Calibration Target Printing
Checkerboard

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What Is Camera Calibration? - Camera Intrinsics & Extrinsics

Intrinsic and extrinsic parameters of a camera explained in 5 minutes


Checkerboard Targets

Are you looking to calibrate your cameras to be as accurate as possible? Our checkerboard calibration targets are printed on a rigid, premium 1/8" Dibond, making them the perfect calibration boards for camera calibration. Print checkerboard targets direct to substrate with a true matte finish, allowing easy detection in your computer vision pipeline.

Helpful Ordering Tips

  1. Order the exact sizes that match your file's artboards; use the keyboard to add decimals if needed.
  2. Upload your own custom files, vector PDF files are preferred for optimal results.
  3. Full-scale files are required to avoid the files being scaled up or down to fit the images on the board's order size. Need a PDF? Don 't have a ready file? Use our online tool to generate patterns.
  4. During the proofing process, always double-check and compare the file size to each board order size (we are not responsible for artwork scaling if the incorrect board sizes are ordered and proofs are approved incorrectly).
  5. If you have questions about the artwork uploaded to an order; please call, email, or start a live chat before sending the art files to be made. Production will begin within 10 mins of approval of artwork. Once production begins, we can not remove approved art files from the production line.

Camera Cailbration Checkerboard, Print-Out Checkerboard, Checkerboard Pattern

While there are many patterns photographers can use, checkerboard calibration is a very popular selection.

With the ease of determining such pattern on images and how straightforward it is to localize the corners of the squares of a checkerboard, this is no surprise.

This guide allows you to familiarize yourself with the camera calibration methods, its purpose, the usage of a checkerboard calibration, and more.

What Is Camera Calibration?

Camera calibration or geometric camera calibration, or camera resectioning, refers to estimating extrinsic and intrinsic parameters of a pinhole camera. Typically, the representation of this camera parameter is in a 3×4 matrix referred to as the camera matrix.

Intrinsic parameters encompass a camera's internal characteristics, for example, focal length, distortion, image center, and skew. Extrinsic parameters cover the camera's world coordinates.

Determining intrinsic parameters is crucial in 3D computer vision since it permits you to approximate the scene's structure within Euclidean space. It also eliminates lens distortion, a contributing factor to reduced accuracy.

You can either use a totally automated assisted calibration or manually collect images captured then process them.

The Calibration Process

Almost similar steps work when calibrating two or more cameras and one camera. Here is a quick breakdown of the camera calibrating process:

  • Choose a pattern. Download it or create your own.
  • Mount your pattern on a flat, rigid surface
  • Take images of your checkerboard target in various orientations and distances.
  • Download photos to compute and pick the above images that are in focus
  • Automatically detect the target and compute the parameters using provided examples.
  • Move your calibration file to a secure location.

While you can use any calibration target, it is essential to note that a checkerboard one tends to provide slightly more accuracy.

Camera Calibration with OpenCV

OpenCV (Open Source Computer Vision Library) is an open-source computer vision library that contains many different functions for computer vision and machine learning. It was created by Intel and originally released in 2000. To decide a 3D point's projection onto an image plane, you should first transform this point from the world coordinate system to your camera's coordinate system with the extrinsic parameters (translation [t] and rotation [R]).

Next, project the point onto an image plane using your camera's intrinsic parameters (In 3D computer graphics, the image plane is that plane in the world which is identified with the plane of the display monitor used to view the image that is being rendered. It is also referred to as screen space. If one makes the analogy of taking a photograph to rendering a 3D image, the surface of the film is the image plane)

Following figure shows the example of algorithm relating 3D points (Xw, Yw, Zw) in world coordinates to its projection (u, v) in the image coordinates are shown below.

3D points

Where P represents the 3×4 Projection matrix that has two parts

  • The intrinsic matrix (K) containing intrinsic parameters
  • the extrinsic parameter (R | t) includes the R- 3 x 3 rotation matrix and the translation vector t (3 x 1).
intrinsic matrix
The intrinsic matrix K represents the upper triangular.
K represents the upper triangular
where,
  • fx, fy represent the y and x focal lengths
  • cx, and cy is the optical centers of y and x coordinates. Using an images center is typically an adequate approximation.
  • Gamma represents the skew between the axes, which is typically 0.

The Purpose of Camera Calibration

The process aims to detect the 3×3 rotation matrix (R), 3×1 translation vector (t), and the 3×3 matrix K using known 3D points (Xw, Yw, Zw) and their image coordinates (u, v).

The camera is termed as calibrated upon attaining extrinsic and intrinsic parameter values.

