undistortion.c File Reference

Functions for undistorting camera images. More...

#include "undistortion.h"
#include <math.h>

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Functions
bool	Dhane_distortion (float x_n, float y_n, float *x_nd, float *y_nd, float k)
	Distort normalized image coordinates with the invertible Dhane method. More...
bool	Dhane_undistortion (float x_nd, float y_nd, float *x_n, float *y_n, float k)
	Undistort distorted normalized image coordinates with the invertible Dhane method. More...
void	normalized_to_pixels (float x_n_, float y_n_, float *x_p, float *y_p, const float *K)
	Transform normalized coordinates to pixel coordinates. More...
void	pixels_to_normalized (float x_p, float y_p, float *x_n_, float *y_n_, const float *K)
	Transform pixel coordinates to normalized coordinates. More...
bool	distorted_pixels_to_normalized_coords (float x_pd, float y_pd, float *x_n, float *y_n, float k, const float *K)
	Transform distorted pixel coordinates to normalized coordinates. More...
bool	normalized_coords_to_distorted_pixels (float x_n, float y_n, float *x_pd, float *y_pd, float k, const float *K)
	Transform normalized coordinates to distorted pixel coordinates. More...

Detailed Description

Functions for undistorting camera images.

The lenses of most cameras distort the image, in the sense that it does not represent a linear projection of points in the world. Specifically, straight lines in the world get curved in the image, as the lens compresses the data more and more towards the edges of the image.

Reading:

1. https://docs.opencv.org/2.4/doc/tutorials/calib3d/camera_calibration/camera_calibration.html (for normal cameras)
2. https://docs.opencv.org/trunk/db/d58/group__calib3d__fisheye.html (for fisheye cameras)
3. Dhane, P., Kutty, K., & Bangadkar, S. (2012). A generic non-linear method for fisheye correction. International Journal of Computer Applications, 51(10). (invertible fisheye model)

Some definitions:

• x_n, y_n: Normalized coordinates, i.e., with no distortion, with (0,0) the center of the image, and x_n = X / Z
• x_nd, y_nd: Distorted normalized coordinates, i.e., with (0,0) the center of the image, but x_nd and y_nd are a nonlinear function of X/Z
• x_n_, y_n_: Normalized coordinates, whether distorted or undistorted.
• x_p, y_p: Pixel coordinates, with (0,0) the start of the image, and x_pd, y_pd in the range [0,width] and [0,height], respectively.
• k: distortion parameters
• K: camera calibration matrix, as a single array in row-major form, so K00, K01, K02, K10, K11, ...

Definition in file undistortion.c.

Function Documentation

bool Dhane_distortion	(	float	x_n,
		float	y_n,
		float *	x_nd,
		float *	y_nd,
		float	k
	)

Distort normalized image coordinates with the invertible Dhane method.

This can be useful for undistorting an entire image. We assume f, the focal length, to be 1 here. That is why it is missing from the below formula.

Parameters

[in]	x_n	The undistorted normalized x coordinate
[in]	y_n	The undistorted normalized y coordinate
[in]	k	The single parameter of Dhane's model, typically found empirically by checking if straight lines in the world are straight in an undistorted image.
[out]	*x_nd	The distorted normalized x coordinate
[out]	*y_nd	The distorted normalized y coordinate

Returns

Whether the distortion was successful

Definition at line 57 of file undistortion.c.

Referenced by normalized_coords_to_distorted_pixels().

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bool Dhane_undistortion	(	float	x_nd,
		float	y_nd,
		float *	x_n,
		float *	y_n,
		float	k
	)

Undistort distorted normalized image coordinates with the invertible Dhane method.

We assume f, the focal length, to be 1 here. That is why it is missing from the below formula.

Parameters

[out]	*x_n	The undistorted normalized x coordinate
[out]	*y_n	The undistorted normalized y coordinate
[in]	k	The single parameter of Dhane's model, typically found empirically by checking if straight lines in the world are straight in an undistorted image.
[in]	x_nd	The distorted normalized x coordinate
[in]	y_nd	The distorted normalized y coordinate

Returns

Whether the distortion was successful

Definition at line 76 of file undistortion.c.

Referenced by distorted_pixels_to_normalized_coords().

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bool distorted_pixels_to_normalized_coords	(	float	x_pd,
		float	y_pd,
		float *	x_n,
		float *	y_n,
		float	k,
		const float *	K
	)

Transform distorted pixel coordinates to normalized coordinates.

Parameters

[out]	*x_n	The undistorted normalized x coordinate
[out]	*y_n	The undistorted normalized y coordinate
[in]	k	The single parameter of Dhane's model, typically found empirically by checking if straight lines in the world are straight in an undistorted image.
[in]	*K	The camera calibration matrix, as a single array in row-major form, so K00, K01, K02, K10, K11, ...
[in]	x_pd	The distorted pixel x coordinate
[in]	y_pd	The distorted pixel y coordinate

Returns

Whether the transformation was successful

Definition at line 128 of file undistortion.c.

References Dhane_undistortion(), and pixels_to_normalized().

Referenced by get_world_position_from_image_points(), and predict_flow_vectors().

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bool normalized_coords_to_distorted_pixels	(	float	x_n,
		float	y_n,
		float *	x_pd,
		float *	y_pd,
		float	k,
		const float *	K
	)

Transform normalized coordinates to distorted pixel coordinates.

Parameters

[in]	x_n	The undistorted normalized x coordinate
[in]	y_n	The undistorted normalized y coordinate
[in]	k	The single parameter of Dhane's model, typically found empirically by checking if straight lines in the world are straight in an undistorted image.
[in]	*K	The camera calibration matrix, as a single array in row-major form, so K00, K01, K02, K10, K11, ...
[out]	*x_pd	The distorted pixel x coordinate
[out]	*y_pd	The distorted pixel y coordinate

Returns

Whether the transformation was successful

Definition at line 146 of file undistortion.c.

References Dhane_distortion(), and normalized_to_pixels().

Referenced by predict_flow_vectors(), and undistort_image_func().

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void normalized_to_pixels	(	float	x_n_,
		float	y_n_,
		float *	x_p,
		float *	y_p,
		const float *	K
	)

Transform normalized coordinates to pixel coordinates.

Parameters

[in]	x_n	The undistorted normalized x coordinate
[in]	y_n	The undistorted normalized y coordinate
[in]	*K	The camera calibration matrix, as a single array in row-major form, so K00, K01, K02, K10, K11, ...
[out]	*x_p	The pixel x coordinate
[out]	*y_p	The pixel y coordinate

Definition at line 100 of file undistortion.c.

Referenced by normalized_coords_to_distorted_pixels().

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void pixels_to_normalized	(	float	x_p,
		float	y_p,
		float *	x_n_,
		float *	y_n_,
		const float *	K
	)

Transform pixel coordinates to normalized coordinates.

Parameters

[out]	*x_n	The undistorted normalized x coordinate
[out]	*y_n	The undistorted normalized y coordinate
[in]	*K	The camera calibration matrix, as a single array in row-major form, so K00, K01, K02, K10, K11, ...
[in]	x_p	The pixel x coordinate
[in]	y_p	The pixel y coordinate

Definition at line 113 of file undistortion.c.

Referenced by distorted_pixels_to_normalized_coords().

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