Single Camera Calibration

MetriCal's camera calibration is a joint process, which includes calibrating intrinsics and extrinsics at the same time. This guide provides tips and best practices specifically for single camera calibration.

Single Camera Calibration Tutorial

Calibration Guidelines

Data Capture Best Practices

DO	DON'T
✅ Keep targets in focus - use a lens focused at infinity when possible.	❌ Capture blurry or out-of-focus images.
✅ Capture the target across the entire field of view, especially near the edges.	❌ Only place the target in a small part of the field of view.
✅ Rotate the target 90° for some captures (or rotate the camera if target is fixed).	❌ Keep the target in only one orientation.
✅ Capture the target from various angles to maximize convergence (aim for 70° or greater).	❌ Only capture the target from similar angles.
✅ Make the target appear as large as possible in the image.	❌ Keep the target too far away from the camera.
✅ Pause between poses to avoid motion blur.	❌ Move the target or camera continuously during capture.

Keep Targets in Focus

This tip is an absolute must when capturing data with cameras. Data that is captured out-of-focus breaks underlying assumptions that are made about the relationship between the image projection and object space; this, in turn, breaks the projection model entirely!

A lens focused at infinity captures objects far away with ease without defocusing, so this is the recommended setting for calibration. Care should be taken, therefore, not to get a target too close to a lens that it blurs out the image. This near-to-far range in which objects are still focused is called a camera's depth of field. Knowing your depth of field can ensure you never get a blurry image in your data.

It should be noted that a lens with a shorter focal length, i.e. wide field of view, tends to stay in focus over larger depths of field.

Consider Your Target Orientations

One of the largest sources of projective compensation comes from $x$ and $y$ correlations in the image space observations. All of these effects are especially noticeable when there is little to no depth variation in the target field.

It is almost always helpful to collect data where the target field is collected at 0° and 90° orientations:

When the object space is captured at 0°:

• $x$ image measurements directly measure $X$ in object space
• $y$ image measurements directly measure $Y$ in object space

When the object space is captured at 90°:

• $x$ image measurements directly measure $Y$ in object space
• $y$ image measurements directly measure $X$ in object space

This process de-correlates errors in $x$ and $y$, because small errors in the $x$ and $y$ image measurements are statistically independent. There is no need to collect more data beyond 0° and 90° rotations; the two orientations alone do enough.

Helping You Help Yourself

Note that the same trick can be applied if the target is static, and the camera is rotated relative to the targets instead.

Consider the Full Field Of View

The bigger the target is in the image, the better.

A common data capture mistake is to only place the target in a small part of the field of view of the camera. This makes it extremely difficult to model radial distortions, especially if the majority of the data is in the center of the extent of the image. To mitigate this, object points should be observed across as much of the camera's field of view as is possible.

It is especially important to get image observations with targets near the periphery of the image, because this where distortion is the greatest, and where it needs to be characterized the best.

As a good rule-of-thumb, a ratio of about 1:1 is good for the target width ($X_c$) compared to the distance to the target ($Z_c$). For a standard 10×7 checkerboard, this would mean:

• 10 squares in the $X$-direction, each of length 0.10m
• 7 squares in the $Y$-direction of length 0.10m
• Held 1m away from the camera during data collection

This gives a ratio of 1:1 in $X$, and 7:10 in $Y$.

In general, increasing the size of the target field is preferred to moving too close to the camera (see "Keep Targets In Focus" above). However, both can be useful in practice.

Maximize the Convergence Angle

The convergence angle of the camera's pose relative to the object space is a major factor in the determination of our focal length $f$, among other parameters. The more the angle changes in a single dataset, the better; In most scenarios, reaching a convergence angle of 70° or greater is recommended.

It is worth noting that other data qualities shouldn't be sacrificed for better angles. It is still important for the image to be in focus and for the targets to be observable.

Advanced Considerations

The Importance of Depth Variation

note

This point is more of a consideration than a requirement. At the very least, it should serve to provide you with more intuition about the calibration data capture process.

Using a single, flat planar target provides very little variation in object space depth $Z$. Restricting object space to a single plane introduces projective compensation in all sorts of ways:

• $f$ to all object space $Z$ coordinates
• $p_1$ and $p_2$ to both $f$ and extrinsic rotations about $X$ and $Y$ (for Brown-Conrady)
• $f$ to $k_1$ through $k_4$ (for Kannala-Brandt)

A non-planar target, or a combination of targets using multiple object spaces helps to mitigate this effect by adding depth variation in $Z$. In general, more depth variation is better.

For those with only a single, planar calibration targets — know that MetriCal can still give great calibration results given the other data capture guidelines are followed.

Running a Single Camera Calibration

Basic Calibration Command

To run a calibration for a single camera, use the following commands:

# Initialize the calibration
metrical init -m /camera:eucm $INIT_PLEX

# Run the calibration
metrical calibrate -o $CAMERA_RESULTS $CAMERA_DATA $INIT_PLEX $OBJ

Where:

• /camera is the topic name for your camera
• eucm is the camera model (other options include pinhole, kb4, etc.)
• $INIT_PLEX is the path to the initialization file
• $CAMERA_RESULTS is the output path for the calibration results
• $CAMERA_DATA is the path to your captured data
• $OBJ is the path to your object space definition

Seeding Larger Calibrations

Single camera intrinsics calibration is often the first step in a multi-stage calibration process. When dealing with complex rigs where cameras are mounted in hard-to-reach positions (e.g., several feet off the ground), it can be beneficial to:

1. Calibrate each camera's intrinsics individually using optimal data for that camera
2. Use these individual calibrations to seed a larger multi-camera or sensor fusion calibration

This approach allows you to get up close to each camera individually to fully cover its field of view, which might not be possible when capturing data for the entire rig simultaneously.

The resulting calibration file from this process can be used as input to subsequent calibrations using the -p flag:

# Save the single camera calibration results
metrical calibrate -o $CAMERA_RESULTS $CAMERA_DATA $INIT_PLEX $OBJ

# Use these results in a subsequent calibration
metrical init -p $CAMERA_RESULTS -m /camera:eucm $NEW_INIT_PLEX

See the Multi-Camera Calibration guide for details on how to combine multiple single-camera calibrations.

Troubleshooting

If you encounter errors during calibration, please refer to our Errors documentation.

Common issues with single camera calibration include:

• No features detected (cal-calibrate-001)
• Initial camera pose estimates failed to converge (cal-calibrate-010)