Cubic surface fitting to image by combination

Abstract

We present a new method for constructing a fitting surface to image data. The new method is based on a supposition that the given image data are sampled from an original scene that can be represented by a surface defined by piecewise quadratic polynomials. The surface representing the original scene is known as the original surface in this paper. Unlike existing methods, which generally construct the fitting surface to the original surface using image data as interpolation data, the new method constructs the fitting surface using the image data as constraints to reverse the sampling process, which improves the approximation precision of the fitting surface. Associated with each data point and its near region, the new method constructs a quadratic polynomial patch locally using the sampling formula as constraint. The quadratic patch approximates the original surface with a quadratic polynomial precision. The fitting surface which approximates the original surface is formed by the combination of all the quadratic polynomial patches. The experiments demonstrate that compared with Bi-cubic and Separable PCC methods, the new method produced resized images with high precision and good quality.