Updated branch Dec 2023.

CALICO: a method for calibrating asynchronous camera networks and/or multicamera systems, version **. December 2023 (Original release November 2019).

Changelog:

• code factoring and reorganization; added April Tags support. January 2024.
• Docker image added March 2020.
• Added incremental method as default, and another overhaul, April 2020.
• Completed refactoring and rewrite; allows use of April tags.

Roadmap

• Contact
• References
• Docker release
• Dependences
• Building
• Running
  • Running from a Docker container
• Input format
• Output format

Comments/Bugs/Problems: amy.tabb@usda.gov, or open an issue on Github.

This README file is produced by Amy Tabb as a companion to a paper: Multi-camera calibration with pattern rigs, including for non-overlapping cameras: CALICO

@article{tabb_calibration_2024
	title = {Multi-camera calibration with pattern rigs, including for non-overlapping cameras: CALICO},
	url = {http://arxiv.org/abs/1903.06811},
	abstract = {},
	urldate = {2024-03-27},
	journal = {arXiv:1903.06811 [cs]},
	author = {Tabb, Amy and Medeiros, Henry and Feldmann, Mitchell J. and Santos, Thiago T.},
	month = mar,
	year = {2024},
	note = {arXiv: 1903.06811},
	keywords = {Computer Science - Computer Vision and Pattern Recognition}
}

Dataset and/or code:

Tabb, Amy, & Feldmann, Mitchell J. (2023). Data and Code from: Calibration of Asynchronous Camera Networks: CALICO (Version v2) [Data set]. Zenodo. http://doi.org/10.5281/zenodo.3520865

@dataset{tabb_amy_2023_3520865,
  author       = {Tabb, Amy and Feldmann, Mitchell J.},
  title        = {Data and Code from: Calibration of Asynchronous 
                   Camera Networks: CALICO},
  month        = nov,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v1},
  doi          = {10.5281/zenodo.3520865},
  url          = {https://doi.org/10.5281/zenodo.3520865}
}

If you use this code in project that results in a publication, please cite at a minimum the paper above, and best practice would be to cite the paper and the dataset. Otherwise, conditions include those of the MIT license concerning the copyright and license notice. However, no guarantees are expressed or implied.

Install Docker, if you haven't already. I endorse uninstalling old versions if you have them floating around.

The image for CALICO is : amytabb/calico-dec2023.

docker pull amytabb/calico-dec2023

CALICO needs to read and write results to disk; to do so with Docker means that we need to mount a portion of your hard drive to a volume in the Docker image.

I used a bind mount below; the Docker image's volume is docker_dir and will not change no matter which machine or dataset you run it on. /full/file/path/on/your/machine is the directory that you want the reading and writing to occur.

Example:

sudo docker run -v /full/file/path/on/your/machine:/docker_dir -it amytabb/calico:latest bash

The bind mount is potentially confusing, so here is an example. Say I have a directory /home/amy/Data/March/ and within March is a directory of images that I want to process with CALICO. I also want to write to a directory within /home/amy/Data/March/. So,

sudo docker run -v /home/amy/Data/March:/docker_dir -it amytabb/calico:latest bash

Creates a container with all of the libraries and a Ubuntu 18.04 operating system, and bash shell (command line), and may look something like:

root@f6feb7ce8c31:/docker_dir# 

but if you take a look at the contents of /host_dir, with ls, they are /home/amy/Data/March/. That's the bind mount magic.

First, suppose we forgot to create the write directory. No problem.

root@f6feb7ce8c31:/host_dir# mkdir write-dir

creates our write directory write-dir.

And from here on out, we issue commands from this Docker container, which is writing to our filesystem. Skip to Running to get details on how to run the code. The only difference is that ./ is not needed before commands when using the Docker version, and the --src-dir=[STRING] has been set up within the Docker image, and does not need to be specified.

This code uses the April Tag libraries, Ceres, OpenCV, OpenMP, and Eigen libraries. Ceres can be used without cmake, but is best used with cmake. I've included instructions for building with cmake, and the specific OpenCV libraries needed, as well as what OpenCV 3.x versions have worked without alteration. Hints for successfully building calico in Ubuntu can be found by reading the Dockerfile in this repository and copying many of the steps.

April Tags, April Robotics lab

April Tags, Michael Kaess' library. This is a port of Michael Kaess' April Tag library, which uses the April Robotics' library, over from BitBucket and updated with a cmake. We used Kalibr as a comparison method for calico and it uses a detection from Michael Kaess' version; so to compare calico to Kalibr, we needed a similar detector. More information about these versions can be found at these two posts: one, two.

