A Volumetric Conformal Mapping Approach for Clustering White Matter Fibers in the Brain

Abstract

The human brain may be considered as a genus-0 shape, topologically equivalent to a sphere. Various methods have been used in the past to transform the brain surface to that of a sphere using harmonic energy minimization methods used for cortical surface matching. However, very few methods have studied volumetric parameterization of the brain using a spherical embedding. Volumetric parameterization is typically used for complicated geometric problems like shape matching, morphing and isogeometric analysis. Using conformal mapping techniques, we can establish a bijective mapping between the brain and the topologically equivalent sphere. Our hypothesis is that shape analysis problems are simplified when the shape is defined in an intrinsic coordinate system. Our goal is to establish such a coordinate system for the brain. The efficacy of the method is demonstrated with a white matter clustering problem. Initial results show promise for future investigation in these parameterization technique and its application to other problems related to computational anatomy like registration and segmentation.

FiberNET: An ensemble deep learning framework for clustering white matter fibers

“…Similar flavors of unsupervised techniques and an understanding of hierarchical clustering of fibers in video analytics have been explored in [10]. We have also explored the unsupervised learning procedures like support vector machines (SVM) and spectral clustering in [6,7]. Though mathematically elegant, these methods come with a baggage of assumptions and thus with their own limitations.…”

Fibernet 2.0: An Automatic Neural Network Based Tool for Clustering White Matter Fibers in the Brain

“…Basing tract definitions on the ROIs they intersect can lead to incorrect splitting or fusion of fiber bundles, or omission of some fibers that belong to the same bundle. The fiber clustering problem is extremely challenging, and has been tackled for over a decade using unsupervised methods such as spectral clustering [1,2] and more recently using model-based supervised methods [3]. Inspired by the success of convolutional neural networks in the computer vision community [4], recently CNNs have begun to be tested for clustering white matter fibers in the brain.…”