### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# ╔═╡ c50e6a44-a639-474b-b644-6eabf21607f2
using Images

# ╔═╡ 728fb778-01a7-11ec-35a0-8de77d55a11b
md"""
# Image Processing
"""

# ╔═╡ ecaaee9c-a9a1-4df9-aad0-0bddbf78d838
md"""
## Objectives
- **Import** images from files or the web
- **Transform** images using julia
- Use **convolutions** to modify and process images
"""

# ╔═╡ 1c73a61f-38b6-4dc5-beda-ff09f6b69f5f
md"""
## Working with Images
To work with images in julia we make use of the Images.jl package.
"""

# ╔═╡ 5a24f453-1898-46ec-ba65-b509499bbb4a
md"""
### Loading Images
We can load images from the working directory using the load() function. Images can be downloaded from the web using the download() function. It is also possible to directly load an image from the web without first saving it locally:
"""

# ╔═╡ 0e5b99c6-5fa7-4221-829d-f1323be4d986
url = "https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/University_of_Cambridge_coat_of_arms.svg/900px-University_of_Cambridge_coat_of_arms.svg.png";

# ╔═╡ 411998eb-628f-4f4b-9e3b-cc8e35faef29
crest = download(url) |> load

# ╔═╡ 5dc5185f-4216-4a4e-b962-62a329ff7287
md"""
### Colours
In julia, an image is nothing but a two dimensional array of colours in RGBA format. It can be accessed like any other array. By default, the images package displays these arrays as the images they represent. Note that due to their matrix representation, the first index is in the y-coordinate.
"""

# ╔═╡ 86b952fe-75e3-497e-b093-be65d240b256
typeof(crest), size(crest)

# ╔═╡ 8a2784ce-75a4-48da-accf-d6e0378b9f29
md"""
The individual colours also get automatically displayed as such:
"""

# ╔═╡ 16b15c51-adfc-46ad-9a27-aed6b11313ec
colour = crest[138,100]

# ╔═╡ 2e4f151a-3f1e-4e20-bd9d-f797659d4538
(colour.r, colour.b, colour.g, colour.alpha)

# ╔═╡ 9a78f3fb-bf87-4bfd-b8c6-1d8cf312cf2c
new_colour = RGBA(0.7, 0.2, 0.5)

# ╔═╡ b531437d-53ae-4776-965c-59a530784899
md"""
### Cropping and Transforming Images
The fact that an image in julia is just a collection of colours allows us to work with images exactly as we would with any other array. Cropping an image is as easy as indexing it at specified ranges:
"""

# ╔═╡ f8d76c61-0249-4f66-956b-0944c6ee7f73
lion = RGB.(crest[40:330,40:330])

# ╔═╡ 6f431d38-606c-4ae7-b258-a6021f7d3194
md"""
Just as with any arrays in julia, we can easily concatinate images by placing them imside square braces. We can use the imresize and inverse functions to trasform the image to our liking:
"""

# ╔═╡ 28a043e2-42fa-4e5d-8b8b-0c2fe49a3efe
imresize([reverse(lion, dims = 2) reverse(lion, dims = 1)], ratio = 1/2)

# ╔═╡ 2f6e6d87-38a1-4508-a9ea-729fdc62706f
md"""
### Modifying Individual Pixels
The colours of an image can easily be modfied using julias broadcasting functionality.
"""

# ╔═╡ 57f011d7-bd87-462a-953e-11d5e2579ce5
function invert(col)
	return RGB(1-col.r, 1-col.g, 1-col.b)
end

# ╔═╡ 7881fdeb-06c6-4eb0-9af3-11865fbacd16
function decolourize(col)
	v = max(col.r, col.g, col.b)
	return RGB(v, v, v)
end

# ╔═╡ 6d3f2788-205a-4855-8264-a5a9d826e8c6
[invert.(lion) decolourize.(lion)]

# ╔═╡ d98f83d1-ec5a-4929-bed7-78ea7cb25552
md"""
## Convolutions
Often we want to modify the pixels of an image depending on its neighbourhood. This is where convolutions come into play. A convolution replaces each pixel of an image by a weighted avarage of its neighbouring pixels, where the weights are given by a small matrix whose entries sum to 1.
"""

