openMVG libraries

Cameras

This module provides different camera models.
Source Github: https://github.com/openMVG/openMVG/tree/master/src/openMVG/cameras

Pinhole camera model

A camera could be approximated by a projective model, often called pinhole projection. The simplest representation of a camera is a light sensible surface (sensor): an image plane, a lens (projective projection) at a given position and orientation in space.

The pinhole camera model. An oriented central projective camera.

The pinhole camera geometry models the projective camera with two sub-parametrizations, intrinsic and extrinsic parameters. Intrinsic parameters model the optic component (without distortion) and extrinsic model the camera position and orientation in space. This projection of the camera is described as:

P3×4=K[R|t]=⎡⎣⎢f∗kuf∗kvcucv1⎤⎦⎥⎡⎣⎢⎢⎢⎢0R3×300txtytz1⎤⎦⎥⎥⎥⎥$$$$

• Intrinsic parameters [f;cu;cv]:
  • $\mathrm{ku},kv:$ scale factor relating pixels to distance (often equal to 1),
  • :$f:$ the focal distance (distance between focal and image plane),
  • cu,cv:the principal point, which would be ideally in the centre of the image.
• Extrinsic parameters [R|t]=[R|−RC]:
  • R: the rotation of the camera to the world frame,
  • 
    $t:$ the translation of the camera. t is not the position of the camera. It is the position of the origin of the world coordinate system expressed in coordinates of the camera-centred coordinate system. The position, C of the camera expressed in world coordinates is C=−R−1t=−RTt(since R is a rotation matrix).

A 3D point is projected in a image with the following formula (homogeneous coordinates):

xi=PXi=K[R|t]Xi$$$$

⎡⎣⎢uiviwi⎤⎦⎥=⎡⎣⎢f∗kuf∗kvcucv1⎤⎦⎥⎡⎣⎢⎢⎢⎢0R3×300txtytz1⎤⎦⎥⎥⎥⎥⎡⎣⎢⎢⎢XiYiZiWi⎤⎦⎥⎥⎥$$$$

OpenMVG Pinhole camera models

• Pinhole intrinsic
  • Pinhole_Intrinsic : public IntrinsicBase
    • classic pinhole camera (Focal + principal point and image size).
  • Pinhole_Intrinsic_Radial_K1 : public Pinhole_Intrinsic
    • classic pinhole camera (Focal + principal point and image size) + radial distortion defined by one factor.
    • can add and remove distortion
  • Pinhole_Intrinsic_Radial_K3 : public Pinhole_Intrinsic
    • classic pinhole camera (Focal + principal point and image size) + radial distortion by three factors.
    • can add and remove distortion
  • Pinhole_Intrinsic_Brown_T2 : public Pinhole_Intrinsic
    • classic pinhole camera (Focal + principal point and image size) + radial distortion by three factors + tangential distortion by two factors.
    • can add and remove distortion
  • Pinhole_Intrinsic_Fisheye : public Pinhole_Intrinsic
    • classic pinhole camera (Focal + principal point and image size) + fish-eye distortion by four factors.
    • can add and remove distortion
• Simple pinhole camera models (intrinsic + extrinsic(pose))

// Setup a simple pinhole camera at origin
// Pinhole camera P = K[R|t], t = -RC
Mat3 K;
K << 1000, 0, 500,
     0, 1000, 500,
     0, 0, 1;
PinholeCamera cam(K, Mat3::Identity(), Vec3::Zero());