP 2021 funding scheme.

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