The projection concept in BIAS follows the idea to represent a camera including all internal (such camera matrix and radial distortion parameters) and external (such as rotation and translation) camera parameters as projection parameters.

The thoughts behind this concept are that it is nice to have one class in which everything is encapsulated which makes it very convenient to represent the projection of points and camera transformations.

Projection Parameters

The concept is to have a base class BIAS::ProjectionParametersBase from which all specialized projection parameters for different camera types are derived. Generally speaking it is a generalization of the PMatrix concept to other camera types:

BIAS::ProjectionParametersPerspective is the standard perspective camera model including radial distortion. It uses the BIAS::KMatrix to store focal length and principle point.
BIAS::ProjectionParametersSpherical is the representation of a spherical or fisheye camera model. It uses the model developed my Scaramuzza to represent fisheye camera parameters.
BIAS::ProjectionParametersCylindric represents a cylindrical camera. This can be used to represent cylindrical panoramas.
BIAS::ProjectionParametersPerspectiveDepth is an extension to BIAS::ProjectionParametersPerspective which enhances the perspective camera parameters by the necessary parameters of a ToF-/PMD-/Kinect-camera. The most important enhancement are the depth deviation parameters which represent the deviation of the measured depth values from the real values. It offers methods to correct these measurements.
BIAS::ProjectionParametersBufferedRay stores the rays of a camera for faster lookup in a lookup table.

The base class BIAS::ProjectionParametersBase has these main functions which can be used to project 2D points to 3D coordinates and 3D coordinates to 2D image points:

HomgPoint2D Project(const HomgPoint3D &X,...): Projects a homogenous 3D point X in world coordinates to 2D image coordinates.
HomgPoint2D ProjectLocal(const Vector3<double> &X,...): Projects a homogenous 3D point X in local coordinates to 2D image coordinates.
HomgPoint3D UnProjectToPoint(const HomgPoint2D& pos, double depth,...): Constructs a 3D point by calculating the ray from the camera center through the pixel position pos and scaling the ray with the value depth which is the distance of the point from the camera center. The resulting 3D point will be in world coordinates.
HomgPoint3D UnProjectToPointLocal(const HomgPoint2D& pos, double depth,...): Constructs a 3D point by calculating the ray from the camera center through the pixel position pos and scaling the ray with the value depth which is the distance of the point from the camera center. The resulting 3D point will be in local coordinates of the camera.
XMLRead(filename) : Loads projection parameters from disk
XMLWrite(filename) : Saves projection parameters to disk

There are also many other functions which can be used to calculate rays from the camera center through image coordinates and to calculate 3D points on unit spheres around the camera. Consult the class documentation for further details.

Projection Rigs

Multicamera setups in BIAS are represented as rigs, consisting of multiple instances of BIAS::ProjectionParametersBase. A rig is BIAS is represented by the class BIAS::Projection. In general it only is a container which internally holds a vector of pointers to BIAS::ProjectionParameterBase objects. The Projection is responsible to maintain the relative transformations between the cameras. In a BIAS::Projection the first camera is considered the "master" camera and is given in absolute world coordinates. All other cameras are considered "slave" cameras and are stored using external parameters relative to this master camera (translation, rotation). Adding ProjectionParameters to the Projection can therefore be done with relative or absolute camera externals and the appropriate function has to be used. Analog to the ProjectionParameters the Projection also has Read and Write functions.

XMLRead(filename) : Loads a projection from disk
XMLWrite(filename) : Saves a projection to disk

Author: Ingo Schiller