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pluto_sample.jl
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### A Pluto.jl notebook ###
# v0.19.42
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 1d5e73f0-d287-11ec-3b24-1fad90c82e3d
begin
import ImageMagick
using PlutoUI
using Images
using Colors
using ColorVectorSpace
using ImageShow
using FileIO
using ImageIO
using Unitful
using ImageFiltering
using OffsetArrays
using Plots
using HypertextLiteral
using LinearAlgebra
using ForwardDiff
using LaTeXStrings
using Plots
using ImageMagick
using TestImages
using ImageView
using ImageTransformations
using LinearAlgebra
using LowRankApprox
using Wavelets
using DSP
# Small patch to make images look more crisp:
# https://github.com/JuliaImages/ImageShow.jl/pull/50
Base.showable(::MIME"text/html", ::AbstractMatrix{<:Colorant}) = false
end
# ╔═╡ 44ed3582-cedb-4ad1-80c7-b7b6b21c27f4
md"""
### Original Grayscale Image
"""
# ╔═╡ 6e74f71f-eeee-45ea-9bfe-1642a593eff8
md"""
### Sampling and Reverse
"""
# ╔═╡ b7379e69-26bd-48a5-b3bb-ab885ee38380
step = @bind s Slider(1:40, show_value=true, default=40)
# ╔═╡ 19830f72-b34f-4d56-9e66-8177aed19e4e
[I[1:s:end, 1:s:end] I[1:s:end, end:-s:1];
I[end:-s:1, 1:s:end] I[end:-s:1, end:-s:1]]
# ╔═╡ 61a316bb-e341-46b5-849b-dd93c19c7149
md"""
### SVD and Low Rank Approximation
"""
# ╔═╡ 90f7cceb-692d-4288-8304-a87408ae28aa
md"""
rank = $(@bind r Slider(1:rank, show_value=true))
"""
# ╔═╡ c2a3fd5e-2a3f-4107-bff7-99e2f94fdb95
begin
P1=plot(colorview(RGB,W[:,:,:,r]),
title="Low Rank Approx 1-100/384",
xaxis=false,
xticks=false,
yaxis=false,
yticks=false,
grid=false);
P2=plot(colorview(RGB,X),
title="Original RGB Image",
xaxis=false,
xticks=false,
yaxis=false,
yticks=false,
grid=false);
plot(P1,P2)
end
# ╔═╡ 430fa7d1-fd50-41aa-ae83-64ec24a8b235
begin
# read image, resize, decompose
XX=imresize(I, ratio=1/4);
(p1,q1)=size(XX);
L=7;
AA=channelview(XX);
RR=Array{Float64}(AA[1,:,:]);
GG=Array{Float64}(AA[2,:,:]);
BB=Array{Float64}(AA[3,:,:]);
# Decomposition Filter
XR=zeros(p1,q1,L);
XG=zeros(p1,q1,L);
XB=zeros(p1,q1,L);
for l=1:L
XR[:,:,l]=dwt(RR, wavelet(WT.haar), l);
XG[:,:,l]=dwt(GG, wavelet(WT.haar), l);
XB[:,:,l]=dwt(BB, wavelet(WT.haar), l);
end
# Splitting
XRapprox=zeros(p1,q1,L);
XGapprox=zeros(p1,q1,L);
XBapprox=zeros(p1,q1,L);
for l=1:L
XRapprox[1:Int(p1/2^l),1:Int(q1/2^l),l]=XR[1:Int(p1/2^l),1:Int(q1/2^l),l];
XGapprox[1:Int(p1/2^l),1:Int(q1/2^l),l]=XG[1:Int(p1/2^l),1:Int(q1/2^l),l];
XBapprox[1:Int(p1/2^l),1:Int(q1/2^l),l]=XB[1:Int(p1/2^l),1:Int(q1/2^l),l];
end
XRdetail=XR-XRapprox;
XGdetail=XG-XGapprox;
XBdetail=XB-XBapprox;
# Composition Filter
YRapprox=zeros(p1,q1,L);
YGapprox=zeros(p1,q1,L);
YBapprox=zeros(p1,q1,L);
YRdetail=zeros(p1,q1,L);
YGdetail=zeros(p1,q1,L);
YBdetail=zeros(p1,q1,L);
for l=1:L
YRapprox[:,:,l]=idwt(XRapprox[:,:,l], wavelet(WT.haar), l);
YGapprox[:,:,l]=idwt(XGapprox[:,:,l], wavelet(WT.haar), l);
YBapprox[:,:,l]=idwt(XBapprox[:,:,l], wavelet(WT.haar), l);
YRdetail[:,:,l]=idwt(XRdetail[:,:,l], wavelet(WT.haar), l);
YGdetail[:,:,l]=idwt(XGdetail[:,:,l], wavelet(WT.haar), l);
YBdetail[:,:,l]=idwt(XBdetail[:,:,l], wavelet(WT.haar), l);
end
# RGB
Wapprox=zeros(3,p1,q1,L+1);
Wdetail=zeros(3,p1,q1,L+1);
Wapprox[:,:,:,1]=AA;
for l=2:L+1
Wapprox[1,:,:,l]=YRapprox[:,:,l-1];
Wapprox[2,:,:,l]=YGapprox[:,:,l-1];
Wapprox[3,:,:,l]=YBapprox[:,:,l-1];
Wdetail[1,:,:,l]=YRdetail[:,:,l-1];
Wdetail[2,:,:,l]=YGdetail[:,:,l-1];
Wdetail[3,:,:,l]=YBdetail[:,:,l-1];
end
end
# ╔═╡ 66a04786-fcca-44a7-84e8-f839cf5fadfa
md"""
### Multiresolution Decomposition
"""
# ╔═╡ 2cefc737-bcb0-4eb1-ae6f-9022bbcc50cb
md"""
