Nonlinear shape restoration of distorted images with Coons transformation

Image shape restoration based on mathematical transformation is a successful approach to nonlinear distortions in computer vision, robot vision and pattern recognition. The key of this process is to find the distortion function and its inverse function. Usually, the distortion function is unknown or unclear. Even in the case of that when the function is known, it remains difficult to compute or estimate the parameters necessary for the restoration. To overcome this problem, in this paper, Coons transformation utilizing the boundary functions for the distorted images have been used to approximate the exact distortion function. The boundary functions are calculated using B-spline curve interpolation, which is coincided with the necessary condition of major elements that constitute a Coons transformation. The performance of the proposed method to nonlinearly distorted images has been demonstrated in experiments with interesting results.