### A Pluto.jl notebook ### # v0.11.13 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 el = $(esc(element)) global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing el end end # ╔═╡ 83eb9ca0-ed68-11ea-0bc5-99a09c68f867 md"_homework 1, version 4_" # ╔═╡ ac8ff080-ed61-11ea-3650-d9df06123e1f md""" # **Homework 1** - _convolutions_ `18.S191`, fall 2020 This notebook contains _built-in, live answer checks_! In some exercises you will see a coloured box, which runs a test case on your code, and provides feedback based on the result. Simply edit the code, run it, and the check runs again. _For MIT students:_ there will also be some additional (secret) test cases that will be run as part of the grading process, and we will look at your notebook and write comments. Feel free to ask questions! """ # ╔═╡ 911ccbce-ed68-11ea-3606-0384e7580d7c # edit the code below to set your name and kerberos ID (i.e. email without @mit.edu) student = (name = "Jazzy Doe", kerberos_id = "jazz") # press the ▶ button in the bottom right of this cell to run your edits # or use Shift+Enter # you might need to wait until all other cells in this notebook have completed running. # scroll down the page to see what's up # ╔═╡ 8ef13896-ed68-11ea-160b-3550eeabbd7d md""" Submission by: **_$(student.name)_** ($(student.kerberos_id)@mit.edu) """ # ╔═╡ 5f95e01a-ee0a-11ea-030c-9dba276aba92 md"_Let's create a package environment:_" # ╔═╡ 65780f00-ed6b-11ea-1ecf-8b35523a7ac0 begin import Pkg Pkg.activate(mktempdir()) end # ╔═╡ 74b008f6-ed6b-11ea-291f-b3791d6d1b35 begin Pkg.add(["Images", "ImageMagick"]) using Images end # ╔═╡ 6b30dc38-ed6b-11ea-10f3-ab3f121bf4b8 begin Pkg.add("PlutoUI") using PlutoUI end # ╔═╡ 67461396-ee0a-11ea-3679-f31d46baa9b4 md"_We set up Images.jl again:_" # ╔═╡ 540ccfcc-ee0a-11ea-15dc-4f8120063397 md""" ## **Exercise 1** - _Manipulating vectors (1D images)_ A `Vector` is a 1D array. We can think of that as a 1D image. """ # ╔═╡ 467856dc-eded-11ea-0f83-13d939021ef3 example_vector = [0.5, 0.4, 0.3, 0.2, 0.1, 0.0, 0.7, 0.0, 0.7, 0.9] # ╔═╡ ad6a33b0-eded-11ea-324c-cfabfd658b56 md"#### Exerise 1.1 👉 Make a random vector `random_vect` of length 10 using the `rand` function. " # ╔═╡ f51333a6-eded-11ea-34e6-bfbb3a69bcb0 random_vect = missing # replace this with your code! # ╔═╡ cf738088-eded-11ea-2915-61735c2aa990 md"👉 Make a function `mean` using a `for` loop, which computes the mean/average of a vector of numbers." # ╔═╡ 0ffa8354-edee-11ea-2883-9d5bfea4a236 function mean(x) return missing end # ╔═╡ 1f104ce4-ee0e-11ea-2029-1d9c817175af mean([1, 2, 3]) # ╔═╡ 1f229ca4-edee-11ea-2c56-bb00cc6ea53c md"👉 Define `m` to be the mean of `random_vect`." # ╔═╡ 2a391708-edee-11ea-124e-d14698171b68 m = missing # ╔═╡ e2863d4c-edef-11ea-1d67-332ddca03cc4 md"""👉 Write a function `demean`, which takes a vector `x` and subtracts the mean from each value in `x`.""" # ╔═╡ ec5efe8c-edef-11ea-2c6f-afaaeb5bc50c function demean(x) return missing end # ╔═╡ 29e10640-edf0-11ea-0398-17dbf4242de3 md"Let's check that the mean of the `demean(random_vect)` is 0: _Due to floating-point round-off error it may *not* be *exactly* 0._" # ╔═╡ 6f67657e-ee1a-11ea-0c2f-3d567bcfa6ea if ismissing(random_vect) md""" !!! info The following cells error because `random_vect` is not yet defined. Have you done the first exercise? """ end # ╔═╡ 73ef1d50-edf0-11ea-343c-d71706874c82 copy_of_random_vect = copy(random_vect); # in case demean modifies `x` # ╔═╡ 38155b5a-edf0-11ea-3e3f-7163da7433fb mean(demean(copy_of_random_vect)) # ╔═╡ a5f8bafe-edf0-11ea-0da3-3330861ae43a md""" #### Exercise 1.2 👉 Generate a vector of 100 zeros. Change the center 20 elements to 1. """ # ╔═╡ b6b65b94-edf0-11ea-3686-fbff0ff53d08 function create_bar() return missing end # ╔═╡ 22f28dae-edf2-11ea-25b5-11c369ae1253 md""" #### Exercise 1.3 👉 Write a function that turns a `Vector` of `Vector`s into a `Matrix`. """ # ╔═╡ 8c19fb72-ed6c-11ea-2728-3fa9219eddc4 function vecvec_to_matrix(vecvec) return missing end # ╔═╡ c4761a7e-edf2-11ea-1e75-118e73dadbed vecvec_to_matrix([[1,2], [3,4]]) # ╔═╡ 393667ca-edf2-11ea-09c5-c5d292d5e896 md""" 👉 Write a function that turns a `Matrix` into a`Vector` of `Vector`s . """ # ╔═╡ 9f1c6d04-ed6c-11ea-007b-75e7e780703d function matrix_to_vecvec(matrix) return missing end # ╔═╡ 70955aca-ed6e-11ea-2330-89b4d20b1795 matrix_to_vecvec([6 7; 8 9]) # ╔═╡ 5da8cbe8-eded-11ea-2e43-c5b7cc71e133 begin colored_line(x::Vector{<:Real}) = Gray.