A non-linear extension of generalized hyperplane approximation (GHA) method is introduced in this letter. Although GHA achieved a high-confidence result in motion parameter estimation by utilizing the supervised learning scheme in histogram of oriented gradient (HOG) feature space, it still has unstable convergence range because it approximates the non-linear function of regression from the feature space to the motion parameter space as a linear plane. To extend GHA into a non-linear regression for larger convergence range, we derive theoretical equations and verify this extension's effectiveness and efficiency over GHA by experimental results.