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Nancy was very busy yesterday. She1.C&up before 7∶00 in the morning. She2.A&her face very quickly and had some3.B&and bread for4.C&. It was a fine day. She went to5.C&early. She had four6.A&in the morning. She7.B&a rest after lunch, and she worked very hard in class8.A&. She played9.A&after school and then went home.10.C&home she bought a pen. When she11.A&home she had a short rest. After that she quickly cooked dinner and12.B&. She13.A&TV for14.B&hour after dinner. Then she did her homework and went to15.A&before ten.1.A、get&&&&B、gets&&&C、got2.A、washed&&&B、did&&&C、washes3.A、relax &&&B、milk&&&C、koala4.A、lunch&&&B、dinner&&C、breakfast5.A、beach&&&B、office&&C、school6.A、classes&&&B、class&&C、rooms7.A、have&&&B、had&&&C、has8.A、all day&&&B、the all day&&C、all a day9.A、volleyball&&B、the basketball&C、the chess10.A.、To her way&B、On her way to&C、On her way11.A、got &&&B、reached to&&C、got to12.A、doing some cleaning B、did some cleaning&C、clean the house13.A、watched&&B、read&&&C、saw14.A、a&&&&B、an&&&C、the15.A、bed&&&B、beds&&&C、the bed
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习题“Nancy was very busy yesterday. She____up before 7∶00 in the morning. She____her face very quickly and had...”的分析与解答如下所示：
这篇短文主要介绍了南希繁忙的一天，早晨她七点以前就起来了。上完一天的课程还做了饭，整理了房间。1.2.3.A、relax放松，动词B、milk牛奶C、koala考拉。根据句意，她早饭吃了牛奶和面包，故选B。4.A、lunch&午饭B、dinner晚饭C、breakfast早饭。根据上下文可知是早饭吃了牛奶和面包，故选C。5.A、beach沙滩B、office办公室C、school学校。根据上下文可知她是个学生，所以她上学早。故选C.6.A、classes课，班级，复数形式B、class课，班级C、rooms房间。根据句意她上午有四节课，故选A。7.8.9.A、volleyball排球B、the basketball篮球C、the chess象棋。根据球类运动和棋类前不加任何冠词，故选A。10.11.当她到达家，她稍事休息了一下。reach，直接加地点，got to到达，如果是地点副词，to要省略掉，根据home是地点副词，故选A12.A、doing some cleaning做清整B、did some cleaning做清整C、clean the house清理房子。在那之后她很快的做了饭，然后做清整。根据and连接并列结构，上句是过去时态，故选过去时态，故选B。13.A、watched看B、read读C、saw看到。根据句意，她看了电视，watch TV看电视，故选A。14.15.
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欢迎来到乐乐题库，查看习题“Nancy was very busy yesterday. She____up before 7∶00 in the morning. She____her face very quickly and had some____and bread for____. It was a fine day. She went to____early. She had four____in the morning. She____a rest after lunch, and she worked very hard in class____. She played____after school and then went home.____home she bought a pen. When she____home she had a short rest. After that she quickly cooked dinner and____. She____TV for____hour after dinner. Then she did her homework and went to____before ten.1.A、getB、getsC、got2.A、washedB、didC、washes3.A、relax B、milkC、koala4.A、lunchB、dinnerC、breakfast5.A、beachB、officeC、school6.A、classesB、classC、rooms7.A、haveB、hadC、has8.A、all dayB、the all dayC、all a day9.A、volleyballB、the basketballC、the chess10.A.、To her wayB、On her way toC、On her way11.A、got B、reached toC、got to12.A、doing some cleaning B、did some cleaningC、clean the house13.A、watchedB、readC、saw14.A、aB、anC、the15.A、bedB、bedsC、the bed”的答案、考点梳理，并查找与习题“Nancy was very busy yesterday. She____up before 7∶00 in the morning. She____her face very quickly and had some____and bread for____. It was a fine day. She went to____early. She had four____in the morning. She____a rest after lunch, and she worked very hard in class____. She played____after school and then went home.____home she bought a pen. When she____home she had a short rest. After that she quickly cooked dinner and____. She____TV for____hour after dinner. Then she did her homework and went to____before ten.1.A、getB、getsC、got2.A、washedB、didC、washes3.A、relax B、milkC、koala4.A、lunchB、dinnerC、breakfast5.A、beachB、officeC、school6.A、classesB、classC、rooms7.A、haveB、hadC、has8.A、all dayB、the all dayC、all a day9.A、volleyballB、the basketballC、the chess10.A.、To her wayB、On her way toC、On her way11.A、got B、reached toC、got to12.A、doing some cleaning B、did some cleaningC、clean the house13.A、watchedB、readC、saw14.A、aB、anC、the15.A、bedB、bedsC、the bed”相似的习题。英语名篇名段背诵精华 01 Life is a chess-board
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http://image.tingclass.net/statics/js/2012
The chess-board is the world:the pieces are the pheno the rules of the game are what we call the laws of nature. The player on the other side is hidden from us. We know that his play is always fair, just and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance.
By Thomas Henry Huxley
棋盘宛如世界：一个个棋子仿佛世间的种种现象：游戏规则就是我们所称的自然法则。竞争对手藏于暗处，不为我们所见。我们知晓，这位对手向来处事公平，正义凛然，极富耐心。然而，我们也明白，这位对手从不忽视任何错误，或者因为我们的无知而做出一丝让步，所以我们也必须为此付出代价。
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订阅每日学英语：Position &
online interactive chessboard with PGN viewer and editor, diagram editor and puzzle editor
set up any position to play against computer or analyze with a chess engine
make diagrams with arrows and selected squares
or animations indicating moves with arrows
create links to your chess positions or embed chessboards on your own pages
design chess puzzles:
the computer replies even if the user goes wrong
the computer tries multiple defenses before admitting success
the user is allowed a choice of alternative solutions
Interactive Chessboards Manifesto
Every chess diagram on the Internet should be interactive in the following ways:
One can generate the FEN of the position that is shown on the diagram.
One can generate the PGN of the game fragment of an animated diagram.
One can easily start an interface that allows making moves on the chessboard to study the position by analysis.
One can easily start an interface for playing the position against computer from both sides.
Play against computer should allow the user to make all the moves by oneself and force the computer to move at any moment.
The positions and game lines that are played out in the two points above should satisfy the first points of always being able to generate the FEN and PGN.
The board can be flipped at any moment so that there is always the choice between having White or Black at the bottom.
The Apronus.com chess service implements this vision.
Additionally, you can make static and animated diagrams as images for posting in your blog or website.
Chess authors can participate in this vision by placing links to Apronus.com pages with the chess content encoded in the links.
For example, you can wrap the &a& HTML tag around any image of a chess position
and put a link into href that encodes the position and directs the user to play against computer at Apronus.com.
The interfaces here provide ready-made HTML code to embed in your pages.
Chess at Apronus.com is free for non-commercial amateur use only.
PGN Viewer and Editor
Puzzle Editor
import PGN
chessboard with dimension
coordinates
(100 = one second)
show diagram in new window to save manually
show diagram in new window to copy the link from there
direct download by the browser
Chess at Apronus.com is free for non-commercial amateur use only.
download PGN file
Chess at Apronus.com is free for non-commercial amateur use only.
