Undistort Image - Retain All Source Pixels

A C++ project using the OpenCV library to produce undistorted image in which all source image pixels are retained.

Implementation

The code is implemented using MS Visual Studio 2012. The project files and the source code are in the folder retained_undistort_image. Source code is in the file main.cpp. Using MS Visual Studio as the IDE, this requires some project setting (i.e. include/lib for OpenCV) in order to build the code.

Code Explanation

We implement two methods to produce undistorted image. The first one is a simple and effortless method using cv::initUndistortRectifyMap and cv::getOptimalNewCameraMatrix. The second one is the reverse distortion technique in which we replicate the way OpenCV's undistort() function works (I believe?) in order to produce the undistorted image.

Input: original (distorted) input image, 3x3 intrinsics matrix (K) and distortion matrix
Output: undistorted images saved into files named undistorted_out1.jpg and undistorted_out2.jpg

Steps

1. Due to the distortion factors, it is most likely that the undistorted image will be bigger or smaller than the original image. To retain the resolution of the input image, we have to compute the image size of the undistorted image. With the four extreme corners of the input image: top-left (0,0), top-right (image_size.width-1, 0), bottom-right (image_size.width-1, image_size.height-1) and bottom-left (0, image_size.height-1), we undistort them to get the corresponding coords in the undistorted image.
   

2. We create undistort image using the effortless method by calling cv::initUndistortRectifyMap and cv::getOptimalNewCameraMatrix.
   

3. We use another technique to create undistort image. That is to do reverse distortion in which we create map matrices that define the correspondence between the undistorted coordinate and distorted (original image) coordinates. Then we call cv::remap to create the undistorted results.
   

The reverse distortion is illustrated as the figure below:

The undistorted function (f_undistorted) is defined as the equation to compute distorted coordinates from undistorted coordinates. Simply speaking, it is to add the distortion to the ideal coordinate points.

Note: In the code, the distortion coefficients: k1, k2, p1 and p2 are only used in the code. That is because the calibration tool usually produce upto k3. However, if you have k3, you can simply modify the distortion coefficient matrix and the function to distort the point.

void distortPoint(cv::Mat &K, cv::Mat &distortionCoef, 
                  double in_x, double in_y, 
		  /*out*/double &out_x, /*out*/double &out_y)
{
    ...
    // Modify the equation here to handle k3
    double r2 = x*x + y*y;
    double kcoef = 1 + k1*r2 + k2*r2*r2;
    double x_ = x*kcoef + 2*p1*x*y + p2*(r2 + 2*x*x);
    double y_ = y*kcoef + p1*(r2 + 2*y*y) + 2*p2*x*y;     
    ...
}