Basic pattern matching: saturday morning hack

The Pattern Perception Zooniverse project asks Zooniversites to classify patterns based upon their (dis)similarity. Yet given the narrow scope of the problem (no rotations, same output every time) it was well worth exploring how a simple covariance based metric would perform. The input to the problem is a set of 7 images, one reference image and six scenarios to compare it to. Below you see the general layout of the image as shown on the Zooniverse website (I’ll use a different image afterwards).

model_run

The basic test would be to calculate x features for all maps and compare the six scenarios to the reference map and record the covariance of each of these comparisons. I then rank and plot the images accordingly. Although I’m pretty certain that any greyscale covariance metric would perform well in this case (including the raw data). However, I added a spatially explicit information based upon the Grey Level Co-occurence Matrix (GLCM) features. This ensures in part the inclusion of some spatial information such as the homogeneity of the images.

When performing this analysis on a set of images this simple approach works rather well. The image below shows you the ranking (from good to worse - top to bottom) of six images (left) compared to the reference image (right) (Fig. 1). This ranking is based upon the covariance of all GLCM metrics. In this analysis map 3 seems not to fall nicely in the sequence (to my human eye / mind). However, all GLCM features are weighted equally in this classification. When I only use the “homogeneity” GLCM feature in a classification a ranking of the images appears more pleasing to the eye (Fig. 2).

A few conclusions can be drawn from this:

  1. Human vision seems to pick up high frequency features more than low frequency ones, in this particular case. However, in general things are a bit more complicated.
  2. In this case, the distribution of GLCM features does not match human perception and this unequal weighing relative to our perception sometimes provides surprising rankings.
  3. Overall the best matched images still remain rather stable throughout suggesting that overall the approach works well and is relatively unbiased.

Further exploration of these patterns can done with a principal component analysis (PCA) on the features as calculated for each pixel. The first PC-score would indicated which pixels cause the majority of the variability across maps 1-6 relative to the reference (if differences are taken first). This indicate regions which are more stable or variable under different model scenarios. Furthermore, the project design lends itself to a generalized mixed model approach, with more statistical power than a simple PCA. This could provide insights in potential drivers of this behaviour (either due to model structure errors or ecological / hydrological processes). A code snippet of the image analysis written in R using the GLCM package is attached below (slow but functional).

[caption id=”attachment_1282” align=”aligncenter” width=”512”]map_comparison Fig 1. An image comparison based upon all GLCM features.[/caption]

[caption id=”attachment_1283” align=”aligncenter” width=”512”]map_comparison_homogeneity Fig 2. An image comparison based upon the homogeneity GLCM feature.[/caption]

# load required libs
require(raster)
require(glcm)

# set timer
ptm <- proc.time()

# load the reference image and calculate the glcm
ref = raster('scenario_reference.tif',bands=1)
ref_glcm = glcm(ref) # $glcm_homogeneity to only select the homogeneity band

# create a mask to kick out values
# outside the true area of interest
mask = ref == 255
mask = as.vector(getValues(mask))

# convert gclm data to a long vector
x = as.vector(getValues(ref_glcm))

# list all maps to compare to
maps = list.files(".","scenario_map*")

# create a data frame to store the output
covariance_output = as.data.frame(matrix(NA,length(maps),2))

# loop over the maps and compare
# with the reference image
for (i in 1:length(maps)){

  # print the map being processed
  print(maps[i])

  # load the map into memory and
  # execute the glcm routine
  map = glcm(raster(maps[i],bands=1)) # $glcm_homogeneity to only select the homogeneity band

  # convert stacks of glcm features to vector
  y = as.vector(getValues(map))

  # merge into matrix
  # mask out border data and
  # drop NA values
  mat = cbind(x,y)
  mat = mat[which(mask != 1),]
  mat = na.omit(mat)

  # put the map number on file
  covariance_output[i,1] = i

  # save the x/y covariance
  covariance_output[i,2] = cov(mat)[1,2]
}

# sort the output based upon the covariance
# in decreasing order (best match = left)
covariance_output = covariance_output[order(covariance_output[,2],decreasing = TRUE),]

# stop timer
print(proc.time() - ptm)

# loop over the covariance output to plot how the maps best
# compare
png("map_comparison.png",width=800,height=1600)
par(mfrow=c(6,2))
for (i in 1:dim(covariance_output)[1]){
  rgb_img = brick(sprintf("scenario_map%s.tif",covariance_output[i,1]))
  ref = brick("scenario_reference.tif")
  plotRGB(rgb_img)
  legend("top",legend=sprintf("Map %s",covariance_output[i,1]),bty='n',cex=3)
  plotRGB(ref)
  legend("top",legend="Reference",bty='n',cex=3)
}
dev.off()

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