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"

[[AbstractTrees]]
git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.3.4"

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

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

[[ArrayInterface]]
deps = ["IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "045ff5e1bc8c6fb1ecb28694abba0a0d55b5f4f5"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "3.1.17"

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

[[AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.0"

[[AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "f31f50712cbdf40ee8287f0443b57503e34122ef"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.3"

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

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

[[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 = "82b2811f5888465d96b38c7bb12d8fb9c25838e1"
uuid = "052768ef-5323-5732-b1bb-66c8b64840ba"
version = "3.3.1"

[[CatIndices]]
deps = ["CustomUnitRanges", "OffsetArrays"]
git-tree-sha1 = "a0f80a09780eed9b1d106a1bf62041c2efc995bc"
uuid = "aafaddc9-749c-510e-ac4f-586e18779b91"
version = "0.2.2"

[[ChainRules]]
deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "2a3ff475414f55f73d368f0d42c6d8b14f46e6f9"
uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
version = "0.8.19"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "be770c08881f7bb928dfd86d1ba83798f76cf62a"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "0.10.9"

[[ChainRulesTestUtils]]
deps = ["ChainRulesCore", "Compat", "FiniteDifferences", "LinearAlgebra", "Random", "Test"]
git-tree-sha1 = "fa5a5b23f3be3f798f655981d5ed05be98ab2042"
uuid = "cdddcdb0-9152-4a09-a978-84456f9df70a"
version = "0.7.13"

[[CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
git-tree-sha1 = "42a9b08d3f2f951c9b283ea427d96ed9f1f30343"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.9.5"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[CommonSubexpressions]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
version = "0.3.0"

[[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"

[[ComputationalResources]]
git-tree-sha1 = "52cb3ec90e8a8bea0e62e275ba577ad0f74821f7"
uuid = "ed09eef8-17a6-5b46-8889-db040fac31e3"
version = "0.3.2"

[[Conda]]
deps = ["JSON", "VersionParsing"]
git-tree-sha1 = "299304989a5e6473d985212c28928899c74e9421"
uuid = "8f4d0f93-b110-5947-807f-2305c1781a2d"
version = "1.5.2"

[[CoordinateTransformations]]
deps = ["LinearAlgebra", "StaticArrays"]
git-tree-sha1 = "6d1c23e740a586955645500bbec662476204a52c"
uuid = "150eb455-5306-5404-9cee-2592286d6298"
version = "0.6.1"

[[CustomUnitRanges]]
git-tree-sha1 = "537c988076d001469093945f3bd0b300b8d3a7f3"
uuid = "dc8bdbbb-1ca9-579f-8c36-e416f6a65cce"
version = "1.0.1"

[[DSP]]
deps = ["Compat", "FFTW", "IterTools", "LinearAlgebra", "Polynomials", "Random", "Reexport", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "c6dc51c5597bffe9100ccea0e850dc99afeeaeeb"
uuid = "717857b8-e6f2-59f4-9121-6e50c889abd2"
version = "0.7.2"

[[DataAPI]]
git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
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"

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

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

[[DiffResults]]
deps = ["StaticArrays"]
git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
version = "1.0.3"

[[DiffRules]]
deps = ["NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "214c3fcac57755cfda163d91c58893a8723f93e9"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "1.0.2"

[[Distances]]
deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.3"

[[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"

[[EllipsisNotation]]
deps = ["ArrayInterface"]
git-tree-sha1 = "8041575f021cba5a099a456b4163c9a08b566a02"
uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
version = "1.1.0"

[[ExprTools]]
git-tree-sha1 = "555eab1f7c501166ba87eeb5d561e9f5e7d167d3"
uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
version = "0.1.4"

[[EzXML]]
deps = ["Printf", "XML2_jll"]
git-tree-sha1 = "0fa3b52a04a4e210aeb1626def9c90df3ae65268"
uuid = "8f5d6c58-4d21-5cfd-889c-e3ad7ee6a615"
version = "1.1.0"

[[FFTViews]]
deps = ["CustomUnitRanges", "FFTW"]
git-tree-sha1 = "70a0cfd9b1c86b0209e38fbfe6d8231fd606eeaf"
uuid = "4f61f5a4-77b1-5117-aa51-3ab5ef4ef0cd"
version = "0.3.1"

[[FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "f985af3b9f4e278b1d24434cbb546d6092fca661"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.4.3"

[[FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3676abafff7e4ff07bbd2c42b3d8201f31653dcc"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.9+8"

[[FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "256d8e6188f3f1ebfa1a5d17e072a0efafa8c5bf"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.10.1"

[[FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays"]
git-tree-sha1 = "a603e79b71bb3c1efdb58f0ee32286efe2d1a255"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.11.8"

