OpenCV中undistortPoints()和projectPoints()之间的区别 [英] Difference between undistortPoints() and projectPoints() in OpenCV

问题描述

根据我的理解，undistortPoints在失真的图像上获取一组点，并计算其坐标在同一图像的未失真版本上的位置.同样，projectPoints将一组对象坐标映射到其相应的图像坐标.

From my understanding, undistortPoints takes a set of points on a distorted image, and calculates where their coordinates would be on an undistorted version of the same image. Likewise, projectPoints maps a set of object coordinates to their corresponding image coordinates.

但是，我不确定projectPoints是将对象坐标映射到变形图像(即原始图像)还是未变形图像(直线)上的一组图像点吗?

However, I am unsure if projectPoints maps the object coordinates to a set of image points on the distorted image (ie. the original image) or one that has been undistorted (straight lines)?

此外，undistortPoints的OpenCV文档指出'该函数将反向转换为projectPoints()'.你能解释一下这是怎么回事吗?

Furthermore, the OpenCV documentation for undistortPoints states that 'the function performs a reverse transformation to projectPoints()'. Could you please explain how this is so?

推荐答案

3.2文档中

Quote from the 3.2 documentation for projectPoints():

将3D投影到图像平面.

Projects 3D points to an image plane.

函数计算 给定内在和内在的3D投影到像平面的投影 外在相机参数.

The function computes projections of 3D points to the image plane given intrinsic and extrinsic camera parameters.

您有参数distCoeffs:

如果向量为空，则假定失真系数为零.

If the vector is empty, the zero distortion coefficients are assumed.

在不失真的情况下，等式为:

With no distorsion the equation is:

使用K固有矩阵和[R | t]外部矩阵或将对象或世界框架中的点转换为摄影机框架的转换.

With K the intrinsic matrix and [R | t] the extrinsic matrix or the transformation that transforms a point in the object or world frame to the camera frame.

对于 undistortPoints() ，参数R:

For undistortPoints(), you have the parameter R:

对象空间中的整齐转换(3x3矩阵).由cv :: stereoRectify计算的R1或R2可以在此处传递.如果矩阵为空，则使用恒等变换.

Rectification transformation in the object space (3x3 matrix). R1 or R2 computed by cv::stereoRectify can be passed here. If the matrix is empty, the identity transformation is used.

反向变换是一种操作，您可以使用固有参数为2D图像点([u, v])计算归一化相机帧([x, y, z=1])中的相应3D点.

The reverse transformation is the operation where you compute for a 2D image point ([u, v]) the corresponding 3D point in the normalized camera frame ([x, y, z=1]) using the intrinsic parameters.

使用外部矩阵，您可以在相机框架中获得该点:

With the extrinsic matrix, you can get the point in the camera frame:

归一化的相机框架是通过除以深度获得的:

The normalized camera frame is obtained by dividing by the depth:

假设没有失真，则图像点为:

Assuming no distortion, the image point is:

假设没有失真的逆向变换":

And the "reverse transformation" assuming no distortion:

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