TPI(dem::Matrix{<:Real})

TPI stands for Topographic Position Index, which is defined as the difference between a central pixel and the mean of its surrounding cells (see Wilson et al 2007, Marine Geodesy 30:3-35).

TRI(dem::Matrix{<:Real})

TRI stands for Terrain Ruggedness Index, which measures the difference between a central pixel and its surrounding cells. This algorithm uses the square root of the sum of the square of the difference between a central pixel and its surrounding cells. This is recommended for terrestrial use cases.

aspect(dem::Matrix{<:Real}, method=Horn())

Aspect is direction of slope, as defined in Burrough, P. A., and McDonell, R. A., (1998, Principles of Geographical Information Systems).

curvature(dem::Matrix{<:Real}; cellsize=1.0)

Curvature is derivative of slope, so the second derivative of the DEM.

hillshade(dem::Matrix{<:Real}; azimuth=315.0, zenith=45.0, cellsize=1.0)

hillshade is the simulated illumination of a surface based on its slope and aspect given a light source with azimuth and zenith angles in °, , as defined in Burrough, P. A., and McDonell, R. A., (1998, Principles of Geographical Information Systems).

multihillshade(dem::Matrix{<:Real}; cellsize=1.0)

multihillshade is the simulated illumination of a surface based on its slope and aspect. Like hillshade, but now using multiple sources as defined in https://pubs.usgs.gov/of/1992/of92-422/of92-422.pdf, similar to GDALs -multidirectional.

Apply the opening operation to A with window size ω.

Apply the opening operation to A with window size ω.

Apply the opening operation to A with window size ω.

pitremoval(dem::Matrix{<:Real})

Remove pits from a DEM Array if the center cell of a 3x3 patch is limit lower or than the surrounding cells.

B, flags = pmf(A; ωₘ, slope, dhₘ, dh₀, cellsize, adjust, erode)

Applies the progressive morphological filter by Zhang et al. (2003) ^[zhang2003] to A.

Output

• B::Array{T,2} Maximum allowable values
• flags::Array{Float64,2} A sized array with window sizes if filtered, zero if not filtered.

Afterwards, one can retrieve the resulting mask for A by A .<= B or flags .== 0..

Arguments

• A::Array{T,2} Input Array
• ωₘ::Real=20. Maximum window size [m]
• slope::Real=0.01 Terrain slope [m/m]
• dhₘ::Real=2.5 Maximum elevation threshold [m]
• dh₀::Real=0.2 Initial elevation threshold [m]
• cellsize::Real=1. Cellsize in [m]

image = pssm(A; exaggeration=2.3, resolution=1.0)

Perceptually Shaded Slope Map by Pingel, Clarke. 2014 ^[pingel2014].

Output

• image::Gray{T,2} Grayscale image

Arguments

• A::Array{Real,2} Input Array
• exaggeration::Real=2.3 Factor to exaggerate elevation
• cellsize::Real=1.0 Size of cell to account for horizontal resolution if different from vertical resolution

roughness(dem::Matrix{<:Real})

Roughness is the largest inter-cell difference of a central pixel and its surrounding cell, as defined in Wilson et al (2007, Marine Geodesy 30:3-35).

mask = skb(A; mean=mean(A))

Applies skewness balancing by Bartels e.a (2006) ^{[bartels2006]} to A. Improved the performance by applying a binary search to find the threshold value.

Output

• mask::BitMatrix Mask of allowed values

mask = skbr(A; iterations=10)

Applies recursive skewness balancing by Bartels e.a (2006) ^{[bartels2006]} to A. Applies skb iterations times to the object (non-terrain) mask, as to include more (sloped) terrain.

Output

• mask::BitMatrix Mask of allowed values

slope(dem::Matrix{<:Real}; cellsize=1.0, method=Horn())

Slope is the rate of change between a cell and its neighbors as defined in Burrough, P. A., and McDonell, R. A., (1998, Principles of Geographical Information Systems).

B = smf(A; ω, slope, dhₘ, dh₀, cellsize)

Applies the simple morphological filter by Pingel et al. (2013) ^[pingel2013] to A.

Output

• B::Array{Float64,2} A filtered version of A

Arguments

• A::Array{T,2} Input Array
• ω::Float64=18. Maximum window size [m]
• slope::Float64=0.01 Terrain slope [m/m]
• cellsize::Float64=1. Cellsize in [m]

spread(points::Matrix{<:Real}, initial::Matrix{<:Real}, friction::Real; distance=Euclidean(), res=1.0)
spread(points::Matrix{<:Real}, initial::Real, friction::Real; distance=Euclidean(), res=1.0)

Optimized (and more accurate) function based on the same friction everywhere.

When the friction is the same everywhere, there's no need for searching the shortest cost path, as one can just take a direct line to the input points.

The calculated cost is more accurate, as there's no 'zigzag' from cell center to cell center.

spread(points::Matrix{<:Real}, initial::Matrix{<:Real}, friction::Matrix{<:Real}; res=1, limit=Inf)

Total friction distance spread from points as by Tomlin (1983) ^[tomlin1983]. This is also the method implemented by PCRaster.

Output

• Array{Float64,2} Total friction distance

Arguments

• points::Matrix{<:Real} Input Array
• initial::Matrix{<:Real} Factor to exaggerate elevation
• friction::Matrix{<:Real} Resolution of cell size
• res=1 Resolution or cell size
• limit=Inf Initial fill value

spread2(points::Matrix{<:Real}, initial::Matrix{<:Real}, friction::Matrix{<:Real}; res=1, limit=Inf, iterations=3)

Pushbroom method for friction costs as discussed by *Eastman (1989) ^{[eastman1989]}. This method should scale much better (linearly) than the ^[tomlin1983] method, but can require more iterations than set by default (3) in the case of maze-like, uncrossable obstacles.

Output

• Array{Float64,2} Total friction distance

Arguments

• points::Matrix{<:Real} Input Array
• initial::Matrix{<:Real} Factor to exaggerate elevation
• friction::Matrix{<:Real} Resolution of cell size
• res=1 Resolution or cell size
• limit=Inf Initial fill value
• iterations=3 Number of pushbroom iterations

Third order finite difference estimator using all 8 neighbors (Horn, 1981).

Maximum Downward Gradient

Second order finite difference estimator using all 4 neighbors (Zevenbergen and Thorne, 1987).