---
title: "Canopy Analysis in R Using ForestTools"
author: "Andrew Plowright"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Canopy analysis in R using Forest Tools}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
```{r global_options, include=FALSE, dpi =  300}
knitr::opts_knit$set(global.par = TRUE)
options(rmarkdown.html_vignette.check_title = FALSE)
```
```{r setup}
library(ForestTools)
```

This short guide will demonstrate how to use the ForestTools package to detect and outline trees from a canopy height model (CHM) derived from a photogrammetric point cloud.

Begin by installing ForestTools.

```{r, eval = FALSE}
install.packages("ForestTools")
```


# Loading sample data

A sample CHM is included in the ForestTools package. It represents a small 1.5 hectare swath of forest in the Kootenay Mountains, British Columbia.

```{r, message = FALSE, warning = FALSE}
# Attach the 'ForestTools' and 'terra' libraries
library(ForestTools)
library(terra)
library(sf)

# Load sample canopy height model
chm <- terra::rast(kootenayCHM)
```

View the CHM using the `plot` function. The cell values are equal to the canopy's height above ground.

```{r, fig.width = 4, fig.height = 2.51}
# Remove plot margins (optional)
par(mar = rep(0.5, 4))

# Plot CHM (extra optional arguments remove labels and tick marks from the plot)
plot(chm, xlab = "", ylab = "", xaxt='n', yaxt = 'n')
```

# Detecting treetops

Dominant treetops can be detected using `vwf`. This function implements the _variable window filter_ algorithm developed by Popescu and Wynne (2004). In short, a moving window scans the CHM and tags a given cell as treetop if it is found to be the highest within the window. The size of the window itself changes dynamically depending on the height of the cell on which it is centered. This is to account for varying crown sizes, with tall trees assumed to have wide crowns and vice versa.

Therefore, the first step is to define the **function that will define the dynamic window size**. Essentially, this function should take a **CHM cell value** (i.e.: the height of the canopy above ground at that location) and return the **radius of the search window**. Here, we will define a simple linear equation, but any function with a single input and output will work. We do not wish for the `vwf` to tag low-lying underbrush or other spurious treetops, and so we also set a minimum height of 2 m using the `minHeight` argument. Any cell with a lower value will not be tagged as a treetop.

```{r}
# Function for defining dynamic window size
lin <- function(x){x * 0.05 + 0.6}

# Detect treetops
ttops <- vwf(chm, winFun = lin, minHeight = 2)
```

We can now plot these treetops on top of the CHM.

```{r, fig.width = 4, fig.height = 2.51}
# Plot CHM
plot(chm, xlab = "", ylab = "", xaxt='n', yaxt = 'n')

# Add dominant treetops to the plot
plot(ttops$geometry, col = "blue", pch = 20, cex = 0.5, add = TRUE)

```

The `ttops` object created by `vwf` in this example contains the spatial coordinates of each detected treetop, as well as two default attributes: _height_ and _winRadius_. These correspond to the tree's height above ground and the radius of the moving window where the tree was located. Note that _winRadius_ **is not necessarily equivalent to the tree's crown radius**.

```{r}
# Get the mean treetop height
mean(ttops$height)
```

# Outlining tree crowns

Canopy height models often represent continuous, dense forests, where tree crowns abut against each other. Outlining discrete crown shapes from this type of forest is often referred to as _canopy segmentation_, where each crown outline is represented by a _segment_. Once a set of treetops have been detected from a canopy height model, the `mcws` function can be used for this purpose.

The `mcws` function implements the `watershed` algorithm from the [imager](https://cran.r-project.org/package=imager/imager.pdf) library. Watershed algorithms are frequently used in topographical analysis to outline drainage basins. Given the morphological similarity between an inverted canopy and a terrain model, this same process can be used to outline tree crowns. However, a potential problem is the issue of _oversegmentation_, whereby branches, bumps and other spurious treetops are given their own segments. This source of error can be mitigated by using a variant of the algorithm known as _marker-controlled watershed segmentation_ (Beucher & Meyer, 1993), whereby the watershed algorithm is constrained by a set of markers -- in this case, treetops.

The `mcws` function also takes a `minHeight` argument, although this value should be lower than that which was assigned to `vwf`. For the latter, `minHeight` defines the lowest expected treetop, whereas for the former it should correspond to the height above ground of the fringes of the lowest trees. 

```{r, fig.width = 4, fig.height = 2.51}
# Create crown map
crowns_ras <- mcws(treetops = ttops, CHM = chm, minHeight = 1.5)

# Plot crowns
plot(crowns_ras, col = sample(rainbow(50), nrow(unique(chm)), replace = TRUE), legend = FALSE, xlab = "", ylab = "", xaxt='n', yaxt = 'n')
```

By default, `mcws` returns a raster, where each crown is given a unique cell value. Depending on the intended purpose of the crown map, it may be preferable to store these outlines as polygons. This can be accomplished by setting the `format` argument to "polygons". As an added benefit, these polygons will inherit the attributes of the treetops from which they were generated, such as _height_.

```{r, fig.width = 4, fig.height = 2.51}
# Create polygon crown map
crowns_poly <- mcws(treetops = ttops, CHM = chm, format = "polygons", minHeight = 1.5)

# Plot CHM
plot(chm, xlab = "", ylab = "", xaxt='n', yaxt = 'n')

# Add crown outlines to the plot
plot(crowns_poly$geometry, border = "blue", lwd = 0.5, add = TRUE)
```

Assuming that each crown has a roughly circular shape, we can use the crown's area to compute its average circular diameter.

```{r}
# Compute area and diameter
crowns_poly[["area"]] <- st_area(crowns_poly)
crowns_poly[["diameter"]] <- sqrt(crowns_poly[["area"]]/ pi) * 2

# Mean crown diameter
mean(crowns_poly$diameter)
```

# References

Popescu, S. C., & Wynne, R. H. (2004). [Seeing the trees in the forest](https://www.ingentaconnect.com/content/asprs/pers/2004/00000070/00000005/art00003). _Photogrammetric Engineering & Remote Sensing, 70_(5), 589-604.

Beucher, S., and Meyer, F. (1993). [The morphological approach to segmentation: the watershed transformation](https://www.researchgate.net/profile/Serge-Beucher/publication/233950923_Segmentation_The_Watershed_Transformation_Mathematical_Morphology_in_Image_Processing/links/55f7c6ce08aeba1d9efe4072/Segmentation-The-Watershed-Transformation-Mathematical-Morphology-in-Image-Processing.pdf). _Mathematical morphology in image processing_, 433-481.
