AUTHOR=Cabon Yann , Suehs Carey , Bommart Sébastien , Vachier Isabelle , Marin Gregory , Bourdin Arnaud , Molinari Nicolas 

TITLE=k-Nearest Neighbor Curves in Imaging Data Classification

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 5 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2019.00022

DOI=10.3389/fams.2019.00022

ISSN=2297-4687

ABSTRACT=Background
Lung disease quantification via medical images 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 the theoretical distance according to the uniform distribution of the air-trapping. This normalization renders images of different size, shape and/or density comparable. The estimated distances for the k nearest neighbor describe the proximity of point patterns over the image. Our approach assumes a defined homogenous space so a completion pretreatment is used. 
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 data for illustrative purpose.
Conclusion
We demonstrate that a parenchyma-cuboid completion method provides the means of characterizing air trapping patterns in a chosen segmentation, and importantly, to compare such patterns between patients and/or images.