Manifest.toml

# This file is machine-generated - editing it directly is not advised

[[AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.0.1"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

[[ArgCheck]]
git-tree-sha1 = "dedbbb2ddb876f899585c4ec4433265e3017215a"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.1.0"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[BFloat16s]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "4af69e205efc343068dc8722b8dfec1ade89254a"
uuid = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"
version = "0.1.0"

[[BangBang]]
deps = ["Compat", "ConstructionBase", "Future", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables", "ZygoteRules"]
git-tree-sha1 = "e239020994123f08905052b9603b4ca14f8c5807"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.3.31"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"

[[CEnum]]
git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.4.1"

[[CUDA]]
deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "DataStructures", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "TimerOutputs"]
git-tree-sha1 = "5e696e37e51b01ae07bd9f700afe6cbd55250bce"
uuid = "052768ef-5323-5732-b1bb-66c8b64840ba"
version = "3.3.4"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "0b0aa9d61456940511416b59a0e902c57b154956"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "0.10.12"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.31.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[CompositionsBase]]
git-tree-sha1 = "455419f7e328a1a2493cabc6428d79e951349769"
uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
version = "0.1.1"

[[ConstructionBase]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f74e9d5388b8620b4cee35d4c5a618dd4dc547f4"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.3.0"

[[ContextVariablesX]]
deps = ["Compat", "Logging", "UUIDs"]
git-tree-sha1 = "fc81d9dd4ffdafb56680f01e6d9db464a6b3689d"
uuid = "6add18c4-b38d-439d-96f6-d6bc489c04c5"
version = "0.1.1"

[[DataAPI]]
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uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.7.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.9"

[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DefineSingletons]]
git-tree-sha1 = "77b4ca280084423b728662fe040e5ff8819347c5"
uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
version = "0.1.1"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.5"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[ExprTools]]
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uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
version = "0.1.6"

[[FLoops]]
deps = ["Compat", "FLoopsBase", "JuliaVariables", "MLStyle", "Serialization", "Setfield", "Transducers"]
git-tree-sha1 = "37d092665146d18e4b980d8a88b4a7d80572c5c3"
uuid = "cc61a311-1640-44b5-9fba-1b764f453329"
version = "0.1.10"

[[FLoopsBase]]
deps = ["ContextVariablesX"]
git-tree-sha1 = "cf3d8b2527be12d204d06aba922b30339a9653dd"
uuid = "b9860ae5-e623-471e-878b-f6a53c775ea6"
version = "0.1.0"

[[FoldsCUDA]]
deps = ["CUDA", "InitialValues", "Transducers", "UnionArrays"]
git-tree-sha1 = "40184fb209ac6024dd3e86ab4495b14cb2cddf38"
repo-rev = "master"
repo-url = "https://github.com/JuliaFolds/FoldsCUDA.jl.git"
uuid = "6cd66ae4-5932-4b96-926d-e73e578e42cc"
version = "0.1.6-DEV"

[[Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"

[[GPUArrays]]
deps = ["AbstractFFTs", "Adapt", "LinearAlgebra", "Printf", "Random", "Serialization", "Statistics"]
git-tree-sha1 = "ececbf05f8904c92814bdbd0aafd5540b0bf2e9a"
uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
version = "7.0.1"

[[GPUCompiler]]
deps = ["DataStructures", "ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "TimerOutputs", "UUIDs"]
git-tree-sha1 = "e8a09182a4440489e2e3dedff5ad3f6bbe555396"
uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
version = "0.12.5"

[[InitialValues]]
git-tree-sha1 = "26c8832afd63ac558b98a823265856670d898b6c"
uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c"
version = "0.2.10"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
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[[JuliaVariables]]
deps = ["MLStyle", "NameResolution"]
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uuid = "b14d175d-62b4-44ba-8fb7-3064adc8c3ec"
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[[LLVM]]
deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
git-tree-sha1 = "1b7ba36ea7aa6fa2278118951bad114fbb8359f2"
uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
version = "4.1.0"

[[LLVMExtra_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b36c0677a0549c7d1dc8719899a4133abbfacf7d"
uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
version = "0.0.6+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"

[[LinearAlgebra]]
deps = ["Libdl"]
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[[LogExpFunctions]]
deps = ["DocStringExtensions", "LinearAlgebra"]
git-tree-sha1 = "7bd5f6565d80b6bf753738d2bc40a5dfea072070"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
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[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

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

[[MicroCollections]]
deps = ["BangBang", "Setfield"]
git-tree-sha1 = "e991b6a9d38091c4a0d7cd051fcb57c05f98ac03"
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[[Mmap]]
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[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[NameResolution]]
deps = ["PrettyPrint"]
git-tree-sha1 = "1a0fa0e9613f46c9b8c11eee38ebb4f590013c5e"
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[[NetworkOptions]]
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[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
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[[OrderedCollections]]
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[[Pkg]]
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uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

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

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

[[Random123]]
deps = ["Libdl", "Random", "RandomNumbers"]
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[[RandomNumbers]]
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[[Reexport]]
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[[Requires]]
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[[SHA]]
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[[Serialization]]
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[[Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
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[[SharedArrays]]
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uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Sockets]]
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[[SparseArrays]]
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[[SpecialFunctions]]
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[[SplittablesBase]]
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[[TOML]]
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[[Tables]]
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[[Tar]]
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[[Test]]
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[[TimerOutputs]]
deps = ["ExprTools", "Printf"]
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[[Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
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[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

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

[[UnionArrays]]
deps = ["Adapt", "Setfield", "Transducers"]
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[[Zlib_jll]]
deps = ["Libdl"]
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[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
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[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

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

Project.toml

[deps]
CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
FLoops = "cc61a311-1640-44b5-9fba-1b764f453329"
FoldsCUDA = "6cd66ae4-5932-4b96-926d-e73e578e42cc"

sedt.jl

using CUDA
using FLoops
using FoldsCUDA

x = CUDA.rand(4, 4)
dt = CuArray{Float32}(undef, size(x))
v = CUDA.ones(Int64, size(x))
z = CUDA.zeros(Float32, size(x) .+ 1)

function squared_euclidean_distance_transform(f::AbstractArray{T,1}, dt, v, z) where {T}
    n = length(f)
    k = 1
    z[1] = -1.0f12
    z[2] = 1.0f12

    # Lower envelope operation
    for q in 2:n
        while true
            s = ((f[q] + q^2) - (f[v[k]] + v[k]^2)) / (2 * q - 2 * v[k])
            if s ≤ z[k]
                k -= 1
            else
                k += 1
                v[k] = q
                z[k] = s
                z[k + 1] = 1.0f12
                break
            end
        end
    end

    # Distance transform operation
    k = 1
    for q in 1:n
        while z[k + 1] < q
            k = k + 1
        end
        dt[q] = (q - v[k])^2 + f[v[k]]
    end
    return dt
end

function sedt(img::CuArray{T,2}, dt, v, z) where {T}
    rows, columns = size(img)
    @floop CUDAEx() for x in 1:rows
        @views squared_euclidean_distance_transform(img[x, :], dt[x, :], v[x, :], z[x, :])
    end

    @floop CUDAEx() for y in 1:columns
        @views squared_euclidean_distance_transform(img[:, y], dt[:, y], v[:, y], z[:, y])
    end
    return dt
end

sedt(x, dt, v, z)