Advanced Raster Analysis: Classification

In this example, we will publish a documented report using R, carry out a supervised and unsupervised classification on a series of raster layers, construct a raster sieve using the clump() function, and work with thematic (categorical maps).

Introduction to Landsat data

Since being released to the public, the Landsat data archive has become an invaluable tool for environmental monitoring. With a historical archive reaching back to the 1970s, the release of these data has resulted in a spur of time series-based methods. In this tutorial, we will work with time series data from the Landsat 7 Enhanced Thematic Mapper (ETM+) sensor. Landsat scenes are delivered via the USGS as several image layers representing the different bands captured by the sensors. In the case of the Landsat 7 Enhanced Thematic Mapper (ETM+) sensor, the bands are shown in the figure below. Using different combinations of these bands can be useful in describing land features and change processes.

Landsat 7 ETM+ bands

Part of a Landsat scene, including bands 2-4 is included in the data provided here. These data have been processed using the LEDAPS framework, so the values contained in this dataset represent surface reflectance, scaled by 10000 (ie. divide by 10000 to get a reflectance value between 0 and 1).

We will begin exploring these data simply by downloading and visualizing them:

To download the data you can clone this GitHub repository (https://github.com/itaiaxelrad/remote-sensing) to your local computer. All the required datasets are located within the data folder.

## Libraries
library(raster)
## Load data
load("data/GewataB2.rda")
load("data/GewataB3.rda")
load("data/GewataB4.rda")
## Check out the attributes
GewataB2
## Some basic statistics using cellStats()
cellStats(GewataB2, stat=max)
cellStats(GewataB2, stat=mean)
# This is equivalent to:
maxValue(GewataB2)
## What is the maximum value of all three bands?
max(c(maxValue(GewataB2), maxValue(GewataB3), maxValue(GewataB4)))
## summary() is useful function for a quick overview
summary(GewataB2)
## Put the 3 bands into a RasterBrick object to summarize together
gewata <- brick(GewataB2, GewataB3, GewataB4)
# 3 histograms in one window (automatic, if a RasterBrick is supplied)
hist(gewata)

When we plot the histogram of the RasterBrick, the scales of the axes and the bin sizes are not equivalent, which could be problematic. This can be solved by adjusting these parameters in hist(), which requires extra consideration. The raster hist() function inherits arguments from the function of the same name from the graphics package. To view additional arguments, type: ?graphics::hist. To ensure that our histograms are of the same scale, we should consider the xlim, ylim, and breaks arguments.

# reset plotting window
par(mfrow = c(1, 1))
hist(gewata, xlim = c(0, 5000), ylim = c(0, 750000), breaks = seq(0, 5000, by = 100))

Note that the values of these bands have been rescaled by a factor of 10000. This is done for file storage considerations. For example, a value of 0.5643 stored as a float takes up more disk space than a value of 5643 stored as an integer. If you prefer reflectance values in their original scale (from 0 to 1), this can easily be done using raster algebra or calc().

A scatterplot matrix can help explore relationships between raster layers. This can be done with the pairs() function of the raster package, which (like hist()) is a wrapper for the same function found in the graphics packages.

pairs(gewata)

Note that both hist() and pairs() compute histograms and scatterplots based on a random sample of raster pixels. The size of this sample can be changed with the argument maxpixels in either function.

Calling pairs() on a RasterBrick reveals potential correlations between the layers themselves. In the case of bands 2-4 of the gewata subset, we can see that bands 2 and 3 (in the visual part of the EM spectrum) are highly correlated, while band 4 contains significant non-redundant information.

In the case of bands 2-4 of the gewata subset, we can see that bands 2 and 3 (in the visual part of the EM spectrum) are highly correlated, while band 4 contains significant non-redundant information. ETM+ band 4 (nearly equivalent to band 5 in the Landsat 8 OLI sensor) is situated in the near-infrared (NIR) region of the EM spectrum and is often used to describe vegetation-related features. We observe a strong correlation between two of the Landsat bands of the gewata subset, but a very different distribution of values in band 4 (NIR). This distribution stems from the fact that vegetation reflects very highly in the NIR range, compared to the visual range of the EM spectrum. A commonly used metric for assessing vegetation dynamics is the normalized difference vegetation index (NDVI), which takes advantage of this fact and is computed from Landsat bands 3 (visible red) and 4 (near infrared).

