CenterIndexedArrays

A CenterIndexedArray is an array indexed symmetrically around its midpoint: the center element is always at index (0, 0, …), and along each dimension of size 2n+1 the valid indices run from -n to n. All dimension sizes must be odd.

A common use case is image registration, where the mismatch between two images is stored as a function of their relative displacement — the center of that array is naturally the zero-displacement case.

Installation

using Pkg
Pkg.add("CenterIndexedArrays")

Basic usage

julia> using CenterIndexedArrays

julia> A = CenterIndexedArray(reshape(1:15, 3, 5))
3×5 CenterIndexedArray(reshape(::UnitRange{Int64}, 3, 5)) with eltype Int64 with indices SymRange(1)×SymRange(2):
 1  4  7  10  13
 2  5  8  11  14
 3  6  9  12  15

julia> A[0, 0]   # center element
8

julia> A[0, -1]  # one step left of center
5

julia> A[-1, 2]  # one step above, two steps right
13

You can also allocate an uninitialized array:

julia> using CenterIndexedArrays

julia> B = CenterIndexedArray{Float64}(undef, 3, 5);

julia> axes(B)
(SymRange(1), SymRange(2))

julia> size(B)
(3, 5)

SymRange axes

The axes of a CenterIndexedArray are SymRange values — unit ranges symmetric around zero. SymRange(n) covers -n:n and has length 2n+1.

julia> using CenterIndexedArrays: SymRange

julia> r = SymRange(3)
SymRange(3)

julia> length(r)
7

julia> first(r), last(r)
(-3, 3)

julia> r[-3], r[3]
(-3, 3)

Interpolation

Wrapping an Interpolations.jl interpolation object enables fractional (sub-integer) indexing, which is useful when computing cross-correlations at non-integer offsets.

julia> using CenterIndexedArrays, Interpolations

julia> dat = collect(reshape(1.0:25.0, 5, 5));

julia> itp = interpolate(dat, BSpline(Linear()));

julia> A = CenterIndexedArray(itp);

julia> A[0, 0]       # center, equivalent to dat[3, 3]
13.0

julia> A[0.5, 0.0]   # fractional index; linearly interpolated
13.5