vignettes/foto-background.Rmd
+ foto-background.RmdThe FOTO (Fourier Transform Textural Ordination) method uses a +principal component analysis (PCA) on radially averaged 2D fourier +spectra to characterize (greyscale) image texture (of canopies). Here, +I’ll explain the underlying algorithm, with a worked example. This +should give you a better insight in how the algorithm works and how some +of the parameters influence your analysis.
+
Note that the three boxes have very different textures.
+
The next step in the algorithm is to transform the data using a +Fourier decomposition.
+
+# fft transform
+fftim_1 <- Mod(stats::fft(im_1))^2
+fftim_2 <- Mod(stats::fft(im_2))^2
+fftim_3 <- Mod(stats::fft(im_3))^2The data now need to be radially averaged, so we calculate the +distance relative to the center of the image.
+
+# calculate distance from the center of the image
+offset <- ceiling(dim(im_1)[1] / 2)
+
+# define distance matrix
+# r is rounded to an integer by zonal
+distance_mask <- sqrt((col(im_1) - offset)^2 + (row(im_1) - offset)^2)We first back convert all data to terra objects
+(rasters), to make the raster math easier.
+# suppress warning on missing extent (which
+# is normal)
+fftim_1 <- terra::rast(fftim_1)
+fftim_2 <- terra::rast(fftim_2)
+fftim_3 <- terra::rast(fftim_3)
+distance_mask <- terra::rast(distance_mask)Below you see the concentric mask and the 2D FFT frequency plot. +Note, unlike most conventional plots the data is not centered on 0.
+ +
For all FFT spectra the data will be radially averaged, removing any
+directional components from the data. The terra zonal()
+function is used to do this efficiently.
+rspec_1 <- rev(
+ terra::zonal(
+ fftim_1,
+ distance_mask,
+ fun = "mean",
+ na.rm = TRUE
+ )[, 2]
+)Plotting the averaged spectra shows subtle differences between the +different textures.
+
Hufkens K (2024). foto: Fourier Transform Textural Ordination. -R package version 1.1, https://github.com/bluegreen-labs/foto. +R package version 1.2, https://github.com/bluegreen-labs/foto.
@Manual{,
title = {foto: Fourier Transform Textural Ordination},
author = {Koen Hufkens},
year = {2024},
- note = {R package version 1.1},
+ note = {R package version 1.2},
url = {https://github.com/bluegreen-labs/foto},
}
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+