Ceres

We are not responsible for whatever it takes to get Ceres to build; but advise that having a recent version of Eigen and Google's glog are helpful to the process.

OpenCV As of this writing, OpenCV is at version 4.9.0 Github. However, this code was written with an earlier version and versions over 4.3.0 result in compilation error. We have successfully run the code with OpenCV 3.4.8 and OpenCV 4.3.0. The OpenCV contributed module is needed to detect aruco patterns. These libraries need to be installed:

• opencv_core
• opencv_imgproc
• opencv_imgcodecs
• opencv_aruco
• opencv_calib3d

OpenMP OpenMP is used to parallelize some sections of the individual camera calibration section. On Ubuntu, to install the library, run sudo apt-get install libgomp1 at a terminal. Now OpenMP is required. Evidently, OpenMP support on MacOS is ... difficult to accomplish. If you have notes on getting this to work on MacOs, let me know so that I can add them to this document. If you cannot get OpenMP working and you have a Mac (or Windows), I suggest using the Docker container to run calico.

This code has been tested on Ubuntu 16.04 and Ubuntu 18.04. You are welcome to convert it to Windows, but I have not. While OpenCV is available from distribution repositories, my long experience with it is has always been to build from the source to get the best results.

These instructions will walk you through cloning to configuring with cmake, and importing to the Eclipse Integrated Development Environment (IDE) (if desired).

1. Clone! Go to the location where you want the project, and from a terminal git clone https://github.com/amy-tabb/calico.git

2. cd calico

3. The code is in src. Create a build directory, mkdir build , cd build.

4. Here's the cmake fun. The way I have the cmake file configured (calico/src/CmakeLists.txt), the last installed version of OpenCV will be used. I don't specify a version. However, you can specify which version of OpenCV is used by altering the the find_package() line:

• find_package( OpenCV 3.4.8 REQUIRED )
• find_package( OpenCV 4 REQUIRED )

Both work and those versions are compatible with CALICO.

5. Configure with cmake. Don't have cmake? (sudo apt-get install cmake). Then from the build folder, you can use any of the following four options below:

• cmake ../src (basic)
• cmake -DCMAKE_BUILD_TYPE=Release ../src (Release configuration)
• cmake -DCMAKE_BUILD_TYPE=Debug ../src (Debug configuration)
• cmake -G"Eclipse CDT4 - Unix Makefiles" -DCMAKE_ECLIPSE_GENERATE_SOURCE_PROJECT=TRUE ../src/ (Create an Eclipse project to import -- it will be in the build folder)

In case you have installed OpenCV and cmake can't find it, you need to specify the location of OpenCVConfig.cmake. Don't know where it is? Find out with locate OpenCVConfig.cmake. Then append

-DCMAKE_PREFIX_PATH=dir

in my case on one machine, this was:

-DCMAKE_PREFIX_PATH=/usr/local/opencv41/lib/cmake/opencv4/

where /usr/local/opencv41/lib/cmake/opencv4/ is the directory containing OpenCVConfig.cmake. Of course, you will substitute whatever the appropriate directory returned from locate OpenCVConfig.cmake was.

6. Then, you can either import the project to Eclipse (if you used the last option), or build from there, or type make. If the everything compiled and linked, and you have an executable named calico, you are ready to go.

7. I highly suggest that you download at least one test dataset from http://doi.org/10.5281/zenodo.3520866. These datasets are in the format needed for CALICO, and you can ensure that everything is correctly configured on your system.

To see the available options, run ./calico-dec2023 with no arguments or --help.:

Printing help for calico, Dec. 2023.
ESSENTIAL FUNCTIONALITY -------------------
--verbose                     No arguments.  Writes additional information during the run.
--create-patterns             No arguments, write charuco or april image patterns from a specification file.
--calibrate                   No arguments, indicates that this dataset is a camera network or multicamera system.
--num-threads                 Number of threads to use.  Default is # returned by omp_get_max_threads();, currently = 24
--charuco                     Using charuco patterns.
--april                       Using AprilTag patterns.

DIRECTORIES AND PATHS ----------------------- 
--input=[STRING]              Mandatory, has to be a directory.
--output=[STRING]             Mandatory, has to be a directory.
--src-dir=[STRING]            Directory where the source code resides relative to where the executable is being run. 
 Specifically, the location of 'detector_params.yml'  Default is ../src/ . 

