Methods, apparatuses and computer programs for determining and using extrinsic calibration of one or more cameras

An apparatus for extrinsic calibration of one or more cameras with respect to a reference coordinate system, the apparatus comprising one or more processors and one or more interfaces, wherein the processor is configured to:

• obtain, via the one or more interfaces, one or more images from one or more cameras, with each camera having a field of view, wherein each image shows an observation of at least one marker of a plurality of markers, wherein the plurality of markers are co-planar with respect to a reference plane,
• estimate, for the one or more cameras, a transformation between a respective camera coordinate system and the reference coordinate system based on an estimated pose of the at least one marker observed in the field of view of the camera relative to the camera coordinate system;
• estimate a pose of the reference plane with respect to the respective one or more camera coordinate systems based on a pre-defined or estimated pose of the reference plane with respect to the reference coordinate system and based on the estimated transformations between the one or more camera coordinate systems and the reference coordinate system;
• estimate planar poses of the plurality of markers with respect to the reference plane;
• and
• simultaneously adjust the planar poses of the plurality of markers and the pose of the reference plane with respect to the respective one or more camera coordinate systems by iteratively reducing an error between a reprojection of the plurality of markers into the respective one or more camera coordinate systems and the position of the respective markers in the images.

A non-transitory, computer-readable medium comprising a program code that, when the program code is executed on a processor, a computer, or a programmable hardware component, causes the processor, computer, or programmable hardware component to perform a method for extrinsic calibration of one or more cameras with respect to a reference coordinate system, the method comprising:

• obtaining one or more images from one or more cameras, with each camera having a field of view, wherein each image shows an observation of at least one marker of a plurality of markers, wherein the plurality of markers are co-planar with respect to a reference plane,
• estimating, for the one or more cameras, a transformation between a respective camera coordinate system and the reference coordinate system based on an estimated pose of the at least one marker observed in the field of view of the camera relative to the camera coordinate system;
• estimating a pose of the reference plane with respect to the respective one or more camera coordinate systems based on a pre-defined or estimated pose of the reference plane with respect to the reference coordinate system and based on the estimated transformations between the one or more camera coordinate systems and the reference coordinate system;
• estimating planar poses of the plurality of markers with respect to the reference plane;
• and
• simultaneously adjusting the planar poses of the plurality of markers and the pose of the reference plane with respect to the respective one or more camera coordinate systems by iteratively reducing an error between a reprojection of the plurality of markers into the respective one or more camera coordinate systems and the position of the respective markers in the images.