# How to upsample an array (or image)

**URL:** <https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415>\
**Category:** New to Julia\
**Tags:** question, images, array\
**Created:** [July 16, 2018, 12:21pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415 "2018-07-16T12:21:01Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![merckxiaan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/merckxiaan/32/4697_2.png) [@merckxiaan](https://discourse.julialang.org/u/merckxiaan)\
**Post date:** [July 16, 2018, 12:21pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/1 "2018-07-16T12:21:02Z")

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I’m wondering how one would go about upsampling an array, I’ve come across [interpolations.jl](https://github.com/JuliaMath/Interpolations.jl), to interpolate the newly created elements in the scaled array but I’m not certain how this can be used to upscale an array. Is there, by any chance, a package that handles array upsampling?

Thanks,  
Jules

---

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**Author:** ![Evizero](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/evizero/32/10118_2.png) [@Evizero](https://discourse.julialang.org/u/Evizero)\
**Post date:** [July 16, 2018, 4:01pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/2 "2018-07-16T16:01:47Z")

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You can use interpolations directly and index with real numbers within the range of valid indices (unless you want to use extrapolations as well). See the readme of the package you linked for more details on the parameters

```julia
julia> using Interpolations

julia> A = interpolate([1. 2; 3 4], BSpline(Linear()), OnGrid())
2×2 interpolate(::Array{Float64,2}, BSpline(Linear()), OnGrid()) with element type Float64:
 1.0 2.0
 3.0 4.0

julia> A[1:0.5:2, 1:0.5:2]
3×3 Array{Float64,2}:
 1.0 1.5 2.0
 2.0 2.5 3.0
 3.0 3.5 4.0

```

Images.jl offers a high-level interface for resizing which uses Interpolations.jl under the hood

```julia
julia> using Images

julia> A = [1. 2; 3 4]
2×2 Array{Float64,2}:
 1.0 2.0
 3.0 4.0

julia> imresize(A, (3, 3))
3×3 Array{Float64,2}:
 1.0 1.5 2.0
 2.0 2.5 3.0
 3.0 3.5 4.0

```

You can also use a mid-level interface - if you wish - to have control over the exact transformation. see `warp` or [https://juliaimages.github.io/latest/indexing.html](https://juliaimages.github.io/latest/indexing.html) for details

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<div class="post-metadata">

**Author:** ![merckxiaan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/merckxiaan/32/4697_2.png) [@merckxiaan](https://discourse.julialang.org/u/merckxiaan)\
**Post date:** [July 16, 2018, 6:24pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/3 "2018-07-16T18:24:20Z")

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Thank you very much!

I guess Images.jl isn’t suitable since I’m using multi-dimensional arrays?

For the interpolations.jl method, how could you taken an array and, for example, double (or triple) it’s size. Say I want to double the following array: `[1. 3 3 4 5 6; 7 8 9 10 11 12]` (2x6)

I’ve tried the following:

```julia
A = interpolate([1. 3 3 4 5 6; 7 8 9 10 11 12], BSpline(Linear()), OnGrid())
A[1:0.5:2, 1:0.5:6]

```

instead of a 4x12 array, I end up with the following:

```julia
3×11 Array{Float64,2}:
 1.0 2.0 3.0 3.0 3.0 3.5 4.0 4.5 5.0 5.5 6.0
 4.0 4.75 5.5 5.75 6.0 6.5 7.0 7.5 8.0 8.5 9.0
 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0

```

I’m not certain of what I should be doing instead so any help would be welcome!

Thanks in advance,  
Jules

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<div class="post-metadata">

**Author:** ![rdeits](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rdeits/32/286_2.png) [@rdeits](https://discourse.julialang.org/u/rdeits)\
**Post date:** [July 16, 2018, 7:32pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/4 "2018-07-16T19:32:37Z")

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You might want to try Images.jl anyway–I don’t think it has any particular restrictions to 2-dimensional arrays (that’s one of it’s best features, in my opinion).