CAMERA CALIBRATION OPTIONS ---------------------------
--non-zero-tangent            No arguments. In the camera calibration part, sets the tangential components of radial distortion (p1, p2) to non-zero.
--non-zero-k3                 No arguments. In the camera calibration part, sets the 3rd radial distortion k value to non-zero.
--fix-pp                      No arguments. In the camera calibration part, sets the principal point to the image center. 
--focal-px=[float]            Initial focal length in pixels for the camera.  Default is max dimension * 1.2 


OPTIONS ON NUMBER OF IMAGES READ/USED; NUMBER OF POINTS USED FOR NETWORK -----------
--max-internal-read=[int]     Integer argument. Sets the number of internal camera calibration images to read. Default is the number of images in the directory 'internal'.
--max-internal-use=[int]      Integer argument. Sets the number of images to use where the pattern is detected in the calibration, from the 'internal' directory. The default is the maximum number of patterns found in . 
--max-external=[int]          Integer argument. Sets the number of images /time instants to read from  the 'external' directory for each camera.
--k=[int]                     Specifies the number of points to use for the minimization of reprojection error, relevant only  for the network case.  The default is 8.
--num-pattern=[int]           Integer argument. Sets the number of points required to estimate the   pose for a pattern.  Default is >=10 for network, >= 4 for rotating.
OPTIONS HOW OFTEN TO RUN GLOBAL MINIMIZATION OF VARIABLES -----------
--perc-ae=[float]             float argument from (0,1]. Global LM optimization of variables for algebraic error occurs after this percentage of variables are solved for. Unspecified, the default is 0.2, so this step will be run 5 times.
--perc-rp=[float]             float argument from (0,1]. Global LM optimization of variables for reprojection error is triggered when this percentage of constraints/equations are added to the model. Unspecified, the default is 0.5, so this step will be run 2 times.

DISPLAY -----------
--camera-size=[float]         Float argument.  Specifies the size of the cameras written, default is 40.
--track-size=[float]          Float argument.  Specifies the size of the track size written, default is 0.5 .
All other arguments are ignored.

Assuming you've downloaded some of the datasets from Zenodo http://doi.org/10.5281/zenodo.3520866, the arguments used to run a sampling is here:

sim1: ./calico-dec2023 --charuco --calibrate --k=8 --perc-ae=0.2 --perc-rp=0.5 --num-threads 24 --input=/home/username/data-calico/sim1/base/ --output=/home/username/data-calico/sim1/result/ --camera-size=40 --track-size=0 --num-pattern=10

mult1: ./calico-dec2023 --charuco --calibrate --k=8 --perc-ae=0.2 --perc-rp=0.5 --num-threads 24 --input=/home/username/data-calico/mult1/base/ --output=/home/username/data-calico/mult1/result/ --camera-size=40 --track-size=0 --num-pattern=10

rot1: ./calico --rotating --input=/home/username/data-calico/rot1/base/ --output=/home/username/data-calico/rot1/result/ --camera-size=40 --track-size=5 --verbose

It is suggested that you generate aruco patterns to use in your own calibrations using the --create-patterns argument.

1. To do so, create an input and output directory.

2. Select whether you will be creating a network (most likely), or rotating case and create the corresponding file network_specification_file.txt or rotate_specification_file.txt detailed in Calibration object specifications.

3. call CALICO using the --create-patterns flag and specify the input and output directories. And example is:

--perc-ae=0.2 --perc-rp=0.5 --num-threads 4 --input=/home/username/datasets/mult-1-base/ --output=/home/username/datasets/mult-1-pattern/ --camera-size=40 --track-size=0.5 --num-pattern=-1 

4. The code create calibration patterns -- in the patterns subdirectory within the output directory. Print and measure the squares. Edit the squareLength_mm parameter in the pattern_square_mmNUMBER.txt files.

As mentioned in Run the image, you start the Docker container from the command line, and then issue commands similar to above. So, start the container running,

sudo docker run -v /home/amy/Data/March/:/docker_dir -it amytabb/calico-dec2023:latest bash

And this will start the container. Suppose we forgot to create a directory for the results.

root@d208fe4482b5:/docker_dir# 

Supposing we forgot to create a directory for the results, we can do so from the terminal here:

root@d208fe4482b5:/docker_dir# mkdir results/

Then, we can call calico. Note that the --src-dir=[STRING] flag is not needed; the paths have already been set to the defaults within the Docker image. For example using the sim-1-base dataset:

root@d208fe4482b5:/docker_dir# calico-dec2023 --input sim-1-base/ --output results/ --network

For most datasets, the input consists of the Image Data and Calibration object specifications.

directory: data Within data are directories, one for each camera. There is no specification on the names, so long at the names are different from each other.

