Geometric Image Transformations

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_MAX = 7,   cv::WARP_FILL_OUTLIERS = 8,   cv::WARP_INVERSE_MAP = 16 }
	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::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.
Mat	cv::getAffineTransform (const Point2f src[], const Point2f dst[])
	Calculates an affine transform from three pairs of the corresponding points.
Mat	cv::getAffineTransform (InputArray src, InputArray dst)
Mat	cv::getPerspectiveTransform (InputArray src, InputArray dst, int solveMethod=DECOMP_LU)
	Calculates a perspective transform from four pairs of the corresponding points.
Mat	cv::getPerspectiveTransform (const Point2f src[], const Point2f dst[], int solveMethod=DECOMP_LU)
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.
Mat	cv::getRotationMatrix2D (Point2f center, double angle, double scale)
	Calculates an affine matrix of 2D rotation.
void	cv::invertAffineTransform (InputArray M, OutputArray iM)
	Inverts an affine transformation.
void	cv::linearPolar (InputArray src, OutputArray dst, Point2f center, double maxRadius, int flags)
	Remaps an image to polar coordinates space.
void	cv::logPolar (InputArray src, OutputArray dst, Point2f center, double M, int flags)
	Remaps an image to semilog-polar coordinates space.
void	cv::remap (InputArray src, OutputArray dst, InputArray map1, InputArray map2, int interpolation, int borderMode=BORDER_CONSTANT, const Scalar &borderValue=Scalar())
	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::warpAffine (InputArray src, OutputArray dst, InputArray M, Size dsize, int flags=INTER_LINEAR, int borderMode=BORDER_CONSTANT, const Scalar &borderValue=Scalar())
	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())
	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.

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.

Enumeration Type Documentation

enum cv::InterpolationFlags

interpolation algorithm

Enumerator
INTER_NEAREST	nearest neighbor interpolation
INTER_LINEAR	bilinear interpolation
INTER_CUBIC	bicubic interpolation
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	Lanczos interpolation over 8x8 neighborhood
INTER_LINEAR_EXACT	Bit exact bilinear interpolation
INTER_MAX	mask for interpolation codes
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	flag, inverse transformation For example, linearPolar or logPolar transforms: flag is not set: \(dst( \rho , \phi ) = src(x,y)\) flag is set: \(dst(x,y) = src( \rho , \phi )\)

enum cv::InterpolationMasks

Enumerator
INTER_BITS
INTER_BITS2
INTER_TAB_SIZE
INTER_TAB_SIZE2

enum cv::WarpPolarMode

Specify the polar mapping mode.

See Also

warpPolar

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

Function Documentation

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.

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

Mat cv::getAffineTransform	(	const Point2f	src[],
		const Point2f	dst[]
	)

Calculates an affine transform from three pairs of the corresponding points.

The function calculates the \(2 \times 3\) matrix of an affine transform so that:

\[\begin{bmatrix} x'_i \\ y'_i \end{bmatrix} = \texttt{map_matrix} \cdot \begin{bmatrix} x_i \\ y_i \\ 1 \end{bmatrix}\]

where

\[dst(i)=(x'_i,y'_i), src(i)=(x_i, y_i), i=0,1,2\]

Parameters

src	Coordinates of triangle vertices in the source image.
dst	Coordinates of the corresponding triangle vertices in the destination image.

See Also

warpAffine, transform

Mat cv::getAffineTransform	(	InputArray	src,
		InputArray	dst
	)

Mat cv::getPerspectiveTransform	(	InputArray	src,
		InputArray	dst,
		int	solveMethod = DECOMP_LU
	)

Calculates a perspective transform from four pairs of the corresponding points.

The function calculates the \(3 \times 3\) matrix of a perspective transform so that:

\[\begin{bmatrix} t_i x'_i \\ t_i y'_i \\ t_i \end{bmatrix} = \texttt{map_matrix} \cdot \begin{bmatrix} x_i \\ y_i \\ 1 \end{bmatrix}\]

where

\[dst(i)=(x'_i,y'_i), src(i)=(x_i, y_i), i=0,1,2,3\]

Parameters

src	Coordinates of quadrangle vertices in the source image.
dst	Coordinates of the corresponding quadrangle vertices in the destination image.
solveMethod	method passed to cv::solve (DecompTypes)

See Also

findHomography, warpPerspective, perspectiveTransform

Mat cv::getPerspectiveTransform	(	const Point2f	src[],
		const Point2f	dst[],
		int	solveMethod = DECOMP_LU
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

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.

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

Mat cv::getRotationMatrix2D	(	Point2f	center,
		double	angle,
		double	scale
	)

Calculates an affine matrix of 2D rotation.

The function calculates the following matrix:

\[\begin{bmatrix} \alpha & \beta & (1- \alpha ) \cdot \texttt{center.x} - \beta \cdot \texttt{center.y} \\ - \beta & \alpha & \beta \cdot \texttt{center.x} + (1- \alpha ) \cdot \texttt{center.y} \end{bmatrix}\]

where

\[\begin{array}{l} \alpha = \texttt{scale} \cdot \cos \texttt{angle} , \\ \beta = \texttt{scale} \cdot \sin \texttt{angle} \end{array}\]

The transformation maps the rotation center to itself. If this is not the target, adjust the shift.

Parameters

center	Center of the rotation in the source image.
angle	Rotation angle in degrees. Positive values mean counter-clockwise rotation (the coordinate origin is assumed to be the top-left corner).
scale	Isotropic scale factor.

See Also

getAffineTransform, warpAffine, transform

void cv::invertAffineTransform	(	InputArray	M,
		OutputArray	iM
	)

Inverts an affine transformation.

The function computes an inverse affine transformation represented by \(2 \times 3\) matrix M:

\[\begin{bmatrix} a_{11} & a_{12} & b_1 \\ a_{21} & a_{22} & b_2 \end{bmatrix}\]

The result is also a \(2 \times 3\) matrix of the same type as M.

Parameters

M	Original affine transformation.
iM	Output reverse affine transformation.

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

Remaps an image to polar coordinates space.

Deprecated:

This function produces same result as cv::warpPolar(src, dst, src.size(), center, maxRadius, flags)

Examples:

samples/cpp/polar_transforms.cpp.

void cv::logPolar	(	InputArray	src,
		OutputArray	dst,
		Point2f	center,
		double	M,
		int	flags
	)

Remaps an image to semilog-polar coordinates space.

Deprecated:

This function produces same result as cv::warpPolar(src, dst, src.size(), center, maxRadius, flags+WARP_POLAR_LOG);

Examples:

samples/cpp/polar_transforms.cpp.

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

Applies a generic geometrical transformation to an image.

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

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

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 method INTER_AREA is not supported by this function.
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.

Note

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

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

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 c::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, 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:

samples/cpp/image_alignment.cpp, samples/cpp/train_HOG.cpp, samples/dnn/colorization.cpp, samples/dnn/object_detection.cpp, and samples/dnn/segmentation.cpp.

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

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.

See Also

warpPerspective, resize, remap, getRectSubPix, transform

Examples:

samples/cpp/image_alignment.cpp.

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

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.

See Also

warpAffine, resize, remap, getRectSubPix, perspectiveTransform

Examples:

samples/cpp/image_alignment.cpp.

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.

Polar remaps reference

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
        warpPolar(src, lin_polar_img, Size(),center, maxRadius, flags);                     // linear Polar
        warpPolar(src, log_polar_img, Size(),center, maxRadius, flags + WARP_POLAR_LOG);    // semilog Polar
        // 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 addiction, 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

Examples:

samples/cpp/polar_transforms.cpp.