cameraParameters

Object for storing camera parameters

Description

The cameraParameters object stores the intrinsic, extrinsic, and lens distortion parameters of a camera.

Creation

You can create a cameraParameters object using the cameraParameters function described here. You can also create a cameraParameters object by using the estimateCameraParameters with an M-by-2-by-numImages array of input image points. M is the number of keypoint coordinates in each pattern.

Syntax

cameraParams = cameraParameters

cameraParams = cameraParameters(Name,Value)

cameraParams = cameraParameters(paramStruct)

Description

cameraParams = cameraParameters creates a cameraParameters object that contains the intrinsic, extrinsic, and lens distortion parameters of a camera.

cameraParams = cameraParameters(Name,Value) sets properties of the cameraParameters object by using one or more name-value arguments. Unspecified properties use default values.

For example, cameraParams = cameraParameters("RadialDistortion",[0 10]) sets the radial lens distortion property, RadialDistortion, as the vector [0 10].

cameraParams = cameraParameters(paramStruct) creates an identical cameraParameters object from an existing cameraParameters object with parameters stored in paramStruct.

Input Arguments

paramStruct — Camera parameters

structure

Camera parameters, specified as a camera parameters structure. To get a paramStruct from an existing cameraParameters object, use the toStruct function.

Properties

Intrinsic Camera Parameters:

K — Camera intrinsic matrix

3-by-3 matrix

Camera intrinsic matrix, specified as a 3-by-3 matrix. The matrix has this format:

$$\left[\begin{array}{ccc}{f}_x& s& c_x\\ 0& f_y& c_y\\ 0& 0& 1\end{array}\right]$$

The coordinates [c_x c_y] represent the optical center (the principal point), in pixels. When the x- and y-axes are exactly perpendicular, the skew parameter s equals 0.

f_x = F*s_x

f_y = F*s_y

• F is the focal length in world units, typically expressed in millimeters.

• s_x and s_y are the number of pixels per world unit in the x- and y-direction respectively.

• f_x and f_y are expressed in pixels.

Intrinsics — Camera intrinsics object

cameraIntrinsics object

This property is read-only.

Camera intrinsics object, stated as a cameraIntrinsics object. The object contains information about camera intrinsic calibration parameters, including lens distortion.

Dependency

You must provide an image size (using the ImageSize property) for the Intrinsics property to be non-empty. The intrinsics for the camera parameters depends on the image size.

ImageSize — Image size

two-element vector

Image size, specified as a two-element vector [mrows ncols].

Camera Lens Distortion:

RadialDistortion — Radial distortion coefficients

[0 0 0] (default) | 2-element vector | 3-element vector

Radial distortion coefficients, specified as either a two- or three-element vector. When you specify a two-element vector, the object sets the third element to 0. Radial distortion is the displacement of image points along radial lines extending from the principal point.

The camera parameters object calculates the radial-distorted location of a point. You can denote the distorted points as (x_distorted, y_distorted), as follows:

x_distorted = x(1 + k₁*r² + k₂*r⁴ + k₃*r⁶)

y_distorted= y(1 + k₁*r² + k₂*r⁴ + k₃*r⁶)

x, y are undistorted pixel locations

k1, k2, and k3 are radial distortion coefficients of the lens

r2 = x2 + y2

Typically, two coefficients are sufficient. For severe distortion, you can include k₃. The undistorted pixel locations appear in normalized image coordinates, with the origin at the optical center. The coordinates are expressed in world units.

TangentialDistortion — Tangential distortion coefficients

[0 0]' (default) | 2-element vector

Tangential distortion coefficients, specified as a two-element vector. Tangential distortion occurs when the lens and the image plane are not parallel. The camera parameters object calculates the tangential distorted location of a point. You can denote the distorted points as (x_distorted, y_distorted). The undistorted pixel locations appear in normalized image coordinates, with the origin at the optical center. The coordinates are expressed in world units.

Tangential distortion occurs when the lens and the image plane are not parallel. The tangential distortion coefficients model this type of distortion.

The distorted points are denoted as (x_distorted, y_distorted):

x_distorted = x + [2 * p₁ * x * y + p₂ * (r² + 2 * x²)]

y_distorted = y + [p₁ * (r² + 2 *y²) + 2 * p₂ * x * y]

• x, y — Undistorted pixel locations. x and y are in normalized image coordinates. Normalized image coordinates are calculated from pixel coordinates by translating to the optical center and dividing by the focal length in pixels. Thus, x and y are dimensionless.

• p₁ and p₂ — Tangential distortion coefficients of the lens.

• r² = x² + y²

Extrinsic Camera Parameters:

PatternExtrinsics — Calibration pattern extrinsics

[] (default) | P-element vector of rigidtform3d objects

This property is read-only.

Calibration pattern extrinsics, specified as a P-element vector of rigidtform3d objects. Each object stores information about the 3-D rotation matrices and the camera translation vectors.

• The R property of each rigidtform3d object describes the 3-D rotation of the camera image plane relative to the corresponding calibration pattern.

• The Translation property of each rigidtform3d object describes the translation t of the camera relative to the corresponding calibration pattern, expressed in world units.

This equation provides the transformation that relates a world coordinate in the checkerboard frame [X Y Z] and the corresponding image point [x y]:

$$w\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=K\left[\begin{array}{cc}R& t\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$$

• w: arbitrary scale factor

• K: camera intrinsic matrix

• R: matrix representing the 3-D rotation of the camera

• t: translation of the camera relative to the world coordinate system

The rigid geometric transformations do not take distortion into consideration. Use the undistortImage function to remove distortion.

RotationVectors — 3-D rotation vectors

[] (default) | P-by-3 matrix

This property is read-only.