We observe a strong correlation between two of the Landsat bands of the gewata subset, but a very different distribution of values in band 4 (NIR). This distribution stems from the fact that vegetation reflects very highly in the NIR range, compared to the visual range of the EM spectrum. A commonly used metric for assessing vegetation dynamics, the normalized difference vegetation index (NDVI), explained in the previous lesson, takes advantage of this fact and is computed from Landsat bands 3 (visible red) and 4 (near infra-red).

There are several ways to calculate NDVI, using direct raster algebra, calc(), or overlay(). Since we will be using NDVI again later in this tutorial, let's calculate it again and store it in our workspace using overlay().

ndvi <- overlay(GewataB4, GewataB3, fun=function(x,y){(x\-y)/(x+y)}) plot(ndvi)

Aside from the advantages of calc() and overlay() regarding memory usage, an additional advantage of these functions is the fact that the result can be written immediately to a file by including the filename = "..." argument, which will allow you to write your results to file immediately, after which you can reload in subsequent sessions without having to repeat your analysis.

Classifying Raster Data

One of the most important tasks in the analysis of remote sensing image analysis is image classification. In classifying the image, we take the information contained in the various bands (possibly including other synthetic bands such as NDVI or principal components). In this tutorial we will explore two approaches for image classification:

Supervised Classification: Random Forest

The Random Forest classification algorithm is an ensemble learning method that is used for both classification and regression. In our case, we will use the method for classification purposes. Here, the random forest method takes random subsets from a training dataset and constructs classification trees using each of these subsets. Trees consist of branches and leaves.

Branches represent nodes of the decision trees, which are often thresholds defined for the measured (known) variables in the dataset. Leaves are the class labels assigned at the termini of the trees. Sampling many subsets at random will result in many trees being built. Classes are then assigned based on classes assigned by all of these trees based on a majority rule as if each class assigned by a decision tree were considered to be a vote.

One major advantage of the Random Forest method is the fact that an Out of the Bag (OOB) error estimate and an estimate of variable performance are performed. For each classification tree assembled, a fraction of the training data is left out and used to compute the error for each tree by predicting the class associated with that value and comparing it with the already known class. This process results in a confusion matrix, which we will explore in our analysis. In addition, an importance score is computed for each variable in two forms: the mean decrease in accuracy for each variable, and the Gini impurity criterion, which will also be explored in our analysis.

We should first prepare the data on which the classification will be done. So far, we have prepared three bands from an ETM+ image in 2001 (bands 2, 3, and 4) as a RasterBrick, and have also calculated NDVI. In addition, there is a Vegetation Continuous Field (VCF) product available for the same period (2000).

For more information on the Landsat VCF product, see here. This product is also based on Landsat ETM+ data and represents an estimate of tree cover (in %). Since this layer could also be useful in classifying land cover types, we will also include it as a potential covariate in the Random Forest classification.

Load the data and check it out

load("data/vcfGewata.rda")
vcfGewata
## class : RasterLayer
## dimensions : 1177, 1548, 1821996 (nrow, ncol, ncell)
## resolution : 30, 30 (x, y)
## extent : 808755, 855195, 817635, 852945 (xmin, xmax, ymin, ymax) ## coord. ref. : +proj=utm +zone=36 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0
## data source : in memory
## names : vcf2000Gewata
## values : 0, 254 (min, max)
plot(vcfGewata)
summary(vcfGewata)
## vcf2000Gewata
## Min. 0
## 1st Qu. 32
## Median 64
## 3rd Qu. 75
## Max. 254
## NA's 8289
hist(vcfGewata)

In the vcfGewata and rasterLayer there are some values much greater than 100 (the maximum tree cover), which are flags for water, clouds, or cloud shadow pixels. To avoid these values, we can assign a value of NA to these pixels so they are not used in the classification.

vcfGewata\[vcfGewata \> 100\] <- NA
plot(vcfGewata)
summary(vcfGewata)
## vcf2000Gewata
## Min. 0
## 1st Qu. 32
## Median 64
## 3rd Qu. 75
## Max. 100
## NA's 13712
hist(vcfGewata)

To perform the classification in R, it is best to assemble all covariate layers (ie. those layers containing predictor variable values) into one RasterBrick object. In this case, we can simply append these new layers (NDVI and VCF) to our existing RasterBrick (currently consisting of bands 2, 3, and 4).