[[FiniteDifferences]]
deps = ["ChainRulesCore", "LinearAlgebra", "Printf", "Random", "Richardson", "StaticArrays"]
git-tree-sha1 = "9a586f04a21e6945f4cbee0d0fb6aebd7b86aa8f"
uuid = "26cc04aa-876d-5657-8c51-4c34ba976000"
version = "0.12.18"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Flux]]
deps = ["AbstractTrees", "Adapt", "CUDA", "CodecZlib", "Colors", "DelimitedFiles", "Functors", "Juno", "LinearAlgebra", "MacroTools", "NNlib", "NNlibCUDA", "Pkg", "Printf", "Random", "Reexport", "SHA", "Statistics", "StatsBase", "Test", "ZipFile", "Zygote"]
git-tree-sha1 = "0b3c6d0ce57d3b793eabd346ccc8f605035ef079"
uuid = "587475ba-b771-5e3f-ad9e-33799f191a9c"
version = "0.12.4"

[[ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "e2af66012e08966366a43251e1fd421522908be6"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.18"

[[Functors]]
deps = ["MacroTools"]
git-tree-sha1 = "a7bb2af991c43dcf5c3455d276dd83976799634f"
uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
version = "0.2.1"

[[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 = "03c3fb77362c08c3722bcef8dec488b708a95d52"
uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
version = "0.12.4"

[[Graphics]]
deps = ["Colors", "LinearAlgebra", "NaNMath"]
git-tree-sha1 = "2c1cf4df419938ece72de17f368a021ee162762e"
uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
version = "1.1.0"

[[IRTools]]
deps = ["InteractiveUtils", "MacroTools", "Test"]
git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
version = "0.4.3"

[[IfElse]]
git-tree-sha1 = "28e837ff3e7a6c3cdb252ce49fb412c8eb3caeef"
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
version = "0.1.0"

[[ImageAxes]]
deps = ["AxisArrays", "ImageCore", "Reexport", "SimpleTraits"]
git-tree-sha1 = "794ad1d922c432082bc1aaa9fa8ffbd1fe74e621"
uuid = "2803e5a7-5153-5ecf-9a86-9b4c37f5f5ac"
version = "0.6.9"

[[ImageBase]]
deps = ["ImageCore", "Reexport"]
git-tree-sha1 = "84677012257b18dfdad166352f0632136cee99f2"
uuid = "c817782e-172a-44cc-b673-b171935fbb9e"
version = "0.1.1"

[[ImageContrastAdjustment]]
deps = ["ColorVectorSpace", "ImageCore", "ImageTransformations", "Parameters"]
git-tree-sha1 = "2e6084db6cccab11fe0bc3e4130bd3d117092ed9"
uuid = "f332f351-ec65-5f6a-b3d1-319c6670881a"
version = "0.3.7"

[[ImageCore]]
deps = ["AbstractFFTs", "Colors", "FixedPointNumbers", "Graphics", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "Reexport"]
git-tree-sha1 = "db645f20b59f060d8cfae696bc9538d13fd86416"
uuid = "a09fc81d-aa75-5fe9-8630-4744c3626534"
version = "0.8.22"

[[ImageDistances]]
deps = ["ColorVectorSpace", "Distances", "ImageCore", "ImageMorphology", "LinearAlgebra", "Statistics"]
git-tree-sha1 = "6378c34a3c3a216235210d19b9f495ecfff2f85f"
uuid = "51556ac3-7006-55f5-8cb3-34580c88182d"
version = "0.2.13"

[[ImageFiltering]]
deps = ["CatIndices", "ColorVectorSpace", "ComputationalResources", "DataStructures", "FFTViews", "FFTW", "ImageCore", "LinearAlgebra", "OffsetArrays", "Requires", "SparseArrays", "StaticArrays", "Statistics", "TiledIteration"]
git-tree-sha1 = "bf96839133212d3eff4a1c3a80c57abc7cfbf0ce"
uuid = "6a3955dd-da59-5b1f-98d4-e7296123deb5"
version = "0.6.21"

[[ImageIO]]
deps = ["FileIO", "Netpbm", "PNGFiles", "TiffImages", "UUIDs"]
git-tree-sha1 = "d067570b4d4870a942b19d9ceacaea4fb39b69a1"
uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
version = "0.5.6"

[[ImageMagick]]
deps = ["FileIO", "ImageCore", "ImageMagick_jll", "InteractiveUtils", "Libdl", "Pkg", "Random"]
git-tree-sha1 = "5bc1cb62e0c5f1005868358db0692c994c3a13c6"
uuid = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
version = "1.2.1"

