# Hand-eye Calibration Result Report

Following hand-eye calibration, AlignPlus generates a hand-eye calibration report. The report contains information about the quality of the captured image and the motion device. The hand-eye calibration is generated for both, checkerboard-based hand-eye calibration and part-based hand-eye calibration. The following subsections describe the salient information contained in this report.

## Checkerboard-based Hand-eye Calibration

The following is an example of a calibration report for a hand-eye calibration result, computed for a two, stationary-camera system that has been hand-eye calibrated using a checkerboard. The report contains eight blocks of significance.

• Block 1 contains information about the pixel resolution(PelSize) of the camera,

• Block 2 contains the locations of the camera in Home2D for stationary-camera systems. For moving camera systems, the camera locations are expressed in Stage2D, which is the coordinate system of the gripper.

• Block 3 contains the overall residual error for the hand-eye calibration

• Blocks 7, 8 contain single view residuals for each camera,

• Blocks 4, 5, 6 contain information about the pose of the motion device during the hand-eye calibration process

PelSize

The PelSize parameter is a measure of the pixel resolution of the camera, expressed in the measurement unit of the calibration target, which is in millimeters. Pel here stands for pixel and PelSize stands for pixel size. The PelSize parameter is the size of the surface that is imaged by each pixel in the camera. For a camera with square pixels, that captures the image of a surface in a manner that is free of non-affine distortion. PelSize is equal to size of the field of view (FOV) divided by the number of pixels in the camera. For a camera with 1600x1200 pixels, that images a FOV of size 12 x 9 mm, the PelSize is 12mm/1600pixel = 0.0075 mm/pixel.

Camera Pose

The pose of stationary cameras do not change relative to the motion device coordinate system and hence Home2D. Therefore for stationary-camera systems, the camera pose is expressed in Home2D. For moving-camera systems, the camera pose is expressed in Stage2D, as the pose of the cameras are fixed relative to the gripper. This information helps the user to verify if the cameras have been installed corrected.

Overall Residuals

The results also include measurement of residual errors, which are indicators of overall quality of the calibration. A good calibration should yield small residual errors. Large residual errors usually indicate bad inputs, examples of which include damaged/inaccurate calibration targets, inaccurate feature extraction, wrong correspondence, inaccurate motion stage, wrong commanded pose, inappropriate lens distortion model, and violations to fundamental requirements.

The residuals are computed in Raw2D and Home2D by mapping the correspondence pairs extracted/computed from all images in the entire hand-eye calibration process. The mapping uses both directions of Raw2DFromHome2D to go to and from Raw2D and Home2D. The unit of the residual errors is pixel in Raw2D and physical units in Home2D. Generally, a residual error of less than 0.25 pixels in Raw2D is considered excellent calibration accuracy.

Single View Residual

Single-view residuals, which are computed from the single-view calibrations for each view of each camera. These residuals are computed in Raw2D and Plate2D, by mapping the correspondence pairs for each view of each camera through the corresponding single-view calibration. Note that the single-view calibrations are not included in the result, only their residuals are. These residuals indicate the quality of the calibration target, feature extractor, correspondence pairs and the selected distortion model. The Raw2D residual errors are in units of pixels, and the Plate2D residual errors are in the physical units of the calibration target. Generally, a residual error of less than 0.1 pixels in Raw2D is considered excellent calibration accuracy.

Uncorrected Home2DFromStage2D

This is the commanded pose of the motion stage. Due to systematic errors in the motion stage, the commanded pose of the motion stage may not match the actual physical pose of the motion stage in Home2D (that is, Home2DFromStage2D). UncorrectedHome2DFromStage2D is used to describe the commanded pose of the motion stage because it represents your best guess of the pose of the motion stage prior to calibration.

Corrected Home2DFromStage2D or Home2DFromStage2D

This is the actual physical pose of the motion stage in Home2D. It defines the relationship between Home2D and Stage2D and is represented by a 2D rigid transform. (In the stationary camera configuration, this is the motion of the motion stage of the object. In the moving camera configuration, this is the motion of the motion stage onto which the cameras are attached – the object platform is stationary in this case.)

Here in this example the UncorrectedHome2DFromStage2D is (2.0, 2.0, 0), but Home2DFromStage2D is (2.003, 1.992).

By comparing expected positions and motion's actual positions, hand-eye calibration can calculate the transform between Stage2D and Home2D.

Estimated Home2DFromStage2D

The hand-eye calibration estimates the Home2DFromStage2D poses at which the images were acquired, from which the correspondence data are extracted. These Home2DFromStage2D poses are useful in checking system consistency. When the correspondence data are consistent with the specified input UncorrectedHome2DFromStage2D poses and there are no systematic errors in the stage motion, the estimated Home2DFromStage2D poses should agree closely with the specified input UncorrectedHome2DFromStage2D. Any significant mismatch indicates inconsistency among the input correspondence data and UncorrectedHome2DFromStage2D poses or systematic errors in the motion stage. This is most likely accompanied by large residual errors if the cause of mismatch is inconsistency between the UncorrectedHome2DFromStage2D pose and the input. When such inconsistency occurs, the user should check their system and correct the source of inconsistency, in order to achieve accurate calibration.

## Part-based Hand-eye Calibration

The summary of part-based hand-eye calibration is very similar except the for the single view residuals, which are not available in part-based calibration. Typically the part-based calibration process generates a sparse set of features in each view, which makes it infeasible to compute single view residuals.