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Detect calibration boards in observed camera images

$ mrgingham /tmp/image*.jpg

# filename x y level
/tmp/image1.jpg - -
/tmp/image2.jpg 1385.433000 1471.719000 0
/tmp/image2.jpg 1483.597000 1469.825000 0
/tmp/image2.jpg 1582.086000 1467.561000 1

$ mrgingham /tmp/image.jpg |
  vnl-filter -p x,y |
  feedgnuplot --domain --lines --points --image /tmp/image.jpg

[ image pops up with the detected grid plotted on top ]

$ mrgingham /tmp/image.jpg |
  vnl-filter -p x,y,level |
  feedgnuplot --domain
              --with 'linespoints pt 7 ps 2 palette'
              --tuplesizeall 3 --image /tmp/image.jpg

[ fancy image pops up with the detected grid plotted on top, detections
  colored by their decimation level ]


As of today (2022-02-27), mrgingham is included in the bleeding-edge versions of Debian and Ubuntu. So if you’re running at least Debian/testing or the not-yet-published Debian 12 (bookworm) or Ubuntu 22.04 (jammy), you can simply

apt install mrgingham libmrgingham-dev

to install the standalone tool and the development library respectively. For older Debian and Ubuntu distros, packages are available in the mrcal repositories. Please see the mrcal installation page.

If running any other distro, you should build mrgingham from source. First, make sure all the build-time dependencies are installed. These are listed in the =debian/control= file:

Build-Depends: ...,

On a Debian-based distro you can:

sudo apt install \
 libopencv-dev   \
 libboost-dev    \
 pkg-config      \
 mawk            \
 perl            \
 python3-all     \
 python3-all-dev \

Replace the package names with their analogues on other distros. Once the dependencies are installed, you


and then the tool can be invoked with



Both chessboard and a square grid of circles are supported. Chessboard are the strongly preferred choice, since the circles cannot produce accurate results: we care about the center point, which we are not directly observing. Thus with closeup and oblique views, the reported circle center and the real circle center could be very far away from each other. Because of this, more work was put into the chessboard detector. Use that one. Really.

These are both nominally supported by OpenCV, but those implementations are slow and not at all robust, in my experience. The implementations here are much faster and work much better. I do use OpenCV here, but only for some core functionality.

Currently mrgingham looks for a square grid of points, with some user-requestable width. Rectangular grids are not supported at this time.


These tools work in two passes:

  1. Look for “interesting” points in the image. The goal is to find all the points we care about, in any order. It is assumed that
    • there will be many outliers
    • there will be no outliers interspersed throughout the points we do care about (this isn’t an unreasonable requirement: areas between chessboard corners have a solid color)
  2. Run a geometric analysis to find a grid in this set of “interesting” points. This will throw out the outliers and it will order the output

If we return any data, that means we found a full grid. The geometric search is fairly anal, so if we found a full grid, it’s extremely likely that it is “right”.

Once again: the current implementation of mrgingham detects only complete chessboards.


This is based on the feature detector described in this paper:

The authors provide a simple MIT-licensed implementation here:

This produces an image of detector response. This library then aggregates these responses by looking at local neighborhoods of high responses, and computing the mean of the position of the points in each candidate neighborhood, weighted by the detector response.

As noted earlier, I look for a square grid, 10x10 points by default. Here that means 10x10 internal corners, meaning a chessboard with 11 squares per side. To ensure robust detections, it is recommended to make the outer squares of the chessboard wider than the inner squares. This would ensure that we see exactly 10 points in a row with the expected spacing. If the outer squares have the same size, the edge of the board might be picked up, and we would see 11 or 12 points instead.

A recommended 10x10 pattern can be printed from this file: chessboard.10x10.pdf. And a recommended 14x14 pattern can be printed from this file: chessboard.14x14.pdf. The denser chessboard containts more data, so fewer observations will be required for convergence of the calibration algorithm. But a higher-res camera is required to reliably detect the corners. A simple tool to generate these .pdf files is included in the mrgingham repository. To make an NxM chessboard figure do make chessboard.NxM.pdf in the mrgingham source tree. N and M must be even integers. Note: today mrgingham requires that N = M=, but eventually this may be lifted, so this tool does not have this requirement.


