Geometric Image Transformations

Detailed Description

The functions in this section perform various geometrical transformations of 2D images. They do not change the image content but deform the pixel grid and map this deformed grid to the destination image. In fact, to avoid sampling artifacts, the mapping is done in the reverse order, from destination to the source. That is, for each pixel \((x, y)\) of the destination image, the functions compute coordinates of the corresponding "donor" pixel in the source image and copy the pixel value:

\[\texttt{dst} (x,y)= \texttt{src} (f_x(x,y), f_y(x,y))\]

In case when you specify the forward mapping \(\left<g_x, g_y\right>: \texttt{src} \rightarrow \texttt{dst}\), the OpenCV functions first compute the corresponding inverse mapping \(\left<f_x, f_y\right>: \texttt{dst} \rightarrow \texttt{src}\) and then use the above formula.

The actual implementations of the geometrical transformations, from the most generic remap and to the simplest and the fastest resize, need to solve two main problems with the above formula:

• Extrapolation of non-existing pixels. Similarly to the filtering functions described in the previous section, for some \((x,y)\), either one of \(f_x(x,y)\), or \(f_y(x,y)\), or both of them may fall outside of the image. In this case, an extrapolation method needs to be used. OpenCV provides the same selection of extrapolation methods as in the filtering functions. In addition, it provides the method BORDER_TRANSPARENT. This means that the corresponding pixels in the destination image will not be modified at all.
• Interpolation of pixel values. Usually \(f_x(x,y)\) and \(f_y(x,y)\) are floating-point numbers. This means that \(\left<f_x, f_y\right>\) can be either an affine or perspective transformation, or radial lens distortion correction, and so on. So, a pixel value at fractional coordinates needs to be retrieved. In the simplest case, the coordinates can be just rounded to the nearest integer coordinates and the corresponding pixel can be used. This is called a nearest-neighbor interpolation. However, a better result can be achieved by using more sophisticated interpolation methods , where a polynomial function is fit into some neighborhood of the computed pixel \((f_x(x,y), f_y(x,y))\), and then the value of the polynomial at \((f_x(x,y), f_y(x,y))\) is taken as the interpolated pixel value. In OpenCV, you can choose between several interpolation methods. See resize for details.

Note

The geometrical transformations do not work with CV_8S or CV_32S images.

Namespaces
namespace	cv::fisheye
	The methods in this namespace use a so-called fisheye camera model.

Enumerations
enum	cv::InterpolationFlags {   cv::INTER_NEAREST = 0 ,   cv::INTER_LINEAR = 1 ,   cv::INTER_CUBIC = 2 ,   cv::INTER_AREA = 3 ,   cv::INTER_LANCZOS4 = 4 ,   cv::INTER_LINEAR_EXACT = 5 ,   cv::INTER_NEAREST_EXACT = 6 ,   cv::INTER_MAX = 7 ,   cv::WARP_FILL_OUTLIERS = 8 ,   cv::WARP_INVERSE_MAP = 16 ,   cv::WARP_RELATIVE_MAP = 32 }
	interpolation algorithm More...
enum	cv::InterpolationMasks {   cv::INTER_BITS = 5 ,   cv::INTER_BITS2 = INTER_BITS * 2 ,   cv::INTER_TAB_SIZE = 1 << INTER_BITS ,   cv::INTER_TAB_SIZE2 = INTER_TAB_SIZE * INTER_TAB_SIZE }
enum	cv::UndistortTypes {   cv::PROJ_SPHERICAL_ORTHO = 0 ,   cv::PROJ_SPHERICAL_EQRECT = 1 }
	cv::undistort mode More...
enum	cv::WarpPolarMode {   cv::WARP_POLAR_LINEAR = 0 ,   cv::WARP_POLAR_LOG = 256 }
	Specify the polar mapping mode. More...

