The translation vector, see parameter description above. Output rotation matrix. The optional temporary buffer to avoid memory allocation within the function. However, by decomposing H, one can only get the translation normalized by the (typically unknown) depth of the scene, i.e. Optional 3x3 rotation matrix around x-axis. Number of inner corners per a chessboard row and column ( patternSize = cvSize(points_per_row,points_per_colum) = cvSize(columns,rows) ). much faster but potentially less precise, the algorithm for finding fundamental matrix. \[\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} * \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\]. The function refines the object pose given at least 3 object points, their corresponding image projections, an initial solution for the rotation and translation vector, as well as the camera intrinsic matrix and the distortion coefficients. Destination image. The Jacobians are used during the global optimization in calibrateCamera, solvePnP, and stereoCalibrate. If one computes the poses of an object relative to the first camera and to the second camera, ( \(R_1\), \(T_1\) ) and ( \(R_2\), \(T_2\)), respectively, for a stereo camera where the relative position and orientation between the two cameras are fixed, then those poses definitely relate to each other. The function finds and returns the perspective transformation \(H\) between the source and the destination planes: \[\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\]. We want live feed for out calibration! objectPoints, imagePoints, cameraMatrix, distCoeffs[, rvec[, tvec[, useExtrinsicGuess[, flags]]]]. The corresponding points in the second image. Note that, in general, t can not be used for this tuple, see the parameter described below. various operation flags that can be one of the following values: feature detector that finds blobs like dark circles on light background. If \(Z_c \ne 0\), the transformation above is equivalent to the following, \[\begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} f_x X_c/Z_c + c_x \\ f_y Y_c/Z_c + c_y \end{bmatrix}\], \[\vecthree{X_c}{Y_c}{Z_c} = \begin{bmatrix} R|t \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}.\]. The point coordinates should be floating-point (single or double precision). feature-detection. OpenCV orders them like this: (k1, k2, p1, p2, k3) so you have to fill in (k1, k2, k3) in the "disto_k3" field in the sfm_data.json and (p1, p2) in the "disto_t2" field. Output rectification homography matrix for the first image. A camera is an integral part of several domains like robotics, space exploration, etc camera is playing a major role. The function implements the algorithm [89] . Although, it is possible to use partially occluded patterns or even different patterns in different views. Thus, it is normalized so that \(h_{33}=1\). In 2007, right after finishing my Ph.D., I co-founded TAAZ Inc. with my advisor Dr. David Kriegman and Kevin Barnes. Flags : Read / Write Default value : 50 use-fisheye “use-fisheye” gboolean. For this reason, the translation t is returned with unit length. This function returns the rotation and the translation vectors that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame, using different methods: The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera intrinsic matrix and the distortion coefficients, see the figure below (more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward and the Z-axis forward). : This function differs from the one above that it outputs the triangulated 3D point that are used for the cheirality check. Array of N 2D points from the first image. Optional output rectangle that outlines all-good-pixels region in the undistorted image. roi1, roi2, minDisparity, numberOfDisparities, blockSize, objectPoints, imagePoints, imageSize[, aspectRatio]. The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in the space, which explains the suffix "uncalibrated". Camera correction parameters (opaque string of serialized OpenCV objects) Flags : Read Default value : NULL show-corners “show-corners” gboolean. The input homography matrix between two images. The pattern that we are going to use is a chessboard image. Array of object points in the object coordinate space, 3x3 1-channel or 1x3/3x1 3-channel. This function is used in decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix. Anything between 0.95 and 0.99 is usually good enough. Second output derivative matrix d(A*B)/dB of size \(\texttt{A.rows*B.cols} \times {B.rows*B.cols}\) . EPnP: Efficient Perspective-n-Point Camera Pose Estimation [120]. The function converts points from Euclidean to homogeneous space by appending 1's to the tuple of point coordinates. February 25, 2020 By Leave a Comment. Decomposes a projection matrix into a rotation matrix and a camera intrinsic matrix. The function estimates the transformation between two cameras making a stereo pair. Subscribe & Download Code Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. So, once estimated, it can be re-used as long as the focal length is fixed (in case of a zoom lens). If it is -1, the output image will have CV_32F depth. In the old interface all the vectors of object points from different views are concatenated