Frontiers in Applied Mathematics and Statistics (May 2019)
k-Nearest Neighbor Curves in Imaging Data Classification
Abstract
Background: Lung disease quantification via medical image analysis is classically difficult. We propose a method based on normalized nearest neighborhood distance classifications for comparing individual CT scan air-trapping distributions (representing 3D segmented parenchyma). Previously, between-image comparisons were precluded by the variation inherent to parenchyma segmentations, the dimensions of which are patient- and image-specific by nature.Method: Nearest neighbor distance estimations are normalized by a theoretical distance according to the uniform distribution of air trapping. This normalization renders images (of different sizes, shapes, and/or densities) comparable. The estimated distances for the k-nearest neighbor describe the proximity of point patterns over the image. Our approach assumes and requires a defined homogeneous space; therefore, a completion pretreatment is applied beforehand.Results: Model robustness is characterized via simulation in order to verify that the required initial transformations do not bias uniformly sampled results. Additional simulations were performed to assess the discriminant power of the method for different point pattern profiles. Simulation results demonstrate that the method robustly recognizes pattern dissimilarity. Finally, the model is applied on real data for illustrative purposes.Conclusion: We demonstrate that a parenchyma-cuboid completion method provides the means of characterizing air-trapping patterns in a chosen segmentation and, importantly, comparing such patterns between patients and images.
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