Functions
void	cv::convertMaps (InputArray map1, InputArray map2, OutputArray dstmap1, OutputArray dstmap2, int dstmap1type, bool nninterpolation=false)
	Converts image transformation maps from one representation to another.
void	cv::getRectSubPix (InputArray image, Size patchSize, Point2f center, OutputArray patch, int patchType=-1)
	Retrieves a pixel rectangle from an image with sub-pixel accuracy.
void	cv::initInverseRectificationMap (InputArray cameraMatrix, InputArray distCoeffs, InputArray R, InputArray newCameraMatrix, const Size &size, int m1type, OutputArray map1, OutputArray map2)
	Computes the projection and inverse-rectification transformation map. In essense, this is the inverse of initUndistortRectifyMap to accomodate stereo-rectification of projectors ('inverse-cameras') in projector-camera pairs.
void	cv::initUndistortRectifyMap (InputArray cameraMatrix, InputArray distCoeffs, InputArray R, InputArray newCameraMatrix, Size size, int m1type, OutputArray map1, OutputArray map2)
	Computes the undistortion and rectification transformation map.
float	cv::initWideAngleProjMap (InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, int destImageWidth, int m1type, OutputArray map1, OutputArray map2, enum UndistortTypes projType=PROJ_SPHERICAL_EQRECT, double alpha=0)
	initializes maps for remap for wide-angle
static float	cv::initWideAngleProjMap (InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, int destImageWidth, int m1type, OutputArray map1, OutputArray map2, int projType, double alpha=0)
void	cv::remap (InputArray src, OutputArray dst, InputArray map1, InputArray map2, int interpolation, int borderMode=BORDER_CONSTANT, const Scalar &borderValue=Scalar(), AlgorithmHint hint=cv::ALGO_HINT_DEFAULT)
	Applies a generic geometrical transformation to an image.
void	cv::resize (InputArray src, OutputArray dst, Size dsize, double fx=0, double fy=0, int interpolation=INTER_LINEAR)
	Resizes an image.
void	cv::undistort (InputArray src, OutputArray dst, InputArray cameraMatrix, InputArray distCoeffs, InputArray newCameraMatrix=noArray())
	Transforms an image to compensate for lens distortion.
void	cv::warpAffine (InputArray src, OutputArray dst, InputArray M, Size dsize, int flags=INTER_LINEAR, int borderMode=BORDER_CONSTANT, const Scalar &borderValue=Scalar(), AlgorithmHint hint=cv::ALGO_HINT_DEFAULT)
	Applies an affine transformation to an image.
void	cv::warpPerspective (InputArray src, OutputArray dst, InputArray M, Size dsize, int flags=INTER_LINEAR, int borderMode=BORDER_CONSTANT, const Scalar &borderValue=Scalar(), AlgorithmHint hint=cv::ALGO_HINT_DEFAULT)
	Applies a perspective transformation to an image.
void	cv::warpPolar (InputArray src, OutputArray dst, Size dsize, Point2f center, double maxRadius, int flags)
	Remaps an image to polar or semilog-polar coordinates space.

Enumeration Type Documentation

InterpolationFlags

enum cv::InterpolationFlags

#include <opencv2/imgproc.hpp>

interpolation algorithm

Enumerator
INTER_NEAREST  Python: cv.INTER_NEAREST	nearest neighbor interpolation
INTER_LINEAR  Python: cv.INTER_LINEAR	bilinear interpolation
INTER_CUBIC  Python: cv.INTER_CUBIC	bicubic interpolation
INTER_AREA  Python: cv.INTER_AREA	resampling using pixel area relation. It may be a preferred method for image decimation, as it gives moire'-free results. But when the image is zoomed, it is similar to the INTER_NEAREST method.
INTER_LANCZOS4  Python: cv.INTER_LANCZOS4	Lanczos interpolation over 8x8 neighborhood
INTER_LINEAR_EXACT  Python: cv.INTER_LINEAR_EXACT	Bit exact bilinear interpolation
INTER_NEAREST_EXACT  Python: cv.INTER_NEAREST_EXACT	Bit exact nearest neighbor interpolation. This will produce same results as the nearest neighbor method in PIL, scikit-image or Matlab.
INTER_MAX  Python: cv.INTER_MAX	mask for interpolation codes
WARP_FILL_OUTLIERS  Python: cv.WARP_FILL_OUTLIERS	flag, fills all of the destination image pixels. If some of them correspond to outliers in the source image, they are set to zero
WARP_INVERSE_MAP  Python: cv.WARP_INVERSE_MAP	flag, inverse transformation
WARP_RELATIVE_MAP  Python: cv.WARP_RELATIVE_MAP

InterpolationMasks

enum cv::InterpolationMasks

#include <opencv2/imgproc.hpp>

Enumerator
INTER_BITS  Python: cv.INTER_BITS
INTER_BITS2  Python: cv.INTER_BITS2
INTER_TAB_SIZE  Python: cv.INTER_TAB_SIZE
INTER_TAB_SIZE2  Python: cv.INTER_TAB_SIZE2

UndistortTypes

enum cv::UndistortTypes

#include <opencv2/imgproc.hpp>

cv::undistort mode

Enumerator
PROJ_SPHERICAL_ORTHO  Python: cv.PROJ_SPHERICAL_ORTHO
PROJ_SPHERICAL_EQRECT  Python: cv.PROJ_SPHERICAL_EQRECT

WarpPolarMode

enum cv::WarpPolarMode

#include <opencv2/imgproc.hpp>

Specify the polar mapping mode.

