Abstract:
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Shapes of anatomical structures can be studied via their boundaries, which form parameterized surfaces. In many applications, in addition to the continuous surface data, we are presented with a set of landmark points selected by the radiologist or doctor. When image contrast is low, there is additional uncertainty in the exact landmark placement. In this talk, we define a framework for statistical analysis of shapes of parameterized surfaces with additional hard (no uncertainty) or soft (uncertainty) landmark constraints. The main difficulty is to appropriately incorporate landmark information in the continuous surface representation. In the case of hard landmarks, we first match them exactly, and then perform further shape analysis under fixed landmark locations. For soft landmarks, we represent the data as a surface in R4, where the first three dimensions contain structural information and the fourth dimension contains the landmarks represented using a mixture of Gaussians where the means and covariances indicate landmark locations and their uncertainties, respectively. The proposed framework allows the user to control the influence of soft landmarks in subsequent shape analysis.
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