[[ImageMagick_jll]]
deps = ["JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "1c0a2295cca535fabaf2029062912591e9b61987"
uuid = "c73af94c-d91f-53ed-93a7-00f77d67a9d7"
version = "6.9.10-12+3"

[[ImageMetadata]]
deps = ["AxisArrays", "ColorVectorSpace", "ImageAxes", "ImageCore", "IndirectArrays"]
git-tree-sha1 = "ae76038347dc4edcdb06b541595268fca65b6a42"
uuid = "bc367c6b-8a6b-528e-b4bd-a4b897500b49"
version = "0.9.5"

[[ImageMorphology]]
deps = ["ColorVectorSpace", "ImageCore", "LinearAlgebra", "TiledIteration"]
git-tree-sha1 = "68e7cbcd7dfaa3c2f74b0a8ab3066f5de8f2b71d"
uuid = "787d08f9-d448-5407-9aad-5290dd7ab264"
version = "0.2.11"

[[ImageProjectiveGeometry]]
deps = ["DSP", "FileIO", "ImageFiltering", "Images", "Interpolations", "LinearAlgebra", "Printf", "PyPlot", "Random", "Statistics"]
git-tree-sha1 = "709233c4470fef4be1338fb1edb2d490596f88f8"
uuid = "b9d14576-938f-5430-9d4c-b7d7de1409d6"
version = "0.3.4"

[[ImageQualityIndexes]]
deps = ["ColorVectorSpace", "ImageCore", "ImageDistances", "ImageFiltering", "OffsetArrays", "Statistics"]
git-tree-sha1 = "1198f85fa2481a3bb94bf937495ba1916f12b533"
uuid = "2996bd0c-7a13-11e9-2da2-2f5ce47296a9"
version = "0.2.2"

[[ImageShow]]
deps = ["Base64", "FileIO", "ImageCore", "OffsetArrays", "Requires", "StackViews"]
git-tree-sha1 = "832abfd709fa436a562db47fd8e81377f72b01f9"
uuid = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
version = "0.3.1"

[[ImageTransformations]]
deps = ["AxisAlgorithms", "ColorVectorSpace", "CoordinateTransformations", "ImageBase", "ImageCore", "Interpolations", "OffsetArrays", "Rotations", "StaticArrays"]
git-tree-sha1 = "0ba10d50a3cf8baf5523db5b76228e70599d9b3e"
repo-rev = "master"
repo-url = "https://github.com/JuliaImages/ImageTransformations.jl.git"
uuid = "02fcd773-0e25-5acc-982a-7f6622650795"
version = "0.8.12"

[[Images]]
deps = ["AxisArrays", "Base64", "ColorVectorSpace", "FileIO", "Graphics", "ImageAxes", "ImageContrastAdjustment", "ImageCore", "ImageDistances", "ImageFiltering", "ImageIO", "ImageMagick", "ImageMetadata", "ImageMorphology", "ImageQualityIndexes", "ImageShow", "ImageTransformations", "IndirectArrays", "OffsetArrays", "Random", "Reexport", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "TiledIteration"]
git-tree-sha1 = "8b714d5e11c91a0d945717430ec20f9251af4bd2"
uuid = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
version = "0.24.1"

[[IndirectArrays]]
git-tree-sha1 = "c2a145a145dc03a7620af1444e0264ef907bd44f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "0.5.1"

[[Inflate]]
git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
version = "0.1.2"

[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2018.0.3+2"

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

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
path = "/Users/dhairyagandhi/.julia/dev/Interpolations"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.3"

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

[[Intervals]]
deps = ["Dates", "Printf", "RecipesBase", "Serialization", "TimeZones"]
git-tree-sha1 = "323a38ed1952d30586d0fe03412cde9399d3618b"
uuid = "d8418881-c3e1-53bb-8760-2df7ec849ed5"
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[[IterTools]]
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version = "1.5.0+0"

[[Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "531474afbc343c3c7cb9b71c2771813c6defd550"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.14"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.1"

[[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"

poc.jl

using ImageTransformations
using StaticArrays
using Interpolations
using ImageCore
using ImageShow
using TestImages
using ChainRules
using ChainRules: NoTangent, ZeroTangent, @not_implemented
using ChainRulesTestUtils
using Zygote

img = Float64.(imresize(testimage("cameraman"), (32, 32)))

function ϕ(p, θ)
    sinθ, cosθ = sincos(θ)
    [p[1]*cosθ - p[2]*sinθ,
     p[1]*sinθ + p[2]*cosθ]
end

function ChainRules.rrule(::typeof(ϕ), p, θ)
    sinθ, cosθ = sincos(θ)
    q = [p[1]*cosθ - p[2]*sinθ,
         p[1]*sinθ + p[2]*cosθ]
    function dϕ(dLdq)
        dϕdθ = [-p[1]*sinθ - p[2]*cosθ,
                p[1]*cosθ - p[2]*sinθ]
        dLdθ = sum(dLdq .* dϕdθ)