Level = $(@bind l Slider(0:L, show_value=true))
"""
# ╔═╡ 2331ce25-2e43-40a3-9537-17aefa359812
begin
Q1=plot(colorview(RGB,Wapprox[:,:,:,l+1]),
title="Approximation",
xaxis=false,
xticks=false,
yaxis=false,
yticks=false,
grid=false);
Q2=plot(colorview(RGB,Wdetail[:,:,:,l+1]),
title="Detail",
xaxis=false,
xticks=false,
yaxis=false,
yticks=false,
grid=false);
plot(Q1,Q2)
end
# ╔═╡ 469d7a59-b027-4d7a-9a24-f219135bfa5e
begin
I=load("char_kway_teow.jpg");
X=imresize(I, ratio=1/4);
(p,q)=size(X);
A=channelview(X);
R=Array{Float64}(A[1,:,:]);
G=Array{Float64}(A[2,:,:]);
B=Array{Float64}(A[3,:,:]);
RU, RS, RV=psvd(R);
GU, GS, GV=psvd(G);
BU, BS, BV=psvd(B);
rank=100;
DR=zeros(p,q,rank);
DG=zeros(p,q,rank);
DB=zeros(p,q,rank);
for r=1:rank
DR[:,:,r]=sum(RS[n]*RU[1:p,n]*(RV[1:q,n])' for n=1:r);
DG[:,:,r]=sum(GS[n]*GU[1:p,n]*(GV[1:q,n])' for n=1:r);
DB[:,:,r]=sum(BS[n]*BU[1:p,n]*(BV[1:q,n])' for n=1:r);
end
Y=zeros(3,p,q,rank+16);
Z=zeros(p,q)
for r=1:4
Y[1,:,:,r]=R;
Y[2,:,:,r]=G;
Y[3,:,:,r]=B;
end
for r=5:8
Y[1,:,:,r]=Z;
Y[2,:,:,r]=Z;
Y[3,:,:,r]=Z;
end
for r=9:rank+8
Y[1,:,:,r]=DR[:,:,r-8];
Y[2,:,:,r]=DG[:,:,r-8];
Y[3,:,:,r]=DB[:,:,r-8];
end
for r=rank+9:rank+12
Y[1,:,:,r]=Z;
Y[2,:,:,r]=Z;
Y[3,:,:,r]=Z;
end
for r=rank+13:rank+16
Y[1,:,:,r]=R;
Y[2,:,:,r]=G;
Y[3,:,:,r]=B;
end
W=zeros(3,p,q,rank);
for r=1:rank
W[1,:,:,r]=DR[:,:,r];
W[2,:,:,r]=DG[:,:,r];
W[3,:,:,r]=DB[:,:,r];
end
end
# ╔═╡ 8e7bcd23-b6c7-49f7-a9a7-d324f228d592
I=load("char_kway_teow.jpg")
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
ColorVectorSpace = "c3611d14-8923-5661-9e6a-0046d554d3a4"
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
DSP = "717857b8-e6f2-59f4-9121-6e50c889abd2"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
ImageFiltering = "6a3955dd-da59-5b1f-98d4-e7296123deb5"
ImageIO = "82e4d734-157c-48bb-816b-45c225c6df19"
ImageMagick = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
ImageShow = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
ImageTransformations = "02fcd773-0e25-5acc-982a-7f6622650795"
ImageView = "86fae568-95e7-573e-a6b2-d8a6b900c9ef"
Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
LowRankApprox = "898213cb-b102-5a47-900c-97e73b919f73"
OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
TestImages = "5e47fb64-e119-507b-a336-dd2b206d9990"
Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
Wavelets = "29a6e085-ba6d-5f35-a997-948ac2efa89a"
[compat]
ColorVectorSpace = "~0.9.8"
Colors = "~0.12.8"
DSP = "~0.7.8"
FileIO = "~1.14.0"
ForwardDiff = "~0.10.28"
HypertextLiteral = "~0.9.4"
ImageFiltering = "~0.7.1"
ImageIO = "~0.6.2"
ImageMagick = "~1.2.2"
ImageShow = "~0.3.5"
ImageTransformations = "~0.9.5"
ImageView = "~0.11.0"
Images = "~0.25.2"
LaTeXStrings = "~1.3.0"
LowRankApprox = "~0.5.2"
OffsetArrays = "~1.11.0"
Plots = "~1.29.0"
PlutoUI = "~0.7.38"
TestImages = "~1.7.1"
Unitful = "~1.11.0"
Wavelets = "~0.9.5"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
julia_version = "1.8.5"
manifest_format = "2.0"
project_hash = "b1620e4528aa44b1833a8ab28fd79605b042f3c8"
[[deps.ATK_jll]]
deps = ["Artifacts", "Glib_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "58c36d8a1beeb12d63921bcfaa674baf30a1140e"
uuid = "7b86fcea-f67b-53e1-809c-8f1719c154e8"
version = "2.36.1+0"
[[deps.AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
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[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
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deps = ["LinearAlgebra"]
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git-tree-sha1 = "62e51b39331de8911e4a7ff6f5aaf38a5f4cc0ae"
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