First, let's rescale the original reflectance values to their original scale. This step is not required for the RF classification, but it might help with the interpretation if you are used to thinking of reflectance as a value between 0 and 1. (On the other hand, for very large raster bricks, it might be preferable to leave them in their integer scale, but we won't go into more detail about that here.)

gewata <- calc(gewata, fun=function(x) x / 10000)
## Make a new RasterBrick of covariates by adding NDVI and VCF layers 
covs <- addLayer(gewata, ndvi, vcfGewata)
plot(covs)

You'll notice that we didn't give our NDVI layer a name yet. It's good to make sure that the raster layer names make sense, so you don't forget which band is which later on. Let's change all the layer names (make sure you get the order right!).

names(covs) <- c("band2", "band3", "band4", "NDVI", "VCF")
plot(covs)

For this example, we will do a very simple classification for 2001 using three classes: forest, cropland, and wetland. While for other purposes it is usually better to define more classes (and possibly fuse classes later), a simple classification like this one could be useful, for example, to construct a forest mask for the year 2001.

# Load the training polygons
load("data/trainingPoly.rda")
# Superimpose training polygons onto NDVI plot
plot(ndvi)
plot(trainingPoly, add = TRUE)

The training classes are labeled as string labels. For this example, we will need to work with integer classes, so we will need to first 'relabel' our training classes. Several approaches could be used to convert these classes to integer codes. In this case, we will first make a function that will reclassify the character strings representing land cover classes into integers based on the existing factor levels.

## Inspect the data slot of the trainingPoly object
trainingPoly@data

## OBJECTID Class
## 0 1 wetland
## 1 2 wetland
## 2 3 wetland
## 3 4 wetland
## 4 5 wetland
## 5 6 forest
## 6 7 forest
## 7 8 forest
## 8 9 forest
## 9 10 forest
## 10 11 cropland
## 11 12 cropland
## 12 13 cropland
## 13 14 cropland
## 14 15 cropland
## 15 16 cropland

# The 'Class' column is actually an ordered factor type
trainingPoly@data$Class

## \[1\] wetland wetland wetland wetland wetland forest forest ## \[8\] forest forest forest cropland cropland cropland cropland ## \[15\] cropland cropland

## Levels: cropland forest wetland
str(trainingPoly@data$Class)

## Factor w/ 3 levels "cropland","forest",..: 3 3 3 3 3 2 2 2 2 2

# We can convert to integer by using the as.numeric() function, # which takes the factor levels
trainingPoly@data$Code <- as.numeric(trainingPoly@data$Class) trainingPoly@data

## OBJECTID Class Code
## 0 1 wetland 3
## 1 2 wetland 3
## 2 3 wetland 3
## 3 4 wetland 3
## 4 5 wetland 3
## 5 6 forest 2
## 6 7 forest 2
## 7 8 forest 2
## 8 9 forest 2
## 9 10 forest 2
## 10 11 cropland 1
## 11 12 cropland 1
## 12 13 cropland 1
## 13 14 cropland 1
## 14 15 cropland 1
## 15 16 cropland 1

To train the raster data, we need to convert our training data to the same type using the rasterize() function. This function takes a spatial object (in this case a polygon object) and transfers the values to raster cells defined by a raster object. Here, we will define a new raster containing those values.

## Assign 'Code' values to raster cells (where they overlap)
classes <- rasterize(trainingPoly, ndvi, field='Code')

You might get warnings like the following:

In '\[<-'('\*tmp\*', cnt, value = p@polygons\[\[i\]\]@Polygons\[\[j\]\]) : implicit list embedding of S4 objects is deprecated.

You can ignore these for now.