(Float64.((hcat(x)'))) colored_line(x::Any) = nothing end # ╔═╡ 56ced344-eded-11ea-3e81-3936e9ad5777 colored_line(example_vector) # ╔═╡ b18e2c54-edf1-11ea-0cbf-85946d64b6a2 colored_line(random_vect) # ╔═╡ d862fb16-edf1-11ea-36ec-615d521e6bc0 colored_line(create_bar()) # ╔═╡ e083b3e8-ed61-11ea-2ec9-217820b0a1b4 md""" ## **Exercise 2** - _Manipulating images_ In this exercise we will get familiar with matrices (2D arrays) in Julia, by manipulating images. Recall that in Julia images are matrices of `RGB` color objects. Let's load a picture of Philip again. """ # ╔═╡ c5484572-ee05-11ea-0424-f37295c3072d philip_file = download("https://i.imgur.com/VGPeJ6s.jpg") # ╔═╡ e86ed944-ee05-11ea-3e0f-d70fc73b789c md"_Hi there Philip_" # ╔═╡ c54ccdea-ee05-11ea-0365-23aaf053b7d7 md""" #### Exercise 2.1 👉 Write a function **`mean_colors`** that accepts an object called `image`. It should calculate the mean (average) amounts of red, green and blue in the image and return a tuple `(r, g, b)` of those means. """ # ╔═╡ f6898df6-ee07-11ea-2838-fde9bc739c11 function mean_colors(image) return missing end # ╔═╡ d75ec078-ee0d-11ea-3723-71fb8eecb040 # ╔═╡ f68d4a36-ee07-11ea-0832-0360530f102e md""" #### Exercise 2.2 👉 Look up the documentation on the `floor` function. Use it to write a function `quantize(x::Number)` that takes in a value $x$ (which you can assume is between 0 and 1) and "quantizes" it into bins of width 0.1. For example, check that 0.267 gets mapped to 0.2. """ # ╔═╡ f6991a50-ee07-11ea-0bc4-1d68eb028e6a begin function quantize(x::Number) return missing end function quantize(color::AbstractRGB) # you will write me in a later exercise! return missing end function quantize(image::AbstractMatrix) # you will write me in a later exercise! return missing end end # ╔═╡ f6a655f8-ee07-11ea-13b6-43ca404ddfc7 quantize(0.267), quantize(0.91) # ╔═╡ f6b218c0-ee07-11ea-2adb-1968c4fd473a md""" #### Exercise 2.3 👉 Write the second **method** of the function `quantize`, i.e. a new *version* of the function with the *same* name. This method will accept a color object called `color`, of the type `AbstractRGB`. _Write the function in the same cell as `quantize(x::Number)` from the last exercise. 👆_ Here, `::AbstractRGB` is a **type annotation**. This ensures that this version of the function will be chosen when passing in an object whose type is a **subtype** of the `AbstractRGB` abstract type. For example, both the `RGB` and `RGBX` types satisfy this. The method you write should return a new `RGB` object, in which each component ($r$, $g$ and $b$) are quantized. """ # ╔═╡ f6bf64da-ee07-11ea-3efb-05af01b14f67 md""" #### Exercise 2.4 👉 Write a method `quantize(image::AbstractMatrix)` that quantizes an image by quantizing each pixel in the image. (You may assume that the matrix is a matrix of color objects.) _Write the function in the same cell as `quantize(x::Number)` from the last exercise. 