Within the individual camera directories, there are the images comprising the dataset OR folders, external and internal.

Images in the internal folder are only used to refine the intrinsic camera calibration parameters, but not to estimate relative transformations between cameras. In general, I have not found that I needed additional images, but difficult acquisitions contexts may benefit from more images. The images in the external directory, or without folders, in the individual camera directory, are ordered by the time variable referenced in the paper.

By this I mean that the 1st image in the camera0 directory was acquired at a corresponding time as the 1st image in the camera1 directory.

The calibration object consists of a two of more cameras that may or may not be asynchronous, and a number of charuco calibration patterns rigidly attached together to create a calibration rig. The transformations between patterns is not needed -- CALICO computes those transformations.

You will need to include a file called network_specification_file.yaml in the input directory. This file will specify the number of patterns and their characteristics; Here is an example with four charuco boards (from sim1, sim2 datasets:

%YAML:1.0
type: charuco
squaresX: 7
squaresY: 9
squareLength: 45
markerLength: 22
margins: 10
numberBoards: 4
arcCode: 11

The aruco dictionary code arcCode parameter provides the dictionary constant used to generate the aruco markers. numberBoards is the number of calibration patterns used to construct the calibration rig.

After those two parameters, the specifications of the boards squaresX, squaresY, squareLength, and markerLength are needed. The X and Y parameters are the number of squares in the chessboard grid, and squarelength is the size of the chessboard squares in pixels. markerLength is the size of the aruco marker in pixels, squarelength < markerLength.

For each calibration pattern, there will also need to be a corresponding pattern_square_mmNUMBER.txt, where NUMBER is the index of that calibration pattern. (Taking a look at the dataset TODO will likely be helpful here.) Each file consists of one parameter, such as:

squareLength_mm 45

where the parameter is the length of the chessboard squares in the charuco pattern, in millimeters.

** VERY IMPORTANT ** The code does not check for this (at the moment, TODO); each dictionary has an upper limit on how many aruco makrers it can generate (last number in the code DICT_4X4_100 means 100 markers). Ensure that the number of patterns in the X-Y grid does not exceed the number in the aruco dictionary you have selected.

enum PREDEFINED_DICTIONARY_NAME {
    DICT_4X4_50 = 0,
    DICT_4X4_100,
    DICT_4X4_250,
    DICT_4X4_1000,
    DICT_5X5_50,
    DICT_5X5_100,
    DICT_5X5_250,
    DICT_5X5_1000,
    DICT_6X6_50,
    DICT_6X6_100,
    DICT_6X6_250,           //10
    DICT_6X6_1000,          //11  
    DICT_7X7_50,
    DICT_7X7_100,
    DICT_7X7_250,
    DICT_7X7_1000,
    DICT_ARUCO_ORIGINAL,
    DICT_APRILTAG_16h5,     ///< 4x4 bits, minimum hamming distance between any two codes = 5, 30 codes
    DICT_APRILTAG_25h9,     ///< 5x5 bits, minimum hamming distance between any two codes = 9, 35 codes
    DICT_APRILTAG_36h10,    ///< 6x6 bits, minimum hamming distance between any two codes = 10, 2320 codes
    DICT_APRILTAG_36h11     ///< 6x6 bits, minimum hamming distance between any two codes = 11, 587 codes
};

The output is stored in the directory you specified with the --output flag. The following subdirectory structure is created:

cameras-incremental
data
patterns
reconstructed-patterns

The arguments used to call the program are in file arguments-calico.txt.

To view the results, take a look at total_results.txt, which is within the output directory. The quantified results are reported according to three metrics: algebraic error (equation 18 in the paper), reprojection error (equation 19 in the paper), and finally reconstruction accuracy error (rae, equations 18 and 19). RAE is reported by mean, median, and standard deviation. Note that not all calibration pattern points may be reconstructed.

If you're running this code, you probably just want a file showing the calibration of the cameras relative to each other.

