Three-dimensional reconstruction of the bony structures involved in the articular complex of the human shoulder using shape-based interpolation and contour-based extrapolation

Here, we propose a 3D reconstruction approach using shape-based interpolation and contour-based extrapolation. This approach aims to generate a 3D geometric model of a human shoulder from a sequence of MR parallel 2D cross-sections. While interpolation generates intermediate slices between every pair of adjacent input slices, extrapolation performs a smooth closing of the external surface of the model. We propose a new interpolation method based on conditional morphological dilation. Our extrapolation approach is based on surface smoothness constraints and gradually shrinks every extreme 2D cross-section of a bony structure towards a point, respectively. Surface rendering is accomplished through the generation of a triangular mesh using a parametric representation of 2D slice contours. After surface rendering, local surface irregularities are smoothed with Taubin's surface fairing algorithm [G. Taubin, (1995)].