👆_ """ # ╔═╡ 25dad7ce-ee0b-11ea-3e20-5f3019dd7fa3 md"Let's apply your method!" # ╔═╡ f6cc03a0-ee07-11ea-17d8-013991514d42 md""" #### Exercise 2.5 👉 Write a function `invert` that inverts a color, i.e. sends $(r, g, b)$ to $(1 - r, 1-g, 1-b)$. """ # ╔═╡ 63e8d636-ee0b-11ea-173d-bd3327347d55 function invert(color::AbstractRGB) return missing end # ╔═╡ 2cc2f84e-ee0d-11ea-373b-e7ad3204bb00 md"Let's invert some colors:" # ╔═╡ b8f26960-ee0a-11ea-05b9-3f4bc1099050 black = RGB(0.0, 0.0, 0.0) # ╔═╡ 5de3a22e-ee0b-11ea-230f-35df4ca3c96d invert(black) # ╔═╡ 4e21e0c4-ee0b-11ea-3d65-b311ae3f98e9 red = RGB(0.8, 0.1, 0.1) # ╔═╡ 6dbf67ce-ee0b-11ea-3b71-abc05a64dc43 invert(red) # ╔═╡ 846b1330-ee0b-11ea-3579-7d90fafd7290 md"Can you invert the picture of Philip?" # ╔═╡ 943103e2-ee0b-11ea-33aa-75a8a1529931 philip_inverted = missing # ╔═╡ f6d6c71a-ee07-11ea-2b63-d759af80707b md""" #### Exercise 2.6 👉 Write a function `noisify(x::Number, s)` to add randomness of intensity $s$ to a value $x$, i.e. to add a random value between $-s$ and $+s$ to $x$. If the result falls outside the range $(0, 1)$ you should "clamp" it to that range. (Note that Julia has a `clamp` function, but you should write your own function `myclamp(x)`.) """ # ╔═╡ f6e2cb2a-ee07-11ea-06ee-1b77e34c1e91 begin function noisify(x::Number, s) return missing end function noisify(color::AbstractRGB, s) # you will write me in a later exercise! return missing end function noisify(image::AbstractMatrix, s) # you will write me in a later exercise! return missing end end # ╔═╡ f6fc1312-ee07-11ea-39a0-299b67aee3d8 md""" 👉 Write the second method `noisify(c::AbstractRGB, s)` to add random noise of intensity $s$ to each of the $(r, g, b)$ values in a colour. _Write the function in the same cell as `noisify(x::Number)` from the last exercise. 👆_ """ # ╔═╡ 774b4ce6-ee1b-11ea-2b48-e38ee25fc89b @bind color_noise Slider(0:0.01:1, show_value=true) # ╔═╡ 7e4aeb70-ee1b-11ea-100f-1952ba66f80f noisify(red, color_noise) # ╔═╡ 6a05f568-ee1b-11ea-3b6c-83b6ada3680f # ╔═╡ f70823d2-ee07-11ea-2bb3-01425212aaf9 md""" 👉 Write the third method `noisify(image::AbstractMatrix, s)` to noisify each pixel of an image. _Write the function in the same cell as `noisify(x::Number)` from the last exercise. 👆_ """ # ╔═╡ e70a84d4-ee0c-11ea-0640-bf78653ba102 @bind philip_noise Slider(0:0.01:8, show_value=true) # ╔═╡ 9604bc44-ee1b-11ea-28f8-7f7af8d0cbb2 # ╔═╡ f714699e-ee07-11ea-08b6-5f5169861b57 md""" 👉 For which noise intensity does it become unrecognisable? You may need noise intensities larger than 1. Why? """ # ╔═╡ bdc2df7c-ee0c-11ea-2e9f-7d2c085617c1 answer_about_noise_intensity = md""" The image is unrecognisable with intensity ... """ # ╔═╡ 81510a30-ee0e-11ea-0062-8b3327428f9d # ╔═╡ e3b03628-ee05-11ea-23b6-27c7b0210532 decimate(image, ratio=5) = image[1:ratio:end, 1:ratio:end] # ╔═╡ c8ecfe5c-ee05-11ea-322b-4b2714898831 philip = let original = Images.load(philip_file) decimate(original, 8) end # ╔═╡ 5be9b144-ee0d-11ea-2a8d-8775de265a1d mean_colors(philip) # ╔═╡ 9751586e-ee0c-11ea-0cbb-b7eda92977c9 quantize(philip) # ╔═╡ ac15e0d0-ee0c-11ea-1eaf-d7f88b5df1d7 noisify(philip, philip_noise) # ╔═╡ e08781fa-ed61-11ea-13ae-91a49b5eb74a md""" ## **Exercise 3** - _Convolutions_ As we have seen in the videos, we can produce cool effects using the mathematical technique of **convolutions**. We input one image $M$ and get a new image $M'$ back. Conceptually we think of $M$ as a matrix. In practice, in Julia it will be a `Matrix` of color objects, and we may need to take that into account. Ideally, however, we should write a **generic** function that will work for any type of data contained in the matrix. A convolution works on a small **window** of an image, i.e. a region centered around a given point $(i, j)$. We will suppose that the window is a square region with odd side length $2\ell + 1$, running from $-\ell, \ldots, 0, \ldots, \ell$. The result of the convolution over a given window, centred at the point $(i, j)$ is a *single number*; this number is the value that we will use for $M'_{i, j}$. (Note that neighbouring windows overlap.) To get started let's restrict ourselves to convolutions in 1D. So a window is just a 1D region from $-\ell$ to $\ell$. """ # ╔═╡ 7fc8ee1c-ee09-11ea-1382-ad21d5373308 md""" --- Let's create a vector `v` of random numbers of length `n=100`. """ # ╔═╡ 7fcd6230-ee09-11ea-314f-a542d00d582e n = 100 # ╔═╡ 7fdb34dc-ee09-11ea-366b-ffe10d1aa845 v = rand(n) # ╔═╡ 7fe9153e-ee09-11ea-15b3-6f24fcc20734 md"_Feel free to experiment with different values!