There is a handy progress="text" argument, which can be passed to many of the raster package functions and can help to monitor processing. Try passing this argument to the rasterize() command above.

## Plotting
# Define a colour scale for the classes (as above)
# corresponding to: cropland, forest, wetland
cols <- c("orange", "dark green", "light blue")
## Plot without a legend
plot(classes, col=cols, legend=FALSE)
## Add a customized legend
legend("topright", legend=c("cropland", "forest", "wetland"), fill=cols, bg="wh ite")

Our goal in preprocessing these data is to have a table of values representing all layers (covariates) with known values/classes. To do this, we will first need to create a version of our RasterBrick only representing the training pixels. Here the mask() function from the raster package will be very useful.

covmasked <- mask(covs, classes)
plot(covmasked)
## Combine this new brick with the classes layer to make our input training dataset
names(classes) <- "class"
trainingbrick <- addLayer(covmasked, classes)
plot(trainingbrick)

Now it's time to add all of these values to a data frame representing all training data. This data frame will be used as input for the RandomForest classification function. We will use getValues() to extract all of the values from the layers of the RasterBrick.

## Extract all values into a matrix
valuetable <- getValues(trainingbrick)

If you print a value table to the console, you will notice that a lot of the rows are filled with NA. This is because all raster cell values have been taken, including those with NA values. We can get rid of these rows by using the na.omit() function.

valuetable <- na.omit(valuetable)

Now we will convert to a data.frame and inspect the first and last 10 rows.

valuetable <- as.data.frame(valuetable)

head(valuetable, n = 10)
## band2 band3 band4 NDVI VCF class
## 1 0.0354 0.0281 0.2527 0.7998575 77 2
## 2 0.0417 0.0301 0.2816 0.8068656 74 2
## 3 0.0418 0.0282 0.2857 0.8203249 72 2
## 4 0.0397 0.0282 0.2651 0.8077054 71 2
## 5 0.0355 0.0263 0.2237 0.7896000 77 2
## 6 0.0396 0.0281 0.2693 0.8110289 75 2
## 7 0.0375 0.0300 0.2817 0.8075072 76 2
## 8 0.0396 0.0263 0.2610 0.8169161 76 2
## 9 0.0354 0.0263 0.2320 0.7963608 76 2
## 10 0.0333 0.0263 0.2113 0.7786195 73 2

tail(valuetable, n = 10)

## band2 band3 band4 NDVI VCF class
## 36211 0.0451 0.0293 0.2984 0.8211779 76 2
## 36212 0.0406 0.0275 0.2561 0.8060649 76 2
## 36213 0.0361 0.0293 0.2179 0.7629450 75 2
## 36214 0.0406 0.0313 0.2222 0.7530572 74 2
## 36215 0.0405 0.0313 0.2222 0.7530572 73 2
## 36216 0.0406 0.0293 0.2646 0.8006125 79 2
## 36217 0.0429 0.0293 0.2774 0.8089338 70 2
## 36218 0.0451 0.0333 0.2900 0.7939994 77 2
## 36219 0.0406 0.0293 0.2689 0.8034876 81 2
## 36220 0.0429 0.0293 0.2434 0.7851118 73 2

Now that we have our training dataset as a data frame, let's convert the class column into a factor (since the values as integers don't have a meaning).

valuetable$class <- factor(valuetable$class, levels = c(1:3))

Now we have a convenient reference table that contains, for each of the three defined classes, all known values for all covariates. Let's visualize the distribution of some of these covariates for each class. To make this easier, we will create 3 different data frames for each of the classes. This is just for plotting purposes, and we will not use these in the actual classification.

val_crop <- subset(valuetable, class \== 1)
val_forest <- subset(valuetable, class \== 2)
val_wetland <- subset(valuetable, class \== 3)

## 1. NDVI
par(mfrow = c(3, 1))
hist(val_crop$NDVI, main = "cropland", xlab = "NDVI", xlim = c(0, 1), ylim = c( 0, 4000), col = "orange")
hist(val_forest$NDVI, main = "forest", xlab = "NDVI", xlim = c(0, 1), ylim = c( 0, 4000), col = "dark green")
hist(val_wetland$NDVI, main = "wetland", xlab = "NDVI", xlim = c(0, 1), ylim = c(0, 4000), col = "light blue")
par(mfrow = c(1, 1))

