How to undo a perspective transform for a single point in opencv

To invert a homography (e.g. perspective transformation) you typically just invert the transformation matrix.

So to transform some points back from your destination image to your source image you invert the transformation matrix and transform those points with the result. To transform a point with a transformation matrix you multiply it from right to the matrix, maybe followed by a de-homogenization.

Luckily, OpenCV provides not only the warpAffine/warpPerspective methods, which transform each pixel of one image to the other image, but there is method to transform single points, too.

Use cv::perspectiveTransform(inputVector, emptyOutputVector, yourTransformation) method to transform a set of points, where

inputVector is a std::vector<cv::Point2f> (you can use a nx2 or 2xn matrix, too, but sometimes that's erroneous). Instead you can use cv::Point3f type, but I'm not sure whether those would be homgeneous coordinate points or 3D points for 3D transformation (or maybe both?).

outputVector is an empty std::vector<cv::Point2f> where the result will be stored

yourTransformation is a double precision 3x3 cv::Mat (like provided by findHomography ) transformation matrix (or 4x4 for 3D points).

Here's a Python example:

import cv2
import numpy as np

# Forward transform
point_transformed = cv2.perspectiveTransform(point_original, trans)

# Reverse transform
inv_trans = np.linalg.pinv(trans)
round_tripped = cv2.perspectiveTransform(point_transformed, inv_trans)

# Now, round_tripped should be approximately equal to point_original