_" # ╔═╡ 80108d80-ee09-11ea-0368-31546eb0d3cc md""" #### Exercise 3.1 You've seen some colored lines in this notebook to visualize arrays. Can you make another one? 👉 Try plotting our vector `v` using `colored_line(v)`. """ # ╔═╡ 01070e28-ee0f-11ea-1928-a7919d452bdd # ╔═╡ 7522f81e-ee1c-11ea-35af-a17eb257ff1a md"Try changing `n` and `v` around. Notice that you can run the cell `v = rand(n)` again to regenerate new random values." # ╔═╡ 801d90c0-ee09-11ea-28d6-61b806de26dc md""" #### Exercise 3.2 We need to decide how to handle the **boundary conditions**, i.e. what happens if we try to access a position in the vector `v` beyond `1:n`. The simplest solution is to assume that $v_{i}$ is 0 outside the original vector; however, this may lead to strange boundary effects. A better solution is to use the *closest* value that is inside the vector. Effectively we are extending the vector and copying the extreme values into the extended positions. (Indeed, this is one way we could implement this; these extra positions are called **ghost cells**.) 👉 Write a function `extend(v, i)` that checks whether the position $i$ is inside `1:n`. If so, return the $i$th component of `v`; otherwise, return the nearest end value. """ # ╔═╡ 802bec56-ee09-11ea-043e-51cf1db02a34 function extend(v, i) return missing end # ╔═╡ b7f3994c-ee1b-11ea-211a-d144db8eafc2 md"_Some test cases:_" # ╔═╡ 803905b2-ee09-11ea-2d52-e77ff79693b0 extend(v, 1) # ╔═╡ 80479d98-ee09-11ea-169e-d166eef65874 extend(v, -8) # ╔═╡ 805691ce-ee09-11ea-053d-6d2e299ee123 extend(v, n + 10) # ╔═╡ 806e5766-ee0f-11ea-1efc-d753cd83d086 md"Extended with 0:" # ╔═╡ 38da843a-ee0f-11ea-01df-bfa8b1317d36 colored_line([0, 0, example_vector..., 0, 0]) # ╔═╡ 9bde9f92-ee0f-11ea-27f8-ffef5fce2b3c md"Extended with your `extend`:" # ╔═╡ 45c4da9a-ee0f-11ea-2c5b-1f6704559137 if extend(v,1) === missing missing else colored_line([extend(example_vector, i) for i in -1:12]) end # ╔═╡ 80664e8c-ee09-11ea-0702-711bce271315 md""" #### Exercise 3.3 👉 Write a function `blur_1D(v, l)` that blurs a vector `v` with a window of length `l` by averaging the elements within a window from $-\ell$ to $\ell$. This is called a **box blur**. """ # ╔═╡ 807e5662-ee09-11ea-3005-21fdcc36b023 function blur_1D(v, l) return missing end # ╔═╡ 808deca8-ee09-11ea-0ee3-1586fa1ce282 let try test_v = rand(n) original = copy(test_v) blur_1D(test_v, 5) if test_v != original md""" !!! danger "Oopsie!" It looks like your function _modifies_ `v`. Can you write it without doing so? Maybe you can use `copy`. """ end catch end end # ╔═╡ 809f5330-ee09-11ea-0e5b-415044b6ac1f md""" #### Exercise 3.4 👉 Apply the box blur to your vector `v`. Show the original and the new vector by creating two cells that call `colored_line`. Make the parameter $\ell$ interactive, and call it `l_box` instead of just `l` to avoid a variable naming conflict. """ # ╔═╡ ca1ac5f4-ee1c-11ea-3d00-ff5268866f87 # ╔═╡ 80ab64f4-ee09-11ea-29b4-498112ed0799 md""" #### Exercise 3.5 The box blur is a simple example of a **convolution**, i.e. a linear function of a window around each point, given by $$v'_{i} = \sum_{n} \, v_{i - n} \, k_{n},$$ where $k$ is a vector called a **kernel**. Again, we need to take care about what happens if $v_{i -n }$ falls off the end of the vector. 👉 Write a function `convolve_vector(v, k)` that performs this convolution. You need to think of the vector $k$ as being *centred* on the position $i$. So $n$ in the above formula runs between $-\ell$ and $\ell$, where $2\ell + 1$ is the length of the vector $k$. You will need to do the necessary manipulation of indices. """ # ╔═╡ 28e20950-ee0c-11ea-0e0a-b5f2e570b56e function convolve_vector(v, k) return missing end # ╔═╡ 93284f92-ee12-11ea-0342-833b1a30625c test_convolution = let v = [1, 10, 100, 1000, 10000] k = [0, 1, 0] convolve_vector(v, k) end # ╔═╡ 5eea882c-ee13-11ea-0d56-af81ecd30a4a colored_line(test_convolution) # ╔═╡ cf73f9f8-ee12-11ea-39ae-0107e9107ef5 md"_Edit the cell above, or create a new cell with your own test cases!