## 2. VCF
par(mfrow = c(3, 1))
hist(val_crop$VCF, main = "cropland", xlab = "% tree cover", xlim = c(0, 100), ylim = c(0, 7500), col = "orange")
hist(val_forest$VCF, main = "forest", xlab = "% tree cover", xlim = c(0, 100), ylim = c(0, 7500), col = "dark green")
hist(val_wetland$VCF, main = "wetland", xlab = "% tree cover", xlim = c(0, 100) , ylim = c(0, 7500), col = "light blue")
par(mfrow = c(1, 1))

## 3. Bands 3 and 4 (scatterplots)
plot(band4 ~ band3, data = val_crop, pch = ".", col = "orange", xlim = c(0, 0.2 ), ylim = c(0, 0.5))
points(band4 ~ band3, data = val_forest, pch = ".", col = "dark green")
points(band4 ~ band3, data = val_wetland, pch = ".", col = "light blue")
legend("topright", legend=c("cropland", "forest", "wetland"), fill=c("orange", "dark green", "light blue"), bg="white")

Try to produce the same scatterplot plot as in #3 looking at the relationship between other bands (e.g. bands 2 and 3, band 4 and VCF, etc.)

We can see from these distributions that these covariates may do well in classifying forest pixels, but we may expect some confusion between cropland and wetland (although the individual bands may help to separate these classes). When performing this classification on large datasets and with a large amount of training data, now may be a good time to save this table using the write.csv() command, in case something goes wrong after this point and you need to start over again.

Now it is time to build the Random Forest model using the training data contained in the table of values we just made. For this, we will use the randomForest package in R, which is an excellent resource for building such types of models. Using the randomForest() function, we will build a model based on a matrix of predictors or covariates (ie. the first 5 columns of valuetable) related to the response (the class column of valuetable).

## Construct a random forest model
# Covariates (x) are found in columns 1 to 5 of valuetable
# Training classes (y) are found in the 'class' column of valuetable ## Caution: this step takes fairly long
# but can be shortened by setting importance=FALSE
library(randomForest)
modelRF <- randomForest(x=valuetable\[ ,c(1:5)\], y=valuetable$class,  importance = TRUE)
## Warning: package 'randomForest' was built under R version 3.3.3 ## randomForest 4.6-12
## Type rfNews() to see new features/changes/bug fixes

Since the random forest method involves the building and testing of many classification trees (the 'forest'), it is a computationally expensive step (and could take a lot of memory for especially large training datasets). When this step is finished, it would be a good idea to save the resulting object with the save() command. Any R object can be saved as an .rda file and reloaded into future sessions using load().

The resulting object from the randomForest() function is a specialized object of class randomForest, which is a large list-type object packed full of information about the model output. Elements of this object can be called and inspected like any list object.

## Inspect the structure and element names of the resulting model modelRF
class(modelRF)
str(modelRF)
names(modelRF)

## Inspect the confusion matrix of the OOB error assessment
modelRF$confusion

# to make the confusion matrix more readable
colnames(modelRF$confusion) <- c("cropland", "forest", "wetland", "class.error" )
rownames(modelRF$confusion) <- c("cropland", "forest", "wetland")

modelRF$confusion

Since we set importance=TRUE, we now also have information on the statistical importance of each of our covariates which we can visualize using the varImpPlot() command.

varImpPlot(modelRF)

The figure above shows the variable importance plots for a Random Forest model showing the mean decrease in accuracy (left) and the decrease in Gini Impurity Coefficient (right) for each variable.

These two plots give two different reports on variable importance (see ?importance()).

First, the mean decrease in accuracy indicates the amount by which the classification accuracy decreased based on the OOB assessment. Second, the Gini impurity coefficient gives a measure of class homogeneity. More specifically, the decrease in the Gini impurity coefficient when including a particular variable is shown in the plot. From Wikipedia:

"Gini impurity is a measure of how often a randomly chosen element from the set would be incorrectly labeled if it were randomly labeled according to the distribution of labels in the subset".