In simple terms, the camera calibration algorithm contains these inputs and outputs.

  • Inputs: A set of images captured containing points with the known 3D world coordinates and 2D image coordinates
  • Outputs: The translation, rotation, and 3×3 intrinsic camera matrix for every image captured.

The camera's intrinsic matrix lacks skew parameters in OpenCV. Therefore, the matrix is as the following figure shows.

matrix assumes form

Text goes here ...

Camera Calibration Methods

Below are the popular kinds of camera calibration.

Calibration Patterns

The best method to calibrate cameras when you have total control of the imaging process is by taking several photos of a pattern or object with known dimensions from various viewpoints. We can either use a checkerboard calibration pattern or circular patterns.

Why Is the Checkerboard Calibration Popular?

Checkerboard calibration patterns are unique and easy to decipher in an image. Moreover, the corners of squares on a checkerboard are suitable for localizing them given their steep gradients in two directions.

Another factor is the relation of these corners, given they lie on the intersection point of checkerboard lines. All these reasons aid in the robust coordinates of the corners of squares within a checkerboard pattern.

Geometric Clues

This is a suitable method when there are geometric clues within a scene, for example, vanishing points and straight lines.

Deep Learning-Based Method

This method allows you camera calibration when there is very minimal control over the imaging process (e.g., when only a single image of the scene exists)

Step By Step Analysis of Camera Calibration

We can split this process into four steps, as discussed below.

Definition of Real World Coordinates Using Checkboard Pattern

Let us fixate the world coordinates using a checkerboard pattern attached to a wall. The corners of the checkerboard's square represent the 3D points.

We can select any corner as the starting point of the world's coordinates. While the Y and X axes are along the wall, the Z-axis flows perpendicularly. Therefore, all points within the checkerboard fall within the XY plane.

We calculate camera parameters using known 3D points (Xw, Yw, Zw) with their respective pixel locations (u,v) on the image while calibrating.

We take images of the pattern with known dimensions from multiple different orientations. With the world coordinate system attached to the checker board and all corner points lying on a plane, we can randomly select Zw for each point to be zero.

Given the equal spacing of points on a checkerboard, we can quickly determine each 3D point coordinate by picking a reference point (0, 0) and getting the remaining points with respect to it.

Take Many Checkerboard Images from Various Viewpoints

The second step involves maintaining the checkerboard in a stationary position and adjusting your camera location for multiple images captured.

Another way to approach this is by keeping your camera fixed while adjusting the pattern to take images from multiple orientations.

Determination of the checkerboard's 2D Coordinates

Given we have multiple images captured and know the 3D position of the checkerboard's points in the world coordinate system, we should now detect the 2D pixel locations of the corners in the pictures.

Identifying Corners

OpenCV comes with findChessboardCorners, an inbuilt function that searches for a checkerboard then decides the corners' coordinates. Following figure bellow is the example usage in a code block:
C++
Identifying checkerboard corners in python C++
Python
Identifying checkerboard corners in python

In which,

  • Image is the source chess board view (must be a colored image or 8-bit grayscale image)
  • patternSize, which denotes how many inner corners on every chessboard, column and row, and column
  • Corners signify detected corners' output array.
  • flags which are the numerous operational flags

Refining Checkerboard Corners

To get a good checkerboard pattern, we need to detect the corners' locations in subpixel accuracy. The cornerSubPix function registers the original image and the corners' locations then searches for the most suitable corner location close to the original location.

The algorithm involves iteration and therefore needs specification of the criteria for termination.

C++
 Refining checkerboard corners in C++
Python
Refining checkerboard corners in Python

In which,

  • Image refers to the input image.
  • Corners are the input corners' initial coordinates and the refined coordinates given for output.
  • winSize is half the side length of your search window
  • zeroZon refers to the half-size of the dead region within the search zone's center, of which the totals don't form part of the following algorithm. The zeroZone is applicable sometimes when avoiding an autocorrelation matrix/ possible singularities. (-1,-1) values indicate that such a size is non-existent.
  • Criteria refer to the basis for the termination of the corner refinement iterative procedure. This means that the corner position refinement process halts after the angular position adjusts by less than criteria.epsilon in an iteration or post the criteria.maxCount iterations.

Calibrate Camera

The last checkerboard calibration step involves passing 3D points in the world coordinate system with their 2D locations across all images to the calibrateCamera method of OpenCV. The implementation relies on Zhengyou Zhang's article. Its Mathematics is quite challenging and needs some basics in linear algebra.

Below is calibrateCamera's syntax example:

C++
Python
Calibrate camera in Python

In which,

  • objectPoints refer to a vector of the 3D image where the exterior vector has its number of elements similar to the pattern views.
  • imagePoints that is the 2D image points' vector.
  • imageSize, which represents what it implies
  • cameraMatrix which is the internal camera matrix
  • distCoeffsthat refers to the coefficient of the lens distortion
  • rvecs, which is a rotation denoted as a 3×1 vector: the vector's size indicates its rotation angle, whereas its direction signifies the rotation axis.
  • tvecs, which is a 3×1 vector that expresses displacement as is like the rvecs

What Is the Diffrence Between Checkboard Targets and Checkerboard Maker Targets?

Accurate calibration of cameras is essential and requires picking the right checkerboard target. While there are various targets to pick from, checkerboard calibration patterns and checkerboard maker targets are some of the most popular.

So what are their differences?

Checkerboard Targets

Chessboard target

The pixel binarization of an image captured by the camera image and determination of its quadrilaterals (black chessboard fields) helps detect chess board corner candidates. Image binarization is the transformation of document image into bi-level document image. Image pixels are separated into dual collection of pixels, i.e. black and white pixels. The main goal of image pixel binarization is the segmentation of document into foreground text and background.

A pixel separation process keeps quads of a particular size organized in an orderly grid structure with dimensions similar to user-specified requirements.

Upon pattern detection, it is straightforward to detect corner locations with extra high accuracy. This is due to corners being typically infinitely small and therefore unbiased under lens distortion or perspective transformations.

The whole chessboard needs to be visible in OpenCV for all images for it to get detected. This makes it challenging to attain details about the farthest ends of images. These image areas are vital for attaining particulars since they properly restrict the lens distortion model.

Upon the checkerboard's detection, you can perform subpixel refinement to detect saddle points with accuracy. This uses similar gray values of pixels in a particular corner position. Moreover, it is more accurate than what you get with integer pixel positions.

For calibration targets to be rotation-invariant, columns should be an odd number while rows even or vice versa. If, for example, both rows and columns are odd, you get a rotation ambiguity of 180-degrees.

With calibration of a single camera, rotation ambiguity is not a big deal. However, during stereo calibration (two or more cameras), the same is unacceptable.

Checkerboard Marker Targets

Checkerboard marker targets are from the traditional checkerboard. They can also utilize similar detection algorithms which software such as Halcon and PhotoModeler can help with.

Checkerboard marker targets contain three circles in the middle. These circles facilitate absolute referencing even when you don't have a full view of the checker board, provided the circles fall within all the images captured.

For this reason, information from an image's periphery can get included. Consequently, it ensures the validity of the fitted lens model in those sections of the image.

For many calibration tasks involving various cameras, this target brings all the advantages of a coded target like the CharuCo target.

Checkerboard marker targets are compatible with OpenCV 4.5+.

Final Thoughts

In both stereo calibration and single-camera calibration, a checkerboard pattern offers an easy way to complete the calibration process. While complicated illumination presents a challenge in camera calibration, this pattern serves as a suitable solution for high-precision calibration. Checkerboard calibration method is improved for high-precision calibration under complicated illumination.

Image Source: Screenshots from https://learnopencv.com/camera-calibration-using-opencv/

Side view of Dibond

Dibond Features

Dibond signage has forever been an industry standard for indoor and outdoor business signs. The material is water, weather, warp resistant and rust proof. It's ultra flat and rigid structure makes Dibond the perfect material for these kind of targets.

  • Light weight
  • Ultra flat surface
  • Anti-reflective surface (flood white finish) pitch black on pure white
  • Rigid and sturdy
  • Water, weather & rust proof

Technical Specifications

  • Material Thickness: .125"
  • Panel Type: Aluminium Composite Panel
  • Temperature Range: from -50°C to +80°C
  • Fire Classification: CLASS P/0/1
  • Physical Weight: 0.78125 lbs per ft.²

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6 months ago by (WA, US)

On second try the board was printed correctly and arrived without damage. I was told on the phone that it would be packaged with a wood frame. But it was basically packaged the same as the previous order which arrived bent. We were just lucky this time that it came through shipping still flat.


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Everything came perfectly and very fast. I worked directly with a member of the team to ensure the file I provided was correct. Thank you very much for all the help.


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8 months ago by (IL, US)

My experience with foamcoreprint was perfect. I had an issue with my product because I provided a non vector image for my calibration. I reached out and Jennifer made it right by providing me with an appropriate vector file and resent out the product in the same day, fixing my mistake. They didn't have to do this but they went above and beyond. I would recommend this product to anyone and if you're unsure about what calibration file to use, reach out to them and they can answer quickly.


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Frequently asked Questions

FAQ

It is a physical object which consists of a specified calibration pattern and whose function is to act as a standard in the measurement and adjustment of the color responsiveness of instruments. The process requires very high accuracy to enable transformation generation with a similar degree of precision.

It is a type of calibration target used in the process of calibrating cameras when taking pictures. It is usually made up of black and white squares that are arranged on a square grid so that they create alternating rows with one black square followed by one white square, then another black square, etc.

These targets are used to calibrate the sensors in a camera. This is done by taking multiple pictures of a checkerboard with the sensor and then comparing them against one another to find out how far off they are from being perfectly aligned. Created by Zhang camera calibration methods involving using fabricated 3D apparatus with painted checkerboard patterns, like two orthogonal planes hinged together. With this technique, the camera records the projection of a 3d scene onto a 2D image plane. As such, it's easy to determine the camera parameters with a camera focus chart.

The most common industry to use a checkerboard calibration target is the military. For soldiers to be able to see at night, they need equipment that can project an image on their retinas for them to be able to see better. These targets are used because they have high contrast, and it's easy for people with normal vision to detect changes in brightness.
The benefits of checkerboard calibration targets are that they allow for the measurement of distortion, which is the bending or stretching of an image as it travels through a lens system. This distortion can make images appear distorted and sometimes even unrecognizable. A checkerboard calibration pattern allows this to be measured by taking two pictures with one camera at different angles relative to another. The difference in these measurements will give you information about how much distortion has occurred. If your lenses are not already calibrated, you should have them checked out before purchasing new ones.

Everything Foam Core Print offers is manufactured to spec or "custom to order," meaning the clients selects the exact finish size down to 100th of an inch. We can manufacture targets as small as 4x4" and as large on one sheet at 48x96 on the Dibond panel.

Standard turn around for these targets is 3 business days and is based on the approval of the art file for the order, not the time of purchase. We do offer next day turnaround as well as same day production. The cut off time for production to begin is 10am PST for "standard" 3 day turnaround, 8am for next day & same day production. The website is fully automated and will generate pricing when you add items to cart so the best way to get pricing is to add all items to your cart and "proceed to checkout" to update your zip code for shipping & turnaround options for grand total pricing. 

Yes, they are water, rust and weatherproof. We direct print onto the face of the Dibond also known as "ACM" at 1000 dpi (dots per inch) for the longest lasting high-resolution print quality. See more info the Dibond material read our artical What are Dibond Signs? Or visit 3A Composites for downloadable full spec sheets.

All products ordered from this category page will automatically get a "flood white" true matte finish. It's this anti-reflective surface "flood white" authentic matte finish that allows for easy detection in your computer vision pipeline because of its optical performance and physical robustness.

The physical weight (.125" Dibond) is 0.78125 lbs per ft.². The formula for weight calculation on your specif dimension product can be figured by multiplying your length x width divided by 144 = Your Physical Weight.

Dibond is a trademarked brand of aluminum composite material. Dibond signage comprises two sheets of aluminum, plastic, or PVC with a layer of polyethylene sandwiched in between. The front, back, and polyethylene core have been sealed with an adhesive, creating a tight, long-lasting bond. Read more about What you need to know about Dibond signs.

ACM (aluminum composite material) is considered off-brand or "generic." Dibond is a trademarked brand of aluminum composite material manufactured by 3A Composites. Foamcoreprint.com only uses genuine Dibond in the manufacturing process.

Dibond's lifespan can vary depending on five key factors. But a general rule of thumb is 5-10 years 

  1. Harsh or extreme weather
  2. How much sunlight exposure your sign has and how often
  3. How often is there salt on the ground from snowfall
  4. The colors selected for the design "Reds and bright oranges often fade first."
  5. Natural elements; hurricanes, tornados, heavy snow, flooding, and hail

radial bend substrate rounded cornersRounded corners refer to the finish of the physical board itself. The edges will have a nice straight cut finish without rounded corners, where round allows smooth rounded corners. The measurements refer to the corners' severity or degrees (radial bend). Rounded corner sizes from less to more dramatic corners;

  • 3/8""
  • 1/4"
  • 1/2" standard
  • 3/4"
  • 1"

No problem! That's is considered a "special" cut option. There are some additional steps for artwork set to run properly through production. See the step by step tutorial on How To Set Up Cut Files. Need help setting up your files for a project? Feel feel to start a live chat or email with the details of your project to get pricing today. 