_" # ╔═╡ 80b7566a-ee09-11ea-3939-6fab470f9ec8 md""" #### Exercise 3.6 👉 Write a function `gaussian_kernel`. The definition of a Gaussian in 1D is $$G(x) = \frac{1}{\sqrt{2\pi \sigma^2}} \exp \left( \frac{-x^2}{2\sigma^2} \right)$$ We need to **sample** (i.e. evaluate) this at each pixel in a region of size $n^2$, and then **normalize** so that the sum of the resulting kernel is 1. For simplicity you can take $\sigma=1$. """ # ╔═╡ 1c8b4658-ee0c-11ea-2ede-9b9ed7d3125e function gaussian_kernel(n) return missing end # ╔═╡ f8bd22b8-ee14-11ea-04aa-ab16fd01826e md"Let's test your kernel function!" # ╔═╡ 2a9dd06a-ee13-11ea-3f84-67bb309c77a8 gaussian_kernel_size_1D = 3 # change this value, or turn me into a slider! # ╔═╡ 38eb92f6-ee13-11ea-14d7-a503ac04302e test_gauss_1D_a = let v = random_vect k = gaussian_kernel(gaussian_kernel_size_1D) if k !== missing convolve_vector(v, k) end end # ╔═╡ b424e2aa-ee14-11ea-33fa-35491e0b9c9d colored_line(test_gauss_1D_a) # ╔═╡ 24c21c7c-ee14-11ea-1512-677980db1288 test_gauss_1D_b = let v = create_bar() k = gaussian_kernel(gaussian_kernel_size_1D) if k !== missing convolve_vector(v, k) end end # ╔═╡ bc1c20a4-ee14-11ea-3525-63c9fa78f089 colored_line(test_gauss_1D_b) # ╔═╡ b01858b6-edf3-11ea-0826-938d33c19a43 md""" ## **Exercise 4** - _Convolutions of images_ Now let's move to 2D images. The convolution is then given by a **kernel** matrix $K$: $$M'_{i, j} = \sum_{k, l} \, M_{i- k, j - l} \, K_{k, l},$$ where the sum is over the possible values of $k$ and $l$ in the window. Again we think of the window as being *centered* at $(i, j)$. A common notation for this operation is $*$: $$M' = M * K.$$ """ # ╔═╡ 7c1bc062-ee15-11ea-30b1-1b1e76520f13 md""" #### Exercise 4.1 👉 Write a function `extend_mat` that takes a matrix `M` and indices `i` and `j`, and returns the closest element of the matrix. """ # ╔═╡ 7c2ec6c6-ee15-11ea-2d7d-0d9401a5e5d1 function extend_mat(M::AbstractMatrix, i, j) return missing end # ╔═╡ 9afc4dca-ee16-11ea-354f-1d827aaa61d2 md"_Let's test it!_" # ╔═╡ cf6b05e2-ee16-11ea-3317-8919565cb56e small_image = Gray.(rand(5,5)) # ╔═╡ e3616062-ee27-11ea-04a9-b9ec60842a64 md"Extended with `0`:" # ╔═╡ e5b6cd34-ee27-11ea-0d60-bd4796540b18 [get(small_image, (i, j), Gray(0)) for (i,j) in Iterators.product(-1:7,-1:7)] # ╔═╡ d06ea762-ee27-11ea-2e9c-1bcff86a3fe0 md"Extended with your `extend`:" # ╔═╡ e1dc0622-ee16-11ea-274a-3b6ec9e15ab5 [extend_mat(small_image, i, j) for (i,j) in Iterators.product(-1:7,-1:7)] # ╔═╡ 3cd535e4-ee26-11ea-2482-fb4ad43dda19 let philip_head = philip[250:430,110:230] [extend_mat(philip_head, i, j) for (i,j) in Iterators.product(-50:size(philip_head,1)+51, (-50:size(philip_head,2)+51))] end # ╔═╡ 7c41f0ca-ee15-11ea-05fb-d97a836659af md""" #### Exercise 4.2 👉 Implement a function `convolve_image(M, K)`. """ # ╔═╡ 8b96e0bc-ee15-11ea-11cd-cfecea7075a0 function convolve_image(M::AbstractMatrix, K::AbstractMatrix) return missing end # ╔═╡ 5a5135c6-ee1e-11ea-05dc-eb0c683c2ce5 md"_Let's test it out! 🎃_" # ╔═╡ 577c6daa-ee1e-11ea-1275-b7abc7a27d73 test_image_with_border = [get(small_image, (i, j), Gray(0)) for (i,j) in Iterators.product(-1:7,-1:7)] # ╔═╡ 275a99c8-ee1e-11ea-0a76-93e3618c9588 K_test = [ 0 0 0 1/2 0 1/2 0 0 0 ] # ╔═╡ 42dfa206-ee1e-11ea-1fcd-21671042064c convolve_image(test_image_with_border, K_test) # ╔═╡ 6e53c2e6-ee1e-11ea-21bd-c9c05381be07 md"_Edit_ `K_test` _to create your own test case!_" # ╔═╡ e7f8b41a-ee25-11ea-287a-e75d33fbd98b convolve_image(philip, K_test) # ╔═╡ 8a335044-ee19-11ea-0255-b9391246d231 md""" --- You can create all sorts of effects by choosing the kernel in a smart way. Today, we will implement two special kernels, to produce a **Gaussian blur** and a **Sobel edge detect** filter. Make sure that you have watched [the lecture](https://www.youtube.com/watch?v=8rrHTtUzyZA) about convolutions! """ # ╔═╡ 7c50ea80-ee15-11ea-328f-6b4e4ff20b7e md""" #### Exercise 4.3 👉 Apply a **Gaussian blur** to an image. Here, the 2D Gaussian kernel will be defined as $$G(x,y)=\frac{1}{2\pi \sigma^2}e^{\frac{-(x^2+y^2)}{2\sigma^2}}$$ """ # ╔═╡ aad67fd0-ee15-11ea-00d4-274ec3cda3a3 function with_gaussian_blur(image) return missing end # ╔═╡ 8ae59674-ee18-11ea-3815-f50713d0fa08 md"_Let's make it interactive. 