Oblique Random Forests for 3-D Vessel Detection Using Steerable Filters and Orthogonal Subspace Filtering

Abstract

We propose a machine learning-based framework using oblique random forests for 3-D vessel segmentation. Two different kinds of features are compared. One is based on orthogonal subspace filtering where we learn 3-D eigenspace filters from local image patches that return task optimal feature responses. The other uses a specific set of steerable filters that show, qualitatively, similarities to the learned eigenspace filters, but also allow for explicit parametrization of scale and orientation that we formally generalize to the 3-D spatial context. In this way, steerable filters allow to efficiently compute oriented features along arbitrary directions in 3-D. The segmentation performance is evaluated on four 3-D imaging datasets of the murine visual cortex at a spatial resolution of 0.7μm. Our experiments show that the learning-based approach is able to significantly improve the segmentation compared to conventional Hessian-based methods. Features computed based on steerable filters prove to be superior to eigenfilter-based features for the considered datasets. We further demonstrate that random forests using oblique split directions outperform decision tree ensembles with univariate orthogonal splits.