This paper presents a method for recovering 3D points from image correspondences using surface characteristics such as mean and Gaussian curvatures. We first give an analysis about how to estimate the mean and Gaussian curvatures from a set of 3D points, and then incorporate the curvature estimation scheme into the reconstruction of 3D points where an optimization process is formulated with the surface curvatures modeled as soft constraints. To analyze the performance of proposed 3D reconstruction method, some simulated data, including the points on surfaces of a plane, a cylinder and a sphere, is generated to test this approach. The experimental results demonstrated that the surface curvature can indeed improve the accuracy of 3D point reconstruction. Some real image data is also tested and the results also support this point.