G: TL;DR: In GIMP, use Tools → Transform Tools → Perspective (or Unified Transform) and drag the four corners of the canvas in the photo until they match a square grid. Then crop. That’s the fastest manual method.

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Method 1 — Fastest: Perspective Tool

1. Open the image in GIMP.
2. Turn on guides if helpful:
   Image → Guides → New Guide by Percent → 50% (Horizontal & Vertical)
3. Select:
   Tools → Transform Tools → Perspective
4. Click the image. A 4-corner grid appears.
5. Drag the four corners until the edges of your photographed canvas line up with the grid so that:
   • vertical edges look vertical
   • horizontal edges look horizontal
6. Click Transform.
7. Use the Crop Tool to crop to the corrected square.

This works because the perspective tool maps your skewed quadrilateral to a rectangle.

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Method 2 — Slightly easier to control: Unified Transform Tool

If the photo has rotation + perspective distortion:

1. Tools → Transform Tools → Unified Transform
2. Drag the corner handles to match the edges of the canvas.
3. Adjust rotation and perspective simultaneously.
4. Apply transform → crop.

This tool is basically GIMP’s closest equivalent to Photoshop’s Free Transform.

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Method 3 — Precise (if the corners are obvious)

1. Use Tools → Transform Tools → Perspective.
2. Zoom in and align each corner exactly with the actual corner of the canvas.
3. Apply transform.

This gives the most accurate result.

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Two practical tips

1. Turn on snapping

View → Snap to Grid
View → Show Grid

Then set grid spacing under:

Image → Configure Grid

2. Overshoot the canvas When correcting perspective, the edges may distort. It's fine — just crop afterward.

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If you want the “one-click” approach

GIMP can do this semi-automatically using G’MIC plugin → Repair → Perspective correction, but it requires installing the plugin.

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If you want, you can drop the photo here, and I can also show the exact corner points to drag. That usually takes about 30 seconds once I see the distortion pattern.

G: You’re running into a specific behavior of GIMP’s transform tools:
If no selection exists, the transform tool automatically grabs the entire layer and distorts it. citeturn0search3

So what you’re seeing is expected — GIMP assumes you want to transform the whole image.

The trick is: you must define the region first, then run the transform.

Below are the two methods that actually behave the way you want.

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Method 1 (closest to what you want): Perspective Tool in Corrective Mode

This is the “fix photographed document” workflow.

Steps

1. Select Free Select Tool (lasso) or Rectangle Select Tool.
2. Draw a selection around the square canvas in the photo.
3. Now choose:
   Tools → Transform Tools → Perspective (Shift+P).

Because a selection exists, the perspective transform now operates only on that selection, not the whole layer. citeturn0search0

4. In Tool Options, set: Direction → Corrective (Backward)
5. Drag the four corner handles to the four corners of the photographed square.
6. Click Transform.
7. Crop.

This workflow literally tells GIMP:
“Take this quadrilateral and flatten it into a rectangle.”

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Method 2 (often easier): Cage Transform

This tool actually lets you draw the region you want to deform, which is closer to what you described wanting.

Steps:

1. Tools → Transform Tools → Cage Transform
2. Click around the four corners of your canvas.
3. Press Enter to finish the cage.
4. Drag the corner nodes to form a perfect square.
5. Press Enter again.

The cage tool works by defining a deformable polygon around an area and then moving the anchor points. citeturn0search15

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The simplest workflow most people actually use

For photographing paper, paintings, canvases, etc:

1. Crop roughly to the object
2. Perspective Tool → Corrective
3. Align the 4 handles to the 4 real corners
4. Apply
5. Scale to a perfect square if needed

That’s the fastest practical workflow. citeturn0search20

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✔ If you want, show the photo.
There is also a very fast 3-step method using the Handle Transform tool that many GIMP users miss, and for a photographed canvas it’s usually the cleanest fix.

G: TL;DR: Yes. What you want is a 4-point perspective correction (homography): pick the four corners of the photographed canvas and map them to a perfect rectangle. In GIMP, the closest built-in tool is the Handle Transform Tool, which lets you place four exact corner points and then force them into a square/rectangle.

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Method that actually does what you described

Handle Transform Tool (best built-in option)

This tool lets you define four source points and then move them to four destination points.

Steps

1. Open the image.

2. Select
   Tools → Transform Tools → Handle Transform
   (shortcut: Shift + L)

3. Click the four corners of your canvas in the photo

   • top-left
   • top-right
   • bottom-right
   • bottom-left

4. Press Enter to activate the transform handles.

5. Now drag those four handles so they form a perfect rectangle or square.
   Use guides or grid for precision:

   • View → Show Grid
   • View → Snap to Grid

6. Press Enter again to apply.

GIMP then computes the full perspective transform and stretches the image so your four points become a perfect rectangle.

This is mathematically the exact operation you're describing.

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Why this works

What you're doing is a projective transform:

skewed quadrilateral  →  perfect rectangle

The computer calculates a mapping so that:

• your chosen 4 points → the rectangle corners
• every other pixel is warped consistently

This is the same math used for:

• document scanning apps
• texture projection
• camera calibration

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Even more automatic (optional)

If you install the G’MIC plugin, it has a filter literally designed for this:

Filters → G’MIC → Repair → Perspective [4 points]

You click the four corners and it automatically outputs a rectangular result.

This behaves exactly like phone “scan document” apps.

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Small trick to make it perfect

After the transform:

1. Image → Canvas Size
2. Set width = height if you want a mathematically perfect square.
3. Crop.

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One conceptual sentence (Japanese practice)

四(よん) つ の 角(かど) を 選(えら)ぶ と、画像(がぞう) を 正方形(せいほうけい) に 変形(へんけい) できる。
— “If you choose four corners, the image can be transformed into a square.”

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If you'd like, I can also show a much faster 20-second workflow many GIMP users use for photographed paintings, because there's one tool hidden in the transform menu that makes this almost trivial.