HTML code to embed in your own page &
with PGN to recreate the chess content
embedded preview
Chess at Apronus.com is free for non-commercial amateur use only.
HTML code to embed in your own page &
with PGN to recreate the chess content
Chess at Apronus.com is free for non-commercial amateur use only.
If this URL is too long, click
to obtain a short one instead.
Chess at Apronus.com is free for non-commercial amateur use only.
Preview of embedded puzzle
Chess at Apronus.com is free for non-commercial amateur use only.
Paste your PGN file below and click
import PGN
Chess at Apronus.com is free for non-commercial amateur use only.Camera Calibration and 3D Reconstruction & OpenCV 2.4.13.6 documentation
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Camera Calibration and 3D Reconstruction
The functions in this section use a so-called pinhole camera model. In this model, a scene view is formed by projecting 3D points into the image plane
using a perspective transformation.
are the coordinates of a 3D point in the world coordinate space
are the coordinates of the projection point in pixels
is a camera matrix, or a matrix of intrinsic parameters
is a principal point that is usually at the image center
are the focal lengths expressed in pixel units.
Thus, if an image from the camera is
scaled by a factor, all of these parameters should
be scaled (multiplied/divided, respectively) by the same factor. The
matrix of intrinsic parameters does not depend on the scene viewed. So,
once estimated, it can be re-used as long as the focal length is fixed (in
case of zoom lens). The joint rotation-translation matrix
is called a matrix of extrinsic parameters. It is used to describe the
camera motion around a static scene, or vice versa, rigid motion of an
object in front of a still camera. That is,
translates
coordinates of a point
to a coordinate system,
fixed with respect to the camera. The transformation above is equivalent
to the following (when
The following figure illustrates the pinhole camera model.
Real lenses usually have some distortion, mostly
radial distortion and slight tangential distortion. So, the above model
is extended as:
are radial distortion coefficients.
are tangential distortion coefficients.
Higher-order coefficients are not considered in OpenCV.
The next figure shows two common types of radial distortion: barrel distortion (typically
and pincushion distortion (typically ).
In the functions below the coefficients are passed or returned as
vector. That is, if the vector contains four elements, it means that
The distortion coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera parameters. And they remain the same regardless of the captured image resolution.
If, for example, a camera has been calibrated on images of
320 x 240 resolution, absolutely the same distortion coefficients can
be used for 640 x 480 images from the same camera while
need to be scaled appropriately.
The functions below use the above model to do the following:
Project 3D points to the image plane given intrinsic and extrinsic parameters.
Compute extrinsic parameters given intrinsic parameters, a few 3D points, and their projections.
Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (every view is described by several 3D-2D point correspondences).
Estimate the relative position and orientation of the stereo camera “heads” and compute the rectification transformation that makes the camera optical axes parallel.
A calibration sample for 3 cameras in horizontal position can be found at opencv_source_code/samples/cpp/3calibration.cpp
A calibration sample based on a sequence of images can be found at opencv_source_code/samples/cpp/calibration.cpp
A calibration sample in order to do 3D reconstruction can be found at opencv_source_code/samples/cpp/build3dmodel.cpp
A calibration sample of an artificially generated camera and chessboard patterns can be found at opencv_source_code/samples/cpp/calibration_artificial.cpp
A calibration example on stereo calibration can be found at opencv_source_code/samples/cpp/stereo_calib.cpp
A calibration example on stereo matching can be found at opencv_source_code/samples/cpp/stereo_match.cpp
(Python) A camera calibration sample can be found at opencv_source_code/samples/python2/calibrate.py
calibrateCamera
Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
C++: double calibrateCamera(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, InputOutputArray cameraMatrix, InputOutputArray distCoeffs, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags=0, TermCriteria criteria=TermCriteria( TermCriteria::COUNT+TermCriteria::EPS, 30, DBL_EPSILON) )
Python: cv2.calibrateCamera(objectPoints, imagePoints, imageSize[, cameraMatrix[, distCoeffs[, rvecs[, tvecs[, flags[, criteria]]]]]]) & retval, cameraMatrix, distCoeffs, rvecs, tvecs
C: double cvCalibrateCamera2(const CvMat* object_points, const CvMat* image_points, const CvMat* point_counts, CvSize image_size, CvMat* camera_matrix, CvMat* distortion_coeffs, CvMat* rotation_vectors=NULL, CvMat* translation_vectors=NULL, int flags=0, CvTermCriteria term_crit=cvTermCriteria( CV_TERMCRIT_ITER+CV_TERMCRIT_EPS,30,DBL_EPSILON) )
Python: cv.CalibrateCamera2(objectPoints, imagePoints, pointCounts, imageSize, cameraMatrix, distCoeffs, rvecs, tvecs, flags=0) & None
Parameters:
objectPoints – In the new interface it is a vector of vectors of calibration pattern points in the calibration pattern coordinate space (e.g. std::vector&std::vector&cv::Vec3f&&). The outer vector contains as many elements as the number of the pattern views. If the same calibration pattern is shown in each view and it is fully visible, all the vectors will be the same. Although, it is possible to use partially occluded patterns, or even different patterns in different views. Then, the vectors will be different. The points are 3D, but since they are in a pattern coordinate system, then, if the rig is planar, it may make sense to put the model to a XY coordinate plane so that Z-coordinate of each input object point is 0.
In the old interface all the vectors of object points from different views are concatenated together.
imagePoints – In the new interface it is a vector of vectors of the projections of calibration pattern points (e.g. std::vector&std::vector&cv::Vec2f&&). imagePoints.size() and objectPoints.size() and imagePoints[i].size() must be equal to objectPoints[i].size() for each i.
In the old interface all the vectors of object points from different views are concatenated together.
point_counts – In the old interface this is a vector of integers, containing as many elements, as the number of views of the calibration pattern. Each element is the number of points in each view. Usually, all the elements are the same and equal to the number of feature points on the calibration pattern.
imageSize – Size of the image used only to initialize the intrinsic camera matrix.
cameraMatrix – Output 3x3 floating-point camera matrix
CV_CALIB_USE_INTRINSIC_GUESS
CV_CALIB_FIX_ASPECT_RATIO
are specified, some or all of
fx, fy, cx, cy
must be initialized before calling the function.
distCoeffs – Output vector of distortion coefficients
of 4, 5, or 8 elements.
rvecs – Output
of rotation vectors (see
) estimated for each pattern view (e.g. std::vector&cv::Mat&&). That is, each k-th rotation vector together with the corresponding k-th translation vector (see the next output parameter description) brings the calibration pattern from the model coordinate space (in which object points are specified) to the world coordinate space, that is, a real position of the calibration pattern in the k-th pattern view (k=0.. M -1).
tvecs – Output vector of translation vectors estimated for each pattern view.
flags – Different flags that may be zero or a combination of the following values:
CV_CALIB_USE_INTRINSIC_GUESS cameraMatrix
contains valid initial values of
fx, fy, cx, cy
that are optimized further. Otherwise, (cx, cy)
is initially set to the image center ( imageSize
is used), and focal distances are computed in a least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate extrinsic parameters. Use
CV_CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global optimization. It stays at the center or at a different location specified when
CV_CALIB_USE_INTRINSIC_GUESS
is set too.
