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This paper focuses on extracting 2D parametric motion regions from uncalibrated images. Our approach simultaneously infers and detects multiple image regions characterized by 2D motions, affine or homography transformations, from noisy initial matches. This approach is based on: (1) a parametric method to detect and extract 2D affine or homography motion regions; (2) the representation of the 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; (6) region refinement based on a hybrid property: motion and color homogeneity. The robustness of the approach is demonstrated with several results.