Automatic Construction of Statistical Shape Models Using Deformable Simplex Meshes with Vector Field Convolution Energy

Background: In the active shape model framework, principal component analysis (PCA) based statistical shape models (SSMs) are widely employed to incorporate high-level a priori shape knowledge of the structure to be segmented to achieve robustness. A crucial component of building SSMs is to establish shape correspondence between all training shapes, which is a very challenging task, especially in three dimensions.

Methods: We propose a novel mesh-to-volume registration based shape correspondence establishment method to improve the accuracy and reduce the computational cost. Specifically, we present a greedy algorithm based deformable simplex mesh that uses vector field convolution as the external energy. Furthermore, we develop an automatic shape initialization method by using a Gaussian mixture model based registration algorithm, to derive an initial shape that has high overlap with the object of interest, such that the deformable models can then evolve more locally. We apply the proposed deformable surface model to the application of femur statistical shape model construction to illustrate its accuracy and efficiency.

Results: Extensive experiments on ten femur CT scans show that the quality of the constructed femur shape models via the proposed method is much better than that of the classical spherical harmonics (SPHARM) method. Moreover, the proposed method achieves much higher computational efficiency than the SPHARM method.

Conclusions: The experimental results suggest that our method can be employed for effective statistical shape model construction.