# ╔═╡ 8aed4282-fec5-47b0-96de-482ef2df9353
md"""
### Bluring
The simplest effect achievable through convolution is a blur. We can choose our weight distribution to be uniform to simply replace each pixels colour with the avarage colour of its neighbours. However, choosing a normal distribution instead gives a much smoother bluring effect, commonly known as a Gaussian Blur.
"""

# ╔═╡ 9ba7fb38-45c2-4667-987e-9237d8e8c7d5
norm(x) = x/sum(x)

# ╔═╡ 89888f4c-b1ae-4330-9c3e-e1161b38c238
uniformBlur(n) = centered(norm(ones(2n+1,2n+1)))

# ╔═╡ a44b2dfb-c249-4d86-9cac-edc0a04a6352
normalBlur(n) = centered(norm([9exp((-9x^2-9y^2)/2n^2) for x in -n:n, y in -n:n]))

# ╔═╡ 99fcee9e-f44e-484a-9095-fab3eb0c9453
[imfilter(lion, uniformBlur(5)) imfilter(lion, normalBlur(10))]

# ╔═╡ b3c172ad-ae05-4cf6-8884-aa3b83951fa8
md"""
### Sharpening
Using negative weight allows us to emphasise regions in the image where different colours are adjacent. We can therefore create a convultion that has a sharpening effect, partially reversing the effect of the previously defined blur.
"""

# ╔═╡ bd927a06-d454-4f3e-9118-caec65da2311
sharpen = centered([0 -1 0; -1 5 -1; 0 -1 0])

# ╔═╡ a4a04ca3-d54c-4a29-84b3-200f76114a7c
[imfilter(lion, normalBlur(4)) imfilter(lion, (normalBlur(4), sharpen)) imfilter(lion, (normalBlur(4), sharpen, sharpen))]

# ╔═╡ 21099433-fab1-403c-8994-268e86541865
md"""
### Edge Detection
Pushing the this idea further, we can define a convolution whose only effect is to find neighbourhoods with different colours. This is essentially the same as finding 'edges' in an image.
"""

# ╔═╡ 7f773bb3-f749-4879-84f9-41fb4ba13e6c
detectEdge = centered([0 -1 0; -1 4 -1; 0 -1 0])

# ╔═╡ d028aa0c-018e-4b3b-89c8-d6c2ca57ae0d
md"""
Note that here the weights sum to $0$ instead of $1$, cancelling similar colours and only highlight pixels that differ substantially from their neighbours in colour. To 'clean up' the resulting image, we decolourize and invert the result:
"""

# ╔═╡ 80a4a6c0-bcca-4a2b-9d7d-79639eac39d1
f(x) = invert(decolourize(x))

# ╔═╡ 7848d3b5-0e75-4617-9f03-ffc9210a92b7
f.([imfilter(lion, detectEdge) imfilter(lion, (normalBlur(2), detectEdge))])

# ╔═╡ 02fc3a3e-f2ea-4def-9508-c64b6086f38f
md"""
As illustrated above, sometimes it is beneficial to first blur the image before applying edge detection resulting in a smoother result.
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.4"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.3"

[[IrrationalConstants]]
git-tree-sha1 = "f76424439413893a832026ca355fe273e93bce94"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.0"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "3d682c07e6dd250ed082f883dc88aee7996bf2cc"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.0"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "c253236b0ed414624b083e6b72bfe891fbd2c7af"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+1"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "0fb723cd8c45858c22169b2e42269e53271a6df7"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.7"

[[MappedArrays]]
git-tree-sha1 = "e8b359ef06ec72e8c030463fe02efe5527ee5142"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.1"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "2ca267b08821e86c5ef4376cffed98a46c2cb205"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.1"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.3"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[Netpbm]]
deps = ["ColorVectorSpace", "FileIO", "ImageCore"]
git-tree-sha1 = "09589171688f0039f13ebe0fdcc7288f50228b52"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.0.1"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "c0f4a4836e5f3e0763243b8324200af6d0e0f90c"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.5"

[[OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
version = "0.3.2"