CV_CALIB_FIX_ASPECT_RATIO The functions considers only
as a free parameter. The ratio
stays the same as in the input
cameraMatrix .
CV_CALIB_USE_INTRINSIC_GUESS
is not set, the actual input values of
are ignored, only their ratio is computed and used further.
CV_CALIB_ZERO_TANGENT_DIST Tangential distortion coefficients
are set to zeros and stay zero.
CV_CALIB_FIX_K1,...,CV_CALIB_FIX_K6 The corresponding radial distortion coefficient is not changed during the optimization. If
CV_CALIB_USE_INTRINSIC_GUESS
is set, the coefficient from the supplied
distCoeffs
matrix is used. Otherwise, it is set to 0.
CV_CALIB_RATIONAL_MODEL Coefficients k4, k5, and k6 are enabled. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function computes
and returns
only 5 distortion coefficients.
criteria – Termination criteria for the iterative optimization algorithm.
term_crit – same as criteria.
The function estimates the intrinsic camera
parameters and extrinsic parameters for each of the views. The algorithm is based on
and . The coordinates of 3D object points and their corresponding 2D projections
in each view must be specified. That may be achieved by using an
object with a known geometry and easily detectable feature points.
Such an object is called a calibration rig or calibration pattern,
and OpenCV has built-in support for a chessboard as a calibration
). Currently, initialization
of intrinsic parameters (when CV_CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration patterns
(where Z-coordinates of the object points must be all zeros). 3D
calibration rigs can also be used as long as initial cameraMatrix is provided.
The algorithm performs the following steps:
Compute the initial intrinsic parameters (the option only available for planar calibration patterns) or read them from the input parameters. The distortion coefficients are all set to zeros initially unless some of CV_CALIB_FIX_K?
are specified.
Estimate the initial camera pose as if the intrinsic parameters have been already known. This is done using
Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error, that is, the total sum of squared distances between the observed feature points imagePoints
and the projected (using the current estimates for camera parameters and the poses) object points objectPoints. See
for details.
The function returns the final re-projection error.
If you use a non-square (=non-NxN) grid and
for calibration, and calibrateCamera returns bad values (zero distortion coefficients, an image center very far from (w/2-0.5,h/2-0.5), and/or large differences between
(ratios of 10:1 or more)), then you have probably used patternSize=cvSize(rows,cols) instead of using patternSize=cvSize(cols,rows) in
calibrationMatrixValues
Computes useful camera characteristics from the camera matrix.
C++: void calibrationMatrixValues(InputArray cameraMatrix, Size imageSize, double apertureWidth, double apertureHeight, double& fovx, double& fovy, double& focalLength, Point2d& principalPoint, double& aspectRatio)
Python: cv2.calibrationMatrixValues(cameraMatrix, imageSize, apertureWidth, apertureHeight) & fovx, fovy, focalLength, principalPoint, aspectRatio
Parameters:
cameraMatrix – Input camera matrix that can be estimated by
imageSize – Input image size in pixels.
apertureWidth – Physical width in mm of the sensor.
apertureHeight – Physical height in mm of the sensor.
fovx – Output field of view in degrees along the horizontal sensor axis.
fovy – Output field of view in degrees along the vertical sensor axis.
focalLength – Focal length of the lens in mm.
principalPoint – Principal point in mm.
aspectRatio –
The function computes various useful camera characteristics from the previously estimated camera matrix.
Do keep in mind that the unity measure ‘mm’ stands for whatever unit of measure one chooses for the chessboard pitch (it can thus be any value).
Combines two rotation-and-shift transformations.
C++: void composeRT(InputArray rvec1, InputArray tvec1, InputArray rvec2, InputArray tvec2, OutputArray rvec3, OutputArray tvec3, OutputArray dr3dr1=noArray(), OutputArray dr3dt1=noArray(), OutputArray dr3dr2=noArray(), OutputArray dr3dt2=noArray(), OutputArray dt3dr1=noArray(), OutputArray dt3dt1=noArray(), OutputArray dt3dr2=noArray(), OutputArray dt3dt2=noArray() )
Python: cv2.composeRT(rvec1, tvec1, rvec2, tvec2[, rvec3[, tvec3[, dr3dr1[, dr3dt1[, dr3dr2[, dr3dt2[, dt3dr1[, dt3dt1[, dt3dr2[, dt3dt2]]]]]]]]]]) & rvec3, tvec3, dr3dr1, dr3dt1, dr3dr2, dr3dt2, dt3dr1, dt3dt1, dt3dr2, dt3dt2
Parameters:
rvec1 – First rotation vector.
tvec1 – First translation vector.
rvec2 – Second rotation vector.
tvec2 – Second translation vector.
rvec3 – Output rotation vector of the superposition.
tvec3 – Output translation vector of the superposition.
d*d* – Optional output derivatives of
with regard to
rvec1, rvec2, tvec1 and tvec2, respectively.
The functions compute:
denotes a rotation vector to a rotation matrix transformation, and
denotes the inverse transformation. See
for details.
Also, the functions can compute the derivatives of the output vectors with regards to the input vectors (see
The functions are used inside
but can also be used in your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a function that contains a matrix multiplication.
computeCorrespondEpilines
For points in an image of a stereo pair, computes the corresponding epilines in the other image.
C++: void computeCorrespondEpilines(InputArray points, int whichImage, InputArray F, OutputArray lines)
C: void cvComputeCorrespondEpilines(const CvMat* points, int which_image, const CvMat* fundamental_matrix, CvMat* correspondent_lines)
Python: cv.ComputeCorrespondEpilines(points, whichImage, F, lines) & None
Parameters:
points – Input points.
matrix of type
vector&Point2f& .
whichImage – Index of the image (1 or 2) that contains the
F – Fundamental matrix that can be estimated using
lines – Output vector of the epipolar lines corresponding to the points in the other image. Each line
is encoded by 3 numbers
For every point in one of the two images of a stereo pair, the function finds the equation of the
corresponding epipolar line in the other image.
From the fundamental matrix definition (see
in the second image for the point
in the first image (when whichImage=1 ) is computed as:
And vice versa, when whichImage=2,
is computed from
Line coefficients are defined up to a scale. They are normalized so that
convertPointsToHomogeneous
Converts points from Euclidean to homogeneous space.
C++: void convertPointsToHomogeneous(InputArray src, OutputArray dst)
Python: cv2.convertPointsToHomogeneous(src[, dst]) & dst
Parameters:
src – Input vector of N-dimensional points.
dst – Output vector of N+1-dimensional points.
The function converts points from Euclidean to homogeneous space by appending 1’s to the tuple of point coordinates. That is, each point (x1, x2, ..., xn) is converted to (x1, x2, ..., xn, 1).
convertPointsFromHomogeneous
Converts points from homogeneous to Euclidean space.
C++: void convertPointsFromHomogeneous(InputArray src, OutputArray dst)
Python: cv2.convertPointsFromHomogeneous(src[, dst]) & dst
Parameters:
src – Input vector of N-dimensional points.
dst – Output vector of N-1-dimensional points.
