How to estimate 2D similarity transformation (linear conformal, nonreflective similarity) in OpenCV?

Question

I\'m trying to search a specific object in input images by matching SIFT descriptors and finding the transformation matrix by RANSAC. The object can only be modified in scene by

Answer 1

You can use find an affine transformation between the point sets using opencv, this is slightly more general than the case you are describing (known as a similarity transform) as it describes shearing transformations of the shapes as well.

It can be performed using the function getAffineTransform(InputArray src, InputArray dst). This takes 2 sets of three points and calculates an affine transform between them.

Answer 2

You can use estimateRigidTransform (I do not know whether it is RANSAC, the code at http://code.opencv.org/projects/opencv/repository/revisions/2.4.4/entry/modules/video/src/lkpyramid.cpp says RANSAC in its comment), the third parameter is set to false in order to get just scale+rotation+translation:

#include <vector>
#include <iostream>
#include "opencv2/video/tracking.hpp"

int main( int argc, char** argv )
{
    std::vector<cv::Point2f> p1s,p2s;

    p1s.push_back(cv::Point2f( 1, 0));
    p1s.push_back(cv::Point2f( 0, 1));
    p1s.push_back(cv::Point2f(-1, 0));
    p1s.push_back(cv::Point2f( 0,-1));

    p2s.push_back(cv::Point2f(1+sqrt(2)/2, 1+sqrt(2)/2));
    p2s.push_back(cv::Point2f(1-sqrt(2)/2, 1+sqrt(2)/2));
    p2s.push_back(cv::Point2f(1-sqrt(2)/2, 1-sqrt(2)/2));
    p2s.push_back(cv::Point2f(1+sqrt(2)/2, 1-sqrt(2)/2));

    cv::Mat t = cv::estimateRigidTransform(p1s,p2s,false);

    std::cout << t << "\n";

    return 0;
}

compiled and tested with OpenCV 2.4.4. The output is:

[0.7071067988872528, -0.7071067988872528, 1.000000029802322;
  0.7071067988872528, 0.7071067988872528, 1.000000029802322]