Topic · Geometry

Stereo vision

Everything on this site about stereo vision, in the order to read it: a page is listed after the pages it builds on. The figures below are the ones those pages use to explain it; each is live: move a slider and it recomputes.

In reading order

  1. Read · read first: Points at Infinity — Horizons, Vanishing Points and the Floor, Triangulation — Two Rays That Almost Meet, From Matches to Motion — Four Cameras, One Right Answer
  2. Read · read first: Lens Distortion — Bending Straight Lines Back

The figures these pages use

Pulled from the pages above. Move a slider and the figure recomputes, exactly as on its page.

From Stereo Depth — Rectification and Z = fB/d › 1. Turn Both Pictures Until the Rows Agree

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Camera: focal length and principal point
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Camera 1: move it and turn it
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Camera 2: move it and turn it
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Turn camera 2 until the rows agree. Camera 1 (blue) already faces straight ahead; camera 2 (rust) is turned 10° in. Turning a camera about its centre needs no new photo, only a remap of its pixels. Press play: camera 2 turns back by 10°, and every point in its picture slides onto the row the same point has in camera 1's picture. Drag the background to turn the scene, or drag a camera to move it. Open the camera panels to move the cameras, or change the focal length and the principal point.

From Stereo Depth — Rectification and Z = fB/d › 2. Disparity

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Camera: focal length and principal point
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Camera 1: move it and turn it
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Camera 2: move it and turn it
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Depth is fB over d. Two cameras facing the same way, B apart. The match in camera 2's picture sits on the same row, d pixels to the left; depth is Z = fB/d. A matching error of Δd pixels smears the point along camera 1's ray (the thick rust band); the strip under the picture enlarges that band. Play Z: d collapses while the error band runs away. Drag the background to turn the scene, or drag a camera to change the baseline. Open the camera panels to move the cameras, or change the focal length and the principal point.

From From Two Photos to a Point Cloud › 1. One Map, Two Jobs

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Camera: focal length and principal point
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Camera 1: move it and turn it
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Camera 2: move it and turn it
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From two photos to a point cloud. The series rig: camera 1 (blue), camera 2 (rust) 1 m to its right and turned in 10°, and the L target's 32 corners plus X. Step through the chain: the lens is undone, camera 2 is turned back until the rows agree, X is matched along its row, and Q turns every pixel and its disparity back into a 3-D point. Drag the background to turn the scene, or drag a camera's centre. Open the camera panels to move the cameras, or change the focal length and the principal point.

From From Two Photos to a Point Cloud › 2. Finding the Match Along a Row

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Cameras: focal length and baseline
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Sliding a window along the row. The blue window sits around x₁ in picture 1. The rust window sits d pixels to its left in picture 2, and its brightness is laid over the blue one so you can see how well they agree. The cost is how different the two windows look; the lowest cost along the row is the match. Play d, or drag the rust window. Open the camera panel to change the focal length or the baseline: the wall stays 4 m away, so the match moves to f B / 4.

Tags that go with it

3-D reconstruction 2Two-view geometry 1