The function converts points homogeneous to Euclidean space using perspective projection. That is, each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). When xn=0, the output point coordinates will be (0,0,0,...).
convertPointsHomogeneous
Converts points to/from homogeneous coordinates.
C++: void convertPointsHomogeneous(InputArray src, OutputArray dst)
C: void cvConvertPointsHomogeneous(const CvMat* src, CvMat* dst)
Python: cv.ConvertPointsHomogeneous(src, dst) & None
Parameters:
src – Input array or vector of 2D, 3D, or 4D points.
dst – Output vector of 2D, 3D, or 4D points.
The function converts 2D or 3D points from/to homogeneous coordinates by calling either
The function is obsolete. Use one of the previous two functions instead.
correctMatches
Refines coordinates of corresponding points.
C++: void correctMatches(InputArray F, InputArray points1, InputArray points2, OutputArray newPoints1, OutputArray newPoints2)
Python: cv2.correctMatches(F, points1, points2[, newPoints1[, newPoints2]]) & newPoints1, newPoints2
C: void cvCorrectMatches(CvMat* F, CvMat* points1, CvMat* points2, CvMat* new_points1, CvMat* new_points2)
Parameters:
F &# fundamental matrix.
points1 – 1xN array containing the first set of points.
points2 – 1xN array containing the second set of points.
newPoints1 – The optimized points1.
newPoints2 – The optimized points2.
The function implements the Optimal Triangulation Method (see Multiple View Geometry for details). For each given point correspondence points1[i] &-& points2[i], and a fundamental matrix F, it computes the corrected correspondences newPoints1[i] &-& newPoints2[i] that minimize the geometric error
is the geometric distance between points
) subject to the epipolar constraint
decomposeProjectionMatrix
Decomposes a projection matrix into a rotation matrix and a camera matrix.
C++: void decomposeProjectionMatrix(InputArray projMatrix, OutputArray cameraMatrix, OutputArray rotMatrix, OutputArray transVect, OutputArray rotMatrixX=noArray(), OutputArray rotMatrixY=noArray(), OutputArray rotMatrixZ=noArray(), OutputArray eulerAngles=noArray() )
Python: cv2.decomposeProjectionMatrix(projMatrix[, cameraMatrix[, rotMatrix[, transVect[, rotMatrixX[, rotMatrixY[, rotMatrixZ[, eulerAngles]]]]]]]) & cameraMatrix, rotMatrix, transVect, rotMatrixX, rotMatrixY, rotMatrixZ, eulerAngles
C: void cvDecomposeProjectionMatrix(const CvMat* projMatr, CvMat* calibMatr, CvMat* rotMatr, CvMat* posVect, CvMat* rotMatrX=NULL, CvMat* rotMatrY=NULL, CvMat* rotMatrZ=NULL, CvPoint3D64f* eulerAngles=NULL )
Python: cv.DecomposeProjectionMatrix(projMatrix, cameraMatrix, rotMatrix, transVect, rotMatrX=None, rotMatrY=None, rotMatrZ=None) & eulerAngles
Parameters:
projMatrix &# input projection matrix P.
cameraMatrix – Output 3x3 camera matrix K.
rotMatrix – Output 3x3 external rotation matrix R.
transVect – Output 4x1 translation vector T.
rotMatrX – Optional 3x3 rotation matrix around x-axis.
rotMatrY – Optional 3x3 rotation matrix around y-axis.
rotMatrZ – Optional 3x3 rotation matrix around z-axis.
eulerAngles – Optional three-element vector containing three Euler angles of rotation in degrees.
The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of a camera.
It optionally returns three rotation matrices, one for each axis, and three Euler angles that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principle axes that results in the same orientation of an object, eg. see . Returned tree rotation matrices and corresponding three Euler angules are only one of the possible solutions.
The function is based on
drawChessboardCorners
Renders the detected chessboard corners.
C++: void drawChessboardCorners(InputOutputArray image, Size patternSize, InputArray corners, bool patternWasFound)
Python: cv2.drawChessboardCorners(image, patternSize, corners, patternWasFound) & None
C: void cvDrawChessboardCorners(CvArr* image, CvSize pattern_size, CvPoint2D32f* corners, int count, int pattern_was_found)
Python: cv.DrawChessboardCorners(image, patternSize, corners, patternWasFound) & None
Parameters:
image – Destination image. It must be an 8-bit color image.
patternSize – Number of inner corners per a chessboard row and column (patternSize = cv::Size(points_per_row,points_per_column)).
corners – Array of detected corners, the output of findChessboardCorners.
patternWasFound – Parameter indicating whether the complete board was found or not. The return value of
should be passed here.
The function draws individual chessboard corners detected either as red circles if the board was not found, or as colored corners connected with lines if the board was found.
findChessboardCorners
Finds the positions of internal corners of the chessboard.
C++: bool findChessboardCorners(InputArray image, Size patternSize, OutputArray corners, int flags=CALIB_CB_ADAPTIVE_THRESH+CALIB_CB_NORMALIZE_IMAGE )
Python: cv2.findChessboardCorners(image, patternSize[, corners[, flags]]) & retval, corners
C: int cvFindChessboardCorners(const void* image, CvSize pattern_size, CvPoint2D32f* corners, int* corner_count=NULL, int flags=CV_CALIB_CB_ADAPTIVE_THRESH+CV_CALIB_CB_NORMALIZE_IMAGE )
Python: cv.FindChessboardCorners(image, patternSize, flags=CV_CALIB_CB_ADAPTIVE_THRESH) & corners
Parameters:
image – Source chessboard view. It must be an 8-bit grayscale or color image.
patternSize – Number of inner corners per a chessboard row and column ( patternSize = cvSize(points_per_row,points_per_colum) = cvSize(columns,rows) ).
corners – Output array of detected corners.
flags – Various operation flags that can be zero or a combination of the following values:
CALIB_CB_ADAPTIVE_THRESH Use adaptive thresholding to convert the image to black and white, rather than a fixed threshold level (computed from the average image brightness).
CALIB_CB_NORMALIZE_IMAGE Normalize the image gamma with
before applying fixed or adaptive thresholding.
CALIB_CB_FILTER_QUADS Use additional criteria (like contour area, perimeter, square-like shape) to filter out false quads extracted at the contour retrieval stage.
CALIB_CB_FAST_CHECK Run a fast check on the image that looks for chessboard corners, and shortcut the call if none is found. This can drastically speed up the call in the degenerate condition when no chessboard is observed.
The function attempts to determine
whether the input image is a view of the chessboard pattern and
locate the internal chessboard corners. The function returns a non-zero
value if all of the corners are found and they are placed
in a certain order (row by row, left to right in every row). Otherwise, if the function fails to find all the corners or reorder
them, it returns 0. For example, a regular chessboard has 8 x 8
squares and 7 x 7 internal corners, that is, points where the black squares touch each other.
The detected coordinates are approximate, and to determine their positions more accurately, the function calls .
You also may use the function
with different parameters if returned coordinates are not accurate enough.
