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### A Pluto.jl notebook ###
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# v0.12.15
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using Markdown
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using InteractiveUtils
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# 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).
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macro bind(def, element)
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quote
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local el = $(esc(element))
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global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
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el
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end
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end
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# ╔═╡ 877df834-f078-11ea-303b-e98273ef98a4
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begin
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using Pkg
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Pkg.activate(tempname())
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end
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# ╔═╡ 0316b94c-eef6-11ea-19bc-dbc959901bb5
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begin
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using Images
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using ImageMagick
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using Statistics
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using LinearAlgebra
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using ImageFiltering
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end
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# ╔═╡ fe19ad0a-ef04-11ea-1e5f-1bfcbbb51302
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using PlutoUI
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# ╔═╡ e196fa66-eef5-11ea-2afe-c9fcb6c48937
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# Poor man's Project.toml
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Pkg.add(["Images",
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"ImageMagick",
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"PlutoUI",
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"Hyperscript",
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"ImageFiltering"])
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# ╔═╡ cb335074-eef7-11ea-24e8-c39a325166a1
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md"""
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# Seam Carving
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1. We use convolution with Sobel filters for "edge detection".
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2. We use that to write an algorithm that removes "uninteresting"
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bits of an image in order to shrink it.
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"""
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# ╔═╡ d2ae6dd2-eef9-11ea-02df-255ec3b46a36
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begin
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example_urls = [
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"https://cdn.shortpixel.ai/spai/w_1086+q_lossy+ret_img+to_webp/https://wisetoast.com/wp-content/uploads/2015/10/The-Persistence-of-Memory-salvador-deli-painting.jpg",
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"https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Gustave_Caillebotte_-_Paris_Street%3B_Rainy_Day_-_Google_Art_Project.jpg/1014px-Gustave_Caillebotte_-_Paris_Street%3B_Rainy_Day_-_Google_Art_Project.jpg",
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"https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Gustave_Caillebotte_-_Paris_Street%3B_Rainy_Day_-_Google_Art_Project.jpg/1014px-Gustave_Caillebotte_-_Paris_Street%3B_Rainy_Day_-_Google_Art_Project.jpg",
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"https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Grant_Wood_-_American_Gothic_-_Google_Art_Project.jpg/480px-Grant_Wood_-_American_Gothic_-_Google_Art_Project.jpg",
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"https://cdn.shortpixel.ai/spai/w_1086+q_lossy+ret_img+to_webp/https://wisetoast.com/wp-content/uploads/2015/10/The-Persistence-of-Memory-salvador-deli-painting.jpg",
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"https://upload.wikimedia.org/wikipedia/commons/thumb/7/7d/A_Sunday_on_La_Grande_Jatte%2C_Georges_Seurat%2C_1884.jpg/640px-A_Sunday_on_La_Grande_Jatte%2C_Georges_Seurat%2C_1884.jpg",
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"https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Van_Gogh_-_Starry_Night_-_Google_Art_Project.jpg/758px-Van_Gogh_-_Starry_Night_-_Google_Art_Project.jpg",
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"https://web.mit.edu/facilities/photos/construction/Projects/stata/1_large.jpg",
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]
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img = load(download(example_urls[2]))
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end
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# ╔═╡ 8340cf20-f079-11ea-1665-f5864bc49cb9
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# ╔═╡ 0b6010a8-eef6-11ea-3ad6-c1f10e30a413
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# arbitrarily choose the brightness of a pixel as mean of rgb
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# brightness(c::AbstractRGB) = mean((c.r, c.g, c.b))
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# Use a weighted sum of rgb giving more weight to colors we perceive as 'brighter'
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# Based on https://www.tutorialspoint.com/dip/grayscale_to_rgb_conversion.htm
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brightness(c::AbstractRGB) = 0.3 * c.r + 0.59 * c.g + 0.11 * c.b
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# ╔═╡ fc1c43cc-eef6-11ea-0fc4-a90ac4336964
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Gray.(brightness.(img))
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# ╔═╡ 82c0d0c8-efec-11ea-1bb9-83134ecb877e
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md"""
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# Edge detection filter
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(Spoiler alert!) Here, we use the Sobel edge detection filter we created in Homework 1.
