A minimum description length approach to statistical shape modeling A minimum description length approach to statistical shape modeling
Paper summary Active Shape Models brought with them the ability to intelligentally deform to various intra-shape variations according to a labelled training set of landmark points. However the dependence of such methods on a low-noise training set marked manually poses challenges due to inter-observer differences which becomes even more pronounced in higher-dimensions (3D). To this end, the authors propose a method that addresses this problem, but introducing automatic shape modelling. The method is based upon the idea of Occam's Razor, or more formally, The minimum description length (MDL). It is the principle formalization of Occam's razor in which the best hypothesis (a model and its parameters) for a given set of data is the one that leads to the best compression of the data. This essentially means that the MDL characteristic can be used to learn from a set of data points, the best hypothesis that fully describes the training data set, but in a compressed form. The authors use a simple two-part coding formulation of MDL, which although does not guarantee a minimum coding length,but does provide a computationally simple functional form to evaluate which is suitable to be used as an objective function for numerical optimization. The proposes objective function is as follows: $F = \sum_{p=1}^{n_g}D^{(1)}\left(\hat{Y}^p, R, \delta \right) + \sum_{q=n_g + 1}^{n_g + n_{min}}D^{2}\left(\hat{Y}^q, R, \delta \right)$ The algorithm proceeds by first parameterizing a single shape using a recursive algorithm. Once the recursive parameterization is complete, optimization of the objective function presented above proceeds. The algorithm first generates a parameterization for each shape recursively, to the same level. Then shapes are sampled according to the correspondence defined by the parameterization. Once this is done, a model is built automatically from the above sampled shapes. This model is then used to calculate the objective function. The parameterization is changed as to converge to an optimal value for the objective function. In order to change the parameterization of the model to converge to an optimal value of objective function, a ``reference" shape is chosen in order to avoid having the points converge to a bad a local minima (all points collapse to single part of the boundary). Due to the non-convex nature of the objective function, optimization is performed using genetic algorithm. The method was tested both qualitatively and quantitatively on several sets of outlines of 2-D biomedical objects. Multiple anatomical sites in human body were chosen to test the model to provide an idea of how the method performs in a variety of shape settings. Quantitatively the models were shown to be highly compact in terms of the MDL. Qualitatively, the models were able to generate shapes that respected the overall shape of the training set, while still maintaining a good amount of deformation without going haywire.

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Summary by Anmol Sharma 1 month ago
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