Sample usage of detecting and drawing chessboard corners:
Size patternsize(8,6); //interior number of corners
Mat gray = ....; //source image
vector&Point2f& corners; //this will be filled by the detected corners
//CALIB_CB_FAST_CHECK saves a lot of time on images
//that do not contain any chessboard corners
bool patternfound = findChessboardCorners(gray, patternsize, corners,
CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
+ CALIB_CB_FAST_CHECK);
if(patternfound)
cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),
TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));
drawChessboardCorners(img, patternsize, Mat(corners), patternfound);
The function requires white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environments. Otherwise, if there is no border and the background is dark, the outer black squares cannot be segmented properly and so the square grouping and ordering algorithm fails.
findCirclesGrid
Finds centers in the grid of circles.
C++: bool findCirclesGrid(InputArray image, Size patternSize, OutputArray centers, int flags=CALIB_CB_SYMMETRIC_GRID, const Ptr&FeatureDetector&& blobDetector=new SimpleBlobDetector() )
Python: cv2.findCirclesGridDefault(image, patternSize[, centers[, flags]]) & retval, centers
Parameters:
image – grid v it must be an 8-bit grayscale or color image.
patternSize – number of circles per row and column ( patternSize = Size(points_per_row, points_per_colum) ).
centers – output array of detected centers.
flags – various operation flags that can be one of the following values:
CALIB_CB_SYMMETRIC_GRID uses symmetric pattern of circles.
CALIB_CB_ASYMMETRIC_GRID uses asymmetric pattern of circles.
CALIB_CB_CLUSTERING uses a special algorithm for grid detection. It is more robust to perspective distortions but much more sensitive to background clutter.
blobDetector – feature detector that finds blobs like dark circles on light background.
The function attempts to determine
whether the input image contains a grid of circles. If it is, the function locates centers of the circles. The function returns a
non-zero value if all of the centers have been found and they have been placed
in a certain order (row by row, left to right in every row). Otherwise, if the function fails to find all the corners or reorder
them, it returns 0.
Sample usage of detecting and drawing the centers of circles:
Size patternsize(7,7); //number of centers
Mat gray = ....; //source image
vector&Point2f& centers; //this will be filled by the detected centers
bool patternfound = findCirclesGrid(gray, patternsize, centers);
drawChessboardCorners(img, patternsize, Mat(centers), patternfound);
The function requires white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environments.
Finds an object pose from 3D-2D point correspondences.
C++: bool solvePnP(InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArray rvec, OutputArray tvec, bool useExtrinsicGuess=false, int flags=ITERATIVE )
Python: cv2.solvePnP(objectPoints, imagePoints, cameraMatrix, distCoeffs[, rvec[, tvec[, useExtrinsicGuess[, flags]]]]) & retval, rvec, tvec
C: void cvFindExtrinsicCameraParams2(const CvMat* object_points, const CvMat* image_points, const CvMat* camera_matrix, const CvMat* distortion_coeffs, CvMat* rotation_vector, CvMat* translation_vector, int use_extrinsic_guess=0 )
Python: cv.FindExtrinsicCameraParams2(objectPoints, imagePoints, cameraMatrix, distCoeffs, rvec, tvec, useExtrinsicGuess=0) & None
Parameters:
objectPoints – Array of object points in the object coordinate space, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points.
vector&Point3f&
can be also passed here.
imagePoints – Array of corresponding image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points.
vector&Point2f&
can be also passed here.
cameraMatrix – Input camera matrix
distCoeffs – Input vector of distortion coefficients
of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
rvec – Output rotation vector (see
) that, together with
tvec , brings points from the model coordinate system to the camera coordinate system.
tvec – Output translation vector.
useExtrinsicGuess – If true (1), the function uses the provided
values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
flags – Method for solving a PnP problem:
CV_ITERATIVE Iterative method is based on Levenberg-Marquardt optimization. In this case the function finds such a pose that minimizes reprojection error, that is the sum of squared distances between the observed projections imagePoints and the projected (using
) objectPoints .
Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang “Complete Solution Classification for the Perspective-Three-Point Problem”. In this case the function requires exactly four object and image points.
CV_EPNP Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the paper “EPnP: Efficient Perspective-n-Point Camera Pose Estimation”.
The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients.
An example of how to use solvePNP for planar augmented reality can be found at opencv_source_code/samples/python2/plane_ar.py
solvePnPRansac
Finds an object pose from 3D-2D point correspondences using the RANSAC scheme.
C++: void solvePnPRansac(InputArray objectPoints, InputArray imagePoints, InputArray cameraMatrix, InputArray distCoeffs, OutputArray rvec, OutputArray tvec, bool useExtrinsicGuess=false, int iterationsCount=100, float reprojectionError=8.0, int minInliersCount=100, OutputArray inliers=noArray(), int flags=ITERATIVE )
Python: cv2.solvePnPRansac(objectPoints, imagePoints, cameraMatrix, distCoeffs[, rvec[, tvec[, useExtrinsicGuess[, iterationsCount[, reprojectionError[, minInliersCount[, inliers[, flags]]]]]]]]) & rvec, tvec, inliers
Parameters:
objectPoints – Array of object points in the object coordinate space, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel, where N is the number of points.
vector&Point3f&
can be also passed here.
imagePoints – Array of corresponding image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, where N is the number of points.
vector&Point2f&
can be also passed here.
cameraMatrix – Input camera matrix
distCoeffs – Input vector of distortion coefficients
of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
rvec – Output rotation vector (see
) that, together with
tvec , brings points from the model coordinate system to the camera coordinate system.
tvec – Output translation vector.
useExtrinsicGuess – If true (1), the function uses the provided
tvec values as initial approximations of the rotation and translation vectors, respectively, and further optimizes them.
iterationsCount – Number of iterations.
reprojectionError – Inlier threshold value used by the RANSAC procedure. The parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier.
minInliersCount – Number of inliers. If the algorithm at some stage finds more inliers than minInliersCount , it finishes.
inliers – Output vector that contains indices of inliers in objectPoints and imagePoints .
flags – Method for solving a PnP problem (see
The function estimates an object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, that is, the sum of squared distances between the observed projections imagePoints and the projected (using
) objectPoints. The use of RANSAC makes the function resistant to outliers. The function is parallelized with the TBB library.
findFundamentalMat
Calculates a fundamental matrix from the corresponding points in two images.
C++: Mat findFundamentalMat(InputArray points1, InputArray points2, int method=FM_RANSAC, double param1=3., double param2=0.99, OutputArray mask=noArray() )
Python: cv2.findFundamentalMat(points1, points2[, method[, param1[, param2[, mask]]]]) & retval, mask
C: int cvFindFundamentalMat(const CvMat* points1, const CvMat* points2, CvMat* fundamental_matrix, int method=CV_FM_RANSAC, double param1=3., double param2=0.99, CvMat* status=NULL )
Python: cv.FindFundamentalMat(points1, points2, fundamentalMatrix, method=CV_FM_RANSAC, param1=1., param2=0.99, status=None) & retval
Parameters:
points1 – Array of
points from the first image. The point coordinates should be floating-point (single or double precision).
points2 – Array of the second image points of the same size and format as
method – Method for computing a fundamental matrix.
CV_FM_7POINT for a 7-point algorithm.