        dLdp = [dLdq[1] * cosθ + dLdq[2] * sinθ,
                -dLdq[1] * sinθ + dLdq[2] * cosθ]
        return NoTangent(), dLdp, dLdθ
    end
    return q, dϕ
end

function τ(X, q)
    etp = extrapolate(interpolate(X, BSpline(Linear())), zero(eltype(X)))
    return etp(q...)
end

function ChainRules.rrule(::typeof(τ), X, q)
    etp = extrapolate(interpolate(X, BSpline(Linear())), zero(eltype(X)))
    Yp = etp(q...)
    function dτ(dLdYp)
        dLdq = dLdYp .* Interpolations.gradient(etp, q...)

        dLdX = @not_implemented(
                "Interpolations doesn't yet support gradient to coefficients"
            )
        return NoTangent(), dLdX, dLdq
    end
    return Yp, dτ
end

# Do some pixel level tests

θ = 0.2
p = [10, 10]
q = ϕ(p, θ)

# test our rrule
# test_rrule(ϕ, p, θ; check_inferred=false) # FIXME
test_rrule(τ, img, q; check_inferred=false)

function f_single_pixel(θ)
    τ(img, ϕ(p, θ))
end

img_p = img[p...]

Zygote.gradient(θ) do θ
    f_single_pixel(θ) - img_p
end # (-0.08925456466517724,)
    
# Now let's put the warp together

function simple_rotate(X, θ)
    out = similar(X)
    for p in CartesianIndices(out)
        q = ϕ(collect(p.I), θ)
        out[p] = τ(X, q)
    end
    out
end

function ChainRules.rrule(::typeof(simple_rotate), X, θ)
    Y = simple_rotate(X, θ)

    function gradient_simple_rotate(dLdY)
        dLdθ = zero(eltype(dLdY))
        lk = ReentrantLock()
        Threads.@threads for p in CartesianIndices(Y)
            tmp = let p = collect(p.I)
                _, dτ = rrule(τ, X, p)
                _, _, dLdq = dτ(dLdY[p])
                _, dϕ = rrule(ϕ, p, θ)
                _, _, dLdθ = dϕ(dLdq)
                return dLdθ
            end
            lock(lk) do
                dLdθ += tmp
            end
        end
        dLdX = @not_implemented(
            "Interpolations doesn't yet support gradient to coefficients"
        )
        return NoTangent(), dLdX, dLdθ
    end
    return Y, gradient_simple_rotate
end

simple_rotate(img, θ) .|> Gray

imgr, gradient_simple_rotate = rrule(simple_rotate, img, θ)

gradient_simple_rotate(ones(eltype(img), size(img)))

# test_rrule(simple_rotate, img, θ; check_inferred=false) # FIXME
    
# do some simple experiment

g(img, θ) = simple_rotate(img, θ)
g(img, θ) .|> Gray

function run2(img = img, θ = 0.5, lr = 1e-2)
# opt = ADAM()
outs = []
FileIO.save("i.gif", ImageShow.gif([img]), fps = 1)
for n in 1:1600
    dθ, = Zygote.gradient(θ) do θ
        sum(abs2, (g(img, θ) .- img))
    end
    θ = θ + lr * dθ

    out = g(img, θ)
    if n % 100 == 0
      println("loss: ", sum(abs2, out - img), ", dθ=", dθ)
    end
    push!(outs, Gray.(out))
end

dθ, = Zygote.gradient(θ) do θ
        sum((g(img, θ) .- img) .^ 2)
    end
println("loss: ", sum(abs2, g(img, θ) - img), ", dθ=", dθ)
FileIO.save("o.gif", ImageShow.gif([outs...]), fps = 50)
end

Project.toml

name = "DiffImages"
uuid = "f2ee3836-eb25-4a50-842c-9baeb5ea126d"
authors = ["SomTambe <tambesom@gmail.com>"]
version = "0.1.0"

[deps]
ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
ColorVectorSpace = "c3611d14-8923-5661-9e6a-0046d554d3a4"
CoordinateTransformations = "150eb455-5306-5404-9cee-2592286d6298"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
ImageCore = "a09fc81d-aa75-5fe9-8630-4744c3626534"
ImageProjectiveGeometry = "b9d14576-938f-5430-9d4c-b7d7de1409d6"
ImageShow = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
ImageTransformations = "02fcd773-0e25-5acc-982a-7f6622650795"
Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
TestImages = "5e47fb64-e119-507b-a336-dd2b206d9990"
Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"