Camera models and calibration

Camera models

A set of classes that model the projective geometry of cameras.

CentralCamera	Create central camera projection model
FishEyeCamera	Create fisheye camera projection model
CatadioptricCamera	Create catadioptric camera projection model
SphericalCamera	Create spherical camera projection model

Calibration

Intrinsic calibration of camera from multiple images

class machinevisiontoolbox.Camera.CentralCamera(f=1, distortion=None, **kwargs)

Create central camera projection model

Parameters:

• f (float, optional) – focal length, defaults to 8mm

• distortion (array_like(5), optional) – camera distortion parameters, defaults to None

• kwargs – arguments passed to CameraBase constructor

A camera object contains methods for projecting 3D points and lines to the image plane, as well as supporting a virtual image plane onto which 3D points and lines can be drawn.

References:

• Robotics, Vision & Control for Python, Section 13.1, P. Corke, Springer 2023.

Seealso:

CameraBase FishEyeCamera SphericalCamera

classmethod images2C(images, gridshape=(7, 6), squaresize=0.025)

Calibrate camera from checkerboard images

Parameters:

• images (ImageSource) – an iterator that returns Image objects

• gridshape (tuple, optional) – number of grid squares in each dimension, defaults to (7,6)

• squaresize (float, optional) – size of the grid squares in units of length, defaults to 0.025

Returns:

camera calibration matrix, distortion parameters, image frames

Return type:

ndarray(3,4), ndarray(5), list of named tuples

The distortion coefficients are in the order \((k_1, k_2, p_1, p_2, k_3)\) where \(k_i\) are radial distortion coefficients and \(p_i\) are tangential distortion coefficients.

Image frames that were successfully processed are returned as a list of named tuples CalibrationFrame with elements:

element	type	description
image	Image	calibration image with overlaid annotation
pose	SE3 instance	pose of the camera with respect to the origin of this image
id	int	sequence number of this image in images

Note:

The units used for squaresize must match the units used for defining 3D points in space.

References:

• Robotics, Vision & Control for Python, Section 13.7, P. Corke, Springer 2023.

Seealso:

C points2C decomposeC SE3

Extrinsic calibration of camera from marker ArUcoBoard

class machinevisiontoolbox.ImageRegionFeatures.ArUcoBoard(layout, sidelength, separation, dict, name=None)

estimatePose(image, camera)

Estimate the pose of the board

Parameters:

• image (Image) – image containing the board

• camera (CentralCamera) – model of the camera, including intrinsics and distortion parameters

Raises:

ValueError – the boards pose could not be estimated

Returns:

Camera pose with respect to board origin, vector of residuals in units of pixels in marker ID order, corresponding marker IDs

Return type:

3-tuple of SE3, numpy.ndarray, numpy.ndarray

Residuals are the Euclidean distance between the detected marker corners and the reprojected corners in the image plane, in units of pixels. The mean and maximum residuals are useful for assessing the quality of the pose estimate.

draw(image, camera, length=0.1, thick=2)

Draw board coordinate frame into image

Parameters:

• image (Image) – image with BGR color order

• length (float, optional) – axis length in metric units, defaults to 0.1

• thick (int, optional) – axis thickness in pixels, defaults to 2

Raises:

ValueError – image must have BGR color order

Draws a coordinate frame into the image representing the pose of the board. The x-, y- and z-axes are drawn as red, green and blue line segments.

Note:

the length is specified in the same units as focal length and pixel size of the camera, and the marker dimensions, typically meters.

chart(filename, dpi=100)

Write ArUco chart to a file

Parameters:

• filename (str) – name of the file to write

• dpi (int, optional) – dots per inch of printer, defaults to 100

PIL is used to write the file, and can support multiple formats (specified by the file extension) such as PNG, PDF, etc.

If a PDF file is written the chart can be printed at 100% scale factor and will have the correct dimensions. The size is of the chart is invariant to the dpi parameter, simply affects the resolution of the image and file size.

Note:

This method assumes that the dimensions given in the constructor are in meters.