Magic Image: Alpha Channel

Mix.install([
  {:evision, "~> 0.1"},
  {:kino, "~> 0.11"},
  {:req, "~> 0.3"},
  {:nx, "~> 0.4"}
])

:ok

Get Images for Front and Back Layers (optional)

Upload your favorite images for this interesting experiment!

Note that the image of the frontlayer should be preferrablly bright, while the image of the backlayer should be relatively dimmed.

But if you don’t have any images at hand, this livebook will load some example images, and you can come back later!

front_layer_input = Kino.Input.image("Frontlayer")
back_layer_input = Kino.Input.image("Backlayer")
Kino.Layout.grid([front_layer_input, back_layer_input], columns: 2)

Load Images

load_layer = fn kino_input, url, save_as ->
  case Kino.Input.read(kino_input) do
    %{file_ref: file_ref, height: height, width: width} ->
      file_ref
      |> Kino.Input.file_path()
      |> File.read!()
      |> Evision.Mat.from_binary({:u, 8}, height, width, 3)
      |> Evision.cvtColor(Evision.Constant.cv_COLOR_BGR2GRAY())

    nil ->
      unless File.exists?(save_as) do
        Req.get!(url, http_errors: :raise, output: save_as, cache: false)
      end

      Evision.imread(save_as, flags: Evision.Constant.cv_IMREAD_GRAYSCALE())
  end
end

front =
  load_layer.(
    front_layer_input,
    "https://raw.githubusercontent.com/cocoa-xu/evision/master/test/testdata/front.jpg",
    "front.jpg"
  )

back =
  load_layer.(
    back_layer_input,
    "https://raw.githubusercontent.com/cocoa-xu/evision/master/test/testdata/back.jpg",
    "back.jpg"
  )

Kino.Layout.grid([front, back], columns: 2)

%Evision.Mat{
  channels: 1,
  dims: 2,
  type: {:u, 8},
  raw_type: 0,
  shape: {667, 1000},
  ref: #Reference<0.3899563693.4086431769.126173>
}

%Evision.Mat{
  channels: 1,
  dims: 2,
  type: {:u, 8},
  raw_type: 0,
  shape: {563, 1000},
  ref: #Reference<0.3899563693.4086431769.126174>
}

Resize Layers to Same Size

resize_layers = fn front_layer, back_layer ->
  {{f_cols, f_rows}, {b_cols, b_rows}} = {front_layer.shape, back_layer.shape}
  {rows, cols} = {round(max(f_rows, b_rows)), round(max(f_cols, b_cols))}
  size = {cols, rows}
  front_canvas = Evision.Mat.full(size, 255.0, :f32)
  back_canvas = Evision.Mat.full(size, 0.0, :f32)

  do_resize = fn layer, canvas ->
    {layer_cols, layer_rows} = layer.shape

    {overlay_rows_start, overlay_cols_start} =
      if layer_cols == cols do
        {0, round((cols - layer_cols) / 2)}
      else
        {round((rows - layer_rows) / 2), 0}
      end

    Evision.Mat.update_roi(
      canvas,
      [
        {overlay_cols_start, overlay_cols_start + layer_cols},
        {overlay_rows_start, overlay_rows_start + layer_rows}
      ],
      Evision.Mat.as_type(layer, :f32)
    )
  end

  front = do_resize.(front_layer, front_canvas)
  back = do_resize.(back_layer, back_canvas)
  {front, back}
end

{f, b} = resize_layers.(front, back)

{%Evision.Mat{
   channels: 1,
   dims: 2,
   type: {:f, 32},
   raw_type: 5,
   shape: {667, 1000},
   ref: #Reference<0.3899563693.4086431768.119728>
 },
 %Evision.Mat{
   channels: 1,
   dims: 2,
   type: {:f, 32},
   raw_type: 5,
   shape: {667, 1000},
   ref: #Reference<0.3899563693.4086431768.119730>
 }}

Adjust Intensity

To achieve best result, the image of the frontlayer should be preferrablly bright, while the image of the backlayer should be generally dimmed.

We can do this by increasing (and decreasing) their pixel intensity accordingly.

front_shift = Kino.Input.range("Frontlayer Intensity Shift", min: -255, max: 255, default: 40)
back_shift = Kino.Input.range("Backlayer Intensity Shift", min: -255, max: 255, default: -10)
Kino.Layout.grid([front_shift, back_shift], columns: 2)

shift_color = fn layer, shift ->
  Nx.add(Evision.Mat.to_nx(layer, Nx.BinaryBackend), shift)
  |> Nx.clip(0, 255)
end

f_ready = shift_color.(f, Kino.Input.read(front_shift))
b_ready = shift_color.(b, Kino.Input.read(back_shift))

#Nx.Tensor<
  f32[667][1000]
  [
    [130.0, 133.0, 137.0, 140.0, 143.0, 147.0, 151.0, 153.0, 159.0, 161.0, 165.0, 167.0, 169.0, 171.0, 173.0, 175.0, 177.0, 179.0, 180.0, 182.0, 183.0, 184.0, 186.0, 187.0, 186.0, 187.0, 188.0, 190.0, 191.0, 191.0, 191.0, 190.0, 189.0, 192.0, 196.0, 198.0, 200.0, 199.0, 195.0, 190.0, 180.0, 161.0, 140.0, 118.0, 93.0, 81.0, 81.0, 79.0, 78.0, 80.0, ...],
    ...
  ]
>