In this case, it seems that Gewata bands 3 and 4 have the highest impact on accuracy, while bands 3 and 2 score highest with the Gini impurity criterion. For especially large datasets, it may be helpful to know this information and leave out less important variables for subsequent runs of the randomForest() function.

Since the VCF layer included NAs (which have also been excluded in our results) and scores relatively low according to the mean accuracy decrease criterion, we can construct an alternate Random Forest model as above, but excluding this layer. We may exclude NAs by using the na.omit() function. The accuracy, as seen in the comparison of confusion matrices, is increased by removing of NAs. Using the system.time() function, one could tell that by excluding NAs the processing time has decreased.

Now we can apply this model to the rest of the image and assign classes to all pixels. Note that for this step, the names of the raster layers in the input brick (here covs) must correspond exactly to the column names of the training table. We will use the predict() function from the raster package to predict class values based on the random forest model we have just constructed. This function uses a pre-defined model to predict the values of raster cells based on other raster layers. This model can be derived by linear regression, for example. In our case, we will use the model provided by the randomForest() function we applied earlier.

## Double-check layer and column names to make sure they match names(covs)
## \[1\] "band2" "band3" "band4" "NDVI" "VCF"

names(valuetable)
## \[1\] "band2" "band3" "band4" "NDVI" "VCF" "class"
## Predict land cover using the RF model

predLC <- predict(covs, model=modelRF, na.rm=TRUE)

## Plot the results
# recall: 1 = cropland, 2 = forest, 3 = wetland
cols <- c("orange", "dark green", "light blue")
plot(predLC, col=cols, legend=FALSE)
legend("bottomright",
 legend=c("cropland", "forest", "wetland"),
 fill=cols, bg="white")

Note that the predict() function also takes arguments that can be passed to writeRaster() (eg. filename = "", so it is a good idea to write to file as you perform this step (rather than keeping all output in memory).

Unsupervised classification: k-means

In the absence of training data, an unsupervised classification can be carried out. Unsupervised classification methods assign classes based on inherent structures in the data without resorting to the training of the algorithm. One such method, the k-means method, divides data into clusters based on Euclidean distances from cluster means in a feature space.

More information on the theory behind k-means clustering

We will use the same layers (from the covs rasterBrick) as in the Random Forest classification for this classification example. As before, we need to extract all values into a data.frame. But this time we will extract all the values since we are not limited to a training dataset.

valuetable <- getValues(covs)
head(valuetable)

Now we will construct a kmeans object using the kmeans() function. Like the Random Forest model, this object packages useful information about the resulting class membership. In this case, we will set the number of clusters to three, presumably corresponding to the three classes defined in our random forest classification.

km <- kmeans(na.omit(valuetable), centers = 3, iter.max = 100, nstart = 10)
# km contains the clusters (classes) assigned to the cells
head(km$cluster)
## \[1\] 2 2 1 1 1 1
unique(km$cluster) # displays unique values
## \[1\] 2 1 3

As in the Random Forest classification, we used the na.omit() argument to avoid any NA values in the valuetable (recall that there is a region of NAs in the VCF layer). These NAs are problematic in the kmeans() function, but omitting them gives us another problem: the resulting vector of clusters (from 1 to 3) is shorter than the actual number of cells in the raster.

In other words, how do we know which clusters to assign to which cells? To answer that question, we need to have a kind of mask raster, indicating where the NA values throughout the cov RasterBrick are located.

## Create a blank raster with default values of 0
rNA <- setValues(raster(covs), 0)
## Loop through layers of covs
## Assign a 1 to rNA wherever an NA is encountered in covs
for(i in 1:nlayers(covs)){
 rNA\[is.na(covs\[\[i\]\])\] <- 1
}
## Convert rNA to an integer vector
rNA <- getValues(rNA)

We now have a vector with a value of 1 indicating where the NA's in the cov brick are. Now that we know where the 'original' NAs are located, we can go ahead and assign the cluster values to a raster. At these NA locations, we will not assign any of the cluster values, instead assigning an NA.