See also

warpPolar

Enumerator
WARP_POLAR_LINEAR  Python: cv.WARP_POLAR_LINEAR	Remaps an image to/from polar space.
WARP_POLAR_LOG  Python: cv.WARP_POLAR_LOG	Remaps an image to/from semilog-polar space.

Function Documentation

convertMaps()

void cv::convertMaps	(	InputArray	map1,
		InputArray	map2,
		OutputArray	dstmap1,
		OutputArray	dstmap2,
		int	dstmap1type,
		bool	nninterpolation = false )

Python:
	cv.convertMaps(	map1, map2, dstmap1type[, dstmap1[, dstmap2[, nninterpolation]]]	) ->	dstmap1, dstmap2

#include <opencv2/imgproc.hpp>

Converts image transformation maps from one representation to another.

The function converts a pair of maps for remap from one representation to another. The following options ( (map1.type(), map2.type()) \(\rightarrow\) (dstmap1.type(), dstmap2.type()) ) are supported:

• \(\texttt{(CV_32FC1, CV_32FC1)} \rightarrow \texttt{(CV_16SC2, CV_16UC1)}\). This is the most frequently used conversion operation, in which the original floating-point maps (see remap) are converted to a more compact and much faster fixed-point representation. The first output array contains the rounded coordinates and the second array (created only when nninterpolation=false ) contains indices in the interpolation tables.
• \(\texttt{(CV_32FC2)} \rightarrow \texttt{(CV_16SC2, CV_16UC1)}\). The same as above but the original maps are stored in one 2-channel matrix.
• Reverse conversion. Obviously, the reconstructed floating-point maps will not be exactly the same as the originals.

Parameters

map1	The first input map of type CV_16SC2, CV_32FC1, or CV_32FC2 .
map2	The second input map of type CV_16UC1, CV_32FC1, or none (empty matrix), respectively.
dstmap1	The first output map that has the type dstmap1type and the same size as src .
dstmap2	The second output map.
dstmap1type	Type of the first output map that should be CV_16SC2, CV_32FC1, or CV_32FC2 .
nninterpolation	Flag indicating whether the fixed-point maps are used for the nearest-neighbor or for a more complex interpolation.

See also

remap, undistort, initUndistortRectifyMap

getRectSubPix()

void cv::getRectSubPix	(	InputArray	image,
		Size	patchSize,
		Point2f	center,
		OutputArray	patch,
		int	patchType = -1 )

Python:
	cv.getRectSubPix(	image, patchSize, center[, patch[, patchType]]	) ->	patch

#include <opencv2/imgproc.hpp>

Retrieves a pixel rectangle from an image with sub-pixel accuracy.

The function getRectSubPix extracts pixels from src:

\[patch(x, y) = src(x + \texttt{center.x} - ( \texttt{dst.cols} -1)*0.5, y + \texttt{center.y} - ( \texttt{dst.rows} -1)*0.5)\]

where the values of the pixels at non-integer coordinates are retrieved using bilinear interpolation. Every channel of multi-channel images is processed independently. Also the image should be a single channel or three channel image. While the center of the rectangle must be inside the image, parts of the rectangle may be outside.

Parameters

image	Source image.
patchSize	Size of the extracted patch.
center	Floating point coordinates of the center of the extracted rectangle within the source image. The center must be inside the image.
patch	Extracted patch that has the size patchSize and the same number of channels as src .
patchType	Depth of the extracted pixels. By default, they have the same depth as src .

See also

warpAffine, warpPerspective

initInverseRectificationMap()

void cv::initInverseRectificationMap	(	InputArray	cameraMatrix,
		InputArray	distCoeffs,
		InputArray	R,
		InputArray	newCameraMatrix,
		const Size &	size,
		int	m1type,
		OutputArray	map1,
		OutputArray	map2 )

Python:
	cv.initInverseRectificationMap(	cameraMatrix, distCoeffs, R, newCameraMatrix, size, m1type[, map1[, map2]]	) ->	map1, map2

#include <opencv2/imgproc.hpp>

Computes the projection and inverse-rectification transformation map. In essense, this is the inverse of initUndistortRectifyMap to accomodate stereo-rectification of projectors ('inverse-cameras') in projector-camera pairs.

