Statistical Shape Modeling (SSM) is a powerful tool to capture the shape variation pattern across a group of shapes belonging to a certain shape class. SSM has seen many promising applications for the purpose of building Patient-Specific Model (PSM) because it avoids unwanted exposure to ionizing radiation from imaging modalities such as CT scanning and has potential as a cost-saving and time-efficient research and clinical tool. All that is needed to reconstruct the patient — specific data is to instantiate the statistical model already generated.

The utility of the statistical model relies on a sufficiently large training set data pool from as many patients as possible; and more importantly, a reasonably good correspondence across the entire training set. As such, the description length has been used as a standard to measure the quality of correspondence and the statistical model, and the desired correspondence found by optimization.

However, the previously proposed optimization schemes are too inefficient to be used for large data sets. We present a new optimization scheme based on B-spline freeform deformation and analytical adjoint sensitivity. This scheme is significantly more efficient in that it makes use of: 1) extraordinary efficiency of direct correspondence manipulation; 2) availability of analytical gradient due to the differentiable shapes and correspondence manipulation; 3) superiority of adjoint method when a large number of design variables are used in optimization.

In the experimental part, we compare the efficiency of our method and current method for some benchmark examples where solutions are known. Additionally, we show the statistical models for a 3D distal femur bone training set. Such models have been previously used in osteosarcoma cases as a bone bank for bone allografts, where shape-matching is very important [1]. The graphical illustration of the training set and preliminary results of the obtained statistical modes are displayed in Figure 1, 2, 3, 4 and 5.

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