In this paper, we propose the volume between two surfaces normalized by the surface area as an invariant quantitative measure for comparing surface reconstruction results. The invariant property of the volume quantity provides the same measure with respect to an arbitrary coordinate system. By normalizing the volume by the surface area, the values of the measure can be compared for different size of images. We also present a computationally simple and efficient way of computing the volume between two surfaces and the surface area using a least-square-error fit plane approximation of a surface patch defined over a rectangular grid. Experiments indicate that the method using a least-square-error fit plane approximation gives equivalent performance as other more complicated and computationally expensive methods. The advantage of this method is that computation is extremely simple and efficient. Similarly, we propose the area between two curves normalized by the arc length as an invariant measure for comparing plane curve reconstruction results
