We present an innovative method estimating multiple 2D motions from uncalibrated images. Our approach robustly and non-iteratively estimates multiple 2D parametric motions, affine or homography, from noisy initial matches without pre-specifying the number of motions This approach is based on: (1) a parametric motion model to detect and extract 2D affine or homography motions; (2) the representation of matching points in decoupled joint image spaces; (3) the characterization of the property associated with affine transformation in the defined spaces; (4) a non-iterative process to extract multiple 2D motions simultaneously based on tensor-voting; (5) local affine to global homography estimation. The major contribution of our work is the extension to our existing affine motion estimation method for homography estimation. The robustness of the approach is demonstrated with several results.