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```math
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\begin{align}
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G_x &= \begin{bmatrix}
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1 & 0 & -1 \\
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2 & 0 & -2 \\
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1 & 0 & -1 \\
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\end{bmatrix}*A\\
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G_y &= \begin{bmatrix}
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1 & 2 & 1 \\
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0 & 0 & 0 \\
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-1 & -2 & -1 \\
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\end{bmatrix}*A
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\end{align}
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```
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Here $A$ is the array corresponding to your image.
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We can think of these as derivatives in the $x$ and $y$ directions.
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Then we combine them by finding the magnitude of the **gradient** (in the sense of multivariate calculus) by defining
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$$G_\text{total} = \sqrt{G_x^2 + G_y^2}.$$
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"""
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# ╔═╡ da726954-eff0-11ea-21d4-a7f4ae4a6b09
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Sy, Sx = Kernel.sobel()
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# ╔═╡ abf6944e-f066-11ea-18e2-0b92606dab85
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(collect(Int.(8 .* Sy)), collect(Int.(8 .* Sx)))
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# ╔═╡ ac8d6902-f069-11ea-0f1d-9b0fa706d769
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md"""
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- blue shows positive values
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- red shows negative values
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$G_x \hspace{180pt} G_y$
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"""
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# ╔═╡ 172c7612-efee-11ea-077a-5d5c6e2505a4
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function shrink_image(image, ratio=5)
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(height, width) = size(image)
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new_height = height ÷ ratio - 1
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new_width = width ÷ ratio - 1
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list = [
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mean(image[
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ratio * i:ratio * (i + 1),
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ratio * j:ratio * (j + 1),
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])
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for j in 1:new_width
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for i in 1:new_height
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]
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reshape(list, new_height, new_width)
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end
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# ╔═╡ fcf46120-efec-11ea-06b9-45f470899cb2
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function convolve(M, kernel)
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height, width = size(kernel)
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half_height = height ÷ 2
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half_width = width ÷ 2
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new_image = similar(M)
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# (i, j) loop over the original image
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m, n = size(M)
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@inbounds for i in 1:m
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for j in 1:n
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# (k, l) loop over the neighbouring pixels
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accumulator = 0 * M[1, 1]
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for k in -half_height:-half_height + height - 1
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for l in -half_width:-half_width + width - 1
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Mi = i - k
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Mj = j - l
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# First index into M
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if Mi < 1
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Mi = 1
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elseif Mi > m
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Mi = m
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end
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# Second index into M
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if Mj < 1
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Mj = 1
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elseif Mj > n
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Mj = n
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end
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accumulator += kernel[k, l] * M[Mi, Mj]
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end
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end
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new_image[i, j] = accumulator
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end
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end
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return new_image
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end
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# ╔═╡ 6f7bd064-eff4-11ea-0260-f71aa7f4f0e5
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function edgeness(img)
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Sy, Sx = Kernel.sobel()
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b = brightness.(img)
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∇y = convolve(b, Sy)
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∇x = convolve(b, Sx)
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sqrt.(∇x.^2 + ∇y.^2)
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end
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# ╔═╡ dec62538-efee-11ea-1e03-0b801e61e91c
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function show_colored_array(array)
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pos_color = RGB(0.36, 0.82, 0.8)
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neg_color = RGB(0.99, 0.18, 0.13)
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to_rgb(x) = max(x, 0) * pos_color + max(-x, 0) * neg_color
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to_rgb.(array) / maximum(abs.(array))
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end
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# ╔═╡ da39c824-eff0-11ea-375b-1b6c6e186182
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# Sx
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# collect(Int.(8 .* Sx))
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show_colored_array(Sx)
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# ╔═╡ 074a58be-f146-11ea-382c-b7ae6c44bf75
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# Sy
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# collect(Int.(8 .* Sy))
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show_colored_array(Sy)
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# ╔═╡ f8283a0e-eff4-11ea-23d3-9f1ced1bafb4
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md"""
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## Seam carving idea
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The idea of seam carving is to find a path from the top of the image to the bottom of the image where the path minimizes the edgness.
