An invariant performance measure for surface reconstruction using the volume between two surfaces

In this paper, we propose the volume between two surfaces normalized by the surface area (interpreted as average distance between two surfaces) as an invariant quantitative measure for comparing surface reconstruction results of the explicit form, z(x,y). 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 novel computationally simple and efficient way of computing the volume between two surfaces and the surface area using a least-squared-error plane approximation of a surface patch defined over a rectangular grid. Experiments indicate that the method gives equivalent performance as other more complicated and computationally expensive methods. The advantages of this new method are that computation is simple and efficient.