Does OpenCV offer a squared norm function for cv::Point?

Question

I have to check several distances between points against a distance threshold. What I can do is taking the square of my threshold and compare it with the squared norm of (a-b), where a and b are the points I am checking.

I know about cv::norm function, but I wonder if there exists a version that doesn't compute the square root (and therefore is faster) or if I should implement it manually.

Answer 1

_{Note from OP:
I accepted this answer as it's the best method one can achieve using OpenCV,
but I think the best solution in this case is going for a custom function.}

---

Yes, it's NORM_L2SQR:

#include <opencv2\opencv.hpp>
#include <vector>
using namespace cv;
using namespace std;

int main()
{
    vector<Point> pts{ Point(0, 2) };

    double n = norm(pts, NORM_L2SQR);
    // n is 4

    return 0;
}

You can see in the function cv::norm in stat.cpp that if you use NORM_L2SQR you don't compute the sqrt on the norm:

...
if( normType == NORM_L2 )
{
    double result = 0;
    GET_OPTIMIZED(normL2_32f)(data, 0, &result, (int)len, 1);
    return std::sqrt(result);
}
if( normType == NORM_L2SQR )
{
    double result = 0;
    GET_OPTIMIZED(normL2_32f)(data, 0, &result, (int)len, 1);
    return result;
}
...

---

Regarding the specific issue:

My actual problem is: I have a vector of points, merge points closer to each other than a given distance. "Merging" means remove one and move the other half way towards the just removed point.

You can probably

• take advantage of the partition function with a predicate that returns true if two points are within a given threshold.
• retrieve all points in the same cluster
• compute the centroid for each cluster

Here the code:

#include <opencv2\opencv.hpp>
#include <vector>
using namespace cv;
using namespace std;

int main()
{
    vector<Point> pts{ Point(0, 2), Point{ 1, 0 }, Point{ 10, 11 }, Point{11,12}, Point(2,2) };

    // Partition according to a threshold
    int th2 = 9;
    vector<int> labels;     
    int n = partition(pts, labels, [th2](const Point& lhs, const Point& rhs) { 
        return ((lhs.x - rhs.x)*(lhs.x - rhs.x) + (lhs.y - rhs.y)*(lhs.y - rhs.y)) < th2;
    });

    // Get all the points in each partition
    vector<vector<Point>> clusters(n);
    for (int i = 0; i < pts.size(); ++i)
    {
        clusters[labels[i]].push_back(pts[i]);
    }

    // Compute the centroid for each cluster
    vector<Point2f> centers;
    for (const vector<Point>& cluster : clusters)
    {
        // Compute centroid
        Point2f c(0.f,0.f);
        for (const Point& p : cluster)
        {
            c.x += p.x;
            c.y += p.y;
        }
        c.x /= cluster.size();
        c.y /= cluster.size();

        centers.push_back(c);
    }

    return 0;
}

will produce the two centers:

centers[0] : Point2f(1.0, 1.3333);
centers[1] : Point2f(10.5, 11.5)