The function computes the joint projection and inverse rectification transformation and represents the result in the form of maps for remap. The projected image looks like a distorted version of the original which, once projected by a projector, should visually match the original. In case of a monocular camera, newCameraMatrix is usually equal to cameraMatrix, or it can be computed by getOptimalNewCameraMatrix for a better control over scaling. In case of a projector-camera pair, newCameraMatrix is normally set to P1 or P2 computed by stereoRectify .

The projector is oriented differently in the coordinate space, according to R. In case of projector-camera pairs, this helps align the projector (in the same manner as initUndistortRectifyMap for the camera) to create a stereo-rectified pair. This allows epipolar lines on both images to become horizontal and have the same y-coordinate (in case of a horizontally aligned projector-camera pair).

The function builds the maps for the inverse mapping algorithm that is used by remap. That is, for each pixel \((u, v)\) in the destination (projected and inverse-rectified) image, the function computes the corresponding coordinates in the source image (that is, in the original digital image). The following process is applied:

\[\begin{array}{l} \text{newCameraMatrix}\\ x \leftarrow (u - {c'}_x)/{f'}_x \\ y \leftarrow (v - {c'}_y)/{f'}_y \\ \\\text{Undistortion} \\\scriptsize{\textit{though equation shown is for radial undistortion, function implements cv::undistortPoints()}}\\ r^2 \leftarrow x^2 + y^2 \\ \theta \leftarrow \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}\\ x' \leftarrow \frac{x}{\theta} \\ y' \leftarrow \frac{y}{\theta} \\ \\\text{Rectification}\\ {[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\ x'' \leftarrow X/W \\ y'' \leftarrow Y/W \\ \\\text{cameraMatrix}\\ map_x(u,v) \leftarrow x'' f_x + c_x \\ map_y(u,v) \leftarrow y'' f_y + c_y \end{array} \]

where \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) are the distortion coefficients vector distCoeffs.

In case of a stereo-rectified projector-camera pair, this function is called for the projector while initUndistortRectifyMap is called for the camera head. This is done after stereoRectify, which in turn is called after stereoCalibrate. If the projector-camera pair is not calibrated, it is still possible to compute the rectification transformations directly from the fundamental matrix using stereoRectifyUncalibrated. For the projector and camera, the function computes homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D space. R can be computed from H as

\[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\]

where cameraMatrix can be chosen arbitrarily.

Parameters

cameraMatrix	Input camera matrix \(A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) .
distCoeffs	Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
R	Optional rectification transformation in the object space (3x3 matrix). R1 or R2, computed by stereoRectify can be passed here. If the matrix is empty, the identity transformation is assumed.
newCameraMatrix	New camera matrix \(A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\).
size	Distorted image size.
m1type	Type of the first output map. Can be CV_32FC1, CV_32FC2 or CV_16SC2, see convertMaps
map1	The first output map for remap.
map2	The second output map for remap.

initUndistortRectifyMap()

void cv::initUndistortRectifyMap	(	InputArray	cameraMatrix,
		InputArray	distCoeffs,
		InputArray	R,
		InputArray	newCameraMatrix,
		Size	size,
		int	m1type,
		OutputArray	map1,
		OutputArray	map2 )

Python:
	cv.initUndistortRectifyMap(	cameraMatrix, distCoeffs, R, newCameraMatrix, size, m1type[, map1[, map2]]	) ->	map1, map2

#include <opencv2/imgproc.hpp>

Computes the undistortion and rectification transformation map.

The function computes the joint undistortion and rectification transformation and represents the result in the form of maps for remap. The undistorted image looks like original, as if it is captured with a camera using the camera matrix =newCameraMatrix and zero distortion. In case of a monocular camera, newCameraMatrix is usually equal to cameraMatrix, or it can be computed by getOptimalNewCameraMatrix for a better control over scaling. In case of a stereo camera, newCameraMatrix is normally set to P1 or P2 computed by stereoRectify .

Also, this new camera is oriented differently in the coordinate space, according to R. That, for example, helps to align two heads of a stereo camera so that the epipolar lines on both images become horizontal and have the same y- coordinate (in case of a horizontally aligned stereo camera).

