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.

This paper presents a modified disparity measurement to recover the depth and a robust method to estimate motion parameters. First, this paper considers phase correspondence for the computation of disparity. It has less computation for disparity than previous methods that use the disparity from correspondence and from correlation. This modified disparity measurement uses the Gabor filter to analyze the local phase property and the exponential filter to analyze the global phase property. These two phases are added to make quasi-linear phases of the stereo image channels which are used for the stereo disparity finding and the structure recovery of scene. Then, we use feature-based correspondence to find the corresponding feature points in temporal image pair. Finally, we combine the depth map and use disparity motion stereo to estimate 3-D motion parameters.