Using interpolations directly, you just need to give the right range indices. `1:0.5:2` is a range with values `[1, 1.5, 2]`, which is why you end up with 3 (instead of 4) rows in the result. If you want 4 elements in your range, you just need to pick the appropriate step size. In this case, it would be exactly `1/3` which you can represent as an exact Rational number in Julia with `1//3`:

```julia
julia> length(1 : 1//3 : 2)
4

```

And you can use that range for to index into the interpolation:

```julia
julia> A[1:1//3:2, 1]
4-element Array{Float64,1}:
 1.0
 3.0
 5.0
 7.0

```

you can do the same with the column indices:

```julia
julia> A[1:1//3:2, 1:5//11:6]
4×12 Array{Float64,2}:
 1.0 1.90909 2.81818 3.0 3.0 3.27273 3.72727 4.18182 4.63636 5.09091 5.54545 6.0
 3.0 3.75758 4.51515 4.78788 4.93939 5.27273 5.72727 6.18182 6.63636 7.09091 7.54545 8.0
 5.0 5.60606 6.21212 6.57576 6.87879 7.27273 7.72727 8.18182 8.63636 9.09091 9.54545 10.0
 7.0 7.45455 7.90909 8.36364 8.81818 9.27273 9.72727 10.1818 10.6364 11.0909 11.5455 12.0

```

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<div class="post-metadata">

**Author:** ![Evizero](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/evizero/32/10118_2.png) [@Evizero](https://discourse.julialang.org/u/Evizero)\
**Post date:** [July 16, 2018, 8:12pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/5 "2018-07-16T20:12:05Z")

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> [@merckxiaan](#):
>
> I guess Images.jl isn’t suitable since I’m using multi-dimensional arrays?

You can do the following

```julia
julia> using Images

julia> A = reshape(1:18, (3,3,2))
3×3×2 Base.ReshapedArray{Int64,3,UnitRange{Int64},Tuple{}}:
[:, :, 1] =
 1 4 7
 2 5 8
 3 6 9

[:, :, 2] =
 10 13 16
 11 14 17
 12 15 18

julia> imresize(A, (5,5,2))
5×5×2 Array{Float64,3}:
[:, :, 1] =
 1.0 2.2 4.0 5.8 7.0
 1.4 2.6 4.4 6.2 7.4
 2.0 3.2 5.0 6.8 8.0
 2.6 3.8 5.6 7.4 8.6
 3.0 4.2 6.0 7.8 9.0

[:, :, 2] =
 10.0 11.2 13.0 14.8 16.0
 10.4 11.6 13.4 15.2 16.4
 11.0 12.2 14.0 15.8 17.0
 11.6 12.8 14.6 16.4 17.6
 12.0 13.2 15.0 16.8 18.0

```

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<div class="post-metadata">

**Author:** ![merckxiaan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/merckxiaan/32/4697_2.png) [@merckxiaan](https://discourse.julialang.org/u/merckxiaan)\
**Post date:** [July 16, 2018, 8:16pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/6 "2018-07-16T20:16:18Z")

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Thank you!  
I think I’ll stick to the Images.jl method for now.

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<div class="post-metadata">

**Author:** ![merckxiaan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/merckxiaan/32/4697_2.png) [@merckxiaan](https://discourse.julialang.org/u/merckxiaan)\
**Post date:** [July 16, 2018, 8:19pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/7 "2018-07-16T20:19:35Z")

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Thanks, it seems that imresize is using bicubic interpolation? There probably is a way to change this?  
It’s not really that important though, you guys already solved my problems! ❤

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<div class="post-metadata">

**Author:** ![Evizero](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/evizero/32/10118_2.png) [@Evizero](https://discourse.julialang.org/u/Evizero)\
**Post date:** [July 18, 2018, 2:37pm UTC](https://discourse.julialang.org/t/how-to-upsample-an-array-or-image/12415/8 "2018-07-18T14:37:36Z")

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> [@merckxiaan](#):
>
> Thanks, it seems that imresize is using bicubic interpolation? There probably is a way to change this?

No it uses linear interpolation, but there is something non-trivial going on. See here for more information: [https://github.com/JuliaImages/ImageTransformations.jl/blob/master/src/resizing.jl#L233-L265](https://github.com/JuliaImages/ImageTransformations.jl/blob/master/src/resizing.jl#L233-L265)