The function actually builds the maps for the inverse mapping algorithm that is used by remap. That is, for each pixel \((u, v)\) in the destination (corrected and rectified) image, the function computes the corresponding coordinates in the source image (that is, in the original image from camera). The following process is applied:

\[\begin{array}{l} x \leftarrow (u - {c'}_x)/{f'}_x \\ y \leftarrow (v - {c'}_y)/{f'}_y \\ {[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\ x' \leftarrow X/W \\ y' \leftarrow Y/W \\ r^2 \leftarrow x'^2 + y'^2 \\ x'' \leftarrow x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4\\ y'' \leftarrow y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\ s\vecthree{x'''}{y'''}{1} = \vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)} {0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)} {0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\ map_x(u,v) \leftarrow x''' f_x + c_x \\ map_y(u,v) \leftarrow y''' f_y + c_y \end{array} \]

where \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) are the distortion coefficients.

In case of a stereo camera, this function is called twice: once for each camera head, after stereoRectify, which in its turn is called after stereoCalibrate. But if the stereo camera was not calibrated, it is still possible to compute the rectification transformations directly from the fundamental matrix using stereoRectifyUncalibrated. For each camera, the function computes homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D space. R can be computed from H as

\[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\]

where cameraMatrix can be chosen arbitrarily.

Parameters

cameraMatrix	Input camera matrix \(A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) .
distCoeffs	Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
R	Optional rectification transformation in the object space (3x3 matrix). R1 or R2 , computed by stereoRectify can be passed here. If the matrix is empty, the identity transformation is assumed. In initUndistortRectifyMap R assumed to be an identity matrix.
newCameraMatrix	New camera matrix \(A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\).
size	Undistorted image size.
m1type	Type of the first output map that can be CV_32FC1, CV_32FC2 or CV_16SC2, see convertMaps
map1	The first output map.
map2	The second output map.

initWideAngleProjMap() [1/2]

float cv::initWideAngleProjMap	(	InputArray	cameraMatrix,
		InputArray	distCoeffs,
		Size	imageSize,
		int	destImageWidth,
		int	m1type,
		OutputArray	map1,
		OutputArray	map2,
		enum UndistortTypes	projType = PROJ_SPHERICAL_EQRECT,
		double	alpha = 0 )

#include <opencv2/imgproc.hpp>

initializes maps for remap for wide-angle

initWideAngleProjMap() [2/2]

float cv::initWideAngleProjMap ( InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, int destImageWidth, int m1type, OutputArray map1, OutputArray map2, int projType, double alpha = 0 )

inlinestatic

#include <opencv2/imgproc.hpp>

remap()

void cv::remap	(	InputArray	src,
		OutputArray	dst,
		InputArray	map1,
		InputArray	map2,
		int	interpolation,
		int	borderMode = BORDER_CONSTANT,
		const Scalar &	borderValue = Scalar(),
		AlgorithmHint	hint = cv::ALGO_HINT_DEFAULT )

Python:
	cv.remap(	src, map1, map2, interpolation[, dst[, borderMode[, borderValue[, hint]]]]	) ->	dst

#include <opencv2/imgproc.hpp>

Applies a generic geometrical transformation to an image.

The function remap transforms the source image using the specified map:

\[\texttt{dst} (x,y) = \texttt{src} (map_x(x,y),map_y(x,y))\]

with the WARP_RELATIVE_MAP flag :

\[\texttt{dst} (x,y) = \texttt{src} (x+map_x(x,y),y+map_y(x,y))\]

where values of pixels with non-integer coordinates are computed using one of available interpolation methods. \(map_x\) and \(map_y\) can be encoded as separate floating-point maps in \(map_1\) and \(map_2\) respectively, or interleaved floating-point maps of \((x,y)\) in \(map_1\), or fixed-point maps created by using convertMaps. The reason you might want to convert from floating to fixed-point representations of a map is that they can yield much faster (2x) remapping operations. In the converted case, \(map_1\) contains pairs (cvFloor(x), cvFloor(y)) and \(map_2\) contains indices in a table of interpolation coefficients.

This function cannot operate in-place.