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In other words, this path **minimizes the number of edges it crosses**
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"""
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# ╔═╡ 025e2c94-eefb-11ea-12cb-f56f34886334
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md"""
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At every step in going down, the path is allowed to go south west, south or south east. We want to find a seam with the minimum possible sum of energies.
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We start by writing a `least_edgy` function which given a matrix of energies, returns
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a matrix of minimum possible energy starting from that pixel going up to a pixel in the bottom most row.
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"""
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# ╔═╡ e5a7e426-2d0c-11eb-07fd-cd587148bd38
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small_img = shrink_image(img, 10)
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# ╔═╡ eff57fca-2d06-11eb-0ef2-f94561e916eb
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function get_seam_map(im)
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m, n = size(im)
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sm = Array{Float64}(undef, size(im))
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sd = Array{Int}(undef, size(im))
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sm[end, :] .= im[end, :]
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for i in m-1:-1:1
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for j in 1:n
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val = im[i,j]
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min_below = 1000.0
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path = 0
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for k in max(1,j-1):min(n,j+1)
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candidate = sm[i+1,k]
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if candidate < min_below
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min_below = candidate
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path = k-j
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end
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end
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sm[i,j] = min_below + val
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sd[i,j] = path
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end
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end
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return sm, sd
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end
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# ╔═╡ 1c01264c-2d08-11eb-0549-076c31bb8fa6
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sm, sd = get_seam_map(edgeness(img))
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# ╔═╡ acc1ee8c-eef9-11ea-01ac-9b9e9c4167b3
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# e[x,y]
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# ↙ ↓ ↘ <--pick the next path which gives the least overall energy
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# e[x-1,y+1] e[x,y+1] e[x+1,y+1]
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#
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# Basic Comp: e[x,y] += min( e[x-1,y+1],e[x,y],e[x+1,y])
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# dirs records which one from (-1==SW,0==S,1==SE)
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function least_edgy(E)
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least_E = zeros(size(E))
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dirs = zeros(Int, size(E))
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least_E[end, :] .= E[end, :] # the minimum energy on the last row is the energy
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# itself
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m, n = size(E)
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# Go from the last row up, finding the minimum energy
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for i in m-1:-1:1
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for j in 1:n
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j1, j2 = max(1, j-1), min(j+1, n)
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e, dir = findmin(least_E[i+1, j1:j2])
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least_E[i,j] += e
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least_E[i,j] += E[i,j]
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dirs[i, j] = (-1,0,1)[dir + (j==1)]
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end
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end
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least_E, dirs
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end
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# ╔═╡ 8b204a2a-eff6-11ea-25b0-13f230037ee1
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# The bright areas are screaming "AVOID ME!!!"
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least_e, dirs = least_edgy(edgeness(img))
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# ╔═╡ 84d3afe4-eefe-11ea-1e31-bf3b2af4aecd
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show_colored_array(least_e)
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# ╔═╡ 50a49b56-2d09-11eb-2d33-8d4cd5896e38
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show_colored_array(sm)
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# ╔═╡ b507480a-ef01-11ea-21c4-63d19fac19ab
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# direction the path should take at every pixel.
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reduce((x,y)->x*y*"\n",
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reduce(*, getindex.(([" ", "↙", "↓", "↘"],), dirs[1:25, 1:76].+3), dims=2, init=""), init="") |> Text
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# ╔═╡ 696cf94e-2d09-11eb-136a-8f360d3a7507
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reduce((x,y)->x*y*"\n",
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reduce(*, getindex.(([" ", "↙", "↓", "↘"],), sd[1:25, 1:76].+3), dims=2, init=""), init="") |> Text
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# ╔═╡ 7d8b20a2-ef03-11ea-1c9e-fdf49a397619
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md"## Remove seams"
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# ╔═╡ f690b06a-ef31-11ea-003b-4f2b2f82a9c3
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md"""
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Compressing an image horizontally involves a number of seams of lowest energy successively.