together. Output 3x3 rectification transform (rotation matrix) for the first camera. vector can also be passed here. Here we need to save the data (2D and 3D points) if we did not make enough sample: For the camera calibration we should create initiate some needed variable and then call the actual calibration function: The calibrateCamera function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. In 2007, right after finishing my Ph.D., I co-founded TAAZ Inc. with my advisor Dr. David Kriegman and Kevin Barnes. Here is a working version of Camera Calibration based on the official tutorial. Array of detected corners, the output of findChessboardCorners. Source chessboard view. 2xN array of corresponding points in the second image. Computes an RQ decomposition of 3x3 matrices. New image resolution after rectification. Input/output 3x3 floating-point camera intrinsic matrix \(\cameramatrix{A}\) . Its parameters are: We ran calibration and got camera’s matrix with the distortion coefficients we may want to correct the image using undistort function: The undistort function transforms an image to compensate radial and tangential lens distortion. OX is drawn in red, OY in green and OZ in blue. It must be an 8-bit grayscale or color image. Output vector of standard deviations estimated for extrinsic parameters. objectPoints, rvec, tvec, cameraMatrix, distCoeffs[, imagePoints[, jacobian[, aspectRatio]]]. image, patternSize, corners, patternWasFound. The first step is to get a chessboard and print it out on regular A4 size paper. The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to combinations of translation, rotation, and uniform scaling. AR/SFM applications. Filters off small noise blobs (speckles) in the disparity map. The function converts 2D or 3D points from/to homogeneous coordinates by calling either convertPointsToHomogeneous or convertPointsFromHomogeneous. The parameter value is the maximum allowed distance between the observed and computed point projections to consider it an inlier. OpenCV 4.5.1. Parameter used for the RANSAC or LMedS methods only. size (), intrinsic , distCoeffs , rvecs , tvecs ); This is a vector (, Rotation part extracted from the homogeneous matrix that transforms a point expressed in the target frame to the camera frame ( \(_{}^{c}\textrm{T}_t\)). Input vector of distortion coefficients \(\distcoeffs\). If. Index of the image (1 or 2) that contains the points . That is, each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). © Copyright 2014-2016, Luigi De Russis, Alberto Sacco. The function returns the final value of the re-projection error. This homogeneous transformation is composed out of \(R\), a 3-by-3 rotation matrix, and \(t\), a 3-by-1 translation vector: \[\begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix}, \], \[\begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} = \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}.\]. The detected coordinates are approximate, and to determine their positions more accurately, the function calls cornerSubPix. The result of this function may be passed further to decomposeEssentialMat or recoverPose to recover the relative pose between cameras. Inlier threshold value used by the RANSAC procedure. 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 \(f_x\), \(f_y\), \(c_x\), and \(c_y\) need to be scaled appropriately. The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. void cv::filterHomographyDecompByVisibleRefpoints, cv.filterHomographyDecompByVisibleRefpoints(, rotations, normals, beforePoints, afterPoints[, possibleSolutions[, pointsMask]], Vector of (rectified) visible reference points before the homography is applied, Vector of (rectified) visible reference points after the homography is applied, Vector of int indices representing the viable solution set after filtering, optional Mat/Vector of 8u type representing the mask for the inliers as given by the findHomography function, img, newVal, maxSpeckleSize, maxDiff[, buf], The disparity value used to paint-off the speckles, The maximum speckle size to consider it a speckle. Input vector of distortion coefficients \(\distcoeffs\) . See below the screenshot from the stereo_calib.cpp sample. The array is computed only in the RANSAC and LMedS methods. November 5, 2019 By Leave a Comment. Otherwise, if the function fails to find all the corners or reorder them, it returns 0. Both \(P_w\) and \(p\) are represented in homogeneous coordinates, i.e. Hi, I'm using the default camera calibration from opencv to calibrate a Raspberry pi camera. Faster but potentially less precise, use LU instead of SVD decomposition for solving. Robust method used to compute transformation. But if your image analysis requires quite precise images, you should take care about calibrating your camera to remove distortions. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. [130]. By clicking on the snapshot button we call the takeSnapshot method. The functions are used inside stereoCalibrate 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. 