First, we will insert these values into the original valuetable data.frame.

## Convert valuetable to a data.frame
valuetable <- as.data.frame(valuetable)
## If rNA is a 0, assign the cluster value at that position valuetable$class\[rNA\==0\] <- km$cluster
## If rNA is a 1, assign an NA at that position
valuetable$class\[rNA\==1\] <- NA

Now we are finally ready to assign these cluster values to a raster. This will represent our final classified raster.

## Create a blank raster
classes <- raster(covs)
## Assign values from the 'class' column of valuetable
classes <- setValues(classes, valuetable$class)
plot(classes, legend=FALSE, col=c("dark green", "orange", "light blue"))

These classes are much more difficult to interpret than those resulting from the random forest classification. We can see from the figure above that there is particularly high confusion between (what we might assume to be) the cropland and wetland classes. Clearly, with a good training dataset, a supervised classification can provide a reasonably accurate land cover classification.

However, unsupervised classification methods like k-means are useful for study areas for which little to no a priori data exist.

Assuming there are no training data available, there is a way we could improve the k-means classification performed in this example. Random forest is computationally faster than k-means. K-means may be improved by setting the maximum variance allowed in each cluster. Beginning with as many clusters as data points, improve clusters by merging neighboring clusters if the resulting cluster's variance is below the threshold, isolating elements that are far if a cluster's variance is above the threshold, or moving some elements between neighboring clusters if it decreases the sum of squared errors.

Applying a raster sieve by clumping

Although the land cover raster we created with the Random Forest method above is limited in the number of thematic classes it has, and we observed some confusion between wetland and cropland classes, it could be useful for constructing a forest mask (since that class performed quite well). To do so, we have to fuse (and remove) non-forest classes, and then clean up the remaining pixels by applying a sieve. To do this, we will make use of the clump() function (detecting patches of connected cells) in the raster package.

## Make an NA-value raster based on the LC raster attributes 
formask <- setValues(raster(predLC), NA)
## Assign 1 to formask to all cells corresponding to the forest
class formask\[predLC\==2\] <- 1
plot(formask, col="dark green", legend = FALSE)

We now have a forest mask that can be used to isolate forest pixels for further analysis. Forest pixels (from the Random Forest classification) have a value of 1, and non-forest pixels have a value of NA.

For some applications, however, we may only be interested in larger forest areas. We may especially want to remove single forest pixels, as they may be a result of errors, or may not fit our definition of forest.

In this section, we will construct 2 types of sieves to remove these types of pixels, following 2 definitions of adjacency. In the first approach, the so-called Queen's Case, neighbors in all 8 directions are considered to be adjacent. If any pixel cell has no neighbors in any of these 8 directions, we will remove that pixel by assigning an NA value.

First, we will use the clump() function in the raster package to identify clumps of raster cells. This function arbitrarily assigns an ID to these clumps.

## Group raster cells into clumps based on the Queen's Case 
if(!file.exists(fn <- "data/clumformask.grd")) {
 forestclumps <- clump(formask, directions=8, filename=fn) } else {
 forestclumps <- raster(fn)
}
plot(forestclumps)

When we inspect the frequency table with freq(), we can see the number of raster cells included in each of these clump IDs.

## Assign freqency table to a matrix
clumpFreq <- freq(forestclumps)
head(clumpFreq)
tail(clumpFreq)

We can use the count column of this frequency table to select clump IDs with only 1 pixel - these are the pixel "islands" that we want to eventually remove from our original forest mask.

## Coerce freq table to data.frame
clumpFreq <- as.data.frame(clumpFreq)
## which rows of the data.frame are only represented by one cell?
str(which(clumpFreq$count\==1))
## which values do these correspond to
str(clumpFreq$value\[which(clumpFreq$count\==1)\])
## Put these into a vector of clump ID's to be removed
excludeID <- clumpFreq$value\[which(clumpFreq$count\==1)\]
## Make a new forest mask to be sieved
formaskSieve <- formask
## Assign NA to all clumps whose IDs are found in excludeID
formaskSieve\[forestclumps %in% excludeID\] <- NA
## Zoom in to a small extent to check the results
# Note: you can define your own zoom by usinge <- drawExtent() e <- extent(c(811744.8, 812764.3, 849997.8, 850920.3))
opar <- par(mfrow=c(1, 2)) # allow 2 plots side-by-side
plot(formask, ext=e, col="dark green", legend=FALSE)
plot(formaskSieve, ext=e, col="dark green", legend=FALSE)
par(opar) 
# reset plotting window