[[OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "923319661e9a22712f24596ce81c54fc0366f304"
uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
version = "3.1.1+0"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "520e28d4026d16dcf7b8c8140a3041f0e20a9ca8"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
version = "0.3.7"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "646eed6f6a5d8df6708f15ea7e02a7a2c4fe4800"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.10"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "2276ac65f1e236e0a6ea70baff3f62ad4c625345"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.2"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
version = "0.1.1"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.1"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "7dff99fbc740e2f8228c6878e2aad6d7c2678098"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.1"

[[Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[Rotations]]
deps = ["LinearAlgebra", "StaticArrays", "Statistics"]
git-tree-sha1 = "2ed8d8a16d703f900168822d83699b8c3c1a5cd8"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.2"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
git-tree-sha1 = "a322a9493e49c5f3a10b50df3aedaf1cdb3244b7"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.6.1"

[[StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
version = "0.1.1"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "62701892d172a2fa41a1f829f66d2b0db94a9a63"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.3.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3240808c6d463ac46f1c1cd7638375cd22abbccb"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.12"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "fed1ec1e65749c4d96fc20dd13bea72b55457e62"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.9"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TiffImages]]
deps = ["ColorTypes", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "OrderedCollections", "PkgVersion", "ProgressMeter"]
git-tree-sha1 = "03fb246ac6e6b7cb7abac3b3302447d55b43270e"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.4.1"

[[TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "52c5f816857bfb3291c7d25420b1f4aca0a74d18"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
version = "0.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
"""

# ╔═╡ Cell order:
# ╟─728fb778-01a7-11ec-35a0-8de77d55a11b
# ╟─ecaaee9c-a9a1-4df9-aad0-0bddbf78d838
# ╟─1c73a61f-38b6-4dc5-beda-ff09f6b69f5f
# ╠═c50e6a44-a639-474b-b644-6eabf21607f2
# ╟─5a24f453-1898-46ec-ba65-b509499bbb4a
# ╠═0e5b99c6-5fa7-4221-829d-f1323be4d986
# ╠═411998eb-628f-4f4b-9e3b-cc8e35faef29
# ╟─5dc5185f-4216-4a4e-b962-62a329ff7287
# ╠═86b952fe-75e3-497e-b093-be65d240b256
# ╟─8a2784ce-75a4-48da-accf-d6e0378b9f29
# ╠═16b15c51-adfc-46ad-9a27-aed6b11313ec
# ╠═2e4f151a-3f1e-4e20-bd9d-f797659d4538
# ╠═9a78f3fb-bf87-4bfd-b8c6-1d8cf312cf2c
# ╟─b531437d-53ae-4776-965c-59a530784899
# ╠═f8d76c61-0249-4f66-956b-0944c6ee7f73
# ╟─6f431d38-606c-4ae7-b258-a6021f7d3194
# ╠═28a043e2-42fa-4e5d-8b8b-0c2fe49a3efe
# ╟─2f6e6d87-38a1-4508-a9ea-729fdc62706f
# ╠═57f011d7-bd87-462a-953e-11d5e2579ce5
# ╠═7881fdeb-06c6-4eb0-9af3-11865fbacd16
# ╠═6d3f2788-205a-4855-8264-a5a9d826e8c6
# ╟─d98f83d1-ec5a-4929-bed7-78ea7cb25552
# ╟─8aed4282-fec5-47b0-96de-482ef2df9353
# ╠═9ba7fb38-45c2-4667-987e-9237d8e8c7d5
# ╠═89888f4c-b1ae-4330-9c3e-e1161b38c238
# ╠═a44b2dfb-c249-4d86-9cac-edc0a04a6352
# ╠═99fcee9e-f44e-484a-9095-fab3eb0c9453
# ╟─b3c172ad-ae05-4cf6-8884-aa3b83951fa8
# ╠═bd927a06-d454-4f3e-9118-caec65da2311
# ╠═a4a04ca3-d54c-4a29-84b3-200f76114a7c
# ╟─21099433-fab1-403c-8994-268e86541865
# ╠═7f773bb3-f749-4879-84f9-41fb4ba13e6c
# ╟─d028aa0c-018e-4b3b-89c8-d6c2ca57ae0d
# ╠═80a4a6c0-bcca-4a2b-9d7d-79639eac39d1
# ╠═7848d3b5-0e75-4617-9f03-ffc9210a92b7
# ╟─02fc3a3e-f2ea-4def-9508-c64b6086f38f
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
