Design and Processing of Invertible Orientation Scores of 3D Images for Enhancement of Complex Vasculature

TL;DR

This paper introduces a novel 3D orientation score framework using invertible transforms and cake-wavelets for enhanced detection of complex vascular structures in noisy biomedical images.

Contribution

It extends 2D orientation scores to 3D with new wavelet designs, enabling invertible transforms and improved vessel enhancement and detection in medical imaging.

Findings

Successful application to real medical data.

Enhanced detection of crossing and elongated structures.

Development of analytical 3D filters using Zernike basis.

Abstract

The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical imaging applications. To handle complex crossing structures in 2D images, 2D orientation scores $U: \mathbb{R} ^ 2\times S ^ 1 \rightarrow \mathbb{C}$ were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores $U: \mathbb{R} ^ 3 \times S ^ 2\rightarrow \mathbb{C}$. First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake-wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. Here we introduce two types of cake-wavelets, the first uses a discrete Fourier transform, the second is designed in the 3D generalized Zernike basis, allowing us to calculate analytical expressions for the spatial filters. Finally, we show two applications of the orientation score transformation. In the first application we propose an extension of crossing-preserving coherence enhancing diffusion via our invertible orientation scores of 3D images which we apply to real medical image data. In the second one we develop a new tubularity measure using 3D orientation scores and apply the tubularity measure to both artificial and real medical data.