We have successfully removed all island pixels from the forest mask using the clump() function. We can adjust our sieve criteria to only directly adjacent (NESW) neighbors: the so-called Rook's Case. To accomplish this, simply repeat the code above, but supply the argument directions=4 when calling clump().

We could take this approach further and apply a minimum mapping unit (MMU) to our forest mask.

We can adjust the above sieve to remove all forest pixels with areas below 0.5 hectares by using the count column of this frequency table to select clump IDs with 5.55 pixels (see computation below).

0.5 hectares = 1⁄2*(10,000 m2) = 5,000 m2 1 px = 30m*30m = 900 m2 5,000 m2 / 900 m2 = 5.55 px

Consider the fact that Landsat pixels are 30m by 30m, and that one hectare is equal to 10000m2.

Working with thematic rasters

As we have seen with the land cover rasters we derived using the random forest or k-means methods above, the values of a raster may be categorical, meaning they relate to a thematic class (e.g. 'forest' or 'wetland') rather than a quantitative value (e.g. NDVI or % Tree Cover). The raster dataset 'lulcGewata' is a raster with integer values representing Land Use and Land Cover (LULC) classes from a 2011 classification (using SPOT5 and ASTER source data).

load("data/lulcGewata.rda")

## Check out the distribution of the values
freq(lulcGewata)

## value count
## \[1,\] 1 396838
## \[2,\] 2 17301
## \[3,\] 3 943
## \[4,\] 4 13645
## \[5,\] 5 470859
## \[6,\] 6 104616
## \[7,\] NA 817794

hist(lulcGewata)

This is a raster with integer values between 1 and 6, but for this raster to be meaningful at all, we need a lookup or attribute table to identify these classes. A data.frame defining these classes is also included in the lesson repository:

load("data/LUTGewata.rda")

LUTGewata
## ID Class
## 1 1 cropland
## 2 2 bamboo
## 3 3 bare soil
## 4 4 coffee plantation
## 5 5 forest
## 6 6 wetland

This data.frame represents a lookup table for the raster we just loaded. The \$ID column corresponds to the values taken on by the LULC raster, and the \$Class column describes the LULC classes assigned. In R it is possible to add an attribute table to a raster. To do this, we need to coerce the raster values to a factor from an integer and add a raster attribute table.

lulc <- as.factor(lulcGewata)
# assign a raster attribute table (RAT)
levels(lulc) <- LUTGewata
lulc
## class : RasterLayer
## dimensions : 1177, 1548, 1821996 (nrow, ncol, ncell)
## resolution : 30, 30 (x, y)
## extent : 808755, 855195, 817635, 852945 (xmin, xmax, ymin, ymax) ## coord. ref. : +proj=utm +zone=36 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0
## data source : in memory
## names : LULC2011_Gewata
## values : 1, 6 (min, max)
## attributes
## ID Class
## from: 1 cropland
## to : 6 wetland

In some cases it might be more useful to visualize only one class at a time. The layerize() function in the raster package does this by producing a RasterBrick object with each layer representing the class membership of each class as a boolean.

classes <- layerize(lulc)
# Layer names follow the order of classes in the LUT
names(classes) <- LUTGewata$Class
plot(classes, legend=FALSE)

Now each class is represented by a separate layer representing class membership of each pixel with 0s and 1s. If we want to construct a forest mask as we did above, this is easily done by extracting the fifth layer of this RasterBrick and replacing 0's with NA's.

forest <- raster(classes, 5)
# is equivalent to
forest <- classes\[\[5\]\]
# or (since the layers are named)
forest <- classes$forest
## Replace 0's (non-forest) with NA's
forest\[forest\==0\] <- NA
plot(forest, col="dark green", legend=FALSE)

Summary

We learned about: