Geometry Reconstruction from Noisy Data using a Radial Basis Function Partition of Unity Method

Manual three-dimensional segmentation of medical images results in noisy data sets representing three-dimensional objects. Based on this data, we look at how to perform a smooth object reconstruction. In particular, we are interested in the diaphragm, which is a thin curved volume. We use a partition of unity method where local object representations in each patch are blended into a global reconstruction. We use principal component analysis of the local data to align the local approximations with the data. Patches are adaptively refined based on local curvature. Due to the independence of the local approximations, we can increase the resolution in the thin dimension locally in each patch. We use infinitely smooth radial basis functions (RBF) to form a level set function with the object surface as its zero level set. Least squares approximation of the location, gradients, and values outside the object is employed to handle the noise in the data set. We evaluate the resulting reconstruction in terms of residual with respect to the initial data, local curvature, and visual appearance. We present guidelines for how to choose the method parameters, and investigate how they affect the result.