The final result is in camera_cali_incremental.txt and has a file format that is similar to, but not exactly like, the Middlebury Multi-View Stereo format. An example of the first three lines of the sim-1 result is:

8
camera_images0 1401.9 0 601.382 0 1402.08 449.69 0 0 1 -0.999983 0.000221258 -0.00585503 -0.000221361 -1 1.69823e-05 -0.00585503 1.82781e-05 0.999983 -336.214 167.961 1503.06 0.00847675 -0.0396309 0 0 0 
camera_images1 1398.49 0 598.732 0 1397.42 448.67 0 0 1 -0.999998 -0.000333189 -0.00195105 0.000332287 -1 0.000462825 -0.0019512 0.000462176 0.999998 666.101 168.9 1496.45 -0.00395854 0.00205396 0 0 0 

The first number in the file is the number of cameras.

Then, on each line, is:

• the directory name for the camera
• k11 k12 k13 k21 k22 k23 k31 k32 k33 (where k11 is the top left entry of the intrinsic camera calibration matrix K, k12 is the top row, second column of K, etc.)
• r11 r12 r13 r21 r22 r23 r31 r32 r33 (where r11 is the top left entry of the rotation matrix R, r12 is the top row, second column of R, etc.)
• t1 t2 t3 (elements of the translation vector t)
• d1 d2 d3 d4 d5 (elements of the distortion vector, property of intrinsic camera calibration)

The camera calibration results are stored in the data subdirectory, and within data, there are directories for each camera. cali_results.txt contains the intrinsic parameters for the camera, and then extNUMBER.img_ext are the original images used for computing the network calibration, with the calibration points identified and undistorted using the intrinisic camera calibration parameters. These images can be checked in case of very poor calibrations.

cameras-incremental holds the calibration results. Within that directory, variables.txt gives the values for individual variables.

EquationNUMBER.png are image files for each foundational relationship. The difference between the image point and reprojected point is shown as a line. Ideally, the difference a small, so you may see a small point. There are rings around the k points that will be used for the reprojection error minimization in step 5.

Camera results are recorded by storing them as .ply files, which can be opened in any 3D model viewer. I use Meshlab, which is free.

It is possible to view the calibration output in directory cameras-incremental. The camera files are within those directories as single_cameras. You can load all of the cameras with all.ply, or load them individually by number.

Alternatively, if you are interested in seeing the movement of the cameras with respect to the calibration objects, camera models are in individual files within the cameras-incremental directory.

The names follow the pattern:

c0_time0.ply
c0_time1.ply
c0_time2.ply
.
.
.
track0.ply

where c0_time0.ply corresponds to "camera 0 at time 0". File track0.ply consists of (generally) line segments connecting the camera locations over time.

Camera and track sizes can be adjusted to increase visability through the --camera-size and --track-size flags.

Reconstructed patterns are written in the reconstructed-patterns directory.

RAE, reconstruction accuracy error, is computed assuming that the pattern has been transformed back to the world coordinate system. In the camera calibration literature, and in the conventions I used in creating CALICO, the world coordinate system is at (0,0,0) and the pattern's points are distributed on the X-Y plane.

To assess the difference between the ideal world coordinate system (as defined by a pattern) and the computed transformation, there are 3D model files that again one can load in their 3D model viewer of choice.

• world-ideal_patternNUMBER.ply is the coordinate system as defined by the calibration pattern,
• patternNUMBERreconstruction-of-id-pattern-points.ply is the reconstruction computed by CALICO, and ideally should overlap world-ideal_patternNUMBER.ply,
• patternNUMBERusing-pattern-transformations.ply is the estimate of the pattern's location relative to the other patterns. For dataset sim-1, the patterns for the sides of a box.

Throughout, NUMBER is the pattern number. If the pattern transformation is not estimated, which does happen, the transformation will be the identity.

(Here's a listing of files for the sim1 dataset.)

pattern0reconstruction-of-id-pattern-points.ply
pattern0using-pattern-transformations.ply
pattern1reconstruction-of-id-pattern-points.ply
pattern1using-pattern-transformations.ply
pattern2reconstruction-of-id-pattern-points.ply
pattern2using-pattern-transformations.ply
pattern3reconstruction-of-id-pattern-points.ply
pattern3using-pattern-transformations.ply
world-ideal_pattern0.ply
world-ideal_pattern1.ply
world-ideal_pattern2.ply
world-ideal_pattern3.ply

• write documentation for the ground truth comparison function.
• Check for bad input : the number of markers specified in the files is greater than the size of the aruco dictionary.
• Check for bad input : alert if markerLength is > squareLength Verbose and write: Add another flag for writing output, as lots of images are currently written.