💫_" # ╔═╡ 7c6642a6-ee15-11ea-0526-a1aac4286cdd md""" #### Exercise 4.4 👉 Create a **Sobel edge detection filter**. Here, we will need to create two separate filters that separately detect edges in the horizontal and vertical directions: ```math \begin{align} G_x &= \left(\begin{bmatrix} 1 \\ 2 \\ 1 \\ \end{bmatrix} \otimes [1~0~-1] \right) * A = \begin{bmatrix} 1 & 0 & -1 \\ 2 & 0 & -2 \\ 1 & 0 & -1 \\ \end{bmatrix}*A\\ G_y &= \left( \begin{bmatrix} 1 \\ 0 \\ -1 \\ \end{bmatrix} \otimes [1~2~1] \right) * A = \begin{bmatrix} 1 & 2 & 1 \\ 0 & 0 & 0 \\ -1 & -2 & -1 \\ \end{bmatrix}*A \end{align} ``` Here $A$ is the array corresponding to your image. We can think of these as derivatives in the $x$ and $y$ directions. Then we combine them by finding the magnitude of the **gradient** (in the sense of multivariate calculus) by defining $$G_\text{total} = \sqrt{G_x^2 + G_y^2}.$$ For simplicity you can choose one of the "channels" (colours) in the image to apply this to. """ # ╔═╡ 9eeb876c-ee15-11ea-1794-d3ea79f47b75 function with_sobel_edge_detect(image) return missing end # ╔═╡ 1b85ee76-ee10-11ea-36d7-978340ef61e6 md""" ## **Exercise 5** - _Lecture transcript_ _(MIT students only)_ Please see the Canvas post for transcript document for week 1 [here](https://canvas.mit.edu/courses/5637/discussion_topics/27880). We need each of you to correct about 100 lines (see instructions in the beginning of the document.) 👉 Please mention the name of the video and the line ranges you edited: """ # ╔═╡ 477d0a3c-ee10-11ea-11cf-07b0e0ce6818 lines_i_edited = md""" Convolution, lines 100-0 (_for example_) """ # ╔═╡ 8ffe16ce-ee20-11ea-18bd-15640f94b839 if student.kerberos_id === "jazz" md""" !!! danger "Oops!" **Before you submit**, remember to fill in your name and kerberos ID at the top of this notebook! """ end # ╔═╡ 5516c800-edee-11ea-12cf-3f8c082ef0ef hint(text) = Markdown.MD(Markdown.Admonition("hint", "Hint", [text])) # ╔═╡ b1d5ca28-edf6-11ea-269e-75a9fb549f1d hint(md"You can find out more about any function (like `rand`) by creating a new cell and typing: ``` ?rand ``` Once the Live Docs are open, you can select any code to learn more about it. It might be useful to leave it open all the time, and get documentation while you type code.") # ╔═╡ f6ef2c2e-ee07-11ea-13a8-2512e7d94426 hint(md"The `rand` function generates (uniform) random floating-point numbers between $0$ and $1$.") # ╔═╡ ea435e58-ee11-11ea-3785-01af8dd72360 hint(md"Have a look at Exercise 2 to see an example of adding interactivity with a slider. You can read the [Interactivity](./sample/Interactivity.jl) and the [PlutoUI](./sample/PlutoUI.jl) sample notebooks _(right click -> Open in new tab)_ to learn more.") # ╔═╡ e9aadeee-ee1d-11ea-3525-95f6ba5fda31 hint(md"`l = (length(k) - 1) ÷ 2`") # ╔═╡ 649df270-ee24-11ea-397e-79c4355e38db hint(md"`num_rows, num_columns = size(M)`") # ╔═╡ 0cabed84-ee1e-11ea-11c1-7d8a4b4ad1af hint(md"`num_rows, num_columns = size(K)`") # ╔═╡ 57360a7a-edee-11ea-0c28-91463ece500d almost(text) = Markdown.MD(Markdown.Admonition("warning", "Almost there!", [text])) # ╔═╡ dcb8324c-edee-11ea-17ff-375ff5078f43 still_missing(text=md"Replace `missing` with your answer.") = Markdown.MD(Markdown.Admonition("warning", "Here we go!", [text])) # ╔═╡ 58af703c-edee-11ea-2963-f52e78fc2412 keep_working(text=md"The answer is not quite right.") = Markdown.MD(Markdown.Admonition("danger", "Keep working on it!", [text])) # ╔═╡ f3d00a9a-edf3-11ea-07b3-1db5c6d0b3cf yays = [md"Great!", md"Yay ❤", md"Great! 