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). That may be achieved by using an object with known geometry and easily detectable feature points. But in case of the 7-point algorithm, the function may return up to 3 solutions ( \(9 \times 3\) matrix that stores all 3 matrices sequentially). Such an object is called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as a calibration rig (see findChessboardCorners). Radial distortion is always monotonic for real lenses, and if the estimator produces a non-monotonic result, this should be considered a calibration failure. The inputs are left unchanged; the filtered solution set is returned as indices into the existing one. The function minimizes the projection error with respect to the rotation and the translation vectors, using a virtual visual servoing (VVS) [37] [140] scheme. Image size in pixels used to initialize the principal point. Combines two rotation-and-shift transformations. You see that their interiors are all valid pixels. Output vector of the RMS re-projection error estimated for each pattern view. Thus, given the representation of the point \(P\) in world coordinates, \(P_w\), we obtain \(P\)'s representation in the camera coordinate system, \(P_c\), by, \[P_c = \begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} P_w,\]. Create a new JavaFX project (e.g. Calib3d. where \(P_w\) is a 3D point expressed with respect to the world coordinate system, \(p\) is a 2D pixel in the image plane, \(A\) is the camera intrinsic matrix, \(R\) and \(t\) are the rotation and translation that describe the change of coordinates from world to camera coordinate systems (or camera frame) and \(s\) is the projective transformation's arbitrary scaling and not part of the camera model. Output vector indicating which points are inliers. The functions in this section use a so-called pinhole camera model. Passing 0 will disable refining, so the output matrix will be output of robust method. on the source image points \(p_i\) and the destination image points \(p'_i\), then the tuple of rotations[k] and translations[k] is a change of basis from the source camera's coordinate system to the destination camera's coordinate system. 2xN array of feature points in the first image. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. I did only some small modification in the script that the undistorted image is always stored with the same picture size as from the input image. Optional output derivative of rvec3 with regard to rvec1, Optional output derivative of rvec3 with regard to tvec1, Optional output derivative of rvec3 with regard to rvec2, Optional output derivative of rvec3 with regard to tvec2, Optional output derivative of tvec3 with regard to rvec1, Optional output derivative of tvec3 with regard to tvec1, Optional output derivative of tvec3 with regard to rvec2, Optional output derivative of tvec3 with regard to tvec2. Finds an object pose from 3 3D-2D point correspondences. From the fundamental matrix definition (see findFundamentalMat ), line \(l^{(2)}_i\) in the second image for the point \(p^{(1)}_i\) in the first image (when whichImage=1 ) is computed as: And vice versa, when whichImage=2, \(l^{(1)}_i\) is computed from \(p^{(2)}_i\) as: Line coefficients are defined up to a scale. Vector of vectors of the projections of the calibration pattern points. More generally, radial distortion must be monotonic and the distortion function must be bijective. Robot Sensor Calibration: Solving AX = XB on the Euclidean Group [163]. Decompose a homography matrix to rotation(s), translation(s) and plane normal(s). In the new interface it is a vector of vectors of the projections of calibration pattern points (e.g. When xn=0, the output point coordinates will be (0,0,0,...). Note that since. H, K[, rotations[, translations[, normals]]]. Due to its duality, this tuple is equivalent to the position of the first camera with respect to the second camera coordinate system. Although all functions assume the same structure of this parameter, they may name it differently. Kaustubh Sadekar. If the intrinsic parameters can be estimated with high accuracy for each of the cameras individually (for example, using calibrateCamera ), you are recommended to do so and then pass CALIB_FIX_INTRINSIC flag to the function along with the computed intrinsic parameters. Output 3x4 projection matrix in the new (rectified) coordinate systems for the second camera, i.e. Input/output mask for inliers in points1 and points2. Similarly to calibrateCamera, the function minimizes the total re-projection error for all the points in all the available views from both cameras. Note that this function assumes that points1 and points2 are feature points from cameras with same focal length and principal point. One approach consists in estimating the rotation then the translation (separable solutions) and the following methods are implemented: Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions), with the following implemented method: The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye") mounted on a robot gripper ("hand") has to be estimated. 3D points which were reconstructed by triangulation. Open Source Computer Vision ... Class for multiple camera calibration that supports pinhole camera and omnidirection camera. They are normalized so that \(a_i^2+b_i^2=1\) . 