CV_FM_8POINT for an 8-point algorithm.
CV_FM_RANSAC for the RANSAC algorithm.
CV_FM_LMEDS for the LMedS algorithm.
param1 – Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise.
param2 – Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct.
mask – Output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in the RANSAC and LMedS methods. For other methods, it is set to all 1’s.
The epipolar geometry is described by the following equation:
is a fundamental matrix,
are corresponding points in the first and the second images, respectively.
The function calculates the fundamental matrix using one of four methods listed above and returns
the found fundamental matrix. Normally just one matrix is found. But in case of the 7-point algorithm, the function may return up to 3 solutions (
matrix that stores all 3 matrices sequentially).
The calculated fundamental matrix may be passed further to
that finds the epipolar lines
corresponding to the specified points. It can also be passed to
to compute the rectification transformation.
// Example. Estimation of fundamental matrix using the RANSAC algorithm
int point_count = 100;
vector&Point2f& points1(point_count);
vector&Point2f& points2(point_count);
// initialize the points here ... */
for( int i = 0; i & point_count; i++ )
points1[i] = ...;
points2[i] = ...;
Mat fundamental_matrix =
findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
findHomography
Finds a perspective transformation between two planes.
C++: Mat findHomography(InputArray srcPoints, InputArray dstPoints, int method=0, double ransacReprojThreshold=3, OutputArray mask=noArray() )
Python: cv2.findHomography(srcPoints, dstPoints[, method[, ransacReprojThreshold[, mask]]]) & retval, mask
C: int cvFindHomography(const CvMat* src_points, const CvMat* dst_points, CvMat* homography, int method=0, double ransacReprojThreshold=3, CvMat* mask=0 )
Python: cv.FindHomography(srcPoints, dstPoints, H, method=0, ransacReprojThreshold=3.0, status=None) & None
Parameters:
srcPoints – Coordinates of the points in the original plane, a matrix of the type
or vector&Point2f& .
dstPoints – Coordinates of the points in the target plane, a matrix of the type
vector&Point2f& .
method – Method used to computed a homography matrix. The following methods are possible:
0 - a regular method using all the points
CV_RANSAC - RANSAC-based robust method
CV_LMEDS - Least-Median robust method
ransacReprojThreshold – Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC method only). That is, if
then the point
is considered an outlier. If
are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10.
mask – Optional output mask set by a robust method ( CV_RANSAC
CV_LMEDS ).
Note that the input mask values are ignored.
The functions find and return the perspective transformation
between the source and the destination planes:
so that the back-projection error
is minimized. If the parameter method is set to the default value 0, the function
uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme.
However, if not all of the point pairs (
) fit the rigid perspective transformation (that is, there
are some outliers), this initial estimate will be poor.
In this case, you can use one of the two robust methods. Both methods, RANSAC and LMeDS , try many different random subsets
of the corresponding point pairs (of four pairs each), estimate
the homography matrix using this subset and a simple least-square
algorithm, and then compute the quality/goodness of the computed homography
(which is the number of inliers for RANSAC or the median re-projection
error for LMeDs). The best subset is then used to produce the initial
estimate of the homography matrix and the mask of inliers/outliers.
Regardless of the method, robust or not, the computed homography
matrix is refined further (using inliers only in case of a robust
method) with the Levenberg-Marquardt method to reduce the
re-projection error even more.
The method RANSAC can handle practically any ratio of outliers
but it needs a threshold to distinguish inliers from outliers.
The method LMeDS does not need any threshold but it works
correctly only when there are more than 50% of inliers. Finally,
if there are no outliers and the noise is rather small, use the default method (method=0).
The function is used to find initial intrinsic and extrinsic matrices.
Homography matrix is determined up to a scale. Thus, it is normalized so that
. Note that whenever an H matrix cannot be estimated, an empty one will be returned.
A example on calculating a homography for image matching can be found at opencv_source_code/samples/cpp/video_homography.cpp
estimateAffine3D
Computes an optimal affine transformation between two 3D point sets.
C++: int estimateAffine3D(InputArray src, InputArray dst, OutputArray out, OutputArray inliers, double ransacThreshold=3, double confidence=0.99)
Python: cv2.estimateAffine3D(src, dst[, out[, inliers[, ransacThreshold[, confidence]]]]) & retval, out, inliers
Parameters:
src – First input 3D point set.
dst – Second input 3D point set.
out – Output 3D affine transformation matrix
inliers – Output vector indicating which points are inliers.
ransacThreshold – Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier.
confidence – Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
The function estimates an optimal 3D affine transformation between two 3D point sets using the RANSAC algorithm.
filterSpeckles
Filters off small noise blobs (speckles) in the disparity map
C++: void filterSpeckles(InputOutputArray img, double newVal, int maxSpeckleSize, double maxDiff, InputOutputArray buf=noArray() )
Python: cv2.filterSpeckles(img, newVal, maxSpeckleSize, maxDiff[, buf]) & None
Parameters:
img – The input 16-bit signed disparity image
newVal – The disparity value used to paint-off the speckles
maxSpeckleSize – The maximum speckle size to consider it a speckle. Larger blobs are not affected by the algorithm
maxDiff – Maximum difference between neighbor disparity pixels to put them into the same blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point disparity map, where disparity values are multiplied by 16, this scale factor should be taken into account when specifying this parameter value.
buf – The optional temporary buffer to avoid memory allocation within the function.
getOptimalNewCameraMatrix
Returns the new camera matrix based on the free scaling parameter.
C++: Mat getOptimalNewCameraMatrix(InputArray cameraMatrix, InputArray distCoeffs, Size imageSize, double alpha, Size newImgSize=Size(), Rect* validPixROI=0, bool centerPrincipalPoint=false )
Python: cv2.getOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, alpha[, newImgSize[, centerPrincipalPoint]]) & retval, validPixROI
C: void cvGetOptimalNewCameraMatrix(const CvMat* camera_matrix, const CvMat* dist_coeffs, CvSize image_size, double alpha, CvMat* new_camera_matrix, CvSize new_imag_size=cvSize(0,0), CvRect* valid_pixel_ROI=0, int center_principal_point=0 )
Python: cv.GetOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, alpha, newCameraMatrix, newImageSize=(0, 0), validPixROI=0, centerPrincipalPoint=0) & None
Parameters:
cameraMatrix – Input camera matrix.
distCoeffs – Input vector of distortion coefficients
of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
imageSize – Original image size.
alpha – Free scaling parameter between 0 (when all the pixels in the undistorted image are valid) and 1 (when all the source image pixels are retained in the undistorted image). See
for details.
new_camera_matrix – Output new camera matrix.
new_imag_size – Image size after rectification. By default,it is set to
imageSize .
validPixROI – Optional output rectangle that outlines all-good-pixels region in the undistorted image. See
roi1, roi2
description in
centerPrincipalPoint – Optional flag that indicates whether in the new camera matrix the principal point should be at the image center or not. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image.
