GitHub

Correlation Maps

The module CorrelationFunctions.Map contains functions which calculate correlation maps, i.e. correlation functions over all possible directions with all possible correlation lengths.

Functions

The following correlation functions are supported:

  • Two point $S_2$ function.
  • Cluster $C_2$ function.
  • Surface-surface $F_{ss}$ function.
  • Surface-void $F_{sv}$ function.
CorrelationFunctions.Map.c2 — Function
c2(image, phase; mode = NonPeriodic())

Calculate $C_2$ (cluster) correlation function for the phase phase in an N-dimensional image.

Examples

julia> c2([1 0; 0 1], 1; mode = Periodic())
2×2 Matrix{Float64}:
 0.5  0.0
 0.0  0.0
source
CorrelationFunctions.Map.s2 — Function
s2(image; mode = NonPeriodic())

Calculate $S_2$ (two point) correlation function for the binary image image.

source
s2(image, phase; mode = NonPeriodic())

Calculate $S_2$ (two point) correlation function for the phase phase in an N-dimensional image.

Examples

julia> s2([1 0; 0 1], 1; mode = Periodic())
2×2 Matrix{Float64}:
 0.5  0.0
 0.0  0.5
source
CorrelationFunctions.Map.cross_correlation — Function
cross_correlation(image1, image2; mode = NonPeriodic())

Calculate cross-correlation function between binary images image1 and image2.

source
cross_correlation(image, p1, p2; mode = NonPeriodic)

Calculate cross-correlation function between phases p1 and p2 in an N-dimensional image.

Examples

julia> cross_correlation([1 0; 0 1], 1, 0; mode = Periodic())
2×2 Matrix{Float64}:
 0.0  0.5
 0.5  0.0
source
CorrelationFunctions.Map.surf2 — Function
surf2(image, phase; mode = NonPeriodic(), filter)

Calculate $F_{ss}$ (surface-surface) correlation function for phase phase on N-dimensional image.

Examples

julia> surf2([1 0; 0 1], 1; mode = Periodic())
2×2 Matrix{Float64}:
 0.125  0.125
 0.125  0.125

See also: Utilities.AbstractKernel

source
CorrelationFunctions.Map.surfvoid — Function
surfvoid(image, phase; mode = NonPeriodic(), filter)

Calculate $F_{sv}$ (surface-void) correlation function for phase phase on N-dimensional image. Phase 0 is considered to be void.

Examples

julia> surfvoid([1 0; 0 1], 1; mode = Periodic())
2×2 Matrix{Float64}:
 0.5  0.5
 0.5  0.5

See also: Utilities.AbstractKernel

source
CorrelationFunctions.Map.average_directions — Function
average_directions(cfmap; len = (cfmap |> size |> minimum) ÷ 2)

Average correlation map cfmap over all directions. The result is a vector of length len with indices being equal to correlation length + 1.

source

You can use usual arrays (of type Array) or CUDA arrays for these functions.