The work reported here is an integral part of a system developed for the automated reconstruction of arbitrary-shaped physical objects using vision systems, three dimensional computer graphics, and B-Spline surface approximation techniques. Digitized planar contour points are automatically fitted in the image and world space to define a minimum number of B-Spline control points using least-squares approximation techniques. The final set of points represent the B-Spline control net of the entire surface of the object. The resulting curves and surfaces can be further interactively modified until a satisfactory fit is obtained. Three parametrization techniques, viz., uniform, chord length, and affine invariant angle method are implemented and adjusted to their local minima using the Newton-Raphson iteration method. The effect of each method on the accuracy of the reconstructed surface is discussed. The techniques were tested using a clay model of a human face. The uniform parametrization performed better with the highest speed of convergence and best least-squares error characteristics. On the other hand, it was less effective in detecting sharp corners as compared to the other two methods. The results also show that there is a minimum number of control points for every surface beyond which there is no error improvement. This is useful in several industrial applications when checking surface accuracy of manufactured parts using Coordinate Measuring Machines (CMM).