Compute Values for Alpha and Grey Channels

Based on the formular given on the Wiki page of alpha blending

$$ \left{\begin{aligned} outA &= src_A + dst_A(1-src_A)\ out{RGB} &= \frac{(src{RGB}src_A + dst{RGB}dstA(1-src_A))}{out_A}\ out_A &= 0 \implies out{RGB} = 0 \end{aligned}\right. $$

If the destination background is opaque, i.e., $dst_A = 1$, we have

$$ \left{\begin{aligned} outA &= 1\ out{RGB} &= src{RGB}src_A + dst{RGB}(1-src_A) \end{aligned}\right. $$

Therefore, for the merged image $I$, given background $B$, we have

$$ \left{\begin{aligned} outA &= 1\ out{G} &= I{G}I_A + B{G}(1-I_A) \end{aligned}\right. $$

where $I_G$ and $I_A$ stands for the grey and alpha channel (of the merged image $I$) respectively.

If the background color is white, i.e., $B_G=255$, then

$$ \left{\begin{aligned} outA &= 1\ out{G} &= I{G}I_A + 255(1-I_A)\ &= \textit{front}{G} \end{aligned}\right. $$

Similarly, when the background color is black ($B_G=0$),

$$ \left{\begin{aligned} outA &= 1\ out{G} &= I{G}I_A + 0(1-I_A)\ &= I{G}IA\ &= \textit{back}{G} \end{aligned}\right. $$

Now we have two unknown variables, $I{G}$ and $I{A}$, and the simultaneous equations

$$ \left{\begin{aligned} \textit{front}{G} &= I{G}I{A} + 255(1-I_A)\ \textit{back}{G} &= I{G}I{A} \end{aligned}\right. $$

therefore, we have

$$ \left{\begin{aligned} I{A} &= 1 - \frac{(front{G} - back{G})}{255}\ I{G} &= \frac{backG}{I{A}} \end{aligned}\right. $$

compute_alpha = fn front, back ->
  Nx.add(back, 255)
  |> Nx.subtract(front)
  |> Nx.clip(0, 255)
  |> Nx.add(1.0e-12)
  |> Nx.clip(0, 255)
end

alpha = compute_alpha.(f_ready, b_ready)

#Nx.Tensor<
  f32[667][1000]
  [
    [182.0, 186.0, 191.0, 194.0, 196.0, 200.0, 205.0, 208.0, 214.0, 214.0, 216.0, 218.0, 220.0, 223.0, 225.0, 229.0, 230.0, 232.0, 232.0, 234.0, 234.0, 235.0, 237.0, 238.0, 236.0, 237.0, 240.0, 243.0, 241.0, 241.0, 242.0, 240.0, 239.0, 242.0, 246.0, 248.0, 250.0, 249.0, 245.0, 240.0, 230.0, 208.0, 186.0, 165.0, 140.0, 129.0, 129.0, 124.0, 127.0, 128.0, ...],
    ...
  ]
>

compute_grey = fn back, alpha ->
  Nx.multiply(back, 255)
  |> Nx.divide(alpha)
end

grey = compute_grey.(b_ready, alpha)

#Nx.Tensor<
  f32[667][1000]
  [
    [182.14285278320312, 182.33871459960938, 182.90576171875, 184.02061462402344, 186.04591369628906, 187.4250030517578, 187.8292694091797, 187.57211303710938, 189.46261596679688, 191.84579467773438, 194.7916717529297, 195.3440399169922, 195.88636779785156, 195.53811645507812, 196.06666564941406, 194.86898803710938, 196.2391357421875, 196.74569702148438, 197.84483337402344, 198.3333282470703, 199.42308044433594, 199.65957641601562, 200.1265869140625, 200.35714721679688, 200.97457885742188, 201.20252990722656, 199.75, 199.38272094726562, 202.09542846679688, 202.09542846679688, 201.2603302001953, 201.875, 201.65272521972656, 202.31405639648438, 203.1707305908203, 203.58871459960938, 204.0, 203.79518127441406, 202.9591827392578, 201.875, 199.56521606445312, 197.3798065185547, 191.93548583984375, 182.36363220214844, 169.39285278320312, 160.11627197265625, 160.11627197265625, 162.4596710205078, 156.61416625976562, 159.375, ...],
    ...
  ]
>

Merge into An Image with Alpha Channel

merged = Evision.merge([grey, grey, grey, alpha])
{cols, rows, _} = merged.shape

{667, 1000, 4}

Visualise

Drag the generated image and hover it over the black background on the right hand-side, and it will “change” from one image (front layer) to the other one (back layer).

[
  ["Generated Image", merged],
  [
    "Black Background",
    Evision.Mat.last_dim_as_channel(Evision.Mat.full({cols, rows, 3}, 0, :u8))
  ]
]
|> Enum.map(fn [label, img] ->
  Kino.Layout.grid([img, Kino.Markdown.new("**#{label}**")], boxed: true)
end)
|> Kino.Layout.grid(columns: 2)

%Evision.Mat{
  channels: 4,
  dims: 2,
  type: {:f, 32},
  raw_type: 29,
  shape: {667, 1000, 4},
  ref: #Reference<0.3899563693.4086431768.119735>
}

Save the Merged Image

Evision.imwrite("merged.png", merged)

true