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"""
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# ╔═╡ 0adf2e18-2d10-11eb-2a27-6de83b5aad3a
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function get_seam_at2(sd, j)
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h = size(sd, 1)
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js = Array{Int}(undef, h)
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js[1] = j
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for i=2:h
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js[i] = js[i-1] + sd[i-1,js[i-1]]
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end
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tuple.(1:h, js)
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end
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# ╔═╡ 977b6b98-ef03-11ea-0176-551fc29729ab
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function get_seam_at(dirs, j)
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m = size(dirs, 1)
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js = fill(0, m)
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js[1] = j
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for i=2:m
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js[i] = js[i-1] + dirs[i-1, js[i-1]]
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end
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tuple.(1:m, js)
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end
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# ╔═╡ 9abbb158-ef03-11ea-39df-a3e8aa792c50
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get_seam_at(dirs, 2)
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# ╔═╡ fe709508-2d10-11eb-02a9-29080b78d44a
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get_seam_at2(dirs, 2)
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# ╔═╡ 14f72976-ef05-11ea-2ad5-9f0914f9cf58
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function mark_path(img, path)
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img′ = copy(img)
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m = size(img, 2)
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for (i, j) in path
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# To make it easier to see, we'll color not just
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# the pixels of the seam, but also those adjacent to it
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for j′ in j-1:j+1
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img′[i, clamp(j′, 1, m)] = RGB(1,0,1)
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end
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end
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img′
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end
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# ╔═╡ cf9a9124-ef04-11ea-14a4-abf930edc7cc
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@bind start_column Slider(1:size(img, 2))
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# ╔═╡ 772a4d68-ef04-11ea-366a-f7ae9e1634f6
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path = get_seam_at2(dirs, start_column)
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# ╔═╡ 081a98cc-f06e-11ea-3664-7ba51d4fd153
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function pencil(X)
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f(x) = RGB(1-x,1-x,1-x)
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map(f, X ./ maximum(X))
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end
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# ╔═╡ 237647e8-f06d-11ea-3c7e-2da57e08bebc
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e = edgeness(img);
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# ╔═╡ c7a7386e-2d11-11eb-3885-056f6d7fb840
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# ╔═╡ 4f23bc54-ef0f-11ea-06a9-35ca3ece421e
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function rm_path(img, path)
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img′ = img[:, 1:end-1] # one less column
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for (i, j) in path
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img′[i, 1:j-1] .= img[i, 1:j-1]
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img′[i, j:end] .= img[i, j+1:end]
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end
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img′
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end
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# ╔═╡ b401f398-ef0f-11ea-38fe-012b7bc8a4fa
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function shrink_n(img, n)
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imgs = []
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marked_imgs = []
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e = edgeness(img)
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for i=1:n
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least_E, dirs = get_seam_map(e)
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_, min_j = findmin(@view least_E[1, :])
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seam = get_seam_at2(dirs, min_j)
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img = rm_path(img, seam)
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# Recompute the energy for the new image
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# Note, this currently involves rerunning the convolution
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# on the whole image, but in principle the only values that
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# need recomputation are those adjacent to the seam, so there
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# is room for a meanintful speedup here.