A Cut option is NOT required; it is a unique finishing option for shapes other than squares or rectangles, drill holes, or a particular size or placement.

  • Special-Cut (custom shape, inside and outside cuts are okay) ** requires additional art set up; check out How to Set Up-Cut Files.

Yes, you can. While Dibond is fairly easy to drill through with the proper home drill and metal bits It is not recommended. Start a live chat and ask a rep about our "special cut" finish option!

No probelm at all! We offfer a free online checkerboard pattern generator to help you create images designed to your owns specific checkerboard calibration requirements.

There are many ways to mount and hang camera calibration targets and Dibond signs; Here is a list of a few hanging methods.

  • Screws and Bolts
  • Flush mount on a wall with drill holes
  • French cleats
  • Hang on walls with 3m adhesive strips or double side Velcro tape
  • Double-sided acrylic VHB tape (great for long terms use)
  • 3M adhesive-backed hooks

File types accepted for checkerboard calibration: Photoshop (PSD, TIFF, EPS, PDF, JPEG, PNG, SVG) **special cut require Illustrator set up (AI, PDF, with all fonts outlined) Any other graphic program capable of creating a PDF, TIFF, EPS, JPEG, PNG, SVG file. However, The best file formats are PDF and AI files. Vector PDFs are our preferred file format. Vector files are created with shapes and colors and will always print at 300dpi at any scale. Check out our free online checkerboard calibration pattern generator and start making vector PDF patterns today! 

There is always a lifespan on any product. If the products are cared for, cleaned, stored away correctly, they will last many years. Our checkerboard calibration techniques use UV-coated permanent LED inks are designed to hold up over time to sunlight. The more direct contact with the daylight your prints have will impact the longevity of your prints. Generally 3-5 years before you notice sunfading to the naked eye. 

Yes, you can print whatever file you like on the back. All pricing is square-foot based; pricing will not change based on the number of uploaded artworks.

Cleaning these targets is simple and very easy. Here is a list of things you'll need along with instructions;

  • Two microfiber cloths
  • One medium-size bowl
  • Dish soap (dove works great)
  • Hot or warm water, a bucket would be great.

Step by Step Instructions

  1. Use the first microfiber cloth and warm water to wash off any easy-to-remove dirt.
  2. Place an empty bowl next to your target.
  3. Add dish soap into the bowl and add warm water.
  4. Soak the microfiber cloth in the soap water and gently wipe down the checker board. 
  5. Be sure not to rub or wipe too hard; pay attention not to scratch the surface. 
  6. Take your second and final microfiber cloth and dry off all remaining water until dry to the touch. 
  7. Repeat steps 4 through 6 until you are happy with the results.

You will need to place the order and fully complete the transaction. Once the order has been placed, you will be directed to the Upload Artwork page. From there, you will be able to upload your image or artwork and view the pre-proof. 

In proofing, you MUST confirm that your Art file matches the order size to avoid scaling up or down. If the PDF file uploaded to the order matches the order size go ahead and send your artwork to print, and production will begin. You can remove and upload image as many times as you like; production will not start until you approve the proofs.

Great question! Please DO NOT send art files to print if you have any questions about your online proofs. Please contact us via live chat, email at info@foamcoreprint.com, or call 855-465-7744 before sending files to print. There is a 10 min window approved proofs can be removed and taken out of the production line; clients can remove approved art files within the 10 min window from the user dashboard in the order history tab.

There is a 10 min window after proofs are approved where they can be removed and taken out of the production line; clients can remove any approved art files within the 10 minutes of approval of that specific art file. 

  1. Sign in to your account
  2. User Dashboard 
  3. Order History  
  4. Locate the Order# in question.
  5. Click "See All Jobs / Details"
  6. Under the Actions section, if the "Replace Artwork" is RED, you are inside the 10-minute window and CAN remove the file by selecting the button.
  7. If the "Replace Artwork" button is "Grayed Out," it is past the time of removal, and production has begun.
To be able to print these camera calibration targets, the most straightforward answer is to hire a professional providing this service. One that we can recommend is foamcoreprint.com. We provide excellent customer support, and our prices are very competitive. If you want more information or would like to order some some, don't hesitate to get in touch with us at info@foamcoreprint.com
The camera calibration method is intended to identify the geometric characteristics of the image creation process. This is a vital step to perform in many computer vision applications, especially when metric information on the scene is needed. Essentially, computer vision uses CNNs and deep learning to perform high-speed, high-volume unsupervised learning on visual information to train machine learning systems to interpret data in a way somewhat resembling how a human eye works.

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