The function computes and returns
the optimal new camera matrix based on the free scaling parameter. By varying
this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original image pixels if there is valuable information in the corners alpha=1 , or get something in between. When alpha&0 , the undistortion result is likely to have some black pixels corresponding to “virtual” pixels outside of the captured distorted image. The original camera matrix, distortion coefficients, the computed new camera matrix, and newImageSize should be passed to
to produce the maps for
initCameraMatrix2D
Finds an initial camera matrix from 3D-2D point correspondences.
C++: Mat initCameraMatrix2D(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, Size imageSize, double aspectRatio=1.)
Python: cv2.initCameraMatrix2D(objectPoints, imagePoints, imageSize[, aspectRatio]) & retval
C: void cvInitIntrinsicParams2D(const CvMat* object_points, const CvMat* image_points, const CvMat* npoints, CvSize image_size, CvMat* camera_matrix, double aspect_ratio=1. )
Python: cv.InitIntrinsicParams2D(objectPoints, imagePoints, npoints, imageSize, cameraMatrix, aspectRatio=1.) & None
Parameters:
objectPoints – Vector of vectors of the calibration pattern points in the calibration pattern coordinate space. In the old interface all the per-view vectors are concatenated. See
for details.
imagePoints – Vector of vectors of the projections of the calibration pattern points. In the old interface all the per-view vectors are concatenated.
npoints – The integer vector of point counters for each view.
imageSize – Image size in pixels used to initialize the principal point.
aspectRatio – If it is zero or negative, both
are estimated independently. Otherwise,
The function estimates and returns an initial camera matrix for the camera calibration process.
Currently, the function only supports planar calibration patterns, which are patterns where each object point has z-coordinate =0.
matMulDeriv
Computes partial derivatives of the matrix product for each multiplied matrix.
C++: void matMulDeriv(InputArray A, InputArray B, OutputArray dABdA, OutputArray dABdB)
Python: cv2.matMulDeriv(A, B[, dABdA[, dABdB]]) & dABdA, dABdB
Parameters:
A – First multiplied matrix.
B – Second multiplied matrix.
dABdA – First output derivative matrix
dABdB – Second output derivative matrix
The function computes partial derivatives of the elements of the matrix product
with regard to the elements of each of the two input matrices. The function is used to compute the Jacobian matrices in
but can also be used in any other similar optimization function.
projectPoints
Projects 3D points to an image plane.
C++: void projectPoints(InputArray objectPoints, InputArray rvec, InputArray tvec, InputArray cameraMatrix, InputArray distCoeffs, OutputArray imagePoints, OutputArray jacobian=noArray(), double aspectRatio=0 )
Python: cv2.projectPoints(objectPoints, rvec, tvec, cameraMatrix, distCoeffs[, imagePoints[, jacobian[, aspectRatio]]]) & imagePoints, jacobian
C: void cvProjectPoints2(const CvMat* object_points, const CvMat* rotation_vector, const CvMat* translation_vector, const CvMat* camera_matrix, const CvMat* distortion_coeffs, CvMat* image_points, CvMat* dpdrot=NULL, CvMat* dpdt=NULL, CvMat* dpdf=NULL, CvMat* dpdc=NULL, CvMat* dpddist=NULL, double aspect_ratio=0 )
Python: cv.ProjectPoints2(objectPoints, rvec, tvec, cameraMatrix, distCoeffs, imagePoints, dpdrot=None, dpdt=None, dpdf=None, dpdc=None, dpddist=None) & None
Parameters:
objectPoints – Array of object points, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel
vector&Point3f& ), where N is the number of points in the view.
rvec – Rotation vector. See
for details.
tvec – Translation vector.
cameraMatrix – Camera matrix
distCoeffs – Input vector of distortion coefficients
of 4, 5, or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
imagePoints – Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or
vector&Point2f& .
jacobian – Optional output 2Nx(10+&numDistCoeffs&) jacobian matrix of derivatives of image points with respect to components of the rotation vector, translation vector, focal lengths, coordinates of the principal point and the distortion coefficients. In the old interface different components of the jacobian are returned via different output parameters.
aspectRatio – Optional “fixed aspect ratio” parameter. If the parameter is not 0, the function assumes that the aspect ratio (fx/fy) is fixed and correspondingly adjusts the jacobian matrix.
The function computes projections of 3D
points to the image plane given intrinsic and extrinsic camera
parameters. Optionally, the function computes Jacobians - matrices
of partial derivatives of image points coordinates (as functions of all the
input parameters) with respect to the particular parameters, intrinsic and/or
extrinsic. The Jacobians are used during the global optimization
function itself can also be used to compute a re-projection error given the
current intrinsic and extrinsic parameters.
By setting rvec=tvec=(0,0,0)
or by setting cameraMatrix to a 3x3 identity matrix, or by passing zero distortion coefficients, you can get various useful partial cases of the function. This means that you can compute the distorted coordinates for a sparse set of points or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
reprojectImageTo3D
Reprojects a disparity image to 3D space.
C++: void reprojectImageTo3D(InputArray disparity, OutputArray _3dImage, InputArray Q, bool handleMissingValues=false, int ddepth=-1 )
Python: cv2.reprojectImageTo3D(disparity, Q[, _3dImage[, handleMissingValues[, ddepth]]]) & _3dImage
C: void cvReprojectImageTo3D(const CvArr* disparityImage, CvArr* _3dImage, const CvMat* Q, int handleMissingValues=0 )
Python: cv.ReprojectImageTo3D(disparity, _3dImage, Q, handleMissingValues=0) & None
Parameters:
disparity – Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit floating-point disparity image.
_3dImage – Output 3-channel floating-point image of the same size as
disparity . Each element of
_3dImage(x,y)
contains 3D coordinates of the point
computed from the disparity map.
perspective transformation matrix that can be obtained with
handleMissingValues – Indicates, whether the function should handle missing values (i.e. points where the disparity was not computed). If handleMissingValues=true, then pixels with the minimal disparity that corresponds to the outliers (see
) are transformed to 3D points with a very large Z value (currently set to 10000).
ddepth – The optional output array depth. If it is -1, the output image will have CV_32F depth. ddepth can also be set to CV_16S, CV_32S or CV_32F.
The function transforms a single-channel disparity map to a 3-channel image representing a 3D surface. That is, for each pixel (x,y) andthe
corresponding disparity d=disparity(x,y) , it computes:
The matrix Q can be an arbitrary
matrix (for example, the one computed by
). To reproject a sparse set of points {(x,y,d),...} to 3D space, use
RQDecomp3x3
Computes an RQ decomposition of 3x3 matrices.
C++: Vec3d RQDecomp3x3(InputArray src, OutputArray mtxR, OutputArray mtxQ, OutputArray Qx=noArray(), OutputArray Qy=noArray(), OutputArray Qz=noArray() )
Python: cv2.RQDecomp3x3(src[, mtxR[, mtxQ[, Qx[, Qy[, Qz]]]]]) & retval, mtxR, mtxQ, Qx, Qy, Qz
C: void cvRQDecomp3x3(const CvMat* matrixM, CvMat* matrixR, CvMat* matrixQ, CvMat* matrixQx=NULL, CvMat* matrixQy=NULL, CvMat* matrixQz=NULL, CvPoint3D64f* eulerAngles=NULL )
Python: cv.RQDecomp3x3(M, R, Q, Qx=None, Qy=None, Qz=None) & eulerAngles
Parameters:
src &# input matrix.
mtxR – Output 3x3 upper-triangular matrix.
mtxQ – Output 3x3 orthogonal matrix.
