cameraIntrinsics

Object for storing intrinsic camera parameters

Description

Store information about a camera’s intrinsic calibration parameters, including lens distortion.

Creation

Syntax

intrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize)

intrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize,PropertyName=Value)

Description

intrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize) returns a camera intrinsics object that contains the focal length and the camera's principal point. The three input arguments set the FocalLength, PrincipalPoint, and ImageSize properties, respectively.

intrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize,PropertyName=Value) specifies options using one or more properties in addition to the previous syntax. For example, RadialDistortion=[0 10] sets the radial lens distortion property, to the vector [0 10].

Properties

FocalLength — Focal length

2-element vector

Focal length in x and y, stored as a 2-element vector [f_x f_y] in pixels.

f_x = F * s_x

f_y = F * s_y

F is the focal length in world units, typically in millimeters. s_x and s_y are the number of pixels per world unit in the x and y direction respectively. Thus, f_x and f_y are in pixels.

The focal length F influences the angle of view and thus affects the area of the scene that appears focused in an image. For a fixed subject distance:

• A short focal length offers a wide angle of view allowing to capture large area of the scene under focus. It emphasizes both the subject and the scene background.

• A long focal length offers a narrow angle of view, thus reducing the area of the scene under focus. It emphasizes more on the subject and restricts the amount of background from being captured.

You cannot set the value of FocalLength after you create the cameraIntrinsics object.

PrincipalPoint — Optical center of camera

two-element vector

Optical center of camera, stored as a two-element vector [cx cy] in pixels. The vector contains the coordinates of the optical center of the camera.

You cannot set the value of PrincipalPoint after you create the cameraIntrinsics object.

ImageSize — Image size produced by the camera

two-element vector

Image size produced by the camera, stored as a two-element vector, [mrows ncols].

You cannot set the value of ImageSize after you create the cameraIntrinsics object.

RadialDistortion — Radial lens distortion coefficients

[0 0] (default) | 2-element vector | 3-element vector | 6-element vector

Radial lens distortion coefficients, specified as a 2-, 3-, or 6-element vector.

• 2-element vector — [k1 k2].

• 3-element vector — [k1 k2 k3].

• 6-element vector — [k1 k2 k3 k4 k5 k6].

In the Robot Operating System (ROS), the 3-element vector is referred to as the plumb_bob model, while the 6-element vector is known as the rational_polynomial model.

Radial distortion is the displacement of image points along radial lines extending from the principal point.

• As image points move away from the principal point (positive radial displacement), image magnification decreases and a pincushion-shaped distortion occurs on the image.

• As image points move toward the principal point (negative radial displacement), image magnification increases and a barrel-shaped distortion occurs on the image.

The camera parameters object calculates the radial-distorted location of a point, denoted as (x_distorted, y_distorted):

$$x_{distorted}=x\left(\frac{1+k_1*r^2+k_2*r^4+k_3*r^6}{1+k_4*r^2+k_5*r^4+k_6*r^6}\right)$$

$$y_{distorted}=y\left(\frac{1+k_1*r^2+k_2*r^4+k_3*r^6}{1+k_4*r^2+k_5*r^4+k_6*r^6}\right)$$

x, y is a undistorted image point in normalized image coordinates in world units, with the origin at the optical center.

r2 = x2 + y2

k1, k2, …, k6 are radial distortion coefficients of the lens. Typically, two coefficients are sufficient and k3, …, k6 are only needed for wide-angle lenses.

TangentialDistortion — Tangential distortion coefficients

[0 0] (default) | two-element vector

Tangential distortion coefficients, specified as a 2-element vector, [p₁ p₂]. 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), as follows:

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

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

x, y are undistorted pixel locations

p1 and p2 are tangential distortion coefficients of the lens

r2 = x2 + y2

The undistorted pixel locations appear in normalized image coordinates, with the origin at the optical center. The coordinates are expressed in world units.

Skew — Camera axes skew

0 (default) | numeric scalar

Camera axes skew, specified as a numeric scalar. If the x and the y axes are exactly perpendicular, then the skew must be 0.

K — Camera intrinsic matrix

Read-only: 3-by-3 identity matrix (default) | 3-by-3 matrix

This property is read-only.

Camera intrinsic matrix, specified as a 3-by-3 matrix. The matrix has the 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 axis 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.

sx and sy are the number of pixels per world unit in the x and y direction respectively.

fx and fy are expressed in pixels.

Examples

Create an Object Containing Fundamental Camera Parameters

Define camera parameters without lens distortion or skew.

Specify the focal length and principal point in pixels.

focalLength    = [800 800]; 
principalPoint = [320 240];
imageSize      = [480 640];

Create a camera intrinsics object.

intrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize)

intrinsics = 
  cameraIntrinsics with properties:

             FocalLength: [800 800]
          PrincipalPoint: [320 240]
               ImageSize: [480 640]
        RadialDistortion: [0 0]
    TangentialDistortion: [0 0]
                    Skew: 0
                       K: [3×3 double]

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced in R2017a

R2024b: Import OpenCV pinhole camera model with six radial distortion coefficients

The cameraIntrinsics has been updated to support OpenCV pinhole camera model with 6 radial distortion coefficients.

R2022b: Supports premultiply matrix convention

Starting in R2022b, many Computer Vision Toolbox™ functions create and perform geometric transformations using the premultiply convention. Accordingly, a property of the cameraIntrinsics object has changed to support the premultiply convention.

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

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