Pinhole camera projection function

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Backlinks:  Pinhole camera model See also: World to camera trafo

Source: Mur-Artal 2017 VI-ORB 3D points unknown_filename.2.png

Projection function unknown_filename.3.png

  • Transforms 3D points into 2D points on image plane unknown_filename.4.png

  • Focal length: unknown_filename.1.png

  • Principal point: unknown_filename.6.png

  • The projection does not consider the distortion due to the lens

    • therefore when extracting image features, first undistort their coordinates
    • only then match to projected points (existing features which have undergone projection from 3D to 2D)

Source:  Lamarca 2019 DefSLAM 3D point: unknown_filename.png

Projection function maps

to a 2D image point (becomes a projected map point)

unknown_filename.9.png unknown_filename.7.png unknown_filename.8.png from camera transformation

Image

  • Set of observations in image: set of keypoints which are matched to map points
  • Normalised keypoint coordinates unknown_filename.5.png

Source: http://www.cse.psu.edu/~rtc12/CSE486/lecture12.pdf unknown_filename.10.png Derivation of the perspective projection