Parameters

src	Source image.
dst	Destination image. It has the same size as map1 and the same type as src .
map1	The first map of either (x,y) points or just x values having the type CV_16SC2 , CV_32FC1, or CV_32FC2. See convertMaps for details on converting a floating point representation to fixed-point for speed.
map2	The second map of y values having the type CV_16UC1, CV_32FC1, or none (empty map if map1 is (x,y) points), respectively.
interpolation	Interpolation method (see InterpolationFlags). The methods INTER_AREA INTER_LINEAR_EXACT and INTER_NEAREST_EXACT are not supported by this function. The extra flag WARP_RELATIVE_MAP can be ORed to the interpolation method (e.g. INTER_LINEAR | WARP_RELATIVE_MAP)
borderMode	Pixel extrapolation method (see BorderTypes). When borderMode=BORDER_TRANSPARENT, it means that the pixels in the destination image that corresponds to the "outliers" in the source image are not modified by the function.
borderValue	Value used in case of a constant border. By default, it is 0.
hint	Implementation modification flags. Set ALGO_HINT_APPROX to use FP16 precision (if available) for linear calculation for faster speed. See AlgorithmHint.

Note

Due to current implementation limitations the size of an input and output images should be less than 32767x32767.

resize()

void cv::resize	(	InputArray	src,
		OutputArray	dst,
		Size	dsize,
		double	fx = 0,
		double	fy = 0,
		int	interpolation = INTER_LINEAR )

Python:
	cv.resize(	src, dsize[, dst[, fx[, fy[, interpolation]]]]	) ->	dst

#include <opencv2/imgproc.hpp>

Resizes an image.

The function resize resizes the image src down to or up to the specified size. Note that the initial dst type or size are not taken into account. Instead, the size and type are derived from the src,dsize,fx, and fy. If you want to resize src so that it fits the pre-created dst, you may call the function as follows:

// explicitly specify dsize=dst.size(); fx and fy will be computed from that.
resize(src, dst, dst.size(), 0, 0, interpolation);

If you want to decimate the image by factor of 2 in each direction, you can call the function this way:

// specify fx and fy and let the function compute the destination image size.
resize(src, dst, Size(), 0.5, 0.5, interpolation);

To shrink an image, it will generally look best with INTER_AREA interpolation, whereas to enlarge an image, it will generally look best with INTER_CUBIC (slow) or INTER_LINEAR (faster but still looks OK).

Parameters

src	input image.
dst	output image; it has the size dsize (when it is non-zero) or the size computed from src.size(), fx, and fy; the type of dst is the same as of src.
dsize	output image size; if it equals zero (None in Python), it is computed as: \[\texttt{dsize = Size(round(fx*src.cols), round(fy*src.rows))}\] Either dsize or both fx and fy must be non-zero.
fx	scale factor along the horizontal axis; when it equals 0, it is computed as \[\texttt{(double)dsize.width/src.cols}\]
fy	scale factor along the vertical axis; when it equals 0, it is computed as \[\texttt{(double)dsize.height/src.rows}\]
interpolation	interpolation method, see InterpolationFlags

See also

warpAffine, warpPerspective, remap

Examples

modules/shape/samples/shape_example.cpp, samples/cpp/image_alignment.cpp, samples/cpp/snippets/epipolar_lines.cpp, samples/cpp/stitching_detailed.cpp, samples/cpp/videowriter.cpp, samples/dnn/colorization.cpp, samples/dnn/segmentation.cpp, samples/facedetect.cpp, and samples/hog_tapi.cpp.

undistort()

void cv::undistort	(	InputArray	src,
		OutputArray	dst,
		InputArray	cameraMatrix,
		InputArray	distCoeffs,
		InputArray	newCameraMatrix = noArray() )

Python:
	cv.undistort(	src, cameraMatrix, distCoeffs[, dst[, newCameraMatrix]]	) ->	dst

#include <opencv2/imgproc.hpp>

Transforms an image to compensate for lens distortion.

The function transforms an image to compensate radial and tangential lens distortion.

The function is simply a combination of initUndistortRectifyMap (with unity R ) and remap (with bilinear interpolation). See the former function for details of the transformation being performed.

Those pixels in the destination image, for which there is no correspondent pixels in the source image, are filled with zeros (black color).

A particular subset of the source image that will be visible in the corrected image can be regulated by newCameraMatrix. You can use getOptimalNewCameraMatrix to compute the appropriate newCameraMatrix depending on your requirements.

The camera matrix and the distortion parameters can be determined using calibrateCamera. If the resolution of images is different from the resolution used at the calibration stage, \(f_x, f_y, c_x\) and \(c_y\) need to be scaled accordingly, while the distortion coefficients remain the same.

