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CalibrateCamera_Telecentric

Header:	AVL.h
Namespace:	avl
Module:	Calibration

Finds the telecentric camera intrinsic parameters from calibration grids.

Applications: Computes camera parameters which need to be calculated only once for each camera, and are a prerequisite for other calibration filters.

Syntax

void avl::CalibrateCamera_Telecentric
(
	const atl::Array<atl::Array<avl::AnnotatedPoint2D>>& inImageGrids,
	float inGridSpacing,
	int inImageWidth,
	int inImageHeight,
	avl::LensDistortionModelType::Type inDistortionType,
	float inImagePointsStandardDeviation,
	avl::TelecentricCameraModel& outCameraModel,
	atl::Optional<avl::TelecentricCameraModel&> outCameraModelStdDev = atl::NIL,
	atl::Optional<float&> outRmsError = atl::NIL,
	atl::Optional<atl::Array<float>&> outMaxReprojectionErrors = atl::NIL,
	atl::Optional<atl::Array<atl::Array<avl::Segment2D> >&> outReprojectionErrorSegments = atl::NIL
)

Parameters

Name	Type	Range	Default	Description
inImageGrids	const Array<Array<AnnotatedPoint2D>>&			For each view, the annotated calibration grid
inGridSpacing	float	0.000001 -		Real-world distance between adjacent grid points.
inImageWidth	int	1 -		Image width, used for initial estimation of principal point.
inImageHeight	int	1 -		Image height, used for initial estimation of principal point.
inDistortionType	LensDistortionModelType::Type		PolynomialWithThinPrism	Lens distortion model
inImagePointsStandardDeviation	float	0.0 -	0.1f	Assumed uncertainty of inImagePoints. Used for robust optimization and outCameraModelStdDev estimation.
outCameraModel	TelecentricCameraModel&
outCameraModelStdDev	Optional<TelecentricCameraModel&>		NIL	Standard deviations of all model parameters, assuming that inImagePoints positions are disturbed with gaussian noise with standard deviation equal to inImagePointsStandardDeviation.
outRmsError	Optional<float&>		NIL	Final reprojection RMS error, in pixels.
outMaxReprojectionErrors	Optional<Array<float>&>		NIL	For each view: the maximum reprojection error among all points.
outReprojectionErrorSegments	Optional<Array<Array<Segment2D> >&>		NIL	For each view: array of segments connecting input image points to grid reprojections.

Optional Outputs

The computation of following outputs can be switched off by passing value atl::NIL to these parameters: outCameraModelStdDev, outRmsError, outMaxReprojectionErrors, outReprojectionErrorSegments.

Description

The filter estimates intrinsic camera parameters - magnification, principal point location and distortion coefficients from a set of planar calibration grids by means of robust minimization of RMS reprojection error - the square root of averaged squared distances between grid points as observed on the image and their associated grid coordinates projected onto image plane using estimated parameters (i.e. grid poses and camera parameters).

A few distortion model types are supported. The simplest - divisional - supports most use cases and has predictable behaviour even when calibration data is sparse. Higher order models can be more accurate, however they need a much larger dataset of high quality calibration points, and are usually needed for achieving high levels of positional accuracy across the whole image - order of magnitude below 0.1 pix. Of course this is only a rule of thumb, as each lens is different and there are exceptions.

Distortion model types are compatible with OpenCV, and are expressed with equations using normalized image coordinates:

Divisional distortion model

Polynomial distortion model

PolynomialWithThinPrism distortion model

where , x' and y' are undistorted, x'' and y'' are distorted normalized image coordinates.

Although every application should be evaluated separately the general guidelines for choosing the right distortion type you will find in table below:

		Required calibration data:		Typical application:	Suggested Lens type:
		Quality:	Quantity:	Typical application:	Suggested Lens type:
Distortion model	Divisional	Average	Average	Robot Guidance	Pinhole
	Polynomial	Very high. Calibration plate should be made of stiff material like metal plate or glass.	Very high evenly distributed across entire ROI. Calculation on areas not covered with calibration plate might be highly inaccurate.	Metrology	Pinhole/Telecentric
	Polynomial with thin prism			Metrology in micrometers	Telecentric

The filter provides a few methods for judging the feasibility of calculated solution.

The outRmsError is the final RMS reprojection error. The main contributor to that value is the random noise in inImageGrids points positions. Model mismatch will also result in increased outRmsError.
The outMaxReprojectionErrors is an array of maximum reprojection errors, per view. It can be used to find suspicious calibration grids.
The outCameraModelStdDev contains standard deviations of all parameters of estimated model, assuming that inImageGrids points positions have a standard deviation equal to inImagePointsStandardDeviation. It can be used to verify the stability of estimated parameters. High values may be a result of data deficiency in a sensitive region (e.g. lack of calibration points at the edges of image when high-order distortion model is used).
The outReprojectionErrorSegments consists of segments connecting input image points to reprojected world points, and thus it can be readily used for visualization of gross errors. The XY scatter plot of residual vectors (obtained by using SegmentVector on the outReprojectionErrorSegments) is a good insight into the residuals distribution, which in ideal case should follow a 2D gaussian distribution centered around point (0,0).

Hints

High accuracy camera calibration needs a considerable amount of high quality calibration points, especially when using more complicated models. Each calibration image should contain hundreds of calibration points, there should be at least a dozen of calibration images, and all the calibration points should span the area/volume of interest. The calibration grids should be as flat and stiff as possible (cardboard is not a proper backing material, thick glass is perfect). Take care of proper conditions when taking the calibration images: minimize motion blur by proper camera and grid mounts, prevent reflections from the calibration surface (ideally use diffusion lighting).

There is no need for camera calibration in the production environment, the camera can be calibrated beforehand. As soon as the camera has been assembled with the lens and lens adjustments (zoom/focus/f-stop rings) have been tightly locked, the calibration images can be taken and camera calibration performed. Of course any modifications to the camera-lens setup void the calibration parameters, even apparently minor ones such as removing the lens and putting it back on the camera in seemingly the same position.

Examples

Usage of outReprojectionErrorSegments for identification of bad association of image points and their grid coordinates in inImageGrids - two points are swapped.

Errors

List of possible exceptions:

Error type	Description
DomainError	Empty input array
DomainError	inGridSpacing needs to be positive