Is there an easy way/algorithm to match 2 clouds of 2D points?

Question

I am wondering if there is an easy way to match (register) 2 clouds of 2d points.

Let\'s say I have an object represented by points and an cluttered 2nd image with t

Answer 1

Here is the function that finds translation and rotation. Generalization to scaling, weighted points, and RANSAC are straight forward. I used openCV library for visualization and SVD. The function below combines data generation, Unit Test , and actual solution.

 // rotation and translation in 2D from point correspondences
 void rigidTransform2D(const int N) {

// Algorithm: http://igl.ethz.ch/projects/ARAP/svd_rot.pdf

const bool debug = false;      // print more debug info
const bool add_noise = true; // add noise to imput and output
srand(time(NULL));           // randomize each time

/*********************************
 * Creat data with some noise
 **********************************/

// Simulated transformation
Point2f T(1.0f, -2.0f);
float a = 30.0; // [-180, 180], see atan2(y, x)
float noise_level = 0.1f;
cout<<"True parameters: rot = "<(2, 2)<0)
    RMSE = sqrt(RMSE/N);

// Final estimate msg
cout<<"Estimate = "<& src, const vector& dst,
        const float* param, const bool* inliers, const Point2f center) {

    const bool all_inliers = (inliers==NULL); // handy when we run QUADRTATIC will all inliers
    unsigned int n = src.size();
    assert(n>0 && n==dst.size());

    float ang_rad = param[0];
    Point2f T(param[1], param[2]);
    float cos_alpha = cos(ang_rad);
    float sin_alpha = sin(ang_rad);

    double RMSE = 0.0;
    int ninliers = 0;
    for (unsigned int i=0; i(2, 2)< best_ninliers) {
            best_ninliers = ninliers;
            best_param[0] = param[0];
            best_param[1] = param[1];
            best_param[2] = param[2];
            best_rmse = cur_rmse;


#ifdef DEBUG_RANSAC
            cout<<" --- Solution improved: "<<
                    best_param[0]<<", "< INLIERS_RATIO_OK) {
#ifdef DEBUG_RANSAC
                cout<<"Breaking early after "<< iter+1<<
                        " iterations; inlier ratio = "<