# 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

### Description

creates a `cameraParams`

= cameraParameters`cameraParameters`

object that contains the intrinsic,
extrinsic, and lens distortion parameters of a camera.

sets properties of
the `cameraParams`

= cameraParameters(Name,Value)`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]
```

.

creates an identical `cameraParams`

= cameraParameters(`paramStruct`

)`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]`

(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*].

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. |

r^{2} =
x^{2} +
y^{2} |

k_{1},
k_{2}, …,
k_{6} are radial
distortion coefficients of the lens. Typically, two coefficients are
sufficient and k_{3}, …,
k_{6} are only needed for
wide-angle lenses. |

`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 * *p*_{1} * *x* *
*y* + *p*_{2}
* (*r*^{2} + 2 *
*x*^{2})]

*y*_{distorted} =
*y* + [*p*_{1}
* (*r*^{2} + 2
**y*^{2}) + 2 *
*p*_{2} * *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.*p*_{1}and*p*_{2}— Tangential distortion coefficients of the lens.*r*^{2}=*x*^{2}+*y*^{2}

## 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`

| `6`

Number of radial distortion coefficients, specified as the number
`2`

, `3`

, or
`6`

.

`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] 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**

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

The `cameraParameters`

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, 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.

## See Also

### Apps

### Classes

`stereoParameters`

|`cameraCalibrationErrors`

|`intrinsicsEstimationErrors`

|`extrinsicsEstimationErrors`

|`cameraIntrinsics`

### Functions

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