🎉", md"Well done!", md"Keep it up!", md"Good job!", md"Awesome!", md"You got the right answer!", md"Let's move on to the next section."] # ╔═╡ 5aa9dfb2-edee-11ea-3754-c368fb40637c correct(text=rand(yays)) = Markdown.MD(Markdown.Admonition("correct", "Got it!", [text])) # ╔═╡ 74d44e22-edee-11ea-09a0-69aa0aba3281 not_defined(variable_name) = Markdown.MD(Markdown.Admonition("danger", "Oopsie!", [md"Make sure that you define a variable called **$(Markdown.Code(string(variable_name)))**"])) # ╔═╡ 397941fc-edee-11ea-33f2-5d46c759fbf7 if !@isdefined(random_vect) not_defined(:random_vect) elseif ismissing(random_vect) still_missing() elseif !(random_vect isa Vector) keep_working(md"`random_vect` should be a `Vector`.") elseif length(random_vect) != 10 keep_working(md"`random_vect` does not have the correct size.") else correct() end # ╔═╡ 38dc80a0-edef-11ea-10e9-615255a4588c if !@isdefined(mean) not_defined(:mean) else let result = mean([1,2,3]) if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif result != 2 keep_working() else correct() end end end # ╔═╡ 2b1ccaca-edee-11ea-34b0-c51659f844d0 if !@isdefined(m) not_defined(:m) elseif ismissing(m) still_missing() elseif !(m isa Number) keep_working(md"`m` should be a number.") elseif m != mean(random_vect) keep_working() else correct() end # ╔═╡ e3394c8a-edf0-11ea-1bb8-619f7abb6881 if !@isdefined(create_bar) not_defined(:create_bar) else let result = create_bar() if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif !(result isa Vector) || length(result) != 100 keep_working(md"The result should be a `Vector` with 100 elements.") elseif result[[1,50,100]] != [0,1,0] keep_working() else correct() end end end # ╔═╡ adfbe9b2-ed6c-11ea-09ac-675262f420df if !@isdefined(vecvec_to_matrix) not_defined(:vecvec_to_matrix) else let input = [[6,7],[8,9]] result = vecvec_to_matrix(input) shouldbe = [6 7; 8 9] if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif !(result isa Matrix) keep_working(md"The result should be a `Matrix`") elseif result != shouldbe && result != shouldbe' keep_working() else correct() end end end # ╔═╡ e06b7fbc-edf2-11ea-1708-fb32599dded3 if !@isdefined(matrix_to_vecvec) not_defined(:matrix_to_vecvec) else let input = [6 7 8; 8 9 10] result = matrix_to_vecvec(input) shouldbe = [[6,7,8],[8,9,10]] shouldbe2 = [[6,8], [7,9], [8,10]] if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif result != shouldbe && result != shouldbe2 keep_working() else correct() end end end # ╔═╡ 4d0158d0-ee0d-11ea-17c3-c169d4284acb if !@isdefined(mean_colors) not_defined(:mean_colors) else let input = reshape([RGB(1.0, 1.0, 1.0), RGB(1.0, 1.0, 0.0)], (2,1)) result = mean_colors(input) shouldbe = (1.0, 1.0, 0.5) shouldbe2 = RGB(shouldbe...) if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif !(result == shouldbe) && !(result == shouldbe2) keep_working() else correct() end end end # ╔═╡ c905b73e-ee1a-11ea-2e36-23b8e73bfdb6 if !@isdefined(quantize) not_defined(:quantize) else let result = quantize(.3) if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif result != .3 if quantize(0.35) == .3 almost(md"What should quantize(`0.2`) be?") else keep_working() end else correct() end end end # ╔═╡ bcf98dfc-ee1b-11ea-21d0-c14439500971 if !@isdefined(extend) not_defined(:extend) else let result = extend([6,7],-10) if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif result != 6 || extend([6,7],10) != 7 keep_working() else correct() end end end # ╔═╡ 7ffd14f8-ee1d-11ea-0343-b54fb0333aea if !@isdefined(convolve_vector) not_defined(:convolve_vector) else let x = [1, 10, 100] result = convolve_vector(x, [0, 1, 1]) shouldbe = [11, 110, 200] shouldbe2 = [2, 11, 110] if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif !(result isa AbstractVector) keep_working(md"The returned object is not a `Vector`.") elseif size(result) != size(x) keep_working(md"The returned vector has the wrong dimensions.") elseif result != shouldbe && result != shouldbe2 keep_working() else correct() end end end # ╔═╡ efd1ceb4-ee1c-11ea-350e-f7e3ea059024 if !