Ellipses from triangles

We present an ellipse finding and fitting algorithm that uses points and tangents, rather than just points, as the basic unit of information. These units are analyzed in a hierarchy: points with tangents are paired into triangles in the first layer and pairs of triangles in the second layer vote for ellipse centers. The remaining parameters are estimated via robust linear algebra: eigen-decomposition and iteratively reweighed least squares. Our method outperforms the state-of-the-art approach in synthetic images and microscopic images of cells.