This isn’t recommended, and exists for legacy compatibility only

The circle finder does mostly what the first stage of the OpenCV circle detector does:

  1. Find a reasonable intensity threshold
  2. Threshold the image
  3. Find blobs
  4. Return centroid of the blobs

This is relatively slow, can get confused by uneven lighting (although CLAHE can take care of that), and is inaccurate: nothing says that the centroid of a blob came from the center of the circle on the calibration board.

Output representation

The mrgingham tool produces its output in a vnlog text table. The columns are:

  • filename: path to the image on disk
  • x, y: detected pixel coordinates of the chessboard corner
  • level: image level used in detecting this corner. Level 0 means “full-resolution”. Level 1 means “half-resolution” and that the noise on this detection has double the standard deviation. Level 2 means “quarter-resolution” and so on.

If no chessboard was found in an image, a single record is output:

filename - - -

The corners are output in a consistent order: starting at the top-left, traversing the grid, in the horizontal direction first. Usually, the chessboard is observed by multiple cameras mounted at a similar orientation, so this consistent order is consistent across cameras.

However, if some cameras in the set are rotated, their observed chessboard corners will not be consistent anymore: the first corner will be “top-left” in pixel coordinates for both, which is at the top of the chessboard for rightside-up cameras, but the bottom of the chessboard for upside-down cameras. This situation is resolved with the mrgingham-rotate-corners tool. It post-processes mrgingham output to reorder detections from rotated cameras. See the manpage of that tool for more detail. Eventually the implementation could be extended to be able to uniquely identify each corner, obviating the need for mrgingham-rotate-corners, but we’re not there today.


The user-facing functions live in mrgingham.hh. Everything is in C++, mostly because some of the underlying libraries are in C++. All functions return a bool to indicate success/failure. All functions put the destination arguments first. All functions return the output points in std::vector<mrgingham::PointDouble& points_out>, an ordered list of found points. The inputs are one of

  • An image filename
  • An OpenCV matrix: cv::Mat& image
  • A set of detected points, that are unordered, and are a superset of the points we’re seeking

The prototypes:

namespace mrgingham
    bool find_circle_grid_from_image_array( std::vector<mrgingham::PointDouble>& points_out,
                                            const cv::Mat& image );

    bool find_circle_grid_from_image_file( std::vector<mrgingham::PointDouble>& points_out,
                                           const char* filename );

    bool find_chessboard_from_image_array( std::vector<mrgingham::PointDouble>& points_out,
                                           const cv::Mat& image,
                                           int image_pyramid_level = -1 );

    int  find_chessboard_from_image_file( std::vector<mrgingham::PointDouble>& points_out,
                                          const char* filename,
                                          int image_pyramid_level = -1 );

    bool find_grid_from_points( std::vector<mrgingham::PointDouble>& points_out,
                                const std::vector<mrgingham::Point>& points );

The arguments should be clear. The only one that needs an explanation is image_pyramid_level:

  • if image_pyramid_level is 0 then we just use the image as is.
  • if image_pyramid_level > 0 then we cut down the image by a factor of 2 that many times. So for example, level 3 means each dimension is cut down by a factor of 2^3 = 8
  • if image_pyramid_level < 0 then we try several levels, taking the first one that produces results


There’re several included applications that exercise the library. The mrgingham-... tools are distributed, and their manpages appear below. The test-... tools are internal.

  • mrgingham takes in images as globs (with some optional manipulation given on the cmdline), finds the grids, and returns them on stdout, as a vnlog
  • mrgingham-observe-pixel-uncertainty evaluates the distribution of corner detections from repeated observations of a stationary scene
  • mrgingham-rotate-corners corrects chessboard detections produced by rotated cameras by reordering the points in the detection stream
  • test-find-grid-from-points ingests a file that contains an unordered set of points with outliers. It the finds the grid, and returns it on stdout
  • test-dump-chessboard-corners is a lower-level tool that just finds the chessboard corner features and returns them on stdout. No geometric search is done.
  • test-dump-chessboard-corners similarly is a lower-level tool that just finds the blob center features and returns them on stdout. No geometric search is done.