Parameters

src	Input (distorted) image.
dst	Output (corrected) image that has the same size and type as src .
cameraMatrix	Input camera matrix \(A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\) .
distCoeffs	Input vector of distortion coefficients \((k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\) of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
newCameraMatrix	Camera matrix of the distorted image. By default, it is the same as cameraMatrix but you may additionally scale and shift the result by using a different matrix.

warpAffine()

void cv::warpAffine	(	InputArray	src,
		OutputArray	dst,
		InputArray	M,
		Size	dsize,
		int	flags = INTER_LINEAR,
		int	borderMode = BORDER_CONSTANT,
		const Scalar &	borderValue = Scalar(),
		AlgorithmHint	hint = cv::ALGO_HINT_DEFAULT )

Python:
	cv.warpAffine(	src, M, dsize[, dst[, flags[, borderMode[, borderValue[, hint]]]]]	) ->	dst

#include <opencv2/imgproc.hpp>

Applies an affine transformation to an image.

The function warpAffine transforms the source image using the specified matrix:

\[\texttt{dst} (x,y) = \texttt{src} ( \texttt{M} _{11} x + \texttt{M} _{12} y + \texttt{M} _{13}, \texttt{M} _{21} x + \texttt{M} _{22} y + \texttt{M} _{23})\]

when the flag WARP_INVERSE_MAP is set. Otherwise, the transformation is first inverted with invertAffineTransform and then put in the formula above instead of M. The function cannot operate in-place.

Parameters

src	input image.
dst	output image that has the size dsize and the same type as src .
M	\(2\times 3\) transformation matrix.
dsize	size of the output image.
flags	combination of interpolation methods (see InterpolationFlags) and the optional flag WARP_INVERSE_MAP that means that M is the inverse transformation ( \(\texttt{dst}\rightarrow\texttt{src}\) ).
borderMode	pixel extrapolation method (see BorderTypes); when borderMode=BORDER_TRANSPARENT, it means that the pixels in the destination image corresponding to the "outliers" in the source image are not modified by the function.
borderValue	value used in case of a constant border; by default, it is 0.
hint	Implementation modification flags. Set ALGO_HINT_APPROX to use FP16 precision (if available) for linear calculation for faster speed. See AlgorithmHint.

See also

warpPerspective, resize, remap, getRectSubPix, transform

Examples

samples/cpp/image_alignment.cpp.

warpPerspective()

void cv::warpPerspective	(	InputArray	src,
		OutputArray	dst,
		InputArray	M,
		Size	dsize,
		int	flags = INTER_LINEAR,
		int	borderMode = BORDER_CONSTANT,
		const Scalar &	borderValue = Scalar(),
		AlgorithmHint	hint = cv::ALGO_HINT_DEFAULT )

Python:
	cv.warpPerspective(	src, M, dsize[, dst[, flags[, borderMode[, borderValue[, hint]]]]]	) ->	dst

#include <opencv2/imgproc.hpp>

Applies a perspective transformation to an image.

The function warpPerspective transforms the source image using the specified matrix:

\[\texttt{dst} (x,y) = \texttt{src} \left ( \frac{M_{11} x + M_{12} y + M_{13}}{M_{31} x + M_{32} y + M_{33}} , \frac{M_{21} x + M_{22} y + M_{23}}{M_{31} x + M_{32} y + M_{33}} \right )\]

when the flag WARP_INVERSE_MAP is set. Otherwise, the transformation is first inverted with invert and then put in the formula above instead of M. The function cannot operate in-place.

Parameters

src	input image.
dst	output image that has the size dsize and the same type as src .
M	\(3\times 3\) transformation matrix.
dsize	size of the output image.
flags	combination of interpolation methods (INTER_LINEAR or INTER_NEAREST) and the optional flag WARP_INVERSE_MAP, that sets M as the inverse transformation ( \(\texttt{dst}\rightarrow\texttt{src}\) ).
borderMode	pixel extrapolation method (BORDER_CONSTANT or BORDER_REPLICATE).
borderValue	value used in case of a constant border; by default, it equals 0.
hint	Implementation modification flags. Set ALGO_HINT_APPROX to use FP16 precision (if available) for linear calculation for faster speed. See AlgorithmHint.

