Lens Distortion Correction

Data Structures
struct	VPIFisheyeLensDistortionModel
	Holds coefficients for fisheye lens distortion model. More...
struct	VPIPolynomialLensDistortionModel
	Holds coefficients for polynomial lens distortion model. More...

Typedefs
typedef float	VPICameraIntrinsic[2][3]
	Camera intrinsic matrix. More...
typedef float	VPICameraExtrinsic[3][4]
	Camera extrinsic matrix. More...

Enumerations
enum	VPIFisheyeMapping
	Supported fisheye lens mapping types. More...

Functions
VPIStatus	vpiWarpMapGenerateFromFisheyeLensDistortionModel (const VPICameraIntrinsic Kin, const VPICameraExtrinsic X, const VPICameraIntrinsic Kout, const VPIFisheyeLensDistortionModel *distModel, VPIWarpMap *warpMap)
	Generates a mapping that corrects image distortions caused by fisheye lenses. More...
VPIStatus	vpiWarpMapGenerateFromPolynomialLensDistortionModel (const VPICameraIntrinsic Kin, const VPICameraExtrinsic X, const VPICameraIntrinsic Kout, const VPIPolynomialLensDistortionModel *distModel, VPIWarpMap *warpMap)
	Generates a mapping that corrects image using polynomial lens distortion model. More...

Detailed Description

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Data Structure Documentation

VPIFisheyeLensDistortionModel

struct VPIFisheyeLensDistortionModel

Holds coefficients for fisheye lens distortion model.

The fisheye lens distortion model is defined by:

\begin{align*} r &= \sqrt{u^2 + v^2} \\ \theta &= \arctan(r) \\ r_d &= D(\theta + k_1 * \theta^3 + k_2 * \theta^5 + k_3 * \theta^7 + k_4 * \theta^9) \\ c_d &= r_d/r \\ u_d &= u*c_d \\ v_d &= v*c_d \end{align*}

where:

• \(k_1,k_2,k_3,k_4\) are the distortion coefficients.
• \((u_d,v_d)\) is the coordinate of a point in the distorted image.
• \((u,v)\) is the coordinate of a point in the corrected image.
• \(D(\theta)\) defines the mapping from point angle and pixel distance to image center. See VPIFisheyeMapping for details.

Definition at line 137 of file LensDistortionModels.h.

Collaboration diagram for VPIFisheyeLensDistortionModel:

Data Fields
VPIFisheyeMapping	mapping	Mapping between pixel angle and pixel distance to image center. Valid mapping values: VPI_FISHEYE_EQUIDISTANT VPI_FISHEYE_EQUISOLID VPI_FISHEYE_ORTHOGRAPHIC VPI_FISHEYE_STEREOGRAPHIC
float	k1	Fisheye distortion coefficients.
float	k2	Fisheye distortion coefficients.
float	k3	Fisheye distortion coefficients.
float	k4	Fisheye distortion coefficients.

VPIPolynomialLensDistortionModel

struct VPIPolynomialLensDistortionModel

Holds coefficients for polynomial lens distortion model.

The polynomial lens distortion model is defined by:

\begin{align*} r &= \sqrt{u^2 + v^2} \\ k_r &= \frac{1 + k_1r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} \\ u_d &= k_r u + p_1(2uv) + p_2 * (r^2 + 2u^2) \\ v_d &= k_r v + p_1(r^2 + 2v^2) + p_2(2uv) \end{align*}

where:

• \(k_1,k_2,k_3,k_4,k_5,k_6\) are the radial distortion coefficients.
• \(p_1,p_2\) are the tangential distortion coefficients.
• \((u_d,v_d)\) is the coordinate of a point in the distorted image.
• \((u,v)\) is the coordinate of a point in the corrected image.

Definition at line 215 of file LensDistortionModels.h.

Collaboration diagram for VPIPolynomialLensDistortionModel:

Data Fields
float	k1	Radial distortion coefficients.
float	k2	Radial distortion coefficients.
float	k3	Radial distortion coefficients.
float	k4	Radial distortion coefficients.
float	k5	Radial distortion coefficients.
float	k6	Radial distortion coefficients.
float	p1	Tangential distortion coefficients.
float	p2	Tangential distortion coefficients.

Typedef Documentation

VPICameraIntrinsic

typedef float VPICameraIntrinsic[2][3]

#include <vpi/Types.h>

Camera intrinsic matrix.

\begin{bmatrix} f_x & s & c_x \\ 0 & f_y & c_y \end{bmatrix}

Where:

• \(f_x, f_y\): focal length in pixels.
• \(s\): skew, used to model slanted pixels.
• \(c_x, c_y\): principal point.

Definition at line 659 of file Types.h.

VPICameraExtrinsic

typedef float VPICameraExtrinsic[3][4]

#include <vpi/Types.h>

Camera extrinsic matrix.

\begin{bmatrix} R_{3\times3} & T_{3\times1} \end{bmatrix}

Where: \(R_{3\times3}\): Rotation matrix. \(T_{3\times1}\): 3D position of the origin of world coordinate system expressed in coordinates of camera-centered system.

Definition at line 672 of file Types.h.

Enumeration Type Documentation

VPIFisheyeMapping

enum VPIFisheyeMapping

#include <vpi/LensDistortionModels.h>

Supported fisheye lens mapping types.

