This paper presents a volumetric approach to reconstructing a smooth surface from a sparse set of parallel binary contours, e.g. those produced via histologic imaging. It creates a volume dataset by interpolating 2D filtered distance fields. The zero isosurface embedded in the computed volume provides the desired result. MPU implicit functions are fit to the input contours, defined as binary images, to produce smooth curves with controllable error bounds. Full 2D Euclidean distance fields are then calculated from the implicit curves. A distance-dependent Gaussian filter is applied to the distance fields to smooth their medial axis discontinuities. Monotonicity-constraining cubic splines are used to construct smooth, blending slices between the input slices. A mesh that approximates the zero isosurface is then extracted from the resulting volume. The effectiveness of the approach is demonstrated on a number of complex, multi-component contour datasets.