Qx – Optional output 3x3 rotation matrix around x-axis.
Qy – Optional output 3x3 rotation matrix around y-axis.
Qz – Optional output 3x3 rotation matrix around z-axis.
The function computes a RQ decomposition using the given rotations. This function is used in
to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix.
It optionally returns three rotation matrices, one for each axis, and the three Euler angles in degrees (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principle axes that results in the same orientation of an object, eg. see . Returned tree rotation matrices and corresponding three Euler angules are only one of the possible solutions.
Converts a rotation matrix to a rotation vector or vice versa.
C++: void Rodrigues(InputArray src, OutputArray dst, OutputArray jacobian=noArray())
Python: cv2.Rodrigues(src[, dst[, jacobian]]) & dst, jacobian
C: int cvRodrigues2(const CvMat* src, CvMat* dst, CvMat* jacobian=0 )
Python: cv.Rodrigues2(src, dst, jacobian=0) & None
Parameters:
src – Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
dst – Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
jacobian – Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial derivatives of the output array components with respect to the input array components.
Inverse transformation can be also done easily, since
A rotation vector is a convenient and most compact representation of a rotation matrix
(since any rotation matrix has just 3 degrees of freedom). The representation is
used in the global 3D geometry optimization procedures like
class StereoBM
Class for computing stereo correspondence using the block matching algorithm.
// Block matching stereo correspondence algorithm class StereoBM
enum { NORMALIZED_RESPONSE = CV_STEREO_BM_NORMALIZED_RESPONSE,
BASIC_PRESET=CV_STEREO_BM_BASIC,
FISH_EYE_PRESET=CV_STEREO_BM_FISH_EYE,
NARROW_PRESET=CV_STEREO_BM_NARROW };
StereoBM();
// the preset is one of ..._PRESET above.
// ndisparities is the size of disparity range,
// in which the optimal disparity at each pixel is searched for.
// SADWindowSize is the size of averaging window used to match pixel blocks
(larger values mean better robustness to noise, but yield blurry disparity maps)
StereoBM(int preset, int ndisparities=0, int SADWindowSize=21);
// separate initialization function
void init(int preset, int ndisparities=0, int SADWindowSize=21);
// computes the disparity for the two rectified 8-bit single-channel images.
// the disparity will be 16-bit signed (fixed-point) or 32-bit floating-point image of the same size as left.
void operator()( InputArray left, InputArray right, OutputArray disparity, int disptype=CV_16S );
Ptr&CvStereoBMState& state;
The class is a C++ wrapper for the associated functions. In particular,
is the wrapper for
StereoBM::StereoBM
The constructors.
StereoBM::StereoBM()
StereoBM::StereoBM(int preset, int ndisparities=0, int SADWindowSize=21)
Python: cv2.StereoBM([preset[, ndisparities[, SADWindowSize]]]) & &StereoBM object&
C: CvStereoBMState* cvCreateStereoBMState(int preset=CV_STEREO_BM_BASIC, int numberOfDisparities=0 )
Python: cv.CreateStereoBMState(preset=CV_STEREO_BM_BASIC, numberOfDisparities=0) & CvStereoBMState
Parameters:
preset – specifies the whole set of algorithm parameters, one of:
BASIC_PRESET - parameters suitable for general cameras
FISH_EYE_PRESET - parameters suitable for wide-angle cameras
NARROW_PRESET - parameters suitable for narrow-angle cameras
After constructing the class, you can override any parameters set by the preset.
ndisparities – the disparity search range. For each pixel algorithm will find the best disparity from 0 (default minimum disparity) to ndisparities. The search range can then be shifted by changing the minimum disparity.
SADWindowSize – the linear size of the blocks compared by the algorithm. The size should be odd (as the block is centered at the current pixel). Larger block size implies smoother, though less accurate disparity map. Smaller block size gives more detailed disparity map, but there is higher chance for algorithm to find a wrong correspondence.
The constructors initialize StereoBM state. You can then call StereoBM::operator() to compute disparity for a specific stereo pair.
In the C API you need to deallocate CvStereoBM state when it is not needed anymore using cvReleaseStereoBMState(&stereobm).
StereoBM::operator()
Computes disparity using the BM algorithm for a rectified stereo pair.
C++: void StereoBM::operator()(InputArray left, InputArray right, OutputArray disparity, int disptype=CV_16S )
Python: cv2.StereoBM.compute(left, right[, disparity[, disptype]]) & disparity
C: void cvFindStereoCorrespondenceBM(const CvArr* left, const CvArr* right, CvArr* disparity, CvStereoBMState* state)
Python: cv.FindStereoCorrespondenceBM(left, right, disparity, state) & None
Parameters:
left – Left 8-bit single-channel image.
right – Right image of the same size and the same type as the left one.
disparity – Output disparity map. It has the same size as the input images. When disptype==CV_16S, the map is a 16-bit signed single-channel image, containing disparity values scaled by 16. To get the true disparity values from such fixed-point representation, you will need to divide each
disp element by 16. If disptype==CV_32F, the disparity map will already contain the real disparity values on output.
disptype – Type of the output disparity map, CV_16S (default) or CV_32F.
state – The pre-initialized CvStereoBMState structure in the case of the old API.
The method executes the BM algorithm on a rectified stereo pair. See the stereo_match.cpp OpenCV sample on how to prepare images and call the method. Note that the method is not constant, thus you should not use the same StereoBM instance from within different threads simultaneously. The function is parallelized with the TBB library.
StereoSGBM
class StereoSGBM
Class for computing stereo correspondence using the semi-global block matching algorithm.
class StereoSGBM
StereoSGBM();
StereoSGBM(int minDisparity, int numDisparities, int SADWindowSize,
int P1=0, int P2=0, int disp12MaxDiff=0,
int preFilterCap=0, int uniquenessRatio=0,
int speckleWindowSize=0, int speckleRange=0,
bool fullDP=false);
virtual ~StereoSGBM();
virtual void operator()(InputArray left, InputArray right, OutputArray disp);
int minDisparity;
int numberOfDisparities;
int SADWindowSize;
int preFilterCap;
int uniquenessRatio;
int P1, P2;
int speckleWindowSize;
int speckleRange;
int disp12MaxDiff;
bool fullDP;
The class implements the modified H. Hirschmuller algorithm
that differs from the original one as follows:
By default, the algorithm is single-pass, which means that you consider only 5 directions instead of 8. Set fullDP=true to run the full variant of the algorithm but beware that it may consume a lot of memory.
The algorithm matches blocks, not individual pixels. Though, setting SADWindowSize=1 reduces the blocks to single pixels.
Mutual information cost function is not implemented. Instead, a simpler Birchfield-Tomasi sub-pixel metric from
is used. Though, the color images are supported as well.
Some pre- and post- processing steps from K. Konolige algorithm
are included, for example: pre-filtering (CV_STEREO_BM_XSOBEL type) and post-filtering (uniqueness check, quadratic interpolation and speckle filtering).
(Python) An example illustrating the use of the Stereo