Triangulate a Point from Two Rays
The two cameras locate one corner in both views.
Triangulate a Point from Two Rays explained visually
The two cameras locate one corner in both views. English captions are optional and start off. The complete transcript follows the written lesson.
What you will learn
The two cameras locate one corner in both views.
A practical question
The tail-light corner has been matched in both camera images. Each observed pixel gives a viewing ray from its camera. If the two rays come from the same physical corner, their geometry lets us estimate a point in three-dimensional space. That's triangulation.
The useful idea
In noisy real measurements, the rays may not meet exactly. We choose a point that best fits the calibrated rays, then project that estimate back into both images to inspect its error. A wrong match can produce an apparently precise number with no physical meaning.
Work through the example
Triangulate a few landmarks at different distances. Compare the reprojected pixels with the points you actually marked. Check whether the estimated locations are in front of both cameras under the chosen convention.
Limits and next step
Save the camera poses, pairs, and errors. Next, we'll see why moving the cameras too close together makes even correct distant matches hard to turn into reliable depth.
Worked example
Use calibrated camera poses and the two observed pixels to recover depth.
Quick check: test your understanding
Try it yourself: In the situation described above, explain the method and one reason its output might be misleading.
Check the reasoning
Triangulation estimates a 3D point from the intersection, or closest fit, of two viewing rays. Noisy pixels make the rays miss, so estimated depth has uncertainty.
What is the main idea behind triangulate a point from two rays?
Triangulation estimates a 3D point from the intersection, or closest fit, of two viewing rays.
How is it used in the example?
Use calibrated camera poses and the two observed pixels to recover depth.
What limitation should be checked?
Noisy pixels make the rays miss, so estimated depth has uncertainty.
Further reading
Programming Computer Vision with Python — Jan Erik Solem.
Original ToolsInVision teaching examples. Editorial approach · Suggest a correction
Accessible referenceLesson 35 transcript147 words · Video transcript · Matches the published narration and captionsOpen transcript
The tail-light corner has been matched in both camera images. Each observed pixel gives a viewing ray from its camera. If the two rays come from the same physical corner, their geometry lets us estimate a point in three-dimensional space. That's triangulation.
In noisy real measurements, the rays may not meet exactly. We choose a point that best fits the calibrated rays, then project that estimate back into both images to inspect its error. A wrong match can produce an apparently precise number with no physical meaning.
Triangulate a few landmarks at different distances. Compare the reprojected pixels with the points you actually marked. Check whether the estimated locations are in front of both cameras under the chosen convention.
Save the camera poses, pairs, and errors. Next, we'll see why moving the cameras too close together makes even correct distant matches hard to turn into reliable depth.