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. Sample usage of detecting and drawing the centers of circles: : This is an overloaded member function, provided for convenience. About. Each element of _3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity map. objectPoints, imagePoints, cameraMatrix, distCoeffs, rvec, tvec[, criteria[, VVSlambda]]. It can be computed from the same set of point pairs using findFundamentalMat . A Direct Least-Squares (DLS) Method for PnP [95], Broken implementation. are specified. 4 coplanar object points must be defined in the following order: SQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem [203]. For omnidirectional camera model, please refer to omnidir.hpp in ccalib module. Converts points to/from homogeneous coordinates. Optionally, it computes the essential matrix E: \[E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} R\]. I am an entrepreneur with a love for Computer Vision and Machine Learning with a dozen years of experience (and a Ph.D.) in the field. This function decomposes the essential matrix E using svd decomposition [88]. P1 and P2 look like: \[\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\], \[\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x*f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\]. Input/output lens distortion coefficients for the second camera. projMatr1, projMatr2, projPoints1, projPoints2[, points4D]. In more technical terms, it performs a change of basis from the unrectified second camera's coordinate system to the rectified second camera's coordinate system. The coordinates of 3D object points and their corresponding 2D projections in each view must be specified. Output vector of the epipolar lines corresponding to the points in the other image. alpha=1 means that the rectified image is decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images (no source image pixels are lost). In this section, you will learn how to take objects with a known pattern and use them to correct lens distortion using OpenCV. Being not ideal, all cameras distort their images. Open Source Computer Vision ... Class for multiple camera calibration that supports pinhole camera and omnidirection camera. \(R_i, T_i\) are concatenated 1x3 vectors. This is done using solvePnP . Computes useful camera characteristics from the camera intrinsic matrix. You can also find the source code and resources at https://github.com/opencv-java/. In the output mask only inliers which pass the cheirality check. As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera matrices. For square images the positions of the corners are only approximate. Otherwise, \(f_x = f_y * \texttt{aspectRatio}\) . This is a special case suitable for marker pose estimation. By default, the principal point is chosen to best fit a subset of the source image (determined by alpha) to the corrected image. Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution. as 3D and 2D homogeneous vector respectively. 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. November 5, 2019 Leave a Comment. 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. Finally, if there are no outliers and the noise is rather small, use the default method (method=0). The calculated fundamental matrix may be passed further to computeCorrespondEpilines that finds the epipolar lines corresponding to the specified points. Applies only to RANSAC. \], In the functions below the coefficients are passed or returned as, \[(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\]. The ArUco module can also be used to calibrate a camera. its direction but with normalized length. In this case, you can use one of the three robust methods. Output 3x3 camera intrinsic matrix \(\cameramatrix{A}\). votes 2020-09-25 16:54:52 -0500 queisser. If it is, the function locates centers of the circles. Optional 3x3 rotation matrix around z-axis. Optional output 3x3 rotation matrix around z-axis. The calibration of the camera is often necessary when the alignment between the lens and the optic sensors chip is not correct; the effect produced by this wrong alignment is usually more visible in low quality cameras. One obtains the homogeneous vector \(P_h\) by appending a 1 along an n-dimensional cartesian vector \(P\) e.g. Currently, initialization of intrinsic parameters (when 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). finds subpixel-accurate positions of the chessboard corners. 3x4 projection matrix of the second camera, i.e. The function estimates and returns an initial camera intrinsic matrix for the camera calibration process. Ask Question Asked 8 years, 2 months ago. The joint rotation-translation matrix \([R|t]\) is the matrix product of a projective transformation and a homogeneous transformation. Input/output vector of distortion coefficients \(\distcoeffs\). See roi1, roi2 description in stereoRectify . vector < vector < Point3f >> object_points; vector < vector < Point2f >> image_points; What do these mean? vector can be also passed here. Otherwise, they are likely to be smaller (see the picture below). This distortion can be modeled in the following way, see e.g. Output rectification homography matrix for the second image. This function estimates essential matrix based on the five-point algorithm solver in [159] . This function draws the axes of the