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.

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.

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

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::Float64=20. Maximum window size [m]
• slope::Float64=0.01 Terrain slope [m/m]
• dhₘ::Float64=2.5 Maximum elevation threshold [m]
• dh₀::Float64=0.2 Initial elevation threshold [m]
• cellsize::Float64=1. Cellsize in [m]

image = pssm(A; exaggeration, resolution)

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
• resolution::Real=1.0 Resolution of cell size

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).

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)

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

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

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