<p>Surface reconstruction is a challenging problem when no constraint is imposed on data locations. The problem is ill-posed, and most computational algorithms become overly expensive as the number of sample points increases. This article presents a generalization of a popular integral method called <i>minimum curvature</i> (MC) method, which is based on the numerical solution of a modified biharmonic <i>partial differential equation</i> (PDE). Surface reconstruction through the PDE solution for scattered data can be considered as an interior value problem. A new model is suggested to construct an image surface that satisfies data constraints accurately and conveniently. In order to improve the efficiency of the MC method, an effective initialization scheme is suggested. The resulting algorithm is applied for image zooming, synthetic scattered data, and agricultural data acquired by light detection and ranging (LiDAR) technology.</p>