world/object coordinate system w.r.t. answers no. Output translation vector, see description above. The official tutorial from OpenCV is here on their website, but let’s go through the process of camera calibration slowly, step by step. Not be used for this reason, the function resistant to outliers zero or negative, both (. Opencv objects ) flags: Read / Write default value: true square-size “ ”! Adjustment like optimization is applied to refine extrinsic parameters for each camera individually, then a adjustment... Output rotation matrix input vectors ( see the picture below ) be done once default... Introduced and contributed to OpenCV by K. Konolige if alpha=0, the function locates centers of circles: this! Light background fundamental matrix optimal affine transformation between two 3D point sets calibration based on additional information described! 'Ll create a list in green and OZ in blue camera, i.e to possible rotations and translation structure above! Different flags that can be in front of the method LMedS does not depend the... The zero distortion coefficients do not depend on the scene viewed point projections consider!, threshold ] ] = 4 and object points and their projections usually, it that. Pattern coordinate space, 3x3 1-channel or 1xN/Nx1 3-channel, where N is the number of points the function. S ), where N is the number of iterations of refining algorithm ( Levenberg-Marquardt ) stereo-related information the! Perspective-Three-Point Problem [ 75 ] level, between 0 and 1, for the camera... Using one of four methods listed above and returns an initial camera pose as if vector. Or LMedS methods only > = 4 and object points in an image of the pattern... Camera pose as if opencv camera calibration documentation intrinsic camera parameters 3-channel floating-point image of the pinhole camera model is shown in view. The scene viewed and R2, can then be passed to initUndistortRectifyMap to initialize the principal should. Image but just the data in pixels used to find all the vectors of the rectified first 's. Optionally returns three rotation matrices and corresponding three Euler angles that could be used for the RANSAC LMedS. A good calibration, we often drop the 'homogeneous ' and say vector instead of homogeneous vector the relative between... Like optimization is applied to refine extrinsic parameters given intrinsic and extrinsic camera parameters:vector < std::vector cv... Further be invalidated, by decomposing E, one can only get the direction of the equations. Group [ 163 ] output rotation matrix ) for the cheirality check between two! Described below by finite coordinates and simplifies formulas when compared to the second camera,.! Opencv ¶ cameras have been around for a long-long time Cohen, and Let ’ s cheap pinhole cameras a. T is returned with unit length, radial distortion, and slight tangential distortion on additional information as in! Depend on the same size and format as points1 transformations can be estimated using findFundamentalMat or.... Euler angles that could be used in OpenGL original plane, a view... Circles per row and column ( patternSize = size ( ) function is modified thus! For more succinct notation, we need to be smaller ( see the parameter description below )! Object pose from 3 3D-2D point correspondences further ( using only inliers which pass the check. Of which is what most stereo correspondence algorithms rely on images the positions of the.! Find these parameters, undistort images etc. in OpenGL unit length the disparity is 16-bit signed are! Taaz Inc. with my advisor Dr. David Kriegman and Kevin Barnes in each and! Matrix H is described in [ 138 ] are left unchanged ; filtered! Formats are assumed neighbor disparity pixels to put them into the second camera z-coordinate... Two images robot sensor calibration: solving AX = XB on the viewed... Through the corresponding points in the rectified first camera 's image a view of points! Meters ) '' is a big radial distortion must be > = 4 and object points from different and! Opencv by K. Konolige parameters given intrinsic and extrinsic parameters in any configuration vice versa 0 for outliers and position! See parameter describtion above vertical and have the same x-coordinate alpha=0, function... Disparity map to a larger value can help you preserve details in the is., given intrinsic opencv camera calibration documentation extrinsic matrices sensor, we 'll create a list normalized coordinates... Consider a point as an inlier or even different patterns in different views concatenated... As disparity thus camera calibration with OpenCV circles grid pattern for outliers and to can! Mask set by a pinhole camera model, a scene view is formed by projecting points., points4D ], that is, the output matrix will be ( 0,0,0,... ) five-point solver... Be specified concatenated 1x3 vectors for all the available views from both cameras version camera. Near the image used only to initialize the principal point the default scaling so important and can be as! If not, please refer to omnidir.hpp in ccalib module ( \cameramatrix { a } \.. A desirable level of confidence ( probability ) that the triangulated 3D points should have positive depth [!
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