Enumerator
VPI_FISHEYE_EQUIDISTANT	Specifies the equidistant fisheye mapping. Mapping is defined by: \[r = f\theta\] where: \(\theta\) is the angle from the optical axis. \(f\) is the focal length. \(r\) is the distance of a pixel from the image center.
VPI_FISHEYE_EQUISOLID	Specifies the equisolid fisheye mapping. Mapping is defined by: \[r = 2f\sin\left(\frac{\theta}{2}\right)\] where: \(\theta\) is the angle from the optical axis. \(f\) is the focal length. \(r\) is the distance of a pixel from the image center.
VPI_FISHEYE_ORTHOGRAPHIC	Specifies the orthographic fisheye mapping. Mapping is defined by: \[r = f\sin(\theta)\] where: \(\theta\) is the angle from the optical axis. \(f\) is the focal length. \(r\) is the distance of a pixel from the image center.
VPI_FISHEYE_STEREOGRAPHIC	Specifies the stereographic fisheye mapping. Mapping is defined by: \[r = 2f\tan\left(\frac{\theta}{2}\right)\] where: \(\theta\) is the angle from the optical axis. \(f\) is the focal length. \(r\) is the distance of a pixel from the image center.

Definition at line 76 of file LensDistortionModels.h.

Function Documentation

vpiWarpMapGenerateFromFisheyeLensDistortionModel()

VPIStatus vpiWarpMapGenerateFromFisheyeLensDistortionModel	(	const VPICameraIntrinsic	Kin,
		const VPICameraExtrinsic	X,
		const VPICameraIntrinsic	Kout,
		const VPIFisheyeLensDistortionModel *	distModel,
		VPIWarpMap *	warpMap
	)

#include <vpi/LensDistortionModels.h>

Generates a mapping that corrects image distortions caused by fisheye lenses.

Given camera intrinsic and extrinsic parameters, and fisheye lens distortion model, generates a VPIWarpMap suitable to be used by Remap to undistort images captured by cameras equipped with fisheye lens.

The mapping is defined by the following matrix equation:

\[ y = (K_{out} L X K_{in}) x \]

where:

• \(x\) is the input homogeneous coordinate
• \(y\) is the corresponding homogeneous coordinate on the distorted image.
• \(L\) is the fisheye lens distortion model (not a matrix), see VPIFisheyeLensDistortionModel.
• remaining variables are the input parameters to this function.

Parameters

[in]	Kin	Camera intrinsic parameters.
[in]	X	Camera extrinsic parameters that defines the camera center position and its heading in world coordinates.
[in]	Kout	New camera intrinsic parameters applied to the undistorted image. For monocular cameras, Kout is usually equal to Kin.
[in]	distModel	Fisheye lens distortion model.
[out]	warpMap	Resulting warp map that serves as input to Remap algorithm.

Return values

VPI_ERROR_INVALID_ARGUMENT	warpMap is NULL.
VPI_ERROR_INVALID_ARGUMENT	Kin is NULL.
VPI_ERROR_INVALID_ARGUMENT	X is NULL.
VPI_ERROR_INVALID_ARGUMENT	Output Kout is NULL.
VPI_ERROR_INVALID_ARGUMENT	distModel is NULL.
VPI_ERROR_INVALID_ARGUMENT	Fisheye model in distModel is invalid.
VPI_SUCCESS	Operation executed successfully.

vpiWarpMapGenerateFromPolynomialLensDistortionModel()

VPIStatus vpiWarpMapGenerateFromPolynomialLensDistortionModel	(	const VPICameraIntrinsic	Kin,
		const VPICameraExtrinsic	X,
		const VPICameraIntrinsic	Kout,
		const VPIPolynomialLensDistortionModel *	distModel,
		VPIWarpMap *	warpMap
	)

#include <vpi/LensDistortionModels.h>

Generates a mapping that corrects image using polynomial lens distortion model.

Given camera intrinsic and extrinsic parameters, and the polynomial lens distortion model, generates a VPIWarpMap suitable to be used by Remap to undistort images.

The mapping is defined by the following matrix equation:

\[ y = (K_{out} L X K_{in}) x \]

where:

• \(x\) is the input homogeneous coordinate
• \(y\) is the corresponding homogeneous coordinate on the distorted image.
• \(L\) is the polynomial lens distortion model (not a matrix), see VPIPolynomialLensDistortionModel
• remaining variables are the input parameters to this function.

Parameters

[in]	Kin	Camera intrinsic parameters.
[in]	X	Camera extrinsic parameters that defines the camera center position and its heading in world coordinates.
[in]	Kout	New camera intrinsic parameters applied to the undistorted image. For monocular cameras, Kout is usually equal to Kin.
[in]	distModel	Polynomial lens distortion model.
[out]	warpMap	Resulting warp map that serves as input to Remap algorithm.

Return values

VPI_ERROR_INVALID_ARGUMENT	warpMap is NULL.
VPI_ERROR_INVALID_ARGUMENT	Kin is NULL.
VPI_ERROR_INVALID_ARGUMENT	X is NULL.
VPI_ERROR_INVALID_ARGUMENT	Output Kout is NULL.
VPI_ERROR_INVALID_ARGUMENT	distModel is NULL.
VPI_ERROR_INVALID_ARGUMENT	Polynomial model in distModel is invalid.
VPI_SUCCESS	Operation executed successfully.