There’s a test suite in test/ It checks all images in test/data/*, and reports which ones produced no data. Currently I don’t ship any actual data. I will at some point.



    mrgingham - Extract chessboard corners from a set of images

      $ mrgingham image*.jpg

      # filename x y level
      image1.jpg - -
      image2.jpg 1385.433000 1471.719000 0
      image2.jpg 1483.597000 1469.825000 0
      image2.jpg 1582.086000 1467.561000 1

      $ mrgingham image.jpg |
        vnl-filter -p x,y,level |
        feedgnuplot --domain \
                    --with 'linespoints pt 7 ps 2 palette' \
                    --tuplesizeall 3 \
                    --image image.jpg

      [ image pops up with the detected grid plotted on top, detections color-coded
        by their decimation level ]

    The mrgingham tool detects chessboard corners from images stored on
    disk. The images are given on the commandline, as globs. Each glob is
    expanded, and each image is processed, possibly in parallel if -j was

    The output is a vnlog text table (<>
    containing columns:

    - filename: path to the image on disk

    - x, y: detected pixel coordinates of the chessboard corner

    - level: image level used in detecting this corner. Level 0 means
    "full-resolution". Level 1 means "half-resolution" and that the noise on
    this detection has double the standard deviation. Level 2 means
    "quarter-resolution" and so on.

    If no chessboard was found in an image, a single record is output:

      filename - - -

    The corners are output in a consistent order: starting at the top-left,
    traversing the grid, in the horizontal direction first. Usually, the
    chessboard is observed by multiple cameras mounted at a similar
    orientation, so this consistent order is consistent across cameras.

    By default we look for a CHESSBOARD, not a grid of circles or Apriltags
    or anything else. By default we apply adaptive histogram equalization
    (CLAHE), then blur with a radius of 1. We then use an adaptive level of
    downsampling when looking for the chessboard. These defaults work very
    well in practice.

    For debugging, pass in --debug. This will dump the various intermediate
    results into /tmp and it will report more stuff on the console. Most of
    the intermediate results are self-plotting data files. Run them. For
    debugging sequence candidates, pass in --debug-sequence x,y where 'x,y'
    are the approximate image coordinates of the start of a given sequence
    (corner on the edge of a chessboard. This doesn't need to be exact;
    mrgingham will report on the nearest corner

    See the mrgingham project documentation for more detail:


        Globs specifying the images to process. May be given more than once

        Finds circle centers instead of chessboard corners. Not recommended
      --gridn N
        Requests detections of an NxN grid of corners. If omitted, N defaults to 10
        Controls image preprocessing. Unless given, we will apply adaptive histogram
        equalization (CLAHE algorithm) to the images. This is EXTREMELY helpful if
        the images aren't illuminated evenly; which applies to most real-world
      --blur RADIUS
        Controls image preprocessing. Applies a gaussian blur to the image after the
        histogram equalization. A light blurring is very helpful with CLAHE, since
        it produces noisy images. By default we will blur with radius = 1. Set to <=
        0 to disable
      --level LEVEL
        Controls image preprocessing. Applies a downsampling to the image (after
        CLAHE and --blur, if those are given). Level 0 means 'use the original
        image'. Level > 0 means downsample by 2**level. Level < 0 means 'try several
        different levels until we find one that works. This is the default.
        Disables corner refinement. By default, the coordinates of reported corners
        are re-detected at less-downsampled zoom levels to improve their accuracy.
        If we do not want to do that, pass --no-refine
      --jobs N
        Parallelizes the processing N-ways. -j is a synonym. This is just like GNU
        make, except you're required to explicitly specify a job count.
        If given, mrgingham will dump various intermediate results into /tmp and it
        will report more stuff on the console. The output is self-documenting
        If given, we report details about sequence matching. Do this if --debug
        reports correct-looking corners (all corners detected, no doubled-up
        detections, no detections inside the chessboard but not on a corner)


    mrgingham-observe-pixel-uncertainty - Evaluate observed point
    distribution from stationary observations