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e = edgeness(img)
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e = rm_path(e, seam)
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push!(imgs, img)
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push!(marked_imgs, mark_path(img, seam))
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end
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imgs, marked_imgs
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end
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# ╔═╡ b1b6b7fc-f153-11ea-224a-2578e8298775
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n_examples = min(200, size(img, 2))
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# ╔═╡ 2eb459d4-ef36-11ea-1f74-b53ffec7a1ed
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# returns two vectors of n successively smaller images
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# The second images have markings where the seam is cut out
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carved, marked_carved = shrink_n(img, n_examples);
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# ╔═╡ 7038abe4-ef36-11ea-11a5-75e57ab51032
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@bind n Slider(1:length(carved))
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# ╔═╡ 2d6c6820-ef2d-11ea-1704-49bb5188cfcc
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md"shrunk by $n:"
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# ╔═╡ 1fd26a60-f089-11ea-1f56-bb6eba7d9651
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function hbox(x, y, gap=16; sy=size(y), sx=size(x))
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w,h = (max(sx[1], sy[1]),
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gap + sx[2] + sy[2])
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slate = fill(RGB(1,1,1), w,h)
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slate[1:size(x,1), 1:size(x,2)] .= RGB.(x)
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slate[1:size(y,1), size(x,2) + gap .+ (1:size(y,2))] .= RGB.(y)
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slate
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end
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# ╔═╡ 44192a40-eff2-11ea-0ec7-05cdadb0c29a
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begin
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img_brightness = brightness.(img)
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∇x = convolve(img_brightness, Sx)
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∇y = convolve(img_brightness, Sy)
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hbox(show_colored_array(∇x), show_colored_array(∇y))
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end
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# ╔═╡ d6a268c0-eff4-11ea-2c9e-bfef19c7f540
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begin
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edged = edgeness(img)
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# hbox(img, pencil(edged))
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hbox(img, Gray.(edgeness(img)) / maximum(abs.(edged)))
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end
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# ╔═╡ 552fb92e-ef05-11ea-0a79-dd7a6760089a
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hbox(mark_path(img, path), mark_path(show_colored_array(least_e), path))
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# ╔═╡ dfd03c4e-f06c-11ea-1e2a-89233a675138
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let
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hbox(mark_path(img, path), mark_path(pencil(e), path));
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end
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# ╔═╡ ca4a87e8-eff8-11ea-3d57-01dfa34ff723
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let
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# least energy path of them all:
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_, k = findmin(least_e[1, :])
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path = get_seam_at(dirs, k)
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hbox(
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mark_path(img, path),
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mark_path(show_colored_array(least_e), path)
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)
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end
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# ╔═╡ fa6a2152-ef0f-11ea-0e67-0d1a6599e779
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hbox(img, marked_carved[n], sy=size(img))
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# ╔═╡ 71b16dbe-f08b-11ea-2343-5f1583074029
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vbox(x,y, gap=16) = hbox(x', y')'
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# ╔═╡ ddac52ea-f148-11ea-2860-21cff4c867e6
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let
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∇y = convolve(brightness.(img), Sy)
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∇x = convolve(brightness.(img), Sx)
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# zoom in on the clock
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vbox(
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hbox(img[300:end, 1:300], img[300:end, 1:300]),
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hbox(show_colored_array.((∇x[300:end, 1:300], ∇y[300:end, 1:300]))...)