@isdefined(extend_mat) not_defined(:extend_mat) else let input = [42 37; 1 0] result = extend_mat(input, -2, -2) if ismissing(result) still_missing() elseif isnothing(result) keep_working(md"Did you forget to write `return`?") elseif result != 42 || extend_mat(input, -1, 3) != 37 keep_working() else correct() end end end # ╔═╡ 115ded8c-ee0a-11ea-3493-89487315feb7 bigbreak = html"




"; # ╔═╡ 54056a02-ee0a-11ea-101f-47feb6623bec bigbreak # ╔═╡ 45815734-ee0a-11ea-2982-595e1fc0e7b1 bigbreak # ╔═╡ 4139ee66-ee0a-11ea-2282-15d63bcca8b8 bigbreak # ╔═╡ 27847dc4-ee0a-11ea-0651-ebbbb3cfd58c bigbreak # ╔═╡ 0001f782-ee0e-11ea-1fb4-2b5ef3d241e2 bigbreak # ╔═╡ 91f4778e-ee20-11ea-1b7e-2b0892bd3c0f bigbreak # ╔═╡ 5842895a-ee10-11ea-119d-81e4c4c8c53b bigbreak # ╔═╡ dfb7c6be-ee0d-11ea-194e-9758857f7b20 function camera_input(;max_size=200, default_url="https://i.imgur.com/SUmi94P.png") """
Enable webcam
""" |> HTML end # ╔═╡ 94c0798e-ee18-11ea-3212-1533753eabb6 @bind gauss_raw_camera_data camera_input(;max_size=100) # ╔═╡ 1a0324de-ee19-11ea-1d4d-db37f4136ad3 @bind sobel_raw_camera_data camera_input(;max_size=100) # ╔═╡ e15ad330-ee0d-11ea-25b6-1b1b3f3d7888 function process_raw_camera_data(raw_camera_data) # the raw image data is a long byte array, we need to transform it into something # more "Julian" - something with more _structure_. # The encoding of the raw byte stream is: # every 4 bytes is a single pixel # every pixel has 4 values: Red, Green, Blue, Alpha # (we ignore alpha for this notebook) # So to get the red values for each pixel, we take every 4th value, starting at # the 1st: reds_flat = UInt8.(raw_camera_data["data"][1:4:end]) greens_flat = UInt8.(raw_camera_data["data"][2:4:end]) blues_flat = UInt8.(raw_camera_data["data"][3:4:end]) # but these are still 1-dimensional arrays, nicknamed 'flat' arrays # We will 'reshape' this into 2D arrays: width = raw_camera_data["width"] height = raw_camera_data["height"] # shuffle and flip to get it in the right shape reds = reshape(reds_flat, (width, height))' / 255.0 greens = reshape(greens_flat, (width, height))' / 255.0 blues = reshape(blues_flat, (width, height))' / 255.0 # we have our 2D array for each color # Let's create a single 2D array, where each value contains the R, G and B value of # that pixel RGB.(reds, greens, blues) end # ╔═╡ f461f5f2-ee18-11ea-3d03-95f57f9bf09e gauss_camera_image = process_raw_camera_data(gauss_raw_camera_data); # ╔═╡ a75701c4-ee18-11ea-2863-d3042e71a68b with_gaussian_blur(gauss_camera_image) # ╔═╡ 1ff6b5cc-ee19-11ea-2ca8-7f00c204f587 sobel_camera_image = Gray.(process_raw_camera_data(sobel_raw_camera_data)); # ╔═╡ 1bf94c00-ee19-11ea-0e3c-e12bc68d8e28 with_sobel_edge_detect(sobel_camera_image) # ╔═╡ Cell order: # ╠═83eb9ca0-ed68-11ea-0bc5-99a09c68f867 # ╟─8ef13896-ed68-11ea-160b-3550eeabbd7d # ╟─ac8ff080-ed61-11ea-3650-d9df06123e1f # ╠═911ccbce-ed68-11ea-3606-0384e7580d7c # ╟─5f95e01a-ee0a-11ea-030c-9dba276aba92 # ╠═65780f00-ed6b-11ea-1ecf-8b35523a7ac0 # ╟─67461396-ee0a-11ea-3679-f31d46baa9b4 # ╠═74b008f6-ed6b-11ea-291f-b3791d6d1b35 # ╟─54056a02-ee0a-11ea-101f-47feb6623bec # ╟─540ccfcc-ee0a-11ea-15dc-4f8120063397 # ╟─467856dc-eded-11ea-0f83-13d939021ef3 # ╠═56ced344-eded-11ea-3e81-3936e9ad5777 # ╟─ad6a33b0-eded-11ea-324c-cfabfd658b56 # ╠═f51333a6-eded-11ea-34e6-bfbb3a69bcb0 # ╟─b18e2c54-edf1-11ea-0cbf-85946d64b6a2 # ╟─397941fc-edee-11ea-33f2-5d46c759fbf7 # ╟─b1d5ca28-edf6-11ea-269e-75a9fb549f1d # ╟─cf738088-eded-11ea-2915-61735c2aa990 # ╠═0ffa8354-edee-11ea-2883-9d5bfea4a236 # ╠═1f104ce4-ee0e-11ea-2029-1d9c817175af # ╟─38dc80a0-edef-11ea-10e9-615255a4588c # ╟─1f229ca4-edee-11ea-2c56-bb00cc6ea53c # ╠═2a391708-edee-11ea-124e-d14698171b68 # ╟─2b1ccaca-edee-11ea-34b0-c51659f844d0 # ╟─e2863d4c-edef-11ea-1d67-332ddca03cc4 # ╠═ec5efe8c-edef-11ea-2c6f-afaaeb5bc50c # ╟─29e10640-edf0-11ea-0398-17dbf4242de3 # ╟─6f67657e-ee1a-11ea-0c2f-3d567bcfa6ea # ╠═38155b5a-edf0-11ea-3e3f-7163da7433fb # ╠═73ef1d50-edf0-11ea-343c-d71706874c82 # ╟─a5f8bafe-edf0-11ea-0da3-3330861ae43a # 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