3D surface reconstruction of the femur and tibia from parallel 2D contours

Segmented structures, such as bones, are typically stored as 2D contours contained on evenly spaced images (slices). Contour interpolation algorithms to turn 2D contours into a 3D surface may differ in their results, causing discrepancies in analysis. This study aimed to create an accurate and consistent algorithm for the interpolation of femur and tibial contours that can be used in computer-assisted surgical navigation systems.

The implemented algorithm performs contour interpolation in a step-by-step manner, determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum-cost cycles in a directed toroidal graph. The algorithm assumes that the contours are ordered. The first step in the algorithm is the determination of branching patterns, followed by the removal of keyholes from contours, optimization of a target function based on the surface area, and mesh triangulation based on the optimization results and mesh seal.

The algorithm was tested on contours segmented on computed tomography images from femoral and tibial specimens; it was able to generate qualitatively good 3D meshes from the set of 2D contours for all the tested examples.

The contour interpolation algorithm proved to be quite effective using optimization based on minimizing the area of the triangles that form the 3D surface. The algorithm can be used for the 3D reconstruction of other types of 2D cuts, but special attention must be paid with the branches, since the proposed algorithm is not designed for complex branching structures.