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)
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end
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# ╔═╡ 15d1e5dc-ef2f-11ea-093a-417108bcd495
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[size(img) size(carved[n])]
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# ╔═╡ Cell order:
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# ╠═877df834-f078-11ea-303b-e98273ef98a4
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# ╠═e196fa66-eef5-11ea-2afe-c9fcb6c48937
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# ╠═0316b94c-eef6-11ea-19bc-dbc959901bb5
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# ╟─cb335074-eef7-11ea-24e8-c39a325166a1
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# ╠═d2ae6dd2-eef9-11ea-02df-255ec3b46a36
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# ╠═8340cf20-f079-11ea-1665-f5864bc49cb9
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# ╠═0b6010a8-eef6-11ea-3ad6-c1f10e30a413
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# ╠═fc1c43cc-eef6-11ea-0fc4-a90ac4336964
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# ╟─82c0d0c8-efec-11ea-1bb9-83134ecb877e
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# ╠═da726954-eff0-11ea-21d4-a7f4ae4a6b09
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# ╠═da39c824-eff0-11ea-375b-1b6c6e186182
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# ╠═074a58be-f146-11ea-382c-b7ae6c44bf75
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# ╠═abf6944e-f066-11ea-18e2-0b92606dab85
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# ╠═44192a40-eff2-11ea-0ec7-05cdadb0c29a
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# ╟─ac8d6902-f069-11ea-0f1d-9b0fa706d769
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# ╠═ddac52ea-f148-11ea-2860-21cff4c867e6
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# ╠═6f7bd064-eff4-11ea-0260-f71aa7f4f0e5
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# ╟─d6a268c0-eff4-11ea-2c9e-bfef19c7f540
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# ╠═172c7612-efee-11ea-077a-5d5c6e2505a4
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# ╟─fcf46120-efec-11ea-06b9-45f470899cb2
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# ╟─dec62538-efee-11ea-1e03-0b801e61e91c
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# ╟─f8283a0e-eff4-11ea-23d3-9f1ced1bafb4
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# ╟─025e2c94-eefb-11ea-12cb-f56f34886334
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# ╠═e5a7e426-2d0c-11eb-07fd-cd587148bd38
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# ╠═eff57fca-2d06-11eb-0ef2-f94561e916eb
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# ╠═1c01264c-2d08-11eb-0549-076c31bb8fa6
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# ╠═acc1ee8c-eef9-11ea-01ac-9b9e9c4167b3
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# ╠═8b204a2a-eff6-11ea-25b0-13f230037ee1
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# ╠═84d3afe4-eefe-11ea-1e31-bf3b2af4aecd
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# ╠═50a49b56-2d09-11eb-2d33-8d4cd5896e38
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# ╠═b507480a-ef01-11ea-21c4-63d19fac19ab
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# ╠═696cf94e-2d09-11eb-136a-8f360d3a7507
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# ╟─7d8b20a2-ef03-11ea-1c9e-fdf49a397619
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# ╠═f690b06a-ef31-11ea-003b-4f2b2f82a9c3
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# ╠═fe19ad0a-ef04-11ea-1e5f-1bfcbbb51302
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# ╠═0adf2e18-2d10-11eb-2a27-6de83b5aad3a
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# ╠═977b6b98-ef03-11ea-0176-551fc29729ab
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# ╠═9abbb158-ef03-11ea-39df-a3e8aa792c50
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# ╠═fe709508-2d10-11eb-02a9-29080b78d44a
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# ╠═772a4d68-ef04-11ea-366a-f7ae9e1634f6
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# ╟─14f72976-ef05-11ea-2ad5-9f0914f9cf58
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# ╠═cf9a9124-ef04-11ea-14a4-abf930edc7cc
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# ╠═552fb92e-ef05-11ea-0a79-dd7a6760089a
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# ╠═081a98cc-f06e-11ea-3664-7ba51d4fd153
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# ╠═237647e8-f06d-11ea-3c7e-2da57e08bebc
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# ╠═dfd03c4e-f06c-11ea-1e2a-89233a675138
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# ╠═ca4a87e8-eff8-11ea-3d57-01dfa34ff723
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# ╠═c7a7386e-2d11-11eb-3885-056f6d7fb840
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# ╠═4f23bc54-ef0f-11ea-06a9-35ca3ece421e
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# ╠═b401f398-ef0f-11ea-38fe-012b7bc8a4fa
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# ╠═b1b6b7fc-f153-11ea-224a-2578e8298775
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# ╠═2eb459d4-ef36-11ea-1f74-b53ffec7a1ed
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# ╠═7038abe4-ef36-11ea-11a5-75e57ab51032
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# ╟─2d6c6820-ef2d-11ea-1704-49bb5188cfcc
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# ╠═fa6a2152-ef0f-11ea-0e67-0d1a6599e779
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# ╟─71b16dbe-f08b-11ea-2343-5f1583074029
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# ╟─1fd26a60-f089-11ea-1f56-bb6eba7d9651
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# ╟─15d1e5dc-ef2f-11ea-093a-417108bcd495
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