Metashape supports four major types of camera: frame camera, fisheye camera, spherical camera and cylindrical camera. In this article, we will consider the results of calibration for the *Frame* type of camera.

This article describes the following sections:

Photogrammetric calibration of cameras is performed to determine the values of the interior orientation parameters of the cameras, including the parameters of distortion of the camera lens. The camera calibration parameters can be input manually, if they have been acquired as a part of precalibration procedure.

## Camera calibration parameters

The following calibration parameters can be determined:

*f *- Focal length measured in pixels (in pixels).

*cx, cy* - Principal point coordinates, i.e. coordinates of lens optical axis interception with sensor plane (in pixels).

*b1, b2* - Affinity and non-orthogonality (skew) coefficients (in pixels).

*k1, k2, k3, k4* - Radial distortion coefficients (dimensionless).

*p1, p2* - Tangential distortion coefficients (dimensionless).

Initial calibration data will be adjusted during the* Align Photos* processing step. Once *Align Photos* processing step is finished adjusted calibration data will be displayed on the *Adjusted tab* of the *Camera Calibration *dialog box.

### Example of "incorrect" calibration

We recommend to review the adjusted values for the cx, cy, b1 and b2 parameters in the *Camera Calibration *dialog. If the values for the parameters are too large (hundreds or more for cx, cy and tens or more for b1, b2), then it may be reasonable to re-align the data set having these parameters fixed.

## Distortion Plot

Metashape provides a number of tools to analyze camera calibration results. To access the *Distortion Plot* choose the corresponding option from context menu of a camera group in the *Camera Calibration* dialog.

### Distortion tab

*Distortion tab*** **in the

*Distortion Plot*dialog window presents an estimated distortion plot for the selected camera.

*Total, Radial, Decentering,*

*Corrections*and

*Residual*options are available in the tab.

*Distortion graph*represents the distortion values and direction according to the adjusted calibration coefficient values. It shows the plot in the discrete vectors mode for a central point in the corresponding image cell. The value of the coefficients calculated by the formula for each point of the image (XY) in the coordinates of the image. The formulas describing the distortion coefficients in Metashape can be found in the user manual in the Appendix C.

*Total -*displays the calculated total value of all camera calibration parameters.*Radial -*displays the total vector for the coefficients k1, k2, k3, k4*.**Decentering -*displays the total vector for the coefficients b1, b2 and p1, p2.*Corrections -*parameters will be displayed in this tab if during optimization process you enabled the*Fit additional corrections,*otherwise the Corrections tab will be blank. It is recommended to enable*Fit additional corrections*feature (see the dialog box below) for the cases where camera distortions are poorly described by the default model (Brown's distortion model is used in Metashape).

*Residuals*option for

*Distortion plot*

*presents residuals graph which allows to evaluate adequacy of the camera description by the applied mathematical model. Note that residuals are averaged per cell of an image and then across all the images in a camera group. Scale reference under the plot indicates the scale of the distortions/residuals.*

Residuals graphanddiagrams forDistortionshave different meaning. The picture of theDistortion plot (distortions graph)represent the distortion values and direction according to the adjusted calibration coefficient values, whereas theResiduals graphrepresents the averaged reprojection errors for the tie points detected on the source images (averaged across all the images of the calibration group and inside the certain "cells" on the images). On a side note:Residuals graph(for the tie point reprojection errors) is also shown on the calibration pages of the report document, while theDistortions graphis not included to the report and is only available fromCamera Calibrationdialog.

### Profile tab

*Profile tab *presents two graphs for radial and decentering distortions and how their values in pixels increase with distance from the center of the photo. The profiles can be saved as images.

### Correlation tab

*Correlation tab* presents:

*Value*column contains the adjusted values of the internal camera orientation parameters. The same values are presented on the*Adjusted*tab of the*Camera Calibration*dialog window.- In the
*Error*column *Correlation values*for internal camera orientation parameters - reflect the degree of correlation between the corresponding parameters.

Metashape calculates covariance matrix for the bundle adjustment results. Covariance matrix captures the uncertainty of the transformation. Covariance matrix diagonal elements are variances, σ_{ii}^{2}; the positive square root of the variance, σ , is called the *standard deviation*.

Covariance matrix off-diagonal elements are covariances, σ_{ij}. The value of each covariance reflects the degree of correlation between the corresponding parameters.