3-D rotation vectors, specified as a P-by-3 matrix containing P rotation vectors. Each vector describes the 3-D rotation of the camera image plane relative to the corresponding calibration pattern. The vector specifies the 3-D axis about which the camera is rotated, where the magnitude is the rotation angle in radians. The PatternExtrinsics property specifies geometric transformation objects with the corresponding 3-D rotation matrices.

Estimated Camera Parameter Accuracy:

MeanReprojectionError — Average Euclidean distance

numeric value

This property is read-only.

Average Euclidean distance between reprojected and detected points, specified as a numeric value in pixels.

ReprojectionErrors — Estimated camera parameters accuracy

[] (default) | M-by-2-by-P array

Estimated camera parameters accuracy, specified as an M-by-2-by-P array of [x y] coordinates. The [x y] coordinates represent the translation in x and y between the reprojected pattern key points and the detected pattern key points. The values of this property represent the accuracy of the estimated camera parameters. P is the number of pattern images that estimates camera parameters. M is the number of keypoints in each image.

ReprojectedPoints — World points reprojected onto calibration images

M-by-2-by-P array

This property is read-only.

World points reprojected onto calibration images, specified as an M-by-2-by-P array of [x y] coordinates. P is the number of pattern images and M is the number of keypoints in each image. Missing points in the pattern's detected keypoints are denoted as [NaN,NaN].

DetectedKeypoints — Detected keypoints in the calibration pattern

[] (default) | M-by-P array

Detected keypoints in the calibration pattern, specified as a logical M-by-P array. M is the number of keypoints in the entire calibration pattern and P specifies the number of calibration images.

Settings for Camera Parameter Estimation:

NumPatterns — Number of calibrated patterns

integer

Number of calibration patterns that estimates camera extrinsics, specified as an integer. The number of calibration patterns equals the number of translation and rotation vectors.

WorldPoints — World coordinates

M-by-2 array | []

World coordinates of key points on calibration pattern, specified as an M-by-2 array. M represents the number of key points in the pattern.

WorldUnits — World points units

"mm" (default) | character vector | string scalar

World points units, specified as a character vector or string scalar. The value describes the units of measure.

EstimateSkew — Estimate skew flag

false (default) | true

Estimate skew flag, specified as a logical scalar. When you set the logical to true, the object estimates the image axes skew. When you set the logical to false, the image axes are exactly perpendicular.

NumRadialDistortionCoefficients — Number of radial distortion coefficients

2 (default) | 3

Number of radial distortion coefficients, specified as the number 2 or 3.

EstimateTangentialDistortion — Estimate tangential distortion flag

false (default) | true

Estimate tangential distortion flag, specified as the logical scalar true or false. When you set the logical to true, the object estimates the tangential distortion. When you set the logical to false, the tangential distortion is negligible.

Examples

Remove Distortion from an Image Using Camera Parameters Object

Use the camera calibration functions to remove distortion from an image. This example creates a cameraParameters object manually, but in practice, you would use the estimateCameraParameters or the Camera Calibrator app to derive the object.

Create a cameraParameters object manually.

k = [715.2699 0 565.6995; 0 711.5281 355.3466; 0 0 1];
radialDistortion = [-0.3361 0.0921]; 
cameraParams = cameraParameters("K",k,"RadialDistortion",radialDistortion)

cameraParams = 
  cameraParameters with properties:

   Camera Intrinsics
                         Intrinsics: [0x0 cameraIntrinsics]

   Camera Extrinsics
                  PatternExtrinsics: [0x1 rigidtform3d]

   Accuracy of Estimation
              MeanReprojectionError: NaN
                 ReprojectionErrors: [0x2 double]
                  ReprojectedPoints: [0x2x0 double]

   Calibration Settings
                        NumPatterns: 0
                  DetectedKeypoints: [0x2 double]
                        WorldPoints: [0x2 double]
                         WorldUnits: 'mm'
                       EstimateSkew: 0
    NumRadialDistortionCoefficients: 2
       EstimateTangentialDistortion: 0

Remove distortion from the images.

I = imread(fullfile(matlabroot,"toolbox","vision","visiondata","calibration","mono","image01.jpg"));
J = undistortImage(I,cameraParams);

Display the original and the undistorted images.

montage({I,J})
title("Original Image (left) vs. Corrected Image (right)")

References

[1] Zhang, Z. "A Flexible New Technique for Camera Calibration." IEEE Transactions on Pattern Analysis and Machine Intelligence 22, no. 11 (November 2000): 1330–34. https://doi.org/10.1109/34.888718.

[2] Heikkila, J., and O. Silven. “A Four-Step Camera Calibration Procedure with Implicit Image Correction.” In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1106–12. San Juan, Puerto Rico: IEEE Comput. Soc, 1997. https://doi.org/10.1109/CVPR.1997.609468.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Use the toStruct function to pass a cameraParameters object into generated code. See the Code Generation for Depth Estimation From Stereo Video example.

Version History

Introduced in R2014a

R2022b: Supports premultiply matrix convention

Starting in R2022b, many Computer Vision Toolbox™ functions create and perform geometric transformations using the premultiply convention. Accordingly, some properties of the cameraParameters object have changed to support the premultiply convention.

• The new K property replaces the old IntrinsicMatrix property. The value of K is the transpose of IntrinsicMatrix.

• The new PatternExtrinsics property replaces the old RotationMatrices and TranslationVectors properties. You can access the rotation matrices and translation vectors by querying the R and Translation properties of the rigidtform3d objects stored in the PatternExtrinsics property. The R property stores a rotation matrix as the transpose of the rotation matrix represented by RotationMatrices.

For more information, see Migrate Geometric Transformations to Premultiply Convention.