      $ observe-pixel-uncertainty '*.png'
        Evaluated 49 observations
        mean 1-sigma for independent x,y: 0.26

      $ mrcal-calibrate-cameras --observed-pixel-uncertainty 0.26 .....
      [ mrcal computes a camera calibration ]

    mrgingham has finite precision, so repeated observations of the same
    board will produce slightly different corner coordinates. This tool
    takes in a set of images (assumed observing a chessboard, with both the
    camera and board stationary). It then outputs the 1-standard-deviation
    statistic for the distribution of detected corners. This can then be
    passed in to mrcal: 'mrcal-calibrate-cameras
    --observed-pixel-uncertainty ...'

    The distribution of the detected corners is assumed to be gaussian, and
    INDEPENDENT in the horizontal and vertical directions. If the x and y
    distributions are each s, then the LENGTH of the deviation of each pixel
    is a Rayleigh distribution with expected value s*sqrt(pi/2) ~ s*1.25


      input                 Either 1: A glob that matches images observing a
                            stationary calibration target. This must be a GLOB. So
                            in the shell pass in '*.png' and NOT *.png. These are
                            processed by 'mrgingham' and the arguments passed in
                            with --mrgingham. Or 2: a vnlog representing corner
                            detections from these images. This is assumed to be a
                            file with a filename ending in .vnl, formatted like
                            'mrgingham' output: 3 columns: filename,x,y

      -h, --help            show this help message and exit
      --show {geometry,histograms}
                            Visualize something. Arguments can be: "geometry":
                            show the 1-stdev ellipses of the distribution for each
                            chessboard corner separately. "histograms": show the
                            distribution of all the x- and y-deviations off the
      --mrgingham MRGINGHAM
                            If we're processing images, these are the arguments
                            given to mrgingham. If we are reading a pre-computed
                            file, this does nothing
      --num-corners NUM_CORNERS
                            How many corners to expect in each image. If this is
                            wrong I will throw an error. Defaults to 100
      --imagersize IMAGERSIZE IMAGERSIZE
                            Optional imager dimensions: width and height. This is
                            optional. If given, we use it to size the "--show
                            geometry" plot


    mrgingham-rotate-corners - Adjust mrgingham corner detections from
    rotated cameras

      # camera A is rightside-up
      # camera B is mounted sideways
      # cameras C,D are upside-down
      mrgingham --gridn N                \
        'frame*-cameraA.jpg'             \
        'frame*-cameraB.jpg'             \
        'frame*-cameraC.jpg'             \
        'frame*-cameraD.jpg' |           \
      mrgingham-rotate-corners --gridn N \
        --90 cameraB --180 'camera[CD]'

    The mrgingham chessboard detector finds a chessboard in an image, but it
    has no way to know whether the detected chessboard was upside-down or
    otherwise rotated: the chessboard itself has no detectable marking to
    make this clear. In the usual case, the cameras as all mounted in the
    same orientation, so they all detect the same orientation of the
    chessboard, and there is no problem. However, if some cameras are
    mounted sideways or upside-down, the sequence of corners will correspond
    to different corners between the cameras with different orientations.
    This can be addressed by this tool. This tool ingests mrgingham
    detections, and outputs them after correcting the chessboard
    observations produced by rotated cameras.

    Each rotation option is an awk regular expression used to select images
    from specific cameras. The regular expression is tested against the
    image filenames. Each rotation option may be given multiple times. Any
    files not matched by any rotation option are passed through unrotated.


This is maintained by Dima Kogan <>. Please let Dima know if something is unclear/broken/missing.


This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version.

Copyright 2017-2021 California Institute of Technology

Copyright 2017-2021 Dima Kogan (


Chessboard corner-finder for a camera calibration system






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