See also

warpAffine, resize, remap, getRectSubPix, perspectiveTransform

Examples

samples/cpp/image_alignment.cpp, samples/cpp/snippets/warpPerspective_demo.cpp, samples/cpp/tutorial_code/features/Homography/homography_from_camera_displacement.cpp, and samples/dnn/text_detection.cpp.

warpPolar()

void cv::warpPolar	(	InputArray	src,
		OutputArray	dst,
		Size	dsize,
		Point2f	center,
		double	maxRadius,
		int	flags )

Python:
	cv.warpPolar(	src, dsize, center, maxRadius, flags[, dst]	) ->	dst

#include <opencv2/imgproc.hpp>

Remaps an image to polar or semilog-polar coordinates space.

Transform the source image using the following transformation:

\[dst(\rho , \phi ) = src(x,y) \]

where

\[\begin{array}{l} \vec{I} = (x - center.x, \;y - center.y) \\ \phi = Kangle \cdot \texttt{angle} (\vec{I}) \\ \rho = \left\{\begin{matrix} Klin \cdot \texttt{magnitude} (\vec{I}) & default \\ Klog \cdot log_e(\texttt{magnitude} (\vec{I})) & if \; semilog \\ \end{matrix}\right. \end{array} \]

and

\[\begin{array}{l} Kangle = dsize.height / 2\Pi \\ Klin = dsize.width / maxRadius \\ Klog = dsize.width / log_e(maxRadius) \\ \end{array} \]

Linear vs semilog mapping

Polar mapping can be linear or semi-log. Add one of WarpPolarMode to flags to specify the polar mapping mode.

Linear is the default mode.

The semilog mapping emulates the human "foveal" vision that permit very high acuity on the line of sight (central vision) in contrast to peripheral vision where acuity is minor.

Option on dsize:

• if both values in dsize <=0 (default), the destination image will have (almost) same area of source bounding circle:

  \[\begin{array}{l} dsize.area \leftarrow (maxRadius^2 \cdot \Pi) \\ dsize.width = \texttt{cvRound}(maxRadius) \\ dsize.height = \texttt{cvRound}(maxRadius \cdot \Pi) \\ \end{array}\]

• if only dsize.height <= 0, the destination image area will be proportional to the bounding circle area but scaled by Kx * Kx:

  \[\begin{array}{l} dsize.height = \texttt{cvRound}(dsize.width \cdot \Pi) \\ \end{array} \]

• if both values in dsize > 0 , the destination image will have the given size therefore the area of the bounding circle will be scaled to dsize.

Reverse mapping

You can get reverse mapping adding WARP_INVERSE_MAP to flags

        // direct transform using warpPolar (replacing deprecated functions)
        warpPolar(src, lin_polar_img, Size(),center, maxRadius, flags);                     // Linear-polar transform
        warpPolar(src, log_polar_img, Size(),center, maxRadius, flags + WARP_POLAR_LOG);    // Log-polar transform
        // inverse transform
        warpPolar(lin_polar_img, recovered_lin_polar_img, src.size(), center, maxRadius, flags + WARP_INVERSE_MAP);
        warpPolar(log_polar_img, recovered_log_polar, src.size(), center, maxRadius, flags + WARP_POLAR_LOG + WARP_INVERSE_MAP);

In addition, to calculate the original coordinate from a polar mapped coordinate \((rho, phi)->(x, y)\):

        double angleRad, magnitude;
        double Kangle = dst.rows / CV_2PI;
        angleRad = phi / Kangle;
        if (flags & WARP_POLAR_LOG)
        {
            double Klog = dst.cols / std::log(maxRadius);
            magnitude = std::exp(rho / Klog);
        }
        else
        {
            double Klin = dst.cols / maxRadius;
            magnitude = rho / Klin;
        }
        int x = cvRound(center.x + magnitude * cos(angleRad));
        int y = cvRound(center.y + magnitude * sin(angleRad));

Parameters

src	Source image.
dst	Destination image. It will have same type as src.
dsize	The destination image size (see description for valid options).
center	The transformation center.
maxRadius	The radius of the bounding circle to transform. It determines the inverse magnitude scale parameter too.
flags	A combination of interpolation methods, InterpolationFlags + WarpPolarMode. Add WARP_POLAR_LINEAR to select linear polar mapping (default) Add WARP_POLAR_LOG to select semilog polar mapping Add WARP_INVERSE_MAP for reverse mapping.

Note

• The function can not operate in-place.
• To calculate magnitude and angle in degrees cartToPolar is used internally thus angles are measured from 0 to 360 with accuracy about 0.3 degrees.
• This function uses remap. Due to current implementation limitations the size of an input and output images should be less than 32767x32767.

See also

cv::remap