2d Convolution

A two-dimensional convolution operator slides the kernel matrix across the target image and records elementwise products. Makes heavy use of the matrix environment in TikZ.

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2d-convolution.tex (56 lines)

\documentclass[tikz]{standalone}

\usetikzlibrary{matrix, positioning}

\begin{document}
\begin{tikzpicture}[
    2d-arr/.style={matrix of nodes, row sep=-\pgflinewidth, column sep=-\pgflinewidth, nodes={draw}}
  ]

  \matrix (mtr) [2d-arr] {
  0 & 1 & 1 & |[fill=orange!30]| 1 & |[fill=orange!30]| 0 & |[fill=orange!30]| 0 & 0\\
  0 & 0 & 1 & |[fill=orange!30]| 1 & |[fill=orange!30]| 1 & |[fill=orange!30]| 0 & 0\\
  0 & 0 & 0 & |[fill=orange!30]| 1 & |[fill=orange!30]| 1 & |[fill=orange!30]| 1 & 0\\
  0 & 0 & 0 & 1 & 1 & 0 & 0\\
  0 & 0 & 1 & 1 & 0 & 0 & 0\\
  0 & 1 & 1 & 0 & 0 & 0 & 0\\
  1 & 1 & 0 & 0 & 0 & 0 & 0\\
  };

  \node[below=of mtr-5-4] {$\mathbf I$};

  \node[right=0.2em of mtr] (str) {$*$};

  \matrix (K) [2d-arr, right=0.2em of str, nodes={draw, fill=teal!30}] {
    1 & 0 & 1 \\
    0 & 1 & 0 \\
    1 & 0 & 1 \\
  };
  \node[below=of K-3-2] {$\mathbf K$};

  \node[right=0.2em of K] (eq) {$=$};

  \matrix (ret) [2d-arr, right=0.2em of eq] {
  1 & 4 & 3 & |[fill=blue!80!black!30]| 4 & 1\\
  1 & 2 & 4 & 3 & 3\\
  1 & 2 & 3 & 4 & 1\\
  1 & 3 & 3 & 1 & 1\\
  3 & 3 & 1 & 1 & 0\\
  };
  \node[below=of ret-4-3] {$\mathbf{I * K}$};

  \draw[dashed, teal] (mtr-1-6.north east) -- (K-1-1.north west);
  \draw[dashed, teal] (mtr-3-6.south east) -- (K-3-1.south west);

  \draw[dashed, blue!80!black] (K-1-3.north east) -- (ret-1-4.north west);
  \draw[dashed, blue!80!black] (K-3-3.south east) -- (ret-1-4.south west);

  \foreach \i in {1,2,3} {
      \foreach \j in {4,5,6} {
          \node[font=\tiny, scale=0.6, shift={(-1.2ex,-2ex)}] at (mtr-\i-\j) {$\times \pgfmathparse{int(mod(\i+\j,2))}\pgfmathresult$};
        }
    }

\end{tikzpicture}
\end{document}

2d-convolution.typ (136 lines)

#import "@preview/cetz:0.4.1": canvas, draw
#import draw: content, line, on-layer, rect

#set page(width: auto, height: auto, margin: 5pt)

#canvas({
  let cell-size = 0.6
  let matrix-sep = 1.5
  let highlight = rgb(255, 200, 150) // orange!30
  let kernel-color = rgb("#9ae7e1") // teal!30
  let result-color = rgb(200, 200, 255) // blue!30

  // Helper to draw a matrix cell
  let draw-cell(pos, value, fill: none, name: none) = {
    rect(
      pos,
      (pos.at(0) + cell-size, pos.at(1) + cell-size),
      fill: fill,
      name: name,
      stroke: .5pt,
    )
    if value != none {
      content(
        (pos.at(0) + cell-size / 2, pos.at(1) + cell-size / 2),
        $#value$,
      )
    }
  }

  // Helper to draw a matrix
  let draw-matrix(origin, shape, values, highlights: (), name: none) = {
    let (rows, cols) = shape
    for ii in range(rows) {
      for jj in range(cols) {
        let pos = (origin.at(0) + jj * cell-size, origin.at(1) - ii * cell-size)
        let idx = ii * cols + jj
        let cell-name = if name != none { name + "-" + str(ii) + "-" + str(jj) }
        draw-cell(
          pos,
          if idx < values.len() { values.at(idx) },
          fill: if (ii, jj) in highlights { highlight },
          name: cell-name,
        )
      }
    }
  }

  // Draw input matrix I
  let input-origin = (0, 4)
  let input-values = (
    ..(0, 1, 1, 1, 0, 0, 0),
    ..(0, 0, 1, 1, 1, 0, 0),
    ..(0, 0, 0, 1, 1, 1, 0),
    ..(0, 0, 0, 1, 1, 0, 0),
    ..(0, 0, 1, 1, 0, 0, 0),
    ..(0, 1, 1, 0, 0, 0, 0),
    ..(1, 1, 0, 0, 0, 0, 0),
  )
  draw-matrix(
    input-origin,
    (7, 7),
    input-values,
    highlights: ((0, 3), (0, 4), (0, 5), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)),
    name: "I",
  )
  content(
    (input-origin.at(0) + 7 * cell-size / 2, 0),
    $bold(I)$,
    name: "I-label",
  )

  // Draw multiplication symbol
  content((rel: (1, 0), to: "I-3-6"), text(size: 18pt)[$*$], name: "times")

  // Draw kernel matrix K
  let kernel-origin = (input-origin.at(0) + 7 * cell-size + matrix-sep, input-origin.at(1) - 2 * cell-size)
  let kernel-values = (1, 0, 1, 0, 1, 0, 1, 0, 1)
  draw-matrix(
    kernel-origin,
    (3, 3),
    kernel-values,
    name: "K",
  )
  // Fill kernel matrix background
  rect("K-0-0.north-west", "K-2-2.south-east", fill: kernel-color, stroke: none)
  // Redraw matrix on top of background
  draw-matrix(kernel-origin, (3, 3), kernel-values, name: "K")
  content(
    (kernel-origin.at(0) + 3 * cell-size / 2, 0),
    $bold(K)$,
    name: "K-label",
  )

  // Draw equals sign
  content((rel: (1, 0), to: "K-1-2"), text(size: 18pt)[$=$], name: "equals")

  // Draw result matrix
  let result-origin = (kernel-origin.at(0) + 3 * cell-size + matrix-sep, input-origin.at(1) - cell-size)
  let result-values = (
    ..(1, 4, 3, 4, 1),
    ..(1, 2, 4, 3, 3),
    ..(1, 2, 3, 4, 1),
    ..(1, 3, 3, 1, 1),
    ..(3, 3, 1, 1, 0),
  )
  draw-matrix(result-origin, (5, 5), result-values, name: "R")
  // Draw highlighted cell in result matrix
  on-layer(-1, rect("R-0-3.north-west", "R-0-3.south-east", fill: result-color, stroke: none))
  content(
    (result-origin.at(0) + 5 * cell-size / 2, 0),
    $bold(I * K)$,
    name: "R-label",
  )

  // Draw connection lines
  let dash-style = (stroke: (dash: "dashed", paint: rgb(150, 220, 200)))
  line("I-0-5.north-east", "K-0-0.north-west", ..dash-style)
  line("I-2-5.south-east", "K-2-0.south-west", ..dash-style)

  let result-style = (stroke: (dash: "dashed", paint: rgb(150, 150, 220)))
  line("K-0-2.north-east", "R-0-3.north-west", ..result-style)
  line("K-2-2.south-east", "R-0-3.south-west", ..result-style)

  // Add small multiplication symbols in highlighted region
  for ii in range(3) {
    for jj in (3, 4, 5) {
      content(
        ("I-" + str(ii) + "-" + str(jj) + ".south-west"),
        text(size: 6pt)[×#calc.rem(ii + jj, 2)],
        anchor: "south-west",
        padding: 1pt,
      )
    }
  }
})