Comparing spatial patterns in raster data using R
2024-07-04
“A spatial pattern is a scale-dependent predictability of the physical arrangement of observations” (Dale, 2000)
Example data
NDVI values derived from Sentinel-2 images for early summer:
CORINE Land Cover:
Visual inspection
Advantages: uses the human ability to recognize patterns and considers many aspects, including local and global similarities, and logical coherence (Hagen-Zanker, 2008).
Disadvantages: the observer’s perspective and the chosen visualization method can heavily influence the results (a subjective process). Also, it can be time-consuming and not suitable for large datasets.
Various aspects of spatial patterns’ comparison
- Data type: continuous, categorical
Various aspects of spatial patterns’ comparison
- Data type: continuous, categorical
- Outcome: raster, single value, multiple values
raster outcome:
single value outcome: 0.21
multiple values outcome:
Various aspects of spatial patterns’ comparison
- Data type: continuous, categorical
- Outcome: raster, single value, multiple values
- Context: non-spatial, spatial
Various aspects of spatial patterns’ comparison
- Data type: continuous, categorical
- Outcome: raster, single value, multiple values
- Context: non-spatial, spatial
- Disjoint areas: no, yes
Raster outcome
Continuous raster data:
Categorical raster data:
Raster outcome
Continuous raster data:
Raster outcome
Categorical raster data:
Single value outcome
Non-disjoint areas
| method | R package |
|---|---|
| Root mean square error | yardstick |
| Mean absolute difference | diffeR |
| Average of Structural Similarity Index | SSIMmap |
RMSE: 0.219
MAD: 0.184
SSIM: 0.638
Single value outcome
Non-disjoint areas
| method | R package |
|---|---|
| The proportion of changed pixels | terra |
| The overall comparison (Pontius 2002) | terra |
| Statistics of the differences between rasters’ values | diffeR |
| Spatial association between regionalizations (Nowosad and Stepinski 2018) | sabre |
Proportion of changed pixels: 0.054
Overall comparison: 0.972
Overall exchange difference: 5280
V-measure: 0.772
Single value outcome
0.037 <- Disimilarity between the distributions -> 0.028
0.069 <- Difference in roughness (focal) -> 0.008
0.019 <- GLCM -> 0.004
1.5402113^{4} <- Difference in Gao’s entropy -> 1.0611691^{4}
Disjoint areas
| method | R package |
|---|---|
| Disimilarity between the distributions | philentropy |
| The difference between average of a focal measure | geodiv |
| The difference between average of a focal measure | GLCMTextures |
| Comparison of the values of the Boltzmann entropy (Gao and Li 2019) | bespatial |
Single value outcome
0.036 <- Difference of SHDI -> 0.03
0.17 <- Difference of ED -> 5.632
0.001 <- Difference of Zhao’s entropy -> 0.002
0.001 <- JS divergence of the spatial signatures -> 0.083
Disjoint areas
| method | R package |
|---|---|
| Comparison of the values of a landscape metric | landscapemetrics |
| Comparison of the values of Zhao’s entropy (Zhao and Zhang 2019) | bespatial |
| Dissimilarity of a spatial signature (Jasiewicz and Stepinski 2013) | motif |
Multiple values outcome
| method | R package |
|---|---|
| The distribution of the difference between values of two rasters | terra |
| Statistics of the differences between rasters’ values calculated at many scales | waywiser |
Multiple values outcome
1 2 3 4 6 7
1 4821 357 2 10 0 0
2 1342 67915 684 389 0 0
3 59 415 33670 2896 9 22
4 122 638 1435 7040 229 24
6 0 3 13 20 2177 37
7 0 0 0 0 3 1995| method | R package |
|---|---|
| The contingency table of the values of two rasters | terra |
Extensions and multidimensional data
The above methods can be extended to compare two sets of raster layers, such as two time-series:
- Treat each layer as a separate raster and compare corresponding layers using the methods described above (a pairwise comparison)
- Compress the data into one dimension (e.g., one raster layer) and then compare such compressed data
- Create temporal or spatiotemporal signatures and compare them using dissimilarity measures
Author: Lorena Abad
R tools
R and its packages provide a wide range of tools for comparing spatial patterns
Remaining issues:
- The current R efforts are rather fragmented, with packages having different interfaces, assumptions, and types of data they can handle
- Not all commonly used methods are implemented in R, e.g., the Complex Wavelet Structural Similarity Index or the Fuzzy Kappa index
- Several packages are not on CRAN, and have minimal documentation and examples
- The efforts needed to develop user tutorials and maintain scientific software are still underappreciated in the scientific community and undervalued in the academic reward system
Method selection
There is almost an unlimited range of possible map comparison methods, and no universal method for assessing the similarity between spatial patterns (Hagen-Zanker, 2008)
The choice of method should depend on (Boots and Csillag, 2006):
- the pattern characteristics to be examined
- the categories/ranges of values involved in the comparison
- the selection of geographic space
- the choice of the unit of computed measures
- the decision if the significance tests are needed
Other considerations include data preprocessing and the scale and extent of comparison (Tewkesbury et al., 2015)
Future directions
Different methods can produce varying outcomes when analyzing differences in spatial patterns, and using a variety of methods may be advisable to gain a comprehensive understanding
Author: Lorena Abad
There is a lack of studies that systematically compare different methods of assessing similarity between spatial patterns, or suggest good practices in their use
The growing number of FOSS tools for spatial raster comparison offers a promising avenue for testing various methods and their application to real-life scenarios