Implementing the Automatic Generation of 3D Statistical Shape Models with ITK

Statistical Shape Models are a popular method for segmenting three-dimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Then, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. In this work, we first present a basic version where spatial locations are used in the MDL cost function; next, we introduce an extended version where any combination of features can be used as a metric. As an example application, we present results based on local curvature measurements. Finally, we present results for synthetic and real-world datasets